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This is to certify that I, Christopher Karolis, being a candidate for the degree of Doctor of Philosophy am fully awareof the policy of the University of New South Wales relating to the retention and use of higher degree theses, namely that the University retains the copies of any thesis submitted for examination, "and is freeto allow the thesis to be consulted or borrowed. Subject to the provisions of the Copyright Act (1968) the University may issue the thesis in whole or part, in photostat or microfilmor other copy medium."
In the light of these provisions I grant the University Librarian permission to publish, or to authorise the publicationof my thesis, in whole or part, as he/she deems fit.
I also authorise the publication by University Microfilms of a 350 word abstractin Dissertation Abstracts International(D.A.I.)
C. KAROLIS
Date.. 4.:.!.:.?5...... THE DIELECTRIC CHARACIERIZATION OF BILA YER LIPID MEMBRANES
by
CHRISTOPHER KAROLIS
A thesis submitted for the degree of DOCTOR OF PHILOSOPHY in the Faculty of Science of the UNNERSITY OF NEW SOUTH WALES
1993 dedicated to my wife and family
"Now faith is being sure of what we hope for and certain of what we do not see"
HEBREWS 11: 1 This is to certify that the work embodied in this thesis has not been previously submitted for the award of a degree in any institution.
C.KAROLIS September, 1993 ACKNOWLEDGMENTS
I am sincerely grateful to the many people who gave me advice, assistance and encouragement during the course of this work.
In particular I am indobted to my supervisor, Professor Hans GL Coster for his positive direction and many uieful and encouraging discussions. I would also like to thank Dr John R Smith for supervisingjl1e for a period of time and reading and correcting this manuscript I am also grateful to the fe1low students (all of whom have since graduated) who were a continuous source of ideas and friendly company during the long hours of measurement and frequent frustrating circumstances. I am particularly grateful to Dr Terry C Chilcott who provided much needed software and liardware support for the BULFIS and.fitting programs and many helpful discussions, often late' at night; Dr Derek R Laver for his advice and assistance during the early stages of this work. -
I am grateful for the ~sistance provided by the Physics Workshop for building much of the experimental apparatus; the Department of Medical illustrations (UNSW) for the illustrations in this manuscript; Cec Williams, JC Ludowici Pty Ltd for providing silicone 'O'-rings; CSIRO for assisting in the calibration of electrical components; Janet Aitken and the Lipid Laboratory, Prince Henry Hospital for extracting lipid from donated red blocxi cells; Sue Murray Jones for looking after many of the administrative problems in the laboratory.
Finally, a very special thank you to my wife, Suzanne and children, Alex, Tony and Tina for their unwaivering love and encouragement through very difficult times; the congregation of St Judes and the healing ministry of St Andrews for taking the role of the arms of Jesus; Dr Lam Po Tang for his medical and social skills; Hilary, Sid and Arnold for their mutual support and love. God bless them all. ABSTRACT
Very low frequency impedance spectrometry has been used to investigate the electrical and geometric properties of solvent free egg lecithin planar bilayers. The structural form of the bilayer and the relationship of the macromolecules in the bilayer provide insights into the manner in which other macromolecules may be accommodated in the bilayer and how ions may traverse the hydrophobic interior. A planar bilayer composed of a single lipid represents the most simple model on which to perform such measurements.
Egg lecithin was selected because of its similarities to the composition of human erythrocyte membranes. The bilayers were formed by dispersing the lipid in n-hexadecane and employing a brush technique to a polycarbonate septum in a thermostatically controlled cell. The cross sectional area of the bilayers was -5x10-6 m2. The mechanical and electrically stability of the apparatus supporting the bilayer was addressed to ensure long term measurements were possible on individual bilayers. Typical stable bilayer life times were 3-20 hours thus ensuring good statistical data. Measurements were performed with an admittance measuring device having a phase resolution of± 0.01 ° and an impedance amplitude accuracy of± 0.1 %. The range of frequencies was 10-2 to 104 Hz. The performance of the measuring apparatus was evaluated with hard-wired electrical models. A Maxwell-Wagner model was found to fit the measured data within the 95% confidence limit.
The capacitance, measured below 10- 1 Hz in 100 mM KCl, was found to be -10% greater than at frequencies > 100 Hz and was typically -7.3±0.3 mF m-2. The capacitance translated to a hydrocarbon region thickness of approximately 2.5 nm when a dielectric constant of 2.2 was used and appeared to be independent of the presence of cholesterol and cyclosporin A which were added to egg lecithin.
Capacitance measurements performed at electrolyte concentrations 1, 10, 100 and 1000 mM
KCl suggest that cholesterol bilayers support a net surface charge of 5.8x10-3 C m-2. The conductance of the bilayers was varied and appeared to depend on the stability of the bilayer. The inclusion of cholesterol and cyclosporin A reduced the bilayer conductance and enhanced the stability of the bilayer. Bilayer conductance varied between 5 mS m-2 for egg lecithin bilayers and 1 mS m·2 for egg lecithin bilayers containing cholesterol and cyclosporin A.
Admittance data, measured over the frequency range lQ-2 to 104 Hz was fitted to a Maxwell
Wagner model and the data interpreted to show the existence of dielectrically different regions of the bilayer. The inclusion of molecules such as cholesterol and cyclosporin A could be identified as occupying the polar-head region of the bilayer.
Measurements of bilayers formed from the lipids extracted from the membranes of human erythrocytes were found to be similar to those recorded for egg lecithin-cholesterol bilayers.
A review of the analogies of lipid bilayers and biological membranes is presented in Chapter 1.
Some discussion of alternative methods of investigation is presented. The statistical mechanics of lipid aggregation and in particular micelle and bilayer formation is reviewed in Chapter 2. In
Chapter 3 the dielectric model of the lipid bilayer, Maxwell-Wagner dispersion and the philosophy of measurement are discussed. The experimental arrangement is presented in
Chapter 4, while Chapter 5 is reserved for a discussion of the method, materials and influences on bilayer formation. The performance of the apparatus and the fitting of the data is examined in detail in this chapter. In Chapter 6 the results of capacitance measurements at frequencies below 10-1 Hz are presented. The analogous measurements of conductance is presented in
Chapter 7. Cholesterol inclusion is discussed in Chapter 8, while Cyclosporin A inclusion is discussed in Chapter 9. In Chapter 10 is presented the multilayer dielectric model of the bilayer and the results for bilayers formed from the lipids of erythrocyte membranes in Chapter 11. Karolis; Thesis: THE DIELECTRIC CJl;.RACTERlZATION OF UPID BILAYERS 1
INDEX
CHAPTER I BIOLOOICAL MEMBRANES AND 11IE BILA YER LIPID MEMBRANE The Importance of Structure to Function
1.1 INfRODUCTION 2 1.2 BIOLOGICAL MEMBRANES 4 1.2.1 Introduction •...... 4 1.2.2 Review of Biological Membrane Models ...... 5 1.2.3 The Dielecn; Properties of Biological Membranes ...... 7 1.3 PLANAR BILA YER LIPID MEMBRANES 8 1.3.1 Introduction ...... 8 1.3.2 Formation and Composition ...... 8 1.3.3 Liposomes ...... 9 1.3.4 Planar Bilayer Lipid Membranes ...... 10 1.3.6 The Dielectric Properties of the Bilayer Lipid Membrane ...... 10 1.4 INVESTIGATIVE METHODS OF MEMBRANE STRUCTURE 12 1.4.1 Introduction •...... 12 1.4.1 X-Ray Diffraction Analysis ...... 12 1.4.3 Electron Microscopy ...... 13 1.4.4 Optical Methods ...... 14 1.4.5 Magnetic Resonance ...... 16 1.5 DISCUSSION 18 1.6 SUMMARY 18
CHAPTER 2 TIIESTATISTICALMECHANICSOFMEMBRANEFORMATION
2.1 INfRODUCTION 20 2.2 LIPIDS 20 2.3 SELF-ASSEMBLY OF LIPID MOLECULES 23 2.3.1 Mechanism of Self-Assembly ...... 23 2.3.2 Thermodynamics of Self Assembly ...... 24 2.3.3 Interaction Free Energies ...... 24 2.3.4 Packing Constraints ...... 25 2.3.5 Theoretical Properties of Vesicles and Bilayers ...... 27 2.4 SUMMARY 28
Index Karolis; Thesis: THE DIEU:CTRJC CHARACTERlZAT/ON OF UPID BILAYERS 11
CHAPTER 3 THE DIELECTRIC MODEL OF THE LIPID BILAYER 3.1 INTRODUCTION 30 3.2 IONS IN SOLUTION 30 3. 2 .1 Introduction ...... 30 3.2.2 Ion Self-Energy ...... 31 3.2.3 Ion Translocation Between Dielectric Media ...... 33 Infinite Media ...... 33 Finite Media ...... 33 3.3 ION-ION INTERACTIONS (DEBYE-HlJCKEL THEORY) 36 3. 3 .1 Introduction ...... 36 3.3.2 The Chemical Potential...... 36 3.3.3 Charge Density Near an Ion ...... 37 3.3.4 Linearization of the Boltzmann Equation ...... 38 3.3.5 Linearized Poisson-Boltzmann Equation ...... 38 3.3.6 Solution to the linearized P-B equation ...... 39 3. 3. 7 The ionic cloud surrounding an ion ...... 40 3.3.8 Thickness of the Ionic Atmosphere ...... 41 3. 3. 9 Partition Coefficient ...... 41 3.4 ION MIGRATION 43 3.4.1 Introduction ...... 43 3.4.2 The Forces Moving Ions ...... 43 3.5 MEMBRANE CONDUCTANCE AND CAPACITANCE 46 3. 5 .1 Introduction ...... 46 3.5.2 Membrane Conductance ...... 46 3.5.3 Membrane Capacitance ...... 48 Effects of unstirred layers ...... 48 The ionic double layer ...... 50 3.5.4 The dielectric constant of the bilayer hydrocarbon interior ...... 55 3.5.5 Non-dielectric charge storage in the bilayer ...... 55 3.6 SUMMARY 56
CHAPTER 4
EXPERIMENTAL ARRANGEMENT 4.1 INTRODUCTION 58 4.2 GENERAL DESCRIPTION 60 4.2.1 Vibration-Free Platform and Faraday cage ...... 60 Mechanical Shock ...... 60 Electrical Shock ...... 60 4.2.2 Lipid Bilayer Chamber Assembly ...... 61 The Polycarbonate Cell and Septum ...... 62 Temperature Control ...... 62 Hydrostatic Pressure Control ...... 63 The Viewing System ...... 63 The Electrode System ...... 64 4.2.2 The Amplifier Assembly ...... 65 4.2.3 Computer Based Data Acquisition System ...... 66 4.2.4 Microprocessor Software ...... 67 4.3 DISCUSSION 69
Index ii ~arolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS iii
CHAPTER 5 ME1HOD AND MATERIALS
5.1 INfRODUCTION 71 5.2 MATERIALS 73 5.2.1 Egg Lecithin ...... 73 5.2.2 Cholesterol ...... 74 5.2.3 Oxidised Cholesterol ...... 75 5.2.4 Cyclosporin A ...... 75 5.2.5 Blood Lipid ...... 76 5.2.6 Aqueous Phase ...... 78 5.2.7 n-Alkane Solvent ...... 79 5.2.8 pH ...... 79 5.3 PLANARBILAYERFORMATION 80 5. 3 .1 Introduction ...... 80 5.3.2 Dynrunics of Formation ...... 80 5.3.3 The Lipid Solvent Mixture ...... 83 5 .4 CALIBRATION - PERFORMANCE OF DATA ACQUISffiON SYSTEM 84 5.4.1 Introduction ...... 84 5.4.2 Amplifier Matching ...... 84 5.4.3 Measurement of Stray Capacitance ...... 85 5.4.4 Calibration of Electrical Standards ...... 86 5.4.5 Performance of the Apparatus ...... 87 5.5 DATA PRESENTATION, REDUCTION AND ANALYSIS 88 5.5.1 Data Presentation ...... 88 5.5.2 Data Reduction ...... 88 5.5.3 Data Analysis by Theoretical Modelling ("Fitting") ...... 90 5.5.4 Performance of the Software ...... 90 5.6 PERFORMANCE OF THE SYSTEM 91 5.6.1 Introduction ...... 91 5.6.2 Method and Materials ...... 91 5.6.3 Results ...... 92 5.6.4 Discussion ...... 93 5.7 SUMMARY 94
CHAPTER 6 THE LOW FREQUENCY CAPACITANCE OF BILAYERS AND ITS RELATION TO THE HYDROCARBON REGION
6.1 INfRODUCTION 96 Electrical Double Layers ...... 96 Frequency of Measurement ...... 91 Area ...... 91 Temperature ...... 98 Dielectric Constant ...... 98 Measurement of Capacitance ...... 100 Egg Lecithin - Cholesterol Bilayers ...... 101
Index iii Karolis; Thesis: THE DIEL.ECTRJC CHARACTERIZATION OF UPID BILAYERS iv
6.2 THEORY 102 6. 2 .1 The Capacitance Equation ...... 102 Ignoring the Gouy-Chapman diffuse double layer and swface charge effects ...... 102 6.2.2 Double Layer Capacitance ...... 103 Ignoring swface charge effects ...... 103 Constant surface charge ...... 104 6. 2. 3 The Dielectric Constant of the Hydrocarbon Interior ...... 105 6.2.4 Temperature Dependence of the Dielectric Constant...... 106 6.2.5 The Interactive Volume ...... 107 6.3 METHOD 109 6.4 RESULTS 110 6.4.1 The Age and Stability of the Bilayers ...... 110 6.4.2 The low frequency, area specific, measured capacitance (Cm) ...... 111 6.4.3 Double layer correction of the measured capacitance (Cg) ...... 112 6.5 DISCUSSION 114 6.5.1 Removal of the double layer capacitance ...... 115 6.5.2 The Thickness of the Hydrocarbon Region ...... 117 6.6 SUMMARY 118
CHAPTER 7 THE CONDUCTANCE OF LIPID BILAYERS
7 .1 INTRODUCTION 120 7.2 THEORY 123 Naked Ion Translocation ...... 123 Hydrated Ion Translocation ...... 123 Translocation via formation of a transmembrane pore ...... 125 Translocation via existing transmembrane pore ...... 126 7.3 METHODANDMATERIALS 128 7.4 RESULTS 128 7 .5 DISCUSSION 129 7.6 SUMMARY 131
CHAPTER 8 CHOLESTEROL INCLUSION IN EGG-LECITHIN BILAYERS (THE DIELECTRIC PICTURE OF STRUCTURE) 8.1 INTRODUCTION 133 8.2 METHOD AND MATERIALS 136 Materials ...... 136 Frequency dependence of bilayer impedance ...... 136 8.3 RESULTS 138 8.4 DISCUSSION 140 8.5 SUMMARY 144
Index iv _Karolis; Thesis: THE DIELECTRJC CHARACTERfZATION OF UP/D 8/UYERS V
CHAPTER 9 TIIE INCLUSION OF CYCLOSPORIN A (CsA) IN EGG LECITIIIN BILAYERS (A DIELECTRIC PICTURE OF STRUCTURE) 9.1 INTRODUCTION 147 9.1.1 Physiochemical Properties ...... 147 9.2 METIIODANDMATERIALS 149 9.3 RESULTS 150 Frequency dependence ofthe capacitance ...... 150 Frequency dependence of the conductance ...... 150 9.4 DISCUSSION 151 9.5 SUMMARY 153
CHAPTER 10 TIIE MULTILAYER DIELECTRIC MODEL OF EGG LECITIIIN BILAYERS
10.1 INTRODUCTION 155 10.2 TIIEORY 156 10.2.1 Model for the frequency dependence of bilayer impedance ...... 156 10.2.2 Least Squares Fitting Algorithm ...... 158 10.2.2 Correlation Index ...... 160 10.2.3 J-Parameters and Confidence Levels for Rejecting a Model ...... 161 10.3 MEIBODANDMATERIALS 162 10.4 RESULTS 163 10.5 DISCUSSION 164 10.5.1 Features of the Multilayer Dielectric Model of the Bilayer ...... 164 The hydrocarbon region (hc) ...... 164 Polar-head regions (Pi) ...... 164 Lecithin bilayers ...... 165 The effect of cholesterol ...... 165 Effect of substituting cholesterol with oxidised cholesterol ...... 166 Effect of including CsA ...... 166 10.6 SUMMARY 167
CHAPTER 11 A STUDY OF BILAYERS FORMED FROM TIIE LIPIDS OF MAMMALIAN ERYTIIROCYTE MEMBRANES
11.1 INTRODUCTION 170 11.2 METIIOD 171 11.3 RESULTS 172 11.4 DISCUSSION 173 11.5 SUMMARY 175
Index V !{arolis; Thesis: THE D/EUCfRJC CHARACTERlZAT/ON OF UPID BILAYERS VI
APPENDIX
Al GLOSSARY OF MAJOR SYMBOLS 176 A2 INDEX OF TABLES AND DIAGRAMS 180 B DATA STORAGE AND PRESENTATION 187
REFERENCES 189
Index vi Karolis; Thesis: THE DIELECTRIC CHARACTERISATION OF UPID Bit.AYERS 1
CHAPTER 1
BIOLOGICAL MEMBRANES AND THE BILA YER LIPID MEMBRANE The Importance of Structure to Function
1.1 INTRODUCTION 2
1.2 BIOLOOICAL MEMBRANES 4 1.2.1 Introduction ...... 4 1.2.2 Review of Biological Membrane Models ...... 5 1.2.3 The Dielectric Properties of Biological Membranes ...... 7
1. 3 PLANAR BILA YER LIPID MEMBRANES 8 1.3.1 Introduction ...... 8 1.3.2 Formation and Composition ...... 8 1.3.3 Liposomes ...... 9 1.3.4 Planar Bilayer Lipid Membranes ...... 10 1. 3. 6 The Dielectric Properties of the Bilayer Lipid Membrane ...... 10
1.4 INVESTIGATIVE METHODS OF MEMBRANE STRUCTURE 12 1.4.1 Introduction ...... ~ ...... 12 1.4.1 X-Ray Diffraction Analysis ...... 12 1.4.3 Electron Microscopy ...... 13 1.4.4 Optical Methods ...... 14 1.4.5 Magnetic Resonance ...... 16
1.5 DISCUSSION 18
1.6 SUMMARY 18
Chapter 1: Biological membranes and the bilayer lipid membrane page 1.1 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF LIPID Bll.AYERS
Rough endoplasmic reticulum
Centrosomes
Ii A
Nucleus Nuclear membrane
Endoplasmic reticulum
B
FIGURE 1. 1 The structure of cells
A: Diagram of a typical animal cell (De Witt, 1976) B: Diagram of a plant cell (Villee, 1977)
Chapter 1: Biological Membranes and the Bilayer Lipid Membrane Karolis; Thesis: THE DIELECTRIC CHARACTERISATION OF UPID BILAYERS 2
1. 1 INTRODUCTION
The notion that all bodies of all plants and animals are composed of cells is the fundamental principle of what has now become accepted as the cell theory. New cells come into being only by the division of previously existing cells (Virchow, 1855). The cell is the smallest representative bit that shows all the characteristics of living things. Each cell contains a nucleus and is surrounded by a plasma membrane. Mammalian red cells lose their nucleus in the process of maturation, and skeletal muscles have several nuclei per cell, but these are rare exceptions to the general rule of one nucleus per cell. In the simplest plants and animals, all the living material is found within a single plasma membrane. The cells of different plants and animals and of different organs within a single plant or animal, present a bewildering variety of sizes, shapes, colours and internal structures, but all have common features. Each cell is surrounded by a plasma membrane, and contains a nucleus and several kinds of subcellular organelles-mitochondria, granular endoplasmic reticulum, smooth endoplasmic reticulum, the
Golgi complex, lysosomes and centrioles, as shown in Figure 1. 1.
The delicate, elastic covering of the cell called the plasma membrane forms an integral part of the cell and plays such vital functions as selective transportation of nutrients and waste. The membrane appears to behave as though it has ultramicroscopic pores through which certain substances pass. The size of these pores determines the maximal size of the molecules that may pass. Factors other than molecular size also appear to be of significance, such as electric charge, hydration and lipid solubility. lnfolding in the plasma membrane may be continuous with channels that extend deep into the interior of the cell, providing paths for the entrance of some materials and for the removal of secretory and excretory products.
Our understanding of the structure and function of biological membranes has progressed slowly in the last 100 years. Despite their abundance, large surface area and importance to life our basic understanding of their composition, molecular conformation and behaviour in normal and stressful conditions is still very crude. The greatest progress in our understanding of membranes, however, has been in biochemical aspects while the least progress has been in
Chapter 1: Biological membranes and the bilayer lipid membrane page 1.2 Karalis; Thesis: THE DIELECTRIC CHARACTERISATION OF UPID BILAYERS 3 structural aspects. It is the latter that this work is concerned with. Electrical impedance measurements on simple synthetic bilayer lipid membranes in this study have been used to provide important information on the molecular conformation of these structures to yield insights into the structure of biological membranes.
Chapter 1: Biological membranes and the bilayer lipid membrane page 1.3 Karolis; Thesis: THE DIEUCIR/C CHARACTERIZATION OF UPID BILAYERS
TABLE 1.1
SOME IMPORT ANT FUNCTIONS OF BIOLOGICAL MEMBRANES (Tien, 1974)
Function Membrane
Penneability barrier to ions and molecules Plasma Ion accumulation or active transport Plasma, nerve Conduction of nerve impulse Nerve axon Conversion of light into chemical energy Thylakoid Conversion of light into electrical energy Visual receptor Oxidative and photosynthetic phosphorylation Mitochondrial, Chloroplast Site of immunological reactions Plasma Protein synthesis Cell organelle Phagocytosis and pinocytosis Plasma
Chapter 1: Biological Membranes and the Bilayer Lipid Membrane Table I.I Karolis; Thesis: THE DIELECTRIC CHARACTERISATION OF UPID BILAYERS 4
1.2 BIOLOGICAL MEMBRANES
1.2 .1 Introduction
Biological membranes are organised assemblies of proteins and lipids which form highly selective permeability barriers. They are the sites of intricate and extensive biochemical activity including transport systems such as molecular pumps and gates which regulate the molecular and ionic composition of the intracellular medium (Table 1.1). Eucaryotic cells also contain internal membranes that form the boundaries of organelles such as mitochondria, chloroplasts, and lysosomes. Functional specialisation in the course of evolution has been closely linked to the formation of these compartments.
Membranes also control the flow of information between cells and their environment. They contain specific receptors for external stimuli. The movement of bacteria toward food, the response of target cells to hormones such as insulin, and the perception of light are examples of processes in which the primary event is the detection of a signal by a specific receptor in a membrane. In turn some membranes generate signals, which may be chemical or electrical.
Thus membranes play a central role in biological communication.
The two most important energy conversion processes in biological systems are carried out by membrane systems that contain highly ordered arrays of enzymes and other proteins.
Photosynthesis, in which light is converted into chemical-bond energy, occurs in the inner membranes of chloroplast's, whereas oxidative phosphorylation, in which adenosine triphosphate (A TP) is formed by the oxidation of fuel molecules, takes place in the inner membranes of mitochondria.
In view of these important and varied functions, it is not surprising that the cell membrane has attracted considerable interest. The basic problem, however, is to correlate this diversity at the molecular level of structure and function.
Chapter l: Biological membranes and the bilayer lipid membrane page 1.4 Karolis; Thesis: THE DIEI.ECTRIC CHARACTERISATION OF UPID BILAYERS
EXTERIOR
LIPOID
INTERIOR
FIGURE 1.2 Schematic drawing of 'molecular conditions' of the cell as proposed by Danielli and Davson ( 1935)
Chapter 1: Biological membranes and the bilayer lipid membrane Figure 1.2 Karolis; Thesis: THE DIELECTRIC CHARACTERISATION OF UPID BILAYERS 5
1.2.2 Review of Biological Membrane Models
In the late 19th Century the existence of a selective permeable barrier enclosing animal and plant cells (invisible under the light microscope), was inferred from their osmotic properties. Overton
(1899) determined the nature of the selective "impregnating substance" to be lipoidal in character and in doing so signalled the importance of membrane composition to physiological function. That the membrane was lipoidal and therefore possessing a dielectric constant of about 3, enabled Fricke (1923) to estimate the membrane thickness (3.3 nm) from capacitance measurements of erythrocyte suspensions. However, it was not until 1925, that some evidence as to the molecular structure of membranes was first reported. Using a modified Langmuir monolayer technique, Gorter and Grendel (1925) measured the area of lipids extracted from red cells and found the area to be approximately twice that of the cell surface. From this they inferred that red cells were "covered by a layer offatty substances two molecules thick". The first detailed hypothesis of membrane structure was not presented until 10 years later by
Danielli and Davson (1935). Their model depicted a bimolecular sheet of lipid, of unspecified thickness, covered on the surface by proteins (Figure 1.2). The similarity between cell surface tensions and surface tensions of oil-protein complexes provided the basic material from which their plasma membrane model was constructed.
During the next thirty years the application of refined physical techniques to the study of membrane structure led to an elaboration of the Danielli-Davson molecular model to include polar pores and establish the amount of lipid material in the membrane and so define the membrane thickness. Among the more important of these techniques were polarisation microscopy, X-ray diffraction and electron microscopy. The first two provided unique information about the molecular order and dimensions of biological structures such as nerve myelin, while the last provided the first direct, detailed image of membranes and demonstrated that the polarisation microscope and X-ray diffraction analyses of nerve myelin were relevant if not crucial to an understanding of certain membrane structures.
Chapter 1: Biological membranes and the bilayer lipid membrane page 1.5 Karolis; Thesis: THE DIELECTRIC CHARACTERTZAT/ON OF UPID BILAYERS
TABLE 1.2
COMPOSITION OF SOME TYPICAL PLASMA MEMBRANES (Jain, 1972)
Type of Cell Protein (%) Lipid (%)
Ox brain myelin 1 8-23 73-78 Human erythrocyte 53 47 Rat muscle 65 1 5 Rat liver 85 1 0 Rod outer segment 40-50 20-40 Chlorophylls 35-55 18-37 Mitochondria (total membrane) 70 30 Mitochondria (inner membrane) 75 25
TABLE 1.3
PHOSPHOLIPID COMPOSITION OF VARIOUS CELLULAR MEMBRANES (Tao, 1982)
MEMBRANE PC PE PS PI PA SP CL LPC LPE PG
Human erythrocyte 26.0 30.1 8.2 8.2 n.r. 27.4 n.r. n.r. n.r. n. r. Bovine erythrocyte 0.0 30.0 11 .4 n.r. 58.6 n.r. n.r. n.r. n.r. n. r. Porcine erythrocyte 25.4 41.3 7.9 <1.0 n.r. 25.4 n.r. n.r. n.r. n. r. Rat erythrocyte 47.5 21.5 10.8 3.5 <0.3 12.8 n.r. 3.8 n.r. n.r. Rat liver plasma 34.9 18.5 9.0 7.3 4.4 17. 7 trace 3.3 n.r. n.r. Nuclear 61.4 22.7 3.6 8.6 <1.0 3.2 0.0 1 .5 0.0 n. r. Inner mitochondrial 45.4 25.3 0.9 5.9 0.7 2.5 17.4 n.r. n.r. 2.1 Outer mitochondrial 49.7 23.2 2.2 12.6 1 .3 5.0 3.4 n.r. n.r. 2.5 Golgi 45.3 17.9 8.9 8.9 6.8 32.9 6.8 0.0 n.r. n.r.
PC, phosphatidylcholine; PE, phosphatidylethanolamine; PS, phosphatidylserine; PI, phosphatidylinositol; PA, phosphatidic acid; SP, sphingomyelin; CL, cardiolipin; LPC, lysophosphatidylcholine; LPE, lysophosphatidylethanolamine; PG, phosphatidylglycerol; n.r., not reported
Chapter 1: Biological Membranes and the Bilayer Lipid Membrane Table 1 .2 and Table 13 Karolis; Thesis: THE DIELECTRIC CHARACTERISATION OF UPID Bll.AYERS 6
The introduction of the electron microscope in the 1930's and its subsequent improvements during the following years provided a tool that could form images of structures which had previously been the subject of conjecture. As new preparatory techniques leading to greatly improved tissue sectioning methods were developed, many different cell membranes and membranous cellular organelles were examined. Robertson (1959) summarised a large body of evidence and concluded that there was a common structure at the surface of a wide variety of cells which he called a unit membrane. On an electron micrograph the structure appeared as two dense lines about 2 nm wide separated by a lighter space of 3.5 nm. The dense lines were equated to proteins and polar groups of other moieties in the membrane, and the lighter interzone spaces to their non polar groups. By referring to the biological membrane as a unit,
Robertson emphasised not only that all three parts of the triple-layered 7.5 nm structure were part of one membrane, but also that all membranes had a similarity of molecular arrangement and origin.
The idea of a common structure for all biological membranes had great appeal. However, the membrane compositional diversity in respect of the protein-lipid ratio (Table 1.2) and lipid composition (Table 1.3), and membrane-associated activities was difficult to reconcile with the unit membrane model. Furthermore, conductivity measurements on pure lipid bilayer structures
(Mueller, Rudin, Tien and Wescott, 1962) were found to be much lower than for real membranes. To account for these differences, it was proposed that protein-lipid interactions be considered to be hydrophobic as well as electrostatic in nature and that the membrane lipids and integral membrane proteins be mobile and that diffusion of these components within the lipid bilayer be possible. This dynamic model became known as the Fluid Mosaic Model and was proposed simultaneously by Singer and Nicholson (1972) and Fox (1972). The surface of a membrane was depicted as a mosaic of patches of lipids, proteins, and glycolipids (Figure
1.3). The integral proteins would span the lipid bilayer or be partially embedded in it. If nothing else, the lipids provide a structural framework for the proteins to move about. Freeze etched electron micrographs (Pinto da Silva and Branton, 1970) and radioactive labelling
(Bretscher, 1971), X-ray diffraction (Engelman, 1970), and electron spin resonance studies
(Tourtellotte, Branton and Keith, 1970) appear to support this view.
Chapter I: Biological membranes and the bilayer lipid membrane page 1.6 Karalis; Thesis: THE DIELECTRIC CHARACTERIZATION OF LIPID BILAYERS
FIGURE 1.3 Fluid Mosaic Model based on Singer and Nicholson (1972)
Chapter 1: Biological Membranes and the Bilayer Lipid Membrane Karolis; Thesis: THE DIELECTRIC CHARACTERISATION OF UPJD BILAYERS 7
The presence of trans membrane protein molecules in the fluid mosaic model putatively accounted for specific electrical and biochemical properties of membranes such as active transport, passive ionic permeability, excitability and membrane AC impedance (Coster and
Hope, 1974). Recent theoretical studies involving thermodynamic and geometric considerations of lipid bilayer packing suggest membranes may be highly convoluted structures (lsraelachvili,
1978).
1. 2. 3 The Dielectric Properties of Biological Membranes
Alternating current membrane impedance studies appear to have their origin with the work of
Hober (1910, 1912, 1913) and later by Philipson (1921) and Fricke (1923) on suspensions of erythrocytes and other cells. Interpretation of the measurements (particularly in respect of the membrane conductance) was handicapped by insufficient knowledge of the fractions of the total current flowing through the cell and through the bathing solution. In some instances, cell geometry was also sufficiently complicated as to make cell surface area calculations at best, only crude estimates. Similar problems occurred with impedance measurements of tissues although the development of intracellular electrodes (Blinks, 1936) overcame many of these difficulties.
The remarkable feature of membrane impedance measurement, summarised by Smith (1977), has been the ubiquitous value of the capacitance, namely 10 mF m2, which was found to be frequency independent above 1 kHz but increase below this frequency. Membrane conductance was considerably more variable between species, but typically in the range 100 to 1 mS m2•
Chapter 1: Biological membranes and the bilayer lipid membrane page 1.7 Karolis; Thesis: THE DIELECTRIC CHARACTER/SAT/ON OF UPID BILAYERS 8
1. 3 PLANAR BILA YER LIPID MEMBRANES
1. 3 .1 Introduction
The amount and composition of the lipids in biological membranes vary considerably from species to species, from tissue to tissue, and even from a membrane of one subcellular organelle to another within the same cell. Under physiological stress due to disease or change in nutrients, the characteristic proportions can vary widely. It appears that, among other factors, the nature of the polar group and the variation in the structure of the hydrocarbon chains are important determinants for molecular packing, permeability properties, lipid-protein interaction, and membrane stability and integrity of the unit membrane. However, it is evident from the above that the bimolecular lipid leaflet is the major structural component of biological membranes and as such knowledge concerning the properties and formation of such a structure would be of considerable significance, both experimentally and theoretically. It is also apparent that a detailed physical description of biological membranes would be best approached by studies of simpler well-defined models. The search for a realistic membrane model led to the discovery of a method for the formation of blackt or bilayer lipid membranes (BLM) in aqueous media.
1. 3. 2 Formation and Composition
Membrane lipids are amphipathic molecules possessing both a hydrophilic and hydrophobic moiety. Under certain conditions they can aggregate in various forms by a self-assembly process in aqueous solutions (Israelachvili, Marcelja and Hom, 1980). Some of these are shown in Figure 1.4. The favoured structure for most phospholipids and glycolipids having two (or more) hydrocarbon chains in aqueous media is a bimolecular sheet rather than structures like micelles which are more suited to single chain lipids. The preference for a bilayer structure is of critical biological importance. A micelle is a limited structure, usually less than
t The term black is descriptive of the bilayer lipid membrane appearance. The black appearance arises from an extremely low reflectivity. Reflection of light at the "rear" face of the bilayer lipid membrane undergoes a 1t phase change and the path difference is very much less than the wavelength of light because the membrane is very thin. "Black" thus implies the thickness is much less than the wavelength of visible light.
Chapter 1: Biological membranes and the bilayer lipid membrane page 1.8 Karolis; Thesis: THE DIELECTRIC CHARACTERISATION OF UPID Bll~YERS 9
20 nm in diameter. In contrast, a bimolecular sheet can have macroscopic dimensions such as a
millimetre or larger.
The formation of a bilayer lipid membrane in aqueous solution involves the creation of two coexisting solution/lipid interfaces, or a biface. The first successful method was described by
Mueller, Rudin, Tien and Wescott in 1962. Their membranes were formed by painting ox-brain
lipids in a chloroform/methanol solvent across a small hole in a vertical septum separating salt
solutions. Since then numerous combinations of lipids and solvents have been used to
successfully produce stable bilayer lipid membranes in a variety of experimental arrangements
(Jain, 1972; Tien, 1974 ).
Hydrophobic interactions are the major driving force for the formation of micelles, bilayer vesicles (liposomes), and planar bilayers. The removal of lipid molecules from the aqueous phase into a bilayer is accompanied by a decrease in the entropy but this is offset by a decrease
also in the energy of hydrophobic interactions between the lipid molecules and water. Water
molecules are removed from the hydrocarbon tails of membrane lipids as these tails congregate
in the non polar interior of the bilayer. This release of water results in a large increase in free energy and brings van der Waals attractive forces into play which favour close packing of the
tails. There are also favourable electrostatic and hydrogen bonding interactions between polar
head groups and water.
A more detailed discussion of the dynamics of planar bilayer lipid membrane formation is
presented in Chapter 5.3.
1.3.3 Liposomes
The two most commonly used models of lipid bilayers have been liposomes and planar bilayer
membranes. Liposomes (or bilayer lipid vesicles) are aqueous compartments enclosed by a
lipid bilayer. They are spherical or slightly elongated in shape and have a diameter several times
the thickness of the bilayer. They are excellent models for permeability studies as the
Chapter 1: Biological membranes and the bilayer lipid membrane page 1.9 Karolis; Thesis: THE D/Eu:Cl'RJC CHARACTERIZATION OF UP/D BILAYERS
9 1 ,~\~\~~1 ltliid!6bl000000 o / :?.,.--0 O'z ,- f (o I (b l 6 6 \) ~ ( C)
~°0\f!e:0 ~J~~ ~6~~ UHUH rrrrrrnr 0 ~J~ nrHrn lU~!JU (dl le) (fl (g) HHHlHJi ___ ~I b~~ 'rJ/ nrnnrnr--- Ip <>--(?~/ JiJbJHt~JJ- __ ~IJ \,0 o-'1 ~ if""-c, if rnnnfrr--- _,.-01~'1'~~,'\~6~"06clo-. t J~UJiHU --- ~ rrnnrnr-- "'°?f'"';,P \a.____ (i) ( j) (h) •
Various aggregated forms of amphipaths: (a) lipid molecule; (b) bulk lipid; (c) lipid solution in water; (d) micelle; (e) emulsion; (f) lipid bilayer at air interfaces; (g) lipid bilayer at water interfaces; (h) myelinic, (i) hexagonal I, (j) hexagonal II phases of phospho lipid dispersion.
The characteristics of these various systems may be summarized as follows.
Structural arrangement (type) b f andg h andj i dande C
% Water• 0 5, 20-50 23-40 34-80 30-99.9 Greater !approximate than 99.9 range)
Physical state Crystalline Liquid Liquid L1qu1d Micellar Solution crystalline. crystalline, crystalline. solution lamellar face-cen tered hexagonal cubic compact
Gross Opaque Clear. fluid, Clear, Clear, VISCOUS Clear, fluid Clear, character solid moderately brittle, very fluid VISCOUS viscous
Freedom of None 2 directions Possibly none 1 direction No re- No re- movement stnct1ons stnct1ons
Microscopic Birefringent Neat soap Isotropic with Middle soap Isotropic Isotropic properties texture angular texture with round (crossed n1colsl bubbles bubbles X-ray data Ring pattern Diffuse halo Diffuse halo Di ff use halo 3-6A at about at about at about 4.sA 4.sA 4.sA Structural 3 dimensions 1 dimension 3 dimensions 2 dimensions None None order
FIGURE 1.4 Aggregated forms of amphipaths (Tien, 1974)
Chapter 1: Biological Membranes and the Bilayer Lipid Membrane Karolis; Thesis: THE DIEIECTR/C CHARACTER/SAT/ON OF UP!D BILAYERS 10 discussion on investigative methods in Section 1.4 will show but they are not well suited to electrical studies.
1. 3 .4 Planar Bilayer Lipid Membranes
The first successful attempt to make membranes with a bimolecular lamellar arrangement of lipids was reported in 1962 by Mueller, Rudin, Tien and Wescott. The method was an extension of that used to make soap bubbles. It consists of painting a suitable mixture of lipid and solvent over a small hole in a septum immersed in a salt solution. Such a membrane is well suited to electrical studies, which cannot be performed on liposomes because of their small size and because the inner compartment of vesicles are not readily accessible to electrodes. The planar bilayer has been used for the impedance studies reported in this thesis.
As a model for biological membranes the Mueller-Rudin bilayer lipid membrane has some important advantages. Its size and geometry, for example, make it suitable for optical studies from which fundamental structural information can be derived. Bilayer lipid membranes, although fragile, are relatively easy to produce and can be accommodated in a wide variety of experimental chambers suitable for both electrical and mechanical measurement as well as water, solute and ion permeability studies. By adjusting the lipid mixture, temperature, ionic concentration of the aqueous phase and its pH in a precisely controlled way the effect of each parameter can be evaluated in isolation or in conjunction with other perturbing influences.
1.3.6 The Dielectric Properties of the Bilayer Lipid Membrane
One can see from Table 1.4, that the bilayer lipid membrane possesses many properties similar to biological membranes. It would seem, therefore, that the lipid matrix of biological membranes plays a significantly more complex role in cellular life than is immediately obvious.
Chapter 1: Biological membranes and the bilayer lipid membrane page 1.10 Karolis; Thesis: THE DIELE.CTRJC CHARACTERIZATION OF UPID BILAYERS
TABLE 1.4
COMPARISON OF SOME PHYSICAL CHARACTERISTICS OF BIMOLECULAR LIPID MEMBRANES (BLM) WITH BIOLOGICAL MEMBRANES (Tien, 1974)
Property Biological Membrane BLM
Thickness (nm) Electron microscopy 4 - 13 6 - 9 X-ray diffraction 4 - 8.5 ~tical methods 4 - 13 Capacitance (assumed dielectric) 3 - 15 4 - 13
Potential difference (mV) - resting 10 - 88 0 - 140
Resistance (W m2) 10-2 - 10 1 o- 1 - 1 as
Breakdown Voltage (mV) 100 100 - 550
Capacitance (mF m-2) 0.5 - 1.3 0.3 - 1.3
Refractive Index -1.6 1.37 - 1.66
Water Permeability (1 o-Sm s-1) 0.25 - 400 8 - 50
lnterfacial Tension (10-3 N m-1) 0.03 - 3.0 0.2 - 6.0
Excitability observed observed
Ion selectivity and specificity observed observed
Excitation by light observed observed
Chapter 1: Biological Membranes and the Bilayer Lipid Membrane Table 1.4 Karalis; Thesis: THE DIELECTRIC CHARACTERISATION OF UPID BILAYERS 11
The first measurements of the capacitance of an artificially produced bilayer lipid membrane were made by Mueller, Rudin, Tien and Wescott (1962). These membranes were formed by painting ox-brain lipids in a chloroform/methanol solvent across a small hole in a septum separating salt solutions. At about the same time Hanai, Haydon and Taylor (1964), reported impedance measurements of bilayer lipid membranes formed from egg lecithin in n-decane. The magnitude of the capacitance was measured to be 3.8 mF m-2 and found to be independent of frequency. The conductance, however, was irreproducible but generally < 10-8 mS m-2 of film. Since then, impedance measurements have been made on bilayer lipid membranes from many different lipid/solvent mixtures in a variety of solutions the results of which have been summarised by Smith (1977). In all these measurements, the same electrodes were used to pass the current and measure the potential difference. The impedances measured were thus those of the membrane, electrodes and bulk electrolyte between the electrodes. The exception was the measurements of Coster and Simons (1968, 1970) where the impedance of the electrodes and bulk electrolyte was measured separately in the absence of a membrane and vectorially subtracted to provide the impedance of the membrane alone.
With the exception of Coster and Simons (1970) the membrane capacitance was found to be independent of frequency in the range 20 Hz to 1 MHz. The membrane capacitance was found to be in the range 3-13 mF m-2 depending on the lipid/solvent composition while the conductance was dependent upon the aqueous salt concentration and membrane composition. It was generally found to lie in the range 10-5 to 10-8 mS m·2 of membrane.
Chapter 1: Biological membranes and the bilayer lipid membrane page 1.11 Karalis; Thesis: THE DIELECTRIC CHARACTERISATION OF UPID BILAYERS 12
1. 4 INVESTIGATIVE METHODS OF MEMBRANE STRUCTURE
1. 4 .1 Introduction
A brief survey of biological membrane models was given in Section 1.2.2. The variety of models proposed over the last 100 years to explain the various functions of the cell membrane and cell organelles has resulted from a diverse array of investigative methods; chemical as well as physical. The more impo1tant physical methods and their application to bilayer studies are described below.
1. 4 .1 X-Ray Diffraction Analysis
Soft X-rays have wavelengths of the order of 10- 10 m, which are small enough to be scattered by individual atoms. The process of X-ray diffraction is the constructive and destructive interference of the scattered radiations and results in a diffraction pattern which is a transform of the scattering sites (or atoms). The diffraction pattern is detected radiographically but may require many hours of exposure.
There are two fundamental aspects associated with X-ray diffraction. The first concerns the need to produce a monochromatic, very fine pencil beam of soft X-rays with which to irradiate the sample; the second concerns the ordered nature of the atomic lattice of the sample. The former is technically easy to accomplish with careful selection of the anode target material, external beam filtration and collimation. A high intensity beam may significantly reduce the exposure time. The second, however, restricts the type of material suitable for investigation.
The success of X-ray diffraction analysis in high-resolution structural studies of proteins, for example, has not been repeated in applications to membrane systems. The combination of the long recording time of diffraction patterns and high degree of motional freedom of membrane components results in a pattern corresponding to both a time- and space-averaged structure.
Most studies have been confined either to systems of natural arrays of membranes (such as myelin) or to arrays stacked artificially by sedimentation and partial dehydration, as they have the advantage of concentrating the scattered radiation in readily recorded Bragg spectra
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FIGURE 1.Sa Electron micrograph of the cell membranes of intestinal cells showing the three-layered structure (m=membrane; is=intercellular space). Magnification x240,000
, , , Densely , staining I portion
I , I I I / 0 '75 A unit membrane ' ' ' ' \
' \ Densely staining portion
FIGURE 1.Sb Electron micrograph of the plasma mebrane from erythrocyte. The schematic diagram shows the interpretation as generally developed by Gorter-Grendel-Davson-Danielli-Robertson (see text). (Jain, 1972).
Chapter 1: Biological Membranes and the Bilayer Lipid Membrane Karolis; Thesis: THE DIELECTRIC CHARACTERISATION OF UP/D BILAYERS 13
Diffraction patterns contain information about the average electron density variation in a direction perpendicular to the plane of the membrane. Such information may provide evidence of the conformation of the hydrocarbon chains in the membrane interior. The general consensus of these studies supports the hypothesis that the basic structural element of the membranes is a bimolecular layer of phospholipids. It appears that the protein component of the membrane does not contribute appreciably to the main lamellar diffraction, and its position in the structure can only be inferred indirectly. The dimensions of the structure are consistent with the idea of hydrated protein layers covering the hydrophilic surfaces of the phospholipid bilayer.
1. 4. 3 Electron Microscopy
The theoretical limit of resolution of electron microscopes is about lQ-13 m. In practice the resolution is about 1 nm. Electrons accelerated to 50 - 100 ke V are readily absorbed in the irradiated matelial. Therefore the biological material must be thinly sectioned ( about 50 nm) with the inevitable result that some distortion occurs. The chemistry of the processes of fixation with heavy metal oxides is not very well understood and some of the stains are not specific.
Osmium tetroxide, for example, interacts with a variety of proteins, with phospholipid polar groups, and with the double bonds of unsaturated carbon chains. It is also possible that as a result of chemical change the hydrocarbon chains may become reorientated to some extent during fixation. Despite these limitations and others (Jain, 1972), Robertson (1960) was able to give considerable support to the 'unit membrane' concept of the biological membrane. The unit membrane as applied to the plasma membrane of an erythrocyte (Figure 1.5) is depicted as a triple layered structure on an electron micrograph, 7 .5 nm wide.
The first quantitative estimates of the thickness of bilayer lipid membranes were made from electron micrographs by Mueller, Rudin, Tien and Westcott in 1964 using OsO4 fixing. From published electron micrographs, a thickness of 6-9 nm was estimated. La(NO3)3 fixing was used by Henn, Decker, Greenawalt and Thompson ( 1967) to reveal a widely varying thickness
(3.75 - 11.6 nm) thought to be due to varying degrees of hydrocarbon solvent retention in the bilayer. The triple layered structure so clearly visible in natural membrane electron microscopy
Chapter l: Biological membranes and the bilayer lipid membrane page 1.13 Karolis; Thesis: THE DIELECTRIC CHARACTERISATION OF UPID BI/AYERS 14 was clearly demonstrated by Ververgaert and Elbers (1971). A peak to peak width was found to be 6 nm or 6.9 nm if the polar layers were taken into account
1. 4. 4 Optical Methods
The optical properties of a lipid bilayer in aqueous solution are assumed to be fundamentally similar to those of thin transparent solids and soap films. The thickness of the bilayer can be determined from reflectance measurements performed at small angles of incidence using visible light and the following relation applied to the 'single-layer' model of the bilayer (Tien, 1974), see Figure 1.6 below :
(1.1)
where, Ii and Ir are the intensity of the incident and refracted light respectively, Re is the reflectance,
bilayer, A. the wavelength of the incident light and 0 the refracted angle. The 'single-layer'
model assumes that the bilayer is isotropic and transparent and ignores the polar group refractive index.
Chapter 1: Biological membranes and the bilayer lipid membrane page 1.14 Karolis; Thesis: THE DIELECTRIC CHARACTERISATION OF LJPID BILAYERS 15
Ii 0 (A.) nw
lr
water bilayer water
FIGURE 1.6 Schematic diagram showing the parameters used in optical studies of lipid bilayers
The refractive index is either assumed to be that of the bulk material or determined from
measurements of the Brewster angle using the following relation
Tan (1.2)
where,
the bilayer and aqueous solution respectively.
To obtain the thickness t, the reflectance at some other angle of incidence i, must also be
measured. The first optical measurements on lipid bilayers made by Huang and Thompson
(1965), Tien and Dawidowicz (1966) and Tien (1967) were performed by comparing the
reflectivity from 'black' and 'silvery' film stages. These authors determined refractive indices
( 1.56-1.66) much higher than any component of the membrane forming solution which range
from 1.41 to 1.49. Cherry and Chapman (1967), on the other hand measured a smaller
Brewster angle for lecithin bilayers, which co1Tesponded to a refractive index of 1.37. In
subsequent optical measurements Cherry and Chapman (1 969) used a quartz plate as a
Chapter 1: Biological membranes and the bilayer lipid membrane page 1 .15 Karolis; Thesis: THE DIELECTRIC CHARACTERISATION OF UPID BILAYERS 16 reflectance standard to confirm their previous results. Cherry and Chapman (1967, 1969) accounted for the discrepancies to the isotropic single-layered model of the bilayer and proposed a more complicated 'triple-layered' model (also Tien, 1967) to include the differences in the refractive indices of the polar groups.
Dilger, Fisher and Haydon (1982) have reviewed the work on optical studies carried out since
1965 and found reflectance measurements are complicated by the existence of microlenses
(White, 1978; Bach and Miller, 1980) and the choice of solute in the aqueous phase. There appears little doubt that for optical measurements the bilayer lipid membrane cannot be considered as consisting of discrete isotropic layers. It is also worth noting that the intensity of the reflected component is 10-s - 10-6 times smaller than the intensity of the incident beam.
1. 4. 5 Magnetic Resonance
Magnetic resonance methods include Nuclear Magnetic Resonance (NMR) and Electron Spin
Resonance (ESR). The questions best answered by magnetic resonance are those concerned with the dynamic properties of membranes. In particular NMR and ESR are sensitive to motions that range from about 10-11 s to a few seconds and therefore particularly useful in examination of the fluid state of the hydrocarbon chains of the membrane interior.
Proton magnetic resonance (p.m.r.) is highly successful in conformational and kinetic chemical studies of simple molecules in motion. The success is due to the sensitivity of the resonance frequency of the proton to the shielding by its electronic environment which opposes the field.
The line shape of the resonance signal depends on the detailed molecular motions of the proton and in general, its half-width decreases with increasing motion. The entire p.m.r. high resolution spectrum covers a range of about 2500 Hz at a central frequency of 100 MHz. The shift of the resonance frequency of a particular chemical group from a standard, the chemical shift, characterises the position of a line in the spectrum.
Chapter I: Biological membranes and lhe bilayer lipid membrane page 1.16 Karalis; Thesis: THE DIELECTRIC CHARACTERISATION OF UPID BILAYERS 17
Line widths are related to the life time of the proton spin in a given orientation relative to the applied magnetic field. The shortening of the life-time of the proton in a given orientation will result in a broadening of the line. As will slow chemical exchange of a proton between functional groups.
In order to characterise the motions of the lipid molecules, probe molecules with nitroxide free radicals are covalently linked to membrane components. The probe is sensitive both to its detailed motion and the polarity of its environment Only the probe resonance is obtained (ESR) and there is no interference from nuclear resonance signals. When the free radical is placed in a static magnetic field, the unpaired electron spin can be oriented either parallel or anti-parallel to the field direction (and independent of the spatial orientation of the electronic orbital). Since the later is energetically favoured a population difference between the two orientations, characterised by the Boltzman distribution, is set up. The energy levels of the free radical in the magnetic field are defined, in the first approximation, by the product of the magnetic moment of the electron and the magnetic field. Transitions between the two energy levels, so as to equate their populations, can be induced by the application of an oscillating magnetic field at right angles to the applied field provided the frequency of the oscillations (v) corresponds to the energy gap between the two levels. The resonance condition is given by
(1.3) where g is the magnetic moment, which is the ratio of the actual moment to a theoretical value known as the Bohr magneton and denoted as Pe, h is Plank's constant and H is the static field experienced by the electron spin. Resonance is observed as an absorption of energy by varying the applied magnetic field H (of the order of 3400 Gauss) at a constant frequency (typically
9.5x1Q9 Hz).
Chapter I: Biological membranes and the bilayer lipid membrane page 1.17 Karolis; Thesis: THE DIELECTRIC CHARACTERISATION OF UPID Bll.AYERS 18
1.5 DISCUSSION
The confonnational, electrical and mechanical similarity between biological membranes and the
Mueller-Rudin-Tien-Wescott lipid bilayer has been established. Examination of the lipid bilayer by electron microscopy and other methods that distort the physical dimensions and behaviour of the bilayer such as ESR, NMR and X-ray diffraction is complimented by the rather more simple methods of impedance spectroscopy and optical methods. The infonnation gained from impedance spectroscopy is not complicated by the presence of multiple bilayers, molecular probes or metallic stains.
1.6 SUMMARY
This chapter outlines the importance of biological membranes to life and reviews the development of membrane models over the last 90 years. The role of lipids in biological membranes and their simple analogue, the bilayer lipid membrane, (BLM), is also discussed and a review of alternative methods used in the elucidation of the structure of both biological and synthetic membranes is presented.
Chapter I: Biological membranes and the bilayer lipid membrane page 1.18 Karolis; Thesis: THE D/El.ECTRIC CHARACTERISATION OF UP/D BILAYERS 19
CHAPTER 2
THE STATISTICAL MECHANICS OF MEMBRANE FORMATION
2.1 INTRODUCTION 20
2.2 LIPIDS 20
2.3 SELF-ASSEMBLY OF LIPID MOLECULES 23
2.3.1 Mechanism of Self-Assembly ...... 23 2.3.2 Thermodynamics of Self Assembly ...... 24 2.3.3 Interaction Free Energies ...... 24 2.3.4 Packing Constraints ...... 25 2.3.5 Theoretical Properties of Vesicles and Bilayers ...... 27
2.4 SUMMARY 28
Chapter 2: The staJistical mechanics of membrane formalion page 2.1 Karolis; Thesis: THE DIELECTRIC CHARACTERISATION OF LIPID B11.4.YERS 20
2 .1 INTRODUCTION
The thermodynamics of the self-assembly of lipid molecules into micelles has been well understood for some time. However, considerations of such concepts as the interaction free energies of molecules, opposing and hydrophobic forces, aggregation number and critical micelle concentration, have almost been ignored in analogous bilayer and vesicle research. The role of geometric factors, on the other hand, such as packing and molecular conformation have, only recently, been introduced in micelle self-assembly theory. By contrast, bilayer and membrane models have been developed using a priori assumptions such as bilayer elasticity, fluid mosaics and lipid packing.
2.2 LIPIDS
Lipids are a group of biomolecules which are defined by their lack of solubility in water and higher solubility in organic solvents such as chloroform. For example fats, and certain vitamins such as A, D, E, and K, and the class of hormones known as steroids are lipids. Their
biological role is varied. They may serve as fuel molecules; as highly concentrated energy
stores; and as components to membranes. As membrane constituents they fall into three major
types; phospholipids, glycolipids and steroids.
Phospholipids, which are abundant in all biological membranes, are derived from either
glycerol, (to form phosphoglycerides), or sphingosine (to form sphingolipids). A
phosphoglyceride consists of a glycerol backbone, two fatty acid chains and a phosphorylated
alcohol.
The fatty acid chains in phospholipids and glycolipids usually contain an even number of
carbon atoms, typically between 14 and 24. The most common fatty acids in animals are the
16- and 18- carbon saturated and unsaturated fatty acids. In general the fatty acids derived
from plant tissue have more double bonds and are more likely to have an odd number of carbon
Chapter 2: The statistical mechanics of membrane formation page 2.2 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID B11.AYERS
r------, 01 GLYCEROL 11:
1 FATTY ACIDS H C - {CH~ - C 1 - 0 - CH PHOSPHATE ALCOHOL I 3 14 1 2 , ______.., (phosphatidic add) (ammine alcohol) r------, I r------1 I I I I :H C-(CHJ- c= C-(CH~ - c:-o-c-H :0 : : 3 7 H H 7 11: :II /H3 : I I I + I , 0, H C - 0 -, p - 0 - CH - CH - N - CH , · ------2 : I 2 2 \ 3:
:o- CH 3 : I------'
FIGURE 2.1 A phosphatidyl choline ( 1-Palmitoyl-2-oleoyl-phosphatidyl choline)
A structural presentation of the components chemically linked to form egg lecithin.
Chapter 2: The Statistical Mechanics of Membrane Formation Figure 2.1 Karolis; Thesis: THE DIELECTRIC CHARACTER/SAT/ON OF LJPID BILAYERS 21 atoms. The length and degree of saturation in membrane lipids have a profound effect on membrane fluidity as will be discussed later.
The numbering of the carbon atoms that has been adopted here is that due to Sundaralingam
(1972). In this convention the glycerol carbon atom to which the polar head group is attached is always designated C-1. In phosphoglycerides, the hydroxyl groups at C-2 and C-3 of glycerol are esterified to the carboxyl groups of two fatty acid chains. The esterification of the C-1 group to phosphoric acid results in the simplest of phosphoglycerides called phosphatidate.
While present only in small amounts in membranes this compound is a key intermediate in the biosynthesis of other phosphoglycerides.
The major phosphoglycerides are derivatives of phosphatidate. The phosphate group of phosphatidate becomes esterified to the hydroxyl group of one of several alcohols. The common alcohol moieties of phosphoglycerides are serine, ethanolamine, choline, glycerol, and inositol. The linking of these components to form phosphatidyl choline (egg lecithin) used extensively in this work is shown in Figure 2.1.
Another class of phospholipid that is important to the structure of membranes is built around sphingosine, an amino alcohol that contains a long, unsaturated hydrocarbon. Ceramide, the basic unit of sphingolipids is formed by reacting a fatty acid to the free amine of sphingosine.
The two most common sphingolipids are sphingomyelin and the cerebrosides.
Another important lipid in some membranes is cholesterol. This steroid is present in eukaryotes but not in prokaryotes. The plasma membranes of cells such as erythrocytes, liver cells, and myleniated nerve cells are rich in cholesterol. The role of cholesterol in the fluid mosaic structure is not clear and is a subject of investigation in this thesis. Its function appears to be to maintain liquidity and stability. A membrane without cholesterol has a well defined melting point below which it is in the gel phase and resists lateral movement of its components. The presence of short hydrocarbon chains or large numbers of double bonds causes the melting temperature to be relatively low. Bacterial and plant membranes, which usually lack cholesterol, remain liquid even at low temperatures. Animal cells, on the other hand, typically
Chapter 2: The statistical mechanics of membrane formation page 23 Karolis; Thesis: THE DJEU:CJ'RJC CHARACTER/SAT/ON OF UPJD BILAYERS 22 have long-chain, relatively saturated hydrocarbons that would by themselves impose a melting temperature above that which the cells normally exist. When cholesterol is added, however, the melting temperature is drastically lowered and the fluid nature maintained in these membranes even at relatively low temperatures. Cholesterol also smears out the 'melting ' process- it is not as distinct as in pure phospholipids.
Chapter 2: The staJistical mechanics of membrane formation page 2.4 Karalis; Thesis: THE DIELECTRIC CHARACTERISATION OF UPJD 8/U.YERS 23
2.3 SELF-ASSEMBLY OF LIPID MOLECULES
A single theory that describes the self assembly of lipid molecules to form both micelle and bilayer structures was introduced by lsraelachvili, Mitchell and Ninham (1977). Their theory rests on the unification of thermodynamics, interaction free energies and molecular geometry to explain previously unexplained properties of micelles, and also explains why diacyl chained lipids form into extended bilayers and vesicles.
2. 3 .1 Mechanism of Self-Assembly
It is the amphiphilic nature of lipids which induces them to aggregate, sometimes into organised structures. Hydrophobic interactions involving the acyl chains cause the molecules to congregate, while the hydrophilic interactions of the head groups imposes the requirement that the head groups remain contact with the water. These two opposing forces result in an optimal surface area per head group at which the total interaction free energy per lipid molecule is a minimum.
The structures that are possible will depend on the optimal surface area and the hydrocarbon tail volume, and are limited by the maximum length that the hydrocarbon chains can extend. Thus, double chained lipids cannot assemble into small micelles because of energy and geometrical constraints while single-chained lipids do not form bilayer structures because entropy considerations favour small lipid aggregate numbers.
Chapter 2: The staJistical mechanics of membrane formalion page 2.5 Karolis; Thesis: THE DIEUCTR/C CHARACTERISATION OF UPID 8/l.AYERS 24
2.3.2 Thermodynamics of Self Assembly
In a system of aggregated structures such as bilayers, in thermodynamic equilibrium, the
chemical potential of all the molecules will be the same and may be expressed as
o kT JXN] µN + N Int_ N = constant, N=l, 2, 3, ..... (2.1)
where,
X N = mole fraction of molecules incorporated into micelles of aggregation number N, 0 µN = the free energy per molecule in the mice/le, k = Boltzmann's constant, T = temperature.
If Mis taken to be any arbitrary reference state of micelles with aggregation number N, and T
is above melting temperature of the hydrocarbon chains, equation (2.1) can be rewritten as
follows:
= .,J XM]: I { XN il M exP!_ N µ~kT - µ~}] (2.2)
2. 3. 3 Interaction Free Energies
The interaction free energy ~ is the sum of two opposing conditions:
(1) An attractive interaction arising from attractive hydrophobic or interfacial tension forces
which may be represented by the product of the 'interfacial free energy per unit area y and a the
molecular area measured at the interface.
(2) A repulsive interaction arising from electrostatic head-group repulsion, steric head-group
repulsion and steric hydrocarbon side-chain repulsion, of the form C/a, where C is a constant
for a given lipid but the magnitude of which will depend on the size of the head-group.
Chapter 2: The statistical mechanics of membrane formation page 2.6 Karolis; Thesis: THE DIELECTRIC CHARACTERISATION OF UPID B11.AYERS 25
The free energy per molecule is thus,
C a (2.3)
The minimum free energy ~(min) is given when
or (2.4)
Thus,
(2.5)
The free energy of each lipid molecule may now be conveniently expressed in terms of its
interfacial free energy and molecular area projected at the interface as follows:
(2.6)
This expression for µ~ exhibits a parabolic (or elastic-type) variation about the minimum
energy, where a0 is the optimal surface area per molecule, at the interface, corresponding to
minimum free energy per molecule in a micelle or bilayer.
2.3.4 Packing Constraints
If phospholipids can pack into structures in which the interfacial contact area per molecule is
close to minimum (i.e. a0 ), it follows from equation (2.2) that the structure with the smallest
aggregation number will be entropically favoured. Geometric expressions may be derived
which relate the hydrocarbon-water interfacial area a, the hydrocarbon chain volume v, the hydrocarbon thickness <>he, and the radius of curvature R of the structure measured at the
interface.
Chapter 2: The statistical mechanics of membrane formation page 2.7 Karolis; Thesis: THE DIEU:CTRIC CHARACTERISATION OF UPID BILAYERS 26
Thus,
(1) For a spherical micelle ofradius R = 6hc
3 2 41tR = 41tR = N or (2.7) 3v a
(2) For a cylindrical micelle of radius R = 6hc
(2.8)
(3) For a spherical bilayer vesicle of outer radius R, for the outer layer of molecules
(2.9)
For a planar bilayer, where in the limit of large R, (R >> 6hc=bilayer half-thickness), via =6hc·
A packing constraint is imposed which limits the thickness of the hydrocarbon region to the maximum extension of the acyl chains, say 6:ax, otherwise an energetically unfavourable void
would exist in the hydrocarbon region. The structure, therefore, with the smallest aggregation number and 6hc ~ 6:ax would be most favoured.
A 'packing parameter', v / (a0 ~ax), can be defined which will determine which aggregate will form.
Chapter 2: The stalistica/ mechanics of membrane formalion page 2.8 Karolis; Thesis: THE DIEUCTRIC CHARACTERISATION OF UPID BILAYERS 27
2. 3. 5 Theoretical Properties of Vesicles and Bilayers
As a consequence of the preceding statements regarding the critical length ~ some lipids will be unable to form small micelles or even small vesicles. For a to remain equal to a0 , and if 6 < a:ax the vesicle radius R cannot be less than a certain critical radius Re given by
~----6he (2.10) 1--v ll~e
For vesicles with R > Re there are no packing restrictions on any of the molecules, so they can assume their minimum energy configuration with a = au.
Thus, for all molecules,
(2.11)
Chapter 2: The statistical mechanics of membrane formation page 2.9 Karolis; Thesis: THE DIELECTRIC CHARACTERISATION OF UPID BIV.YERS 2.8
2.4 SUMMARY
A brief description of the molecules that make up the principle matrix of membranes such as lecithin and cholesterol is given. The manner in which these macro-molecules can assemble to form stable structures such as miscelles, lyposomes and planar bilayers has been presented using a statistical mechanical model. The packing constraints of phospholipids and interaction free energies are considered with respect to bilayers.
page 2.10 Chapter 2: The statistical mechanics of membrane formation Karolis; Thesis: THE DIELECTRIC CHARACTER/ZIJ'JON OF UPID BILAYERS 29
CHAPTER 3
THE DIELECTRIC MODEL OF THE LIPID BILA YER
3.1 INTRODUCTION 30
3.2 IONS IN SOLUTION 30 3.2.1 Introduction ...... 30 3.2.2 Ion Self-Energy ...... 31 3.2.3 Ion Translocation Between Dielectric Media ...... 33 Infinite Media ...... 3 3 Finite Media ...... 33
3.3 ION-ION INTERACTIONS (DEBYE-HlJCKEL THEORY) 36 3. 3 .1 Introduction ...... 36 3.3.2 The Chemical Potential...... 36 3.3.3 Charge Density Near an Ion ...... 37 3.3.4 Linearization of the Boltzmann Equation ...... 38 3.3.5 Linearized Poisson-Boltzmann Equation ...... 38 3.3.6 Solution to the linearized P-B equation ...... 39 3. 3. 7 The ionic cloud surrounding an ion ...... 40 3.3.8 Thickness of the Ionic Atmosphere ...... 41 3. 3. 9 Partition Coefficient ...... 41
3.4 ION MIGRATION 43 3.4.1 Introduction ...... 43 3.4.2 The Forces Moving Ions ...... 43
3.5 MEMBRANE CONDUCTANCE AND CAPACITANCE 46 3. 5 .1 Introduction ...... 46 3. 5. 2 Membrane Conductance ...... 46 3.5.3 Membrane Capacitance ...... 48 Effects of unstirred layers ...... 48 The ionic double layer ...... 50 3.5.4 The dielectric constant of the bilayer hydrocarbon interior ...... 55 3.5.5 Non-dielectric charge storage in the bilayer ...... 55
3.6 SUMMARY 56
Chapter 3: The Dielectric Model of the Lipid Bilayer page 3.1 Karolis; Thesis: THE DIEUCTRJC CHARACTERIZATION OF UPID BILAYERS
WEAK ELECTROLYTE
WEAK ELECTROLYTE
FIG. 3.1 Schematic drawing of the membrane model proposed by Gorter and Grendel (1925)
Chapter 3: The Dielectric Model of the Lipid Bilayer Figure 3.1 Karolis; Thesis: THE D/EIECTRIC CHARACTERIZAIION OF UPID BILAYERS 30
3 .1 INTRODUCTION
The biological membrane model proposed by Gorter and Grendel (1925) depicted the membrane as consisting of three distinct regions bounded by a weak electrolyte (Figure 3.1).
Two interfacial regions are represented by the polar groups of the lipid molecules in contact with the molecules of the external bulk medium and a hydrocarbon interior, consisting of the hydrophobic tails of the amphiphile.
The membrane, in conjunction with the external aqueous solution, therefore, acts as a complex electrodiffusion system involving a double double layer. The movement of ions and their interaction with the local field govern the behaviour of and the events at the biological membrane surface.
In this chapter the forces and energy associated with ions in a membrane bounded by a binary univalent electrolyte are examined.
3.2 IONS IN SOLUTION
3. 2 .1 Introduction
Bilayer lipid membranes have a measurable conductivity (see Table 1.4) despite the very low dielectric constant associated with the hydrocarbon interior (E = 2.1). This conductivity must be associated with ion transfer across the membrane. To examine this question one must determine the free energy difference of ions in the external aqueous phase (electrolyte) and in the lipoidal membrane (or more particularly the hydrocarbon interior).
Chapter 3: The Dielectric Model of the Lipid Bilayer page 3.2 Karolis; Thesis: THE DIEL£CTRIC CHARACTERlZATION OF UP/D BILAYERS 31
3.2.2 Ion Self-Energy
By virtue of an ion's electrostatic field it will possess a self-energy when present in a dielectric medium. The self energy is numerically equal to the energy required to transfer a charged sphere from a vacuum into a continuum (Born, 1920). In the Born model, the ion is viewed as a rigid sphere, radius R, bearing a charge ze0 (e0 is the electronic charge and z is the valency), and the interactions betwem the charged sphere and the continuum are considered to be solely electrostatic in nature.
The electrostatic potential ~ the surface of a charged sphere is given by
(3.1)
where Xr is the electric force operating on a unit charge in a medium of dielectric constant £ and r is the distance from the charged sphere.
From Coulomb's Law
(3.2)
and it follows
(3.3)
= (3.4)
Chapter 3: The Dielectric Model of the Lipid Bilayer page 33 Karolis; Thesis: THE DIEUCTRJC CHARACTERIZATION OF UPID BILAYERS 32
The electrostatic field E, associated with this potential is given by
q,r E= r (3.5) while the total energy W, stored in the electrostatic field of a charged sphere in a medium having a dielectric constant E is
W=-EoE i E 2 dt (3.6) 2 't
For r< R, E = 0 (3.7)
ze0 For r ~ R, E = --- (3.8) 41tE0Er2 and
(3.9)
Equation (3.9) represents the se/f-energyt of an ion, radius R, in a dielectric medium E, with
charge ze0 •
t The self energy of a K+ and c1-l ion in water was calculated to be 6.5 kJ mol-1 and 4.8 kJ mol-1 respectively. This compares with the ion self energies in a dielectric medium Ehc=2.1, of 248 kJ mo1-l and 182 kJ moi- 1 respectively, which strongly suggests that these ions are unlikely to exsist in the hydrocarbon region of the membrane.
Chapter 3: The Dielectric Model of the Lipid Bilayer page 3.4 Karolis; Thesis: THE DIEl.£CTRIC CHARACTERIZATION OF UP/D BILAYERS 33
3. 2. 3 Ion Translocation Between Dielectric Media
In.finite Media
The self-energy of an ion situated in a medium of dielectric E2, but remote from an interface with another medium having a dielectric constant E 1, can be shown to be the Born energy difference,
W(oo) (3.10)
Finite Media
In the vicinity of the interface the electric field is no longer Coulombic because the induced charges in the other medium disturb the original field. The true potential of an ion of charge e0 located at a point P(x,y ,z) in medium 2 may be obtained by the method of electrostatic images
(Duckworth 1965), where a fictitious charge -tle0 is introduced at the image point P'(-x,y,z) in
medium 1.
The electrostatic potential of the ion is then given by the relations,
(1 + t})eo \J'1=---- (x:s;O) 41tEaE1P
t}eo (x~O) (3.11)
in which p and p' are the distances measured from P and P' respectively.
Chapter 3: The Dielectric Model of the Lipid Bilayer page 3.5 Karolis; Thesis: THE DIELECTRJC CHARACTERIZATION OF UPJD BILAYERS 34
If, £1 - Ez i}=-- (3.12) £1 + Ez and the following boundary conditions are fulfilled by equations (3.11) at the interlace (x=O),
(3.13)
the force F(x) between the ion and its image is equal to,
-i}e2 F(x) = 2 o (3.14) (41te0) ez(2x)
If e2 < e1, F < 0 (attractive force), there is a reduced self energy W(x) such that,
00 W(oo) - W(x) = -1 F(x)dr
i}eo = x>r (3.15) 47t£0 EzX
It follows,
-i}e2 W(x) = 0 (-oo < X <-r) (3.16) 41t£0 £1X and
2 2 0 W(x)= e [l--- l] - i}eo (r < X < oo) (3.17) 47tEoP Ez £1 81tE0EzX
Chapter 3: The Dielectric Model of the Lipid Bilayer page 3.6 Karolis; Thesis: THE DJEI.ECI'RlC CHARACTERfZATION OF UPID BILAYERS 35
Extending this to a membrane which is considered to be a thin film of dielectric in contact with another medium of finite thickness requires the introduction of multiple image charges.
Neumke and Lailger (1969) have shown that the potential is a rapidly varying function of position only when the ion is very close to the interface (x < 4r). They also showed that the
Born energy in the membrane is approximately constant for 95% of the width of the membrane and essentially has the same value as that for an infinitely thick membrane.
Parsegian (1969), however, considered the effect of the finite thickness of the membrane hydrocarbon region on the ion self energy compared to the self energy in the bulk hydrocarbon and deduced that the change in energy is - 1.4 (R/Ohc), which is very small for membranes only 4-10 nm thick.
Chapter 3: The Dielectric Model of the Lipid Bilayer page 3.7 Karolis; Thesis: THE DIELECI'RIC CHARACTERTZATJON OF UPJD 811.4.YERS 36
3.3 ION-ION INTtRACTIONS (DEBYE-HUCKEL THEORY)
3. 3 .1 Introduction
Ion-ion interactions affectthe equilibrium properties of ionic solutions and interfere with the drift of ions under an externally applied electric field. The degree to which these interactions affect the properties of solutions will depend on the ion population density and, therefore, also on the nature of the electrolyte. The Debye-Hiickel approach was to consider the effect of the time-average spatial distribution of ions about a single reference ion.
3. 3. 2 The Chemical Potential
The free energy of ion-ion interactions is the electrostatic work required to charge a solution of discharged ions. For a single species, the partial free energy change arising from the interactions of one ionic species with the ionic assembly is called the chemical potential change,
(3.19) where NA is Avogadro's number, W is the work required to charge a single ion to a final charge Zieo and q, is the electrostatic potential at the ion surface ('I'= Zieo/Eri), where ri is the ion radius and E the dielectric constant of the medium.
Chapter 3: The Dielectric Model of the lipid Bilayer page 3.8 Karolis; Thesis: THE D/El.£CTRJC CHARACTERIZATION OF UPJD BILAYERS 37
3.3.3 Charge Density Near an Ion
For a spherically symmetrical charge distribution, the relation between the electrostatic potential and the charge density Pr around a given ion at a distance r from the ion, is given by
Poisson's equation,
_1 _!_[r2d'I'] = _ 41t p (3.20) r2 dr dr e r
The concentration of ions (single species) in any volume element in a system in equilibrium can be described by a Boltzmann distribution,
n = 0 0 exp[-;] (3.21) where W is the self energy difference of an ion located first in the bulk solution where the concentration is n and some other place where the concentration differs for some reason.
Alternatively it may be considered as the work that must be done by a hypothetical agency against the time average of the electrical and other forces between ions in producing a concentration change. For no concentration change, n = n0 and W = 0.
If short range interactions (such as dispersion interactions) are excluded and only simple coulombic forces apply, W is the Born energy difference described by Equation 3.10. If short range forces such as image forces are included W takes the form of Equation 3.17.
Chapter 3: The Dielectric Model of the Lipid Bilayer page 3.9 Karolis; Thesis: THE DIELECIRJC CHARACTERIZATION OF UPID BILAYERS 38
3. 3. 4 Linearization of the Boltzmann Equation
We have from Equation (3.21) an expression for the excess charge density in a volume element dv, distance r from the central ion centre,
(3.22)
For systems in which the average electrostatic potential 'Pr is small (weak electrolytes),
(3.23)
3.3.5 Linearized Poisson-Boltzmann Equation
From Equations (3.20) and (3.23)
(3.24)
which is the linearized P-B equation.
Defining a new constant x2,
(3.25)
we have
J_ d'l'r] = x2q, (3.26) 2dr~[r2 dr r r
page 3.10 Chapter 3: The Dielectric Model of the lipid Bilayer Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BIUYERS 39
3. 3. 6 Solution to the linearized P-B equation
The general solution to Equation (3.26) can be expressed in the form
µ = Ae-xr + Bexr (3.27)
where, A and B are constants, and µ is a dummy variable defined by
µ = q,r r
As r ~ oo, q,r ~ 0, therefore, B = 0,
and
Ae-xr q, =-- (3.28) r r
It follows from Equation (3.25), as nf ~ 0 for a very weak electrolyte, X ~ 0.
Therefore,
e-xr ~ 1,
(3.29)
For a point charge:
(3.30)
Thus,
(3.31)
Chapter 3: The Dielectric Model of the Lipid Bilayer page 3.11 Karolis; Thesis: THE DIEUCI'RJC CHARACTERIZA.TION OF UPID Sil.AYERS 40
3. 3. 7 The ionic cloud surrounding an ion
From Equation (3.20) and the linearized Poisson-Boltzman equation it can be shown that the charge density around an ion can be expressed in the form
e 2 (3.32) Pr = --x41t 'I' r
Using the result of Equation (3.31 ), it follows,
(3.33)
The charge contained within a thin spherical shell of the ionic cloud is a function of r.
(3.34)
which is a maximum when r = x- 1 (the Debye-Hilckel reciprocal length)
The potential \flcloud due to the ionic cloud at some point in the system is independent of rand
given by
(3.35)
It follows that the chemical potential change of Equation (3.19) may be written
(3.36)
Chapter 3: The Dielectric Model of the lipid Bilayer page 3.12 Karolis; Thesis: THE DIEU:.CTRJC CHARACTERIZATION OF UPID BILAYERS 41
3. 3. 8 Thickness of the Ionic Atmosphere
It follows from the Debye-Hiickel theory that the ionic atmosphere around an ion is both concentration and type dependent. Bockris and Reddy ( 1970) have shown that for monovalent ions the thickness of the ionic atmosphere varies between 0.1 nm and 30 nm for concentrations 10-1 and 104 mol m-3 respectively.
3. 3. 9 Partition Coefficient
The partition coefficient is a measure of the probability that an ion in equilibrium may exist in a dielectric medium relative to another. For a system in equilibrium consisting of a membrane bounded by a reservoir of electrolyte, the partition coefficient is simply the ratio of the concentration of ions in the membrane and in the electrolyte.
Thus, using the Boltzmann Equation (3.21), the partition coefficient reduces to the expression,
nm W(co) = e kT (3.37) where, nm is the concentration of ions in the membrane.
If one assumes that monovalent ions have a 0.1 nm radius and the dielectric constant of the lipoidal membrane to be 2.2 and for water to be 80, the partition coefficient can be shown to be
- 10-54, which is too small to explain the measured de conductance of biological and bilayer lipid membranes. The small changes to the dielectric constant of water due to the presence of ions (Table 2.23, Bockris and Reddy, 1970) do not significantly alter the ratio.
The dielectric constant in the primary solvation sheath surrounding an ion is of the order of 6, yet using this value in place of 80 only increases the value of the partition coefficient by x1018, which is insufficient to explain the measured de conductance.
Chapter 3: The Dielectric Model of the Lipid Bilayer page 3.13 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 42
If one assumes that the ions are surrounded by an excess charge, as described by Debye
H tickel, the virtual-radius of the ion is at least an order of magnitude greater than the crystal radius. Such large ions could account for the conductance by increasing the partition coefficient to 10-6•
Chapter 3: The Dielectric Model of the Lipid Bilayer page 3.14 Karolis; Thesis: THE D/EUCTRJC CHARACTERIZATION OF UPID BIUYERS 43
3. 4 ION MIGRATION
3. 4 .1 Introduction
A flux (rate of transport) of ions can come about in three ways. If there is a difference in the concentration of ions in different regions of the electrolyte, the resulting concentration gradient produces a flow of ions; a process termed diffusion. A flow of charge under the influence of an electrostatic field is called conduction or migration. Whole liquid movement due to pressure, density or temperature differences is referred to as hydrodynamic flow and will not be discussed further.
There are at least two ways in which ions can pass through a membrane: by going out of solution on one side, into solution in the membrane and redissolving in the solution on the other side; or by passing via holes or pores (filled with water) that are part of the membrane structure.
The properties of the membrane which may influence permeation by ions are: its thickness; the solubility of ions in the membrane; the electric charge on the surface; the sign and density of this charge; the breadth, width and tortuosity of the pores; the electric charge in the pores; and the mobility of the ions in the pores.
3.4.2 The Forces Moving Ions
The total driving force for ionic transport is the negative gradient of the electrostatic potential plus the chemical potential, called the electrochemical potential (Giiggenheim 1929). The electrochemical potential takes the form (in units of J mol-1),
µ = µo + RT In(yc) + zF'I' + PVP (3.38) where µ 0 is the chemical potential, R the Gas constant, T the absolute temperature, z the valency, F the Faraday constant, 'I' the electric potential, P the hydrostatic pressure and Yp the partial molar volume, y the activity coefficient and c the ion concentration.
Chapter 3: The Dielectric Model of the lipid Bilayer page 3.15 Karolis; Thesis: THE D/EUCTRJC CHARACTERTZAT/ON OF UPID BILAYERS 44
In units of electron volts and for ideal solutions without hydrodynamic influences (Hope,
1971 ), the electrochemical potential µj for species j is given by
(3.39) where µf is the standard chemical potential, k is the Boltzmann constant, T the absolute temperature, Cj the ion concentration, z the ion valency, eO the electronic charge and 'I' the electric potential. The chemical activity "{Cj has been replaced by the concentration Cj for simplicity.
For the one dimensional case, the force Xj on ions j is
(3.40)
d O kT d d = --(µ-) - --(c-) - z-e -('I') (3.41) dx J C· dx J J 0 dx J
The electrical current Jj carried by the ionic species j is given by
(3.42)
where Dj is the diffusion constant and is related to the absolute mobility, Uj by the Einstein relation: kT D-=-u· (3.43) J z-e J J 0 It follows from Equations (3.41) and (3.42)
(3.44)
which is the generalised form of the Nemst-Planck equation.
Chapter 3: The Dielectric Model of the Lipid Bilayer page 3.16 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 45
In the bulk solution,
dµ~ _J =0 (3.45) dx and Equation (3.40) reduces to the standard form of the Nemst-Planck equation
(3.46)
page 3.17 Chapter 3: The Dielectric Model of the Lipid Bilayer Karolis; Thesis: THE DIELECTRIC CHARACfERflATION OF UPID BILAYERS 46
3.5 MEMBRANE CONDUCTANCE AND CAPACITANCE
3. 5 .1 Introduction
Exact analytic solutions of the Nemst-Planck-Poisson equations are possible for systems in equilibrium (Jj=O). Initially, consideration was given to deriving the ionic concentrations in a binary electrolyte as a function of distance from either a point charge or a charged sheet. In this way Gouy (1910) and Chapman (1913) obtained an exact solution for what has become known as the ionic double layer. Special cases were also considered. For example Bartlett and
Kromhout (1952) and Landahl (1953) investigated the semi-permeable membrane, while
Overbeek (1956) and Dainty and Hope (1961) considered the immobilisation of ions of one sign.
Approximate solutions were obtained by Mauro (1962) who examined regions of smeared fixed charge, while Karreman (1964) considered the adsorption of ions onto fixed charges. The
Donnan (1911) approach was to consider electroneutrality throughout each region. A comprehensive treatment has been provided by Briggs, Hope and Robertson (1961).
3.5 .2 Membrane Conductance
If one assumes that the concentration of ions is every where uniform in the membrane
(Planck's assumption), and the field gradient is constant (Goldman, 1943)t
d d2 dx (c} = 0 (Planck); -('I')= 0 (Goldman) (3.47) dx2
t The electrical potential 'I' within the membrane is related to the space-charge density p by Poisson's equation ct2\j//dx2 = -4,tp/E. As Lliuger and Neumke ( 1973) pointed out. the Goldman approximation is valid so long as
111'1'1 « kT /e 0 ( or 26 mV). The ion concentration Cj • therefore. must fullfill the inequality
Cj«2£mkT/1t(e0 d)2.
Chapter 3: The Dielectric Model of the lipid Bilayer page 3.18 Karolis; Thesis: THE DIEIECTRJC CHARACTERfZATION OF UPID 8/lJt.YERS 47
Then, d'¥ - =constant dx
V -d (3.48) where, V is the externally applied potential and d is the membrane thickness. The Nernst
Planck equation (3.42) reduces to
q2Dc V J = - kT d, where q = ze0 (3.49)
The membrane conductance, ( (resistance )- 1) is, therefore, given by
q2Dc G =- kTd (3.50) or, alternatively
G= quc (3.51) d where u is the mobility.
A modified form of the Nernst-Planck equation was used by Neumke and Uiuger (1969) to examine the current-voltage characteristics of bilayer lipid membranes. In their analysis the standard chemical potential was equated to a position dependent potential energy function which could be calculated by the method of electrical images to account for the finite thickness of the membrane and the proximity of some ions to the water/membrane interface (see section
3.2.3). In doing so, the conductance exhibited non-linear current-voltage characteristics.
However, for low ionic strengths and voltages, satisfactory agreement between theory and experiment was established.
Chapter 3: The Dielectric Model of the lipid Bilayer page 3.19 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID Bll~YERS 48
3. S. 3 Membrane Capacitance
The analogy between a planar lipid bilayer immersed in an electrolyte and a parallel plate
capacitor has been widely accepted and provided reasonable results for bilayer thickness
(Hanai, Haydon and Taylor, 1964; White, 1970a, b; Fettiplace, Andrews and Haydon, 1971;
Ashcroft, Thulbom, Smith, Coster and Sawyer, 1980). The model assumes electrical neutrality
within a bilayer of pure a homogeneous phase bounded at each discrete interface by an aqueous medium in which the charge concentrations are everywhere uniform. The capacitance, therefore is seen to be due entirely to the interfacial polarisation occurring at the water interfaces. In this way the geometrical capacitance (Lauger, Lesslauer, Marti and Richter,
1967) can be expressed as Cg = e0 e/d, where e is the dielectric constant of the bilayer interior and d is the thickness of this region. There are several sources of uncertainty associated with this simplistic view of the membrane capacitance which will now be discussed.
Effects of unstirred layers
The difference in ion transport numbers between the bilayer and adjacent solutions will, under the action of an applied potential, cause electrolyte concentration changes at the bilayer-solution interfaces. The regions of enhanced and depleted concentrations due to this phenomena are referred to as unstirred layers and result in the development of as time-variant non-ohmic conductance across a pseudo 'composite bilayer'. The thickness of unstirred regions has been estimated to be about 0.2 mm (Segal, 1967; Holtz and Finkelstein, 1970; Lerche and Wolfe,
1975). For steady current flow the concentration changes that take place at the phase boundaries are complicated by local osmotic flows and diffusion potentials. Barry and Hope
(1969) considered these perturbing influences in water flow rates in electroosmotic experiments which had hitherto been neglected. For biological relevant electrolyte concentrations (such as used in this work), the unstirred layers originating from univalent ions with, for example, transport number ratios in the bilayer of 100:2 (i.e. the bilayer is perm-selective), but with similar ion mobilities in the bulk solution, were found to generate significant potentials for current densities> 103 nA m-2. The greater the current density the more rapidly the potentials
Chapter 3: The Dielectric Model of the Lipid Bilayer page 3.20 Karolis; Thesis: THE DIEU:CTRIC CHARACTERIZAIJON OF UPID BILAYERS 49 approached extremely high values. Similar results were obtained by Macdonald (1976) who also showed that the reverse current potential profiles were influenced by the different time dependencies for the ohmic drop and potentials to develop. The larger the differences in transport number between the bilayer and the bulk solution the greater the time dependent changes in the total potential and therefore the charge storage.
Smith (1977), examined the case for sinusoidal current flow using the model of Barry and
Hope (1969) and deduced the concentration profiles as a function of the current flow in complex form. The constant field approximation (using a small alternating current voltage) was employed to determine the impedance of the bilayer for perfectly stirred solutions and imperfectly stirred systems. The result was that the contribution to the impedance arising from unstirred layers could be identified as a separate series term. The total capacitance of the
'composite' bilayer (which included the bilayer and unstirred regions), was determined to be as high as 1 F m-2 at 0.05 Hz. It is assumed, however, in this work, that the transport numbers of the anions and cations are similar to one another in both the solutiont and the bilayer (Uiuger and Neumke, 1973; Ashcroft, 1979) and therefore the effects discussed above should not appear in unmodified planar lipid bilayers.
t The transport numbers for K+ and Cl· in solution are approximately equal (within 0.1 %).
Chapter 3: The Dielectric Model of the lipid Bilayer page 3.21 Karolis; Thesis: THE DIEUCTRJC CHARACTERIZATION OF UPJD BILAYERS 50
The ionic double layer
The total measured direct current electrical capacitance and the effect of the double layer capacitance was investigated by Ui.uger, Lesslauer, Marti and Richter (1967).
Consider a bilayer to be of uniform thickness (with edges at x=-d and x=O), with infinite resistance (i.e. within the film the electrolyte concentration was zero) immersed in a univalent electrolyte solution of concentration n0 • The dielectric constants of the bilayer and solution were
Eb and Ew, respectively. The two surfaces of the sheet are assumed to carry a uniform charge density When a potential difference V = '¥ x=oo - q, x=-oo (3.52) is impressed across the bilayer, the concentration of the cations, n+ and anions n_ are given by the Boltzmann relations n = n ecj>(x) (3.53) - 0 and $(x) is given by ze0 $(x) = kT {'P(x) - 'P(oo), for Q ~ X ~ 00 (3.54) ze0 } $(x) = kT {'P(x) - '¥(-00) , for -oo ~ X ~ -d (3.55) k is the Boltzmann constant, T is the absolute temperature, e0 is the electronic charge, 'If is the electrical potential and z is the valency of the ion (= 1). Chapter 3: The Dielectric Model of the Lipid Bilayer page 3.22 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID Bll~YERS 51 The Poisson equation for a planar bilayer can be written as (3.56) where the net charge density at any point is given by (3.57) Since, d2<1> = zeo d2'¥ (3.58) dx2 kT dx2 it follows d2<1> = (3.59) dx2 substituting for n+ and n_ , 2 2 ') d = 81tz e~n 0 (3.60) dx2 twkT sinh ') . h = K- sm (3.61) where, K= (3.62) is the reciprocal Debye- Htickel length. Chapter 3: The Dielectric Model of the lipid Bilayer page 3.23 Karolis; Thesis: THE DIEUCTRIC CHARACTERIZATION OF UPID Bit.AYERS 52 For the following boundary conditions V 'I'(± co) =±2 , and ( d'I') - 0 (3.63) dx x::oo - the solution to Equation (3.62) is given by V 2kT { 1 - tanh ( ~ )e-lCX] 'l'(x) = - + -I (3.64) 2 ze0 1 + tan h ( 2a ) e -1CX where, [ ~ - 'l'(o)] (3.65) a= 2kT Assuming 11+ = n_ = 0, d\j//dx = constant across the bilayer (Goldman Approximation), and 'l'(x) = 2x d+ d '1'(0), (-d~x~O) (3.66) it follows Ew V zeo Kd-sinha + 2a = -- (3.67) Eb 2 kT Now the capacitance per unit area C = crN, where cr is the total charge per unit area given by ze foo cr = k; Jo (n+ - n_)dx (3.68) Chapter 3: The Dielectric Model of the lipid Bilayer page 3.24 Karolis; Thesis: THE DIELECTRIC CHARACTERfZATJON OF UP/D Bll~YERS 53 It follows from Equation (3.67), C = C sinha. (3.69) g 2a.£b -d- + Sinha. Kl Ew where, (geometrical capacitance per unit area) (3.70) For small V, i.e. V<< kT/e0 < 25 mV, a. is very small and Equation (3.70) reduces to (3.71) and 1 d 2 -=--+-- c EbEo E0 Ew 1C (3.72) = [ geome~c cap. + double l~yer cap. ] For relatively high concentrations 1/K is small and the double layer capacitance is very small. C, therefore, approaches the geometric capacitance Cg. The same analysis was used by Everitt and Haydon ( 1968) to calculate the capacitance of a charged membrane. If the membrane carries a fixed surface charge crf which is neutralised by an equal but opposite diffuse charge cr1. page 3.25 Chapter 3: The Dielectric Model of the Lipid Bilayer Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UP/D BILAYERS 54 Thus ~= - cr~. When V>O, an additional diffuse charge appears on each side of the membrane referred to as a polarisation charge crp. Thus, for the right side of the membrane cr = roo pdx - cr1 (3.73) P Jo d\J' as x--too - --t O · ' dx ' d\J' d\J' x = 0, dx = dx )x=0 (3.74) membrane capacitance C = crrfV, reduces to (3.75) when V << membrane surface potential (Overbeek, 1952). Thus the ionic double layer can be neglected only when the bilayer has a large net surface charge or when the ion concentration is > 0.1 molar. For example, the double layer capacitance for a chargeless bilayer having a hydrocarbon region 2.8 nm thick in a 10- 1 molar solution would be 719 mF m-2. This would result in only a 2% correction to estimates of thickness. A more detailed discussion is given in Chapter 6. Chapter 3: The Dielectric Model of the Lipid Bilayer page 3.26 Karolis; Thesis: THE DIELECTRIC CHARACTERfZATION OF UPID BILAYERS 55 3. S. 4 The dielectric constant of the bilayer hydrocarbon interior The dielectric behaviour of the hydrocarbon interior of the bilayer may not assume the properties of a bulk hydrocarbon. Ohki (1968) deduced significant differences between the polarizability of well structured two-molecule thick models and bulk solutions with the same degree of order. The dielectric constant in the axis of the molecules (usual direction of the applied electric field) was about 50% greater than in the perpendicular direction. The results, however, were not in agreement with experiment. Huang and Levitt (1977) were able to show that the results of Ohki were erroneous because of inappropriate selection of the boundary conditions and deduced that the dielectric constant of the appropriate bulk hydrocarbon could be used for lipid bilayers. The above discussion assumes a pure hydrocarbon medium. The incorporation of water molecules in the bilayer interior, however, could significantly alter the dielectric properties of the bilayer core. Schatzberg (1963, 1968) has shown that water solubility increases with the alkane chain length, when expressed in terms of a mole fraction and is of the order of 0.4 Kg m-3 (or 2.5 mole m-3) at 25°C. The effect of temperature is to nearly double the solubility when the temperature is raised from 25°C to 40°C. Thus, according to Schatzberg, the ratio of the number of water molecules to hexadecane molecules could be as high as 1: 1000 (i.e. 0.0023 moles of water per 3.4 moles hexadecane). Such a figure would do little to affect the bulk hydrocarbon dielectric constant. 3. S. S Non-dielectric charge storage in the bilayer Non-dielectric charge storage due to uneven anion and cation concentrations in the bilayer would contribute to the total measured bilayer capacitance. Such space charge effects, however, have been shown.by Neumcke, Walz and Lauger (1970) and more recently by Ashcroft (1979) to play a negligible role in capacitance measurements where the ion concentrations are low and the applied voltage is< 25 mV. Chapter 3: The Dielectric Model of the Lipid Bilayer page 3.27 Karolis; Thesis: THE D/EUCfRJC CHARACTERfZATION OF UPID B/l,,AYERS 56 3.6 SUMMARY A model of the behaviour of ions in dielectric media has been presented. The forces that act on ions and their ability to translocate between media of differing dielectric constant has been shown to be intimately related to the ion self energy and the dielectric constant. The very low dielectric constant associated with the hydrocarbon interior of the bilayer prohibits ion movement through this region without a facility such as a hydrated pore. The effects of unstirred layers and the electric double layer on capacitance are presented. page 3.28 Chapter 3: The Dielectric Model of the Lipid Bilayer Karolis; Thesis: THE DIELECTRIC CHARACTERfZATION OF UPID Bll.AYERS 57 CHAPTER 4 EXPERIMENTAL ARRANGEMENT 4.1 INTRODUCTION 58 4.2 GENERAL DESCRIPTION 60 4.2.1 Vibration-Free Platform and Faraday cage ...... 60 Mechanical Shock ...... 60 Electrical Shock ...... 60 4.2.2 Lipid Bilayer Chamber Assembly ...... 61 The Polycarbonate Cell and Septum ...... 62 Temperature Control ...... 62 Hydrostatic Pressure Control ...... 63 The Viewing System ...... 63 The Electrode System ...... 64 4.2.2 The Amplifier Assembly ...... 65 4.2.3 Computer Based Data Acquisition System ...... 66 4.2.4 Microprocessor Software ...... 67 4.3 DISCUSSION 69 Chapter 4: Experimenlal Arrangemenl page 4.1 Karalis; Thesis: THE D/El.ECIRJC CHARACTERIZATION OF UPID BILAYERS 58 4.1 INTRODUCTION The formation of a bilayer lipid membrane separating two aqueous phases is conceptually simple: two compartments are separated by a thin partition and communicate through an aperture in this partition. The compartments are filled with an aqueous medium and a (thick) film of amphipathic lipid is formed in the aperture separating the aqueous phases. The thick film spontaneously thins by draining to form a ring or annulus of bulk phase lipid around the margin of the aperture. At equilibrium, a metastable bilayer lipid membrane continues to separate the aqueous phases. In this work membranes were formed in salt solutions in a chamber assembly using the film drainage method of Mueller, Rudin, Tien and Wescott (1962). Their formation was monitored under strong white light illumination with a low powered microscope (x15). While draining, a digitally synthesised 1 Hz sine wave was applied across the membrane via Ag-AgCl electrodes straddling the membrane. The applied current was measured by the potential developed across a known high impedance, while the AC potential developed across the membrane was measured by a separate pair of Ag-AgCl electrodes. The current and voltage signals were individually amplified before sampling by a custom built computer system described by Laver (1983) and Chilcott (1988). The digitally synthesised sine wave was phase-locked to the sampling of the current-voltage wave signals which were also stored. Such data allows the capacitance and conductance of the membrane to be calculated on line. (The electronic apparatus is described in detail in section 4.3). In this way the progress of membrane formation could be monitored electrically by monitoring the membrane capacitance. When the capacitance and conductance at 1 Hz remained steady (for a given temperature), impedance measurements were begun. On completion of the measurement of the chosen spectrum of impedance with frequency, the data was stored on floppy disk for analysis ('FITTING') at some later stage. Chapter 4: Experimental Arrangement page 4.2 Karolis; Thesis: THE DIELECTRIC CHARACTERfZAT/ON OF UPID BILAYERS 59 The dielectric impedance measurements discussed above and in Chapter 3, however, placed important constraints on the system. The most important of these was the length of time the bilayers remained intact after reaching equilibrium and the high precision required of the impedance measurement. These criteria were addressed in the experimental arrangement. Chapter 4: Experimental Arrangement page 4.3 FIGURE 4.1 Experimental system consisting of the vibration free platform supporting the Faraday cage with viewing system in front (centre); BULFIS computer (right). The membrane chamber assembly and amplifiers are siutated in the Faraday cage. FIGURE 4. 2 Experimental arrangement of the viewing system; the membrane chamber assembly and amplifiers. The syringe (centre bottom) was used to maintain equal hydrostatic pressure in both halves of the BLM cell (centre). Karolis; Thesis: THE DIELECTRIC CHARACTERfZATION OF UP/D BILAYERS 60 4.2 GENERAL DESCRIPTION The experimental system, shown in Figure 4.1 consisted of the following main components: (a) A 'vibration-free' platform (b) Membrane chamber assembly (c) Computer based, four terminal impedance measuring system (BULFISt) 4. 2 .1 Vibration-Free Platform and Faraday cage Mechanical Shock A lipid bilayer is a structure only a few nm thick covering an area as large as 6 mm2 (in this work). Despite this apparent fragility many types of bilayer lipid membrane are remarkably resilient to different types of mechanical stress (Warrant, 1985). Mechanical shock, however, mainly from vibrations through the floor, is an important exception. To reduce the effects of such vibrations a platfonn was constructed, consisting of the following: A water ballast tank was made from 0.01 m thick perspex sheet with dimensions 1 x 0.5 x 0.25 m3• It was filled with distilled water and sealed with a soft rubber strip. The tank was supported by 6 soft springs situated on a rigid aluminium framed table. The radius of the spring loop and its Y oung's modulus were matched against the weight of the ballast tank to minimise shock transmissions from the floor. The only sources of mechanical shock to a bilayer were thus reduced to air currents, and through connecting electrical leads which were never allowed to be taut (Figure 4.2). Electrical Shock The dielectric strength of most lipid bilayers is about 1<>4 V mm-1. These extremely high field strengths are a clear indication of the excellent insulating properties of lipid bilayers. Because of t BULFIS: Biophysics Ultra Low Frequency Impedance Spectrometer Chapter 4: Experimental Arrangement page 4.4 FIGURE 4.3 a FIGURE 4.3 Close up views of the bilayer chamber and amplifier assembly. The current electrodes are thicker than the voltage electrodes. The temperature transducer is located in the rear half of the beaker into which the polycarbonate cell is immersed FIGURE 4.3 b Karolis; Thesis: THE DIELECTRIC CHARACTERfZ.4.TION OF UPID BILAYERS 61 their small thickness, however, such field strengths are reached with only 100 m V across the bilayer. The voltage-current relationships are ohmic up to approximately 50 m V and electrical breakdown occurs around 150 m V for lecithin/cholesterol BLM. The probability of breakdown is a function of both the duration and magnitude of the applied voltage. They are, nevertheless, susceptible to electrical transients and atmospheric charges and must be electrically shielded. One such method is to surround the sensitive measuring apparatus with a Faraday cage. The Faraday cage shown in Figure 4.1 consisted of an aluminium box, measuring 0.75 x 0.5 x 0.5 m3 with front face removed, and grounded through the mains supply. 4.2.2 Lipid Bilayer Chamber Assembly The bilayer lipid membrane chamber assembly, shown in Figure 4.3, consisted of the following items: a modified 50 ml Pyrex beaker; a polycarbonate cell which included the septum; a Peltier heating/cooling device; a temperature transducer; a syringe to adjust the hydrostatic pressure in one half of the polycarbonate cell; a white light source and a low powered microscope. The cell, shown in Figure 4.4, was suspended in the beaker with stainless steel clips attached to a Perspex lid. A neoprene 'O'-ring was incorporated in the lid to prevent movement of the cell when wiping the septum with lipid. The temperature transducer, (Parameters, AD590F), was housed in a small closed ended Perspex cylinder filled with heat conducting silicone elastomer, and was suspended in the beaker via a hole in the lid. The bottom of the Pyrex beaker was ground flat so that good contact could be made with the Peltier heating unit which was attached to a copper block with heat conducting epoxy. The electrical supply to the heating unit was situated remote from the Faraday cage, while the connecting leads were supported at a junction mounted on the supporting table to reduce the likelihood of mechanical shock. The beaker was surrounded by a layer of low density polystyrene foam for insulation purposes. Chapter 4: Experimental Arrangement page 4.5 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF LIPID BILAYERS E ,, I''1 :I ',I ) 1", ~ U I L ------1·,~f ___ , B p FIGURE 4.4 a Schematic diagram of the lipid bilayer chamber assembly. B : modified beaker with ground glass bottom C : polycarbonate cell, consisting of two parts, screwed together against a silicone 'O'-ring E : current (large) and voltage (small) silver electrodes P : Peltier device, for heating and cooling S : stainless steel spring supporting the cell in the beaker The temperature transducer, not indicated, was located in the rear half of the cell. FIGURE 4.4 b The three components of the polycarbonate cell. Chapter 4: Experimental Arrangement Karolis; Thesis: THE DIELE.CIRIC CHARACTERflATJON OF UP/D BILAYERS 62 The Polycarbo,aa,te Cell and Septum Polycarbonate was chosen for the septum material for its low dielectric constant (about 2.1), high electrical resistance, chemical inertness and low contact angle at the lipid/water interfacet. The cell was constructed in two parts which could be sealed together on an 'O'-ring with stainless steel keys. A schematic diagram of the cell and the chamber is shown in Figure 4.4. Provision for the electrodes and vinyl tubing (connected to a reservoir for hydrostatic pressure adjustment) were made in the 'male' section of the cell. The hole on which the membranes were to be painted was manufactured on the face of the 'male' section. The hole was prepared with a smooth boundary and sharp edge. The diameter of the hole was measured with a travelling microscope. The average of several diameters was taken to be the diameter of the hole. Electrical insulation between the inside of the cell and the bulk of the aqueous solution was maintained by the 'O' ring when a membrane had formed across the hole. The 'O'-rings (Ludowici type BS1806-116) were made from a medical grade silicone compound (Ludowici type SL1125M) which was inert to the electrolytes and solvents used in this work. Temperature Control The temperature of the electrolyte and therefore the bilayer lipid membrane was adjusted by manual operation of a 0-5 V D.C. power supply driving a solid state Peltier device (Cambion PIN 601-4000). The Peltier device was mounted on a copper block imbedded in an aluminium stand. Thermal contact with the ground glass bottom beaker containing the electrolyte and the copper block was enhanced with heat conducting epoxy. In order to avoid soiling the beaker, however, a thin mylar sheet was placed between the beaker and the epoxy. t The impedance of bilayer lipid membranes have been measured to be as high as 109 n. The electrical studies performed in this work, therefore, required the sides of the membrane to be electrically insulated from one another better than 1012 n for a 0.1 % error in the impedance. This constraint plus the need to use a material inert to the electrolytes and solvents commonly used in this type of work placed important restrictions on the design of the cell. To further complicate matters it was also important to be able to clean the cell between experiments and therefore dismantlling and assembly needed to be fairly easy. Chapter 4: Experimental Arrangement page 4.6 Karalis; Thesis: THE D/EUCTRJC CHARACTERlZAT/ON OF UPID BILAYERS 63 The temperature was monitored by a solid state temperature transducer (Analog Devices 590F) placed inside a closed ended acrylic rod filled with silicone compound having good thermal characteristics, high viscosity and electrically inert. The transducer was calibrated against a platinum thermocouple and found to be accurate (within 0.15 °C) in the range 20 - 50 °C. The rod was suspended in the electrolyte and the voltage displayed digitally outside the Faraday cage. Uneven heat conduction from the beaker was minimised by surrounding the beaker with low density polystyrene foam. Hydrostatic Pressure Control A disadvantage of a bilayer lipid membrane chamber system consisting of two unequal volumes of electrolyte is differential evaporation of the electrolyte in the two sections of the chamber. The differential evaporation resulted a hydrostatic pressure gradient across the membrane which was corrected by adjusting the electrolyte volume in one half of the chamber with a micrometer adjustable syringe containing a small quantity of the electrolyte. Apart from evaporation, expansion and contraction of the polycarbonate cell during heating and cooling also resulted in a hydrostatic pressure gradient. The overall corrections necessary were easily controlled with the micrometer adjustable syringe and a well set-up viewing system. The Viewing System The cell and beaker assembly, just described, was small and compact and could be readily rotated to optimise the viewing angle and were situated near the centre of the Faraday cage. There were no mechanical linkages between the viewing system and the cell. The bifocal microscope, shown in Figure 4.2 was mounted on a separate floor mounted stand and could be adjusted in position independently of the vibration-free platform and thus without disturbing the bilayer lipid membrane cell assembly. The light source consisted of a 12 volt DC (very low ripple) supply, quartz-iodide projector lamp and reflector to which was attached a quartz fibre Chapter 4: Experimental Arrangement page 4.7 Karolis; Thesis: T HE DIEIECTR/C CHARACTER/7AT/ON OF UPID 8/l~YERS FIGURE 4.5 Experimental arrangement used to photograph each bilayer. Long surviving bilayers were photographed many times; usually coinciding with the commencement of a new sequence of measurements. Chapter 4: Experimental Arrangement Karolis; Thesis: THE DIELECTRIC CHARACTERfZATION OF UPID BILAYERS 64 flexible light pipe. (DC power had to be used to avoid circuits close to the membrane system which carried very large AC currents which would otherwise introduce noise into the system). By carefully manipulating the direction of the light source and adjusting the viewing angle the characteristic interference fringes associated with a thin oily sheet could be seen. While in the transition phase from a thick lipid sheet to a black bilayer membrane the light reflected off the membrane gave it the appearance of bright shiny sheet of oil when planar or flat. Small hydrostatic pressure differences across the membrane due to differential evaporation in the two parts of the cell caused the membrane to bow as evidenced by the disappearance of the planar bright sheet and its replacement with a small highlighted region on a dark background. By moving the light source up and down it was possible to determine which way the membrane had bowed and therefore which way to correct with a compensating reservoir located in a screw adjustable syringe mounted on the microscope stand. Photographs of the membrane could be taken by substituting one of the two ocular lenses of the microscope with an SLR camera body (Nikormat, FfN as shown in Figure 4.5). In order to determine the black membrane area (required in the specific capacitance measurements) a method described by White, (1970a) and Kolarov, Scheludko and Exerowa (1968) was used. This consisted of directing the light source to a mirror situated behind the membrane and photographing the membrane with transmitted light. From the resulting negative an enlarged drawing of the torus and septum was produced. The outlines of these were transferred to a computer via a digitised signal and processed to give a ratio which was a measure of the fraction of the septum area that was occupied by a black membrane. The Electrode System Four electrodes were used in this work. Two for the voltage signals and two for the current signals. The advantages of a four terminal system in this work have already been described in Chapter 3. The electrodes, shown in Figure 4.3, consisted of silver wire freshly coated with silver chloride (Ag/AgCl) by electrolytic deposition in a concentrated solution of potassium Chapter 4: Experimental Arrangement page 4.8 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID Bll.AYERS 65 chloride. The main advantage of using Ag/AgCl electrodes in measuring potential differences is that they have a well defined electrode-solution potential. The current injecting electrodes were made of pure silver wire, 1.5 mm diameter. The wire was lightly sanded with a fine emery cloth to remove any oxides and cleaned thoroughly before use. The voltage electrodes were made from Teflon coated silver wire (Medwire Corp., Mt Vernon, N.Y.). The silver wire was 0.2 mm diameter bare and 0.3 mm diameter with the Teflon coating. An exposed 2 mm tip was treated in the same way as the current electrodes. The voltage measuring electrodes were situated as close as practicable either side of the membrane to reduce the voltage drop that would occur across the aqueous phase between the electrodes and the membrane. The Teflon coating ensured that the voltage measured refers to the potential at the exposed tip of the electrode. Both pairs of electrodes were connected to a Teflon junction block located in an acrylic arm which was attached to a micrometer adjustment mechanism mounted on a separate rigid stand adjacent to the chamber assembly. In this way it was possible to move the electrodes in and out of position even after the membrane had formed. The separation of the electrodes from the cell facilitated cleaning and exchange of systems and so reduced the possibility of systematic errors. 4.2.2 The Amplifier Assembly The amplifier assembly was physically located close to the bilayer lipid membrane chamber and was contained in an earthed aluminium housing. All high impedance current paths, including the current and voltage electrode mountings (which were made from 6 mm diameter brass rods approximately 100 mm long), and the electrical standards were mounted on a 12 mm thick Teflon block. The electrodes were connected to the amplifier housing with short leads and gold plated jacks. The amplifiers consisted of two independent circuits built around the National LF352 (Figure 4.6). This device is a monolithic JFET input instrumentation amplifier having a very high input Chapter 4: Experimental Arrangement page 4.9 Karolis; Thesis: THE DIELECTRIC CHARACTERIZ.ATION OF UPID BILAYERS +15 V 1M + guard input+ -15 V OUTPUT input - - guard External offset -15 V Figure 4.6 Schematic diagram of the amplifier circuitry Chapter 4: Experimental Arrangement Figure 4.6 Karolis; Thesis: THE D/El.ECTRJC CHARACTERIZAf'ION OF UPID BILAYERS 66 impedance (2x1012 Q) and extremely low bias current (3 pA). This was more than adequate for the impedance measurements encountered in this work which were typically less than 109 Q. In addition, the high common-mode rejection ratio (100 db at 100 Hz) and low gain non-linearity (0.02%) assured minimal corrections were necessary to their response with frequency (discussed in Chapter 5.4). The gain was set at 33, (Ro = 33K; RA= 100K and Ra = lOK). Situated outside the Faraday cage was placed an external-offset device to compensate for any DC offsets induced by the amplifiers and which might be so large as to shift the Current/Voltage characteristics of the membrane into the non-linear region. The output stage utilised an operational amplifier (National LM741), set with a gain of 10 to drive the low impedance co-axial cable between the amplifier and the computer. In addition to these devices a voltage divider was used to reduce the sine wave signal amplitude emanating from the computer from 5 V (peak-to-peak) to 10 mV. The divider, situated below the water ballast tank with its casing earthed to the Faraday cage, was designed with a frequency response that filtered out high frequency noise which might emanate from the computer data acquisition system. 4.2.3 Computer Based Data Acquisition System To meet the requirements of high precision impedance data collection described above, Bell, Coster and Smith (1975) developed a computer based 4-terminal measuring system capable of measuring the impedance magnitude with an accuracy of 0.3% and phase angle resolution of better than 0.2% in the frequency range 0.1 - 100 Hz. Since that time improvements by Chilcott (1988) have significantly improved the efficiency and speed of the data acquisition by automation and extended the range of frequencies suitable for measurement from 0.003 Hz - 44.4 kHz (consisting of 44 individual frequencies). The apparatus, shown schematically in Figure 4.7 consisted of a DEC PDP 11/03 microprocessor interfaced to a programmable signal generator, a control board and two transient-storage boards. The function of the microprocessor was limited to initiating signal Chapter 4: Experimental Arrangement page 4.10 Karolis; Thesis: THE DIELECTRIC CHARACTER/7.AT/ON OF UPID BILAYERS VISUAL FLOPPY DISPLAY DISK UNIT DRIVE LSI 11 FREQUENCY MICROPROCESSOR DIVIDER .. SIGNAL TOBLM FROM BLM ANALOGUE MEMORY TO DIGITAL CONVERTER TRANSIENT RECORDER BOARD (2 OFF) FIGURE 4.7 Block diagram of signal generator and data aquisition system, the Biophysics Ultra Low Frequency Impedance Spectrometer (BULFIS) Chapter 4: Experimental Arrangement Figure 4.7 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 67 generation, sampling and storage. A sinusoidal signal was digitally generated from a table stored in a 12 bit random access memory - RAM (Mostek MK4118) designed to function as a shift register. This table was loaded into the 'shift register' memory under software control and at a rate determined by a programmable clock situated on the control board. The clock was driven by a 10 MHz crystal oscillator (accuracy 1/106) and provided 50 clocking rates between 1 MHz and 0.0426 Hz in increasing steps of xl.414 or x21/2. Pulses from the clock were used to load consecutive values from the table into a 12 bit digital-to-analog converter -DAC (type DAC7541). The output signal from the DAC was smoothed by filtering. The two transient-storage boards (one each for the current and voltage signals, respectively, from the amplifier stage), consisted of a 12 bit analog to digital converter - ADC (DATEL EH12B3) and a 16 bit 'shift register' (MK4118). The ADCs were used to digitise the analog data arriving from the differential amplifiers while the shift registers were used to transiently store the data before analysis to yield the amplitude and phase of each signal. 4. 2. 4 Microprocessor Software As indicated previously, the microprocessor was not involved in real-time data acquisition. However, it was involved in transferring essential information from floppy disk to the control board where it was used to set the limits of operation of the signal generator and transient storage boards. The operations included the range of frequencies to be used, the signal amplitude at each frequency, the number of repeat cycles required for averaging at each frequency, the DC offsets and filtering at each frequency. Collectively these parameters constituted a 'frequency data file' which was periodically adjusted as required. The software was written in assembler machine language by TC Chilcott and JR Smith of this laboratory. As the data was collected and stored in microprocessor memory, under software, a least squares fitting routine (Smith, 1977) was initiated to fit a theoretical sine wave function to the current and voltage signals. The method employed 16 bit integer arithmetic in conjunction with a 16 bit sinusoidal table thereby minimising the computation time. The amplitude ratio and Chapter 4: Experimental Arrangement page 4.11 Karolis; Thesis: THE DIEI.LCTRIC CHARACTERfZATION OF UPID BILAYERS 68 phase difference were detennined from the fitted data and the normalised fit parameters for the least squares fitting stored for each channel. Essential to these computations were corrections for differences in response of the instrumentation amplifiers. A calibration procedure, outlined in the next chapter was used to derive a ratio of sensitivities and phase corrections of the current and voltage channels over the frequency range of the measuring device and these too were stored in the frequency file. The normalised fit parameters were calculated by summing the square of the differences between all the experimental and theoretical data points, and was normalised by dividing the sum of the squares of the experimental data points. Ideally this parameter should be zero, but a sufficiently small value of this parameter was used as a criteria for accepting data to be reliable. The sum of the normalised fit parameters of both the current and voltage channels was stored with the amplitude ratio and phase difference between the current and voltage signals in an 'impedance data file' and are referred to as 'unprocessed' data in the following chapter. Chapter 4: Experimental Arrangement page 4.12 Karolis; Thesis: THE DIELECTRJC CHARACTERlZATION OF UPID BILAYERS 69 4.3 DISCUSSION The dielectric behaviour of lipid bilayers is not static, particularly during the thinning phase. In addition, the area of the bilayer will likely increase slowly with time either through drainage or under hydrostatic pressure differences. The greater the length of time, however, that the bilayer remains stable (or at least very slowly changing) the greater the opportunities exist for the gathering of reliable statistical data. For this reason much attention was given to the experimental arrangement. The unpredictable nature of bilayers especially during their formation would impose restrictions on the complexity of the bilayer cell. It was this part of the apparatus that required frequent changing and cleaning and therefore was designed to be readily dismantled and cleaned and assembled. The choice of materials and the cleaning processes are discussed in the next chapter. Chapter 4: Experimental Arrangemenl page 4.13 Karolis; Thesis: THE D/El.ECI'RJC CHARACTERIZ.ATJON OF UPID BILAYERS 70 CHAPTER 5 METHOD AND MATERIALS 5.1 INTRODUCTION 71 5.2 MATERIALS 73 5.2.1 Egg Lecithin ...... 73 5.2.2 Cholesterol ...... 74 5.2.3 Oxidised Cholesterol ...... 75 5.2.4 Cyclosporin A ...... 75 5.2.5 Blood Lipid ...... 76 5.2.6 Aqueous Phase ...... 78 5.2.7 n-Alkane Solvent ...... 79 5.2.8 pH ...... 79 5.3 PLANAR BILA YER FORMATION 80 5. 3 .1 Introduction ...... 80 5.3.2 Dynrunics of Formation ...... 80 5.3.3 The Lipid Solvent Mixture ...... 83 5.4 CALIBRATION - PERFORMANCE OF DATA ACQUISIDON SYSTEM 84 5.4.1 Introduction ...... 84 5.4.2 Amplifier Matching ...... 84 5.4.3 Measurement of Stray Capacitance ...... 85 5.4.4 Calibration of Electrical Standards ...... 86 5.4.5 Performance of the Apparatus ...... 87 5.5 DATA PRESENTATION, REDUCTION AND ANALYSIS 88 5. 5 .1 Data Presentation ...... 88 5.5.2 Data Reduction ...... 88 5.5.3 Data Analysis by Theoretical Modelling ("Fitting") ...... 90 5.5.4 Performance of the Software ...... 90 5.6 PERFORMANCE OF THE SYSTEM 91 5.6.1 Introduction ...... 91 5.6.2 Method and Materials ...... 91 5.6.3 Results ...... 92 5.6.4 Discussion ...... 93 5.7 SUMMARY 94 Chapter 5: Method and Materials page 5.1 Karolis; Thesis: THE D/El.ECTRJC CHARACTERIZATION OF UPID BILAYERS 71 S .1 INTRODUCTION The precise chemical composition of a lipid bilayer, even the most simple formed from a lipid solution of phosphatidyl choline and n-decane, is not known with certainty. This is because the actual composition of a lipid bilayer differs from the bulk lipid characteristics due to differential adsorption and thinning at the biface. Ideally one would like to be able to generate lipid bilayers consisting only of lipid but this is not possible since ultimately a thermodynamic equilibrium must be established between the alkane and lipid in the bilayer and the alkane and lipid in the torus which contains the lipid-in-alkane solution from which the membrane forms. Ultimately also, the lipids in the bilayer must be in equilibrium with the molecules of the lipid in the aqueous phase. The 'time-constant' for this last equilibrium to be established may be, however, very long in comparison with the equilibration time with the torus. The use of an n-alkane solvent to disperse the lipid will inevitably result in some solvent retention in the bilayer. The quantity remaining will depend on a number of factors, such alkane chain length and temperature as well as the lipid itself. For example, the longer the alkane chain length and the lower the temperature the less solvent retention in the bilayer (White, 1970a; Coster and Laver, 1986) and the closer the membrane is to being a pure planar lipid bilayer. The number of lipid materials used successfully for bilayer studies has grown since 1962. These include extracts of brains, eggs, chloroplasts, red blood cells, and of bacteria, oxidised cholesterol, carotenoid pigments, synthetic lipids and other interface-active agents. In addition to these materials, liquid hydrocarbons (hexane to hexadecane) and/or other organic solvents are generally required. The physical characteristics of membranes formed from different combinations of lipids and solvents vary quite widely (Tien, 1974 and Jain, 1972). The reasons for the variations are not always clear. By restricting the model to relatively simple molecules a clearer interpretation of the physical structure of the bilayer may be inferred. The physical properties of the lipid bilayer such as its mechanical stability, permeability, conductance and capacitance have also been shown to be greatly affected by the presence of even trace amounts of foreign materials and drugs. To avoid these perturbing Chapter 5: Method and Materials page 5.2 Karolis; Thesis: THE DIELECTRIC CHARACTERfZATION OF UPID BILAYERS 72 influences/artefacts all glassware used in the storage of bulk materials and lipid mixtures such as test-tubes, lipid bilayer chamber and cleaning beakers were carefully and thoroughly cleaned before being used. They were soaked in a dilute solution of chromic and sulphuric acid for 24 hours; rinsed in running tap water (mineral impurity of 50-100 ppm) for a further 24 hours; boiled in distilled water several times, rinsed in AR-grade ethanol three times and finally in chloroform three times. The polycarbonate cell, acrylic temperature transducer holder, silicone 'O'-rings, teflon coated Ag-electrodes, and assembly tools were treated in the same way except the acid treatment was replaced by a hot detergent solution and the chloroform rinse was dispensed with. Disposable plastic gloves were worn while assembling the lipid bilayer chamber and accessories. All equipment used in the preparation of bilayers was cleaned thoroughly between experiments while those components not in immediate use were kept in a dust free storage cabinet. The organic preparations described below were dissolved in highly volatile liquids and were kept for several years. Evaporation of the solvent during this time, would have altered the molar concentration of the preparations and may have led to oxidation of the egg phosphatidyl choline which would ultimately result in the formation of unstable membranes (Huang, Wheeldon and Thompson, 1964). Selection of the glassware in which the organic preparations were to be stored was, therefore, very important. To reduce the risks of contamination by leaching only borosilicate glassware was used. A screw top (Kimax type, with teflon lined plastic top) test tube was found to have a sufficiently effective seal. The test tubes were tested by weighing them with a few millilitres of chloroform and reweighing them after being placed in a low vacuum for 24 hours and then being left to stand for one week at room temperature. The change in weight of the chloroform due to leakage evaporation was less than .01 %. Chapter 5: Method and Materials page 53 Karol.is; Thesis: THE DIELECTRIC CHARACTERIZATION OF LIPID BILAYERS FIGURE 5. 1 a: Space-filling model of a b: Atom numbering and notation for phosphatidylcholine molecule torsion angles for phosphatidylcholine (Stryer, 1975) (Hauser et al , 1 981) FIGURE 5.2 FIGURE 5.3 Space-filiing model of cholesterol Space-filling model of cyclosporin A (Stryer, 1975) (Knott, 1 987) Chapter 5: Method and Materials Figures5.J, 5 Karolis; Thesis: THE DIELECTRIC CHARACTERIZ.ATION OF UPID Bll.AYERS 73 5.2 MATERIALS 5.2.1 Egg Lecithin Lecithin or 1-,2-diacylphosphatidylcholine (IUPAC-IUB, 1978) is a neutral phospholipid and is generally the major fraction of the total phospholipid occurring in biological membranes (see Table 1.2). The polar head consists of a phosphate and a trimethylammonium group separated by two methylene groups allowing two zwitterionic forms: one in which the separation of the charges is maximal and the other in which a reduced separation of charges results from an internal linkage between the phosphate and trimethylammonium groups in the same molecule. These ionic charges are of considerable interest in relation to lipid-protein interactions and to ionic transport in the membrane as well as the detailed structure of the lipid bilayer structure. A schematic representation is shown in Figure 5.1. Also of great interest is the role of the acyl chains of lecithin in relation to permeability characteristics, membrane thickness and the conformation of the chains in the presence of compounds with cyclic structure such as cholesterol. The composition of the acyl chains of egg lecithin can vary widely depending on the extraction method (Lundberg, 1973) as shown in Tables 5.1 and 5.2. The average molecular weight was found by Lundberg (1973) to be 768 and by Small (1967) to be 775. The density was estimated to be 1.018 kg m-3, and the average molecular weight of the fatty acids to be 273.4 (Lundberg, 1973). The lecithin was obtained from Sigma Chemical Co. (Type VII-E) in a 10 ml ampoule of chloroform, (1 g of lecithin in a 10 ml ampoule of chloroform; 0.1302 moles). The solution was stored at -4 oc in a 13 ml Kimax test tube and sealed with a Teflon-lined screw cap. From this bulk solution a small aliquot of 100 ml (10 mg or 0.013 mole) was pipetted into a clean 5 ml Kimax screw top test tube as required. The chloroform was evaporated off in a vacuum oven at room temperature for 4 hours and the solute stored at -4 °C for later use or dispersed in 0.5 ml of n-hexadecane (0.0017 mole) for immediate bilayer production. A fresh mixture was used at least every other day. Chapter 5: Method and Materials page 5.4 Karolis; Thesis: THE DIEUCTRIC CHARACTERIZATION OF UP/D BILAYERS TABLE 5.1 ANALYTICAL DATA OF ISOLATED EGG LECITHIN % Reference Reference Reference Reference Composition (A) ( B) (C) (D) Nitrogen 1.82 1.79 1.82 Phosphorous 4.02 3.90 3.97 3.94 Glycerol 12.00 Fatty Acids 71.20 70.00 69.50 70.30 REF (A) : Lundberg, B., (1973) REF (B) : Hanahan et al, (1951) REF (C) : Tattrie, (1959) TABLE 5.2 % FATTY ACID COMPOSITION OF ISOLATED EGG LECITHIN Fatty Carbon Double REFERENCE acid atoms bonds ( A) ( B) ( C) ( D) ( E) ( F) ( E) Myristic 14 0 0.1 Palmitic 1 6 0 35.9 32.0 37.7 35.7 36.0 26.2 29.8 Palmitoleic 1 6 1 0.9 1 .0 3.1 1.4 2.0 0.9 Stearic 1 8 0 18.4 16.0 9.2 14.9 14.2 1 5. 1 16. 7 Oleic 18 28.7 30.0 32.9 37.0 35.3 31.9 32.4 Linoleic 18 2 13.9 17.0 17.0 12.4 9.9 12.2 16.3 Linolenate 1 8 3 0.4 Arachidonic 20 4 2.2 1.2 5.4 3.8 Other 22 6 1.4 7.2 REF (A) : Lundberg, B. (1973) REF (B) : Hanahan, Turner and Jayko (1951) REF (C) : Tattrie (1959) REF (D) : Singleton, Gray, Brown and White (1961) REF (E) : Laboratory Supply P/L (1975) REF (F) : Fettiplace, Andrews and Haydon (1971) REF (G) : Huang, Wheeldon and Thompson (1964) Chapter 5: Method and Materials Tables 5 .1 and 5 .2 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF LJPID Bll~YERS 74 5.2.2 Cholesterol The group of crystalline alcohols known as the steroids ( i.e. any substance which is a derivative of the condensed ring system cyclopentanoperhydrophenanthrene) are classified as lipids under the definition given in section 1.2.1. Sterols are those members of the steroid class which contain an hydroxyl group capable of forming an ester, (Gur and James, 1971). The single hydroxyl group located at the 3-carbon atom (C-3) of cholesterol, shown in Figure 5.2, provides the polar moiety of this amphipath while the rest is essentially non-polar. Cholesterol denotes a unique substance of definite molecular constitution and stereochemistry different from all of its isomers. The ring system is about 1 nm long and about 0.5 nm wide. The side chain, when fully extended is 1 nm long. On its own, pure cholesterol is not capable of forming stable membranes. When mixed with lecithin, however, cholesterol appears to induce a number physical changes to the membrane. The conformation of the cholesterol molecule in lecithin membranes and the changes it induces are discussed in Chapter 6. The density of cholesterol was taken to be 1.067 Kg m- 3 and the molecular weight 386.67 (Handbook of Chemistry and Physics, 1984). A freshly synthesised clear crystalline sample was provided by Dr K. Barrow (School of Biochemistry, University of New South Wales) and stored in the dark at -4 °C. In order that a known quantity could be mixed with lecithin a bulk solution was prepared by dissolving a known weight of cholesterol in a chloroform-methanol mixture (3: 1, v:v). A concentration of 0.25 g in 10 ml of solvent (i.e 0.0648 moles) was chosen as convenient. The preparation was stored at -4 °c in a 13 ml Kimax test tube. Chapter 5: Method and Materials page 5.5 Karolis; Thesis: THE DIEI.ECTRIC CHARACTERIZATION OF I.JPID BILAYERS 75 5. 2. 3 Oxidised Cholesterol Almost by accident, Tien ( 1966) discovered that cholesterol, left standing in laboratory at room temperature was capable of producing stable bilayers. The same sample when freshly crystallised from methanol was not capable of forming stable bilayers. He attributed the change in stability to oxidation products of cholesterol 7-dehydrocholesterol. The difference between unoxidised and oxidised cholesterol on lecithin bilayers is discussed in Chapter 6. Oxidised cholesterol was prepared by bubbling oxygen through a sample prepared in the manner just described for about 6 hours. To avoid changing the concentration of cholesterol the oxygen was saturated with chloroform and methanol by bubbling it through a bulk solution of chloroform and methanol (3:1, v:v) before passing through the cholesterol sample. The oxidised cholesterol sample (0.0648 moles in 10 ml) was also stored in the dark at -4 °c. 5.2.4 Cyclosporin A Cyclosporin A (CsA) is a potent immunosuppressive agent which has proven effective in facilitating organ graft survival across major and minor histocompatability barriers in a number of species including man (Green, 1981). CsA inhibits T-cell activation (Andrus and Lafferty, 1982) and is non-myelosuppressive (Borel et al,1976; Borel et al, 1977; Hellmann and Goldman, 1980; Gordon and Singer, 1979), but is associated with both renal (Atkinson, Biggs and Hayes, 1983; Hamilton, Calne, Evans, Henderson, Thiru and White, 1981; Klintmalm, Iwatsuki and Starzl, 1981), hepatic (Klintmalm, lwatsuki and Starzl, 1981) and central nervous system toxicity in man. There is, however, no information on its tissue distribution or its distribution in membranes. Chapter 5: Method and Materials page 5.6 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS TABLE 5.3 LIPIDS OF THE NORMAL HUMAN RED CELL MEMBRANE (Cooper 1970) LIPID µg/10 µmoVlO cells cells Cholesterol 12.67 32.8 Lipid phosphorous l.23 Phospholipid 30.72 3.97 Glycolipid 1.12 l.0 Free fatty acid 0.81 2.6 % of total phospholipid Sphingomyelin 25.2 Lecithin 31.0 Phosphatidyl serine ( +inositol) 13.5 Phosphatidy l ethanolammine 27.3 Lysolecithin l.3 Other (e.g. polyglycerol phosphatide, phosphatidic acid) l.7 TABLE 5.4 PREDOMINANT FATTY ACIDS OF PHOSPHOLIPIDS IN NORMAL HUMEN RED CELL MEMBRANE (Cooper 1970) Fatty phosphatidyl- phosphatidyl- lecithin sphingomyelin acid ethanolammine serine % % % % 16:0 14.2 3.6 33.0 32.4 18:0 12.8 38.6 12.8 7.9 18:1 17.6 8.1 20.0 2.2 18:2 6.4 2.9 22.4 2.0 20:4 22.7 23.8 6.7 0.8 22:0 0.8 l.0 1.3 8.7 22:5 & 22:6 13.0 11.5 l.3 1.0 24:0 & 24:1 0.6 6.2 0.3 38.6 Chapter 5: Method and Materials Tables 5 .3 and 5 .4 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID Bll.AYERS 76 Structurally, Cyclosporin is a cyclic polypeptide consisting of 11 amino acids, among them a characteristic unsaturated C-9 amino acid that is unique to this substance (Petcher et al, 1976). Amino acid composition, configuration (Figure 5.3), molecular weight (1202.64) and most other physiochemical properties have been defined by Ruegger, Kuhn, Lichti, Loosli, Hunguenin, Quiquerez and von Wurtburg, (1976). This compound is insoluble in water but dissolves in organic solvents such as ethanol. Cyclosporin was provided by Professor Jim Biggs, St Vincents Hospital, Sydney in two forms: (a) Ampoule for intramuscular injection consisted of the following: Cyclosporin-A 200 mg Ethanol 20 mg Benzyl Alcohol 10 mg Migliol (2 ml) 1912 mg (neutral oil) (b) Cyclosporin powder in the pure form. This substance was dissolved in chloroform and prepared with the lipid-cholesterol mixture prior to the addition of the alkane solvent. Chemical formula: C62H111N11O12 Molecular Weight: 1202.5 5.2.5 Blood Lipid The lipids of mature red cells are confined to the membrane. The major composition of the human red cell membrane are cholesterol and the phospholipids listed in Table 5.3. On a weight basis phospholipids account for approximately 70% of human red cell lipids. The cholesterol: phospholipid mole ratio is approximately 0.8 (Cooper, 1970). Glycosphingolipids account for 2% of human red cell lipids by weight, and small amounts of free fatty acids are also present. Chapter 5: Method and Materials page 5.7 Karolis; Thesis: THE DIEUCTR/C CHARACTERfZATION OF UPID BILAYERS 77 The red cell membrane does not appear to contain either glycerides or sterol esters. Analysis of red cell ghosts confinn that all the lipid present in the mature red cell resides in the membrane. The extraction of lipids from red blood cells is relatively easy in small quantities and has been described many times. The quantity of lipid required to produce bilayers necessitated the use of 450 ml whole blood. The red cells were packed by low centrifuging for about 20 minutes and the plasma and buffy coat removed by aspiration. The white cells were also removed by aspirating the supernatant from 4 separate washes with an isotonic phosphate buffer and centrifuging for 20 minutes. The washing procedure was performed immediately after the blood was obtained from the donor and carried out at 4 °c. The haematocrit volume was about 200 ml after washing. The lipid extraction procedure was essentially that outlined by Dodge, Mitchell and Hanahan, 1963. All glassware used in the process had been washed in chromic acid, rinsed vigorously in tap water for several hours and rinsed thoroughly with distilled water. Just prior to being used all glassware were rinsed with chloroform and the filter papers were soaked in chloroform. The method was as follows : (a) 10 ml of packed red cells were added, with stirring, to 50 ml methanol and allowed to stand for 5 minutes. 50 ml chloroform was added, with stirring, and the mixture allowed to stand for 10 minutes. The solution was then filtered (No. 1 Whatman filter paper) into a flat-bottomed flask chilled with crushed ice. The residue was re-extracted twice. The filtrate was reddish and on standing overnight in the refrigerator a slight precipitate was seen to line the flask. (b) The filtrate was evaporated down on a rota evaporator, under water vacuum while the flask was heated by water bath at 30 °C. The concentrate was a creamy pink suspension of about 20-25 ml. Chapter 5: Method and Materials page 5.8 Karolis; Thesis: THE DIEU:CTRJC CHARACTERIZATION OF UP/D BILAYERS 78 (c) The concentrated filtrate was extracted with 10 x its volume of chloroform (e.g.20 ml of filtrate required 5 x 40 ml of chloroform). Each extraction was allowed to stand 5 minutes before filtration with a No. 1 Whatman filter paper. 1 volume of methanol and 0. 7 5 volume of 0.1 N KCl was added to the filtrate and mixed by inverting (not shaking) to avoid forming an emulsion. The mixture was allowed to stand overnight at 4 °c, when good separation into two layers was obtained. (d) The upper layer was syphoned off by water suction. The lower layer was poured into a clean cylinder and evaporated to dryness on the rota evaporator as before. (e) The lipid was dissolved in a small amount (4 ml) of chloroform and left overnight at 4 °c. A fine precipitate developed which was filtered out on a No. 1 Whatman filter paper. The paper was washed with 0.5 ml chloroform. The solution was evaporated down under nitrogen, (Temperature < 25 °C), to a constant weight. The lipid was dissolved in chloroform in the proportion 1 gm/10 ml. 5.2.6 Aqueous Phase A frequent source of contamination can arise from the water phase. The preparation of fresh salt solutions for each experiment was tedious while the use of a bulk supply was susceptible to contamination. To avoid the uncertainties from having a bulk supply it was decided to make a large number of 100 ml aliquots under very clean conditions. The glass containers used to store the solutions were sealed and sterilised. 100 ml was sufficient for two experiments. Any unused sample was discarded if not used within 3 days of being opened. Once open the vial was closed after use. Chapter 5: Method and Materials page 5.9 Karolis; Thesis: THE DIELE.CTRJC CHARACTERIZATION OF UPID Bll.AYERS 79 Two salt solutions were prepared: (a) KCl in the concentrations 0.1, 1, 10, and 100 mM and 1 Molar (b) Ringer in the concentrations lx and 5x. Ringer's solution consisted of the following : Compound Concentration Concentration (mM) K m-3 NaCl 154.00 9.0 KCI 5.38 0.4 CaClz.6Hz0 1.14 0.25 NaHCO3 0.2 The dielectric constant of Ringer solution was estimated to be 75 (Bockris and Reddy, 1977; p157). 5.2. 7 n-Alkane Solvent It has been shown (Fettiplace, Andrews and Haydon 1971; Laver 1984, p76) that the capacitance and composition of black lipid film depends strongly on the hydrocarbon solvent used in their formation. n-hexadecane was selected for this work because it had been shown to be largely absent from black bilayers at normal temperatures (Coster and Laver, 1986). 11-hexadecane (99%) was obtained from Sigma Chemical Co., St Louis. 5.2.8 pH The pH of whole blood varies between 7.3 to 7 .5. The pH of the aqueous preparations described in 5.2.6 were adjusted from their typical value of 5.6 to 7.2 by the addition of small quantities of KOH (or HCl if over corrected). Chapter 5: Method and Malerials page 5.10 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 80 5.3 PLANAR BILA YER FORMATION 5. 3 .1 Introduction Methods describing bilayer production were discussed in Chapter 1. The method used in this work consisted of wiping a small quantity of lipid, dispersed in n-hexadecane, over a carefully prepared hole (about 2 mm diameter) in a polycarbonate septum with a #17 syringe. At room temperature the lipid and solvent did not mix readily. The lipid, which formed a thin fatty smear at the bottom of a small test tube after completely evaporating the chloroform, required coaxing from the glass walls to mix with the solvent and invariably resulted in a clumpy mixture which was useless for painting. Mixing was improved by warming the contents of the test tube in hot water and then quickly transferring a small aliquot to the septum. A fresh septum usually required wetting with the lipid mixture before a sufficient amount of the substrate was present to act as a torus. 5.3.2 Dynamics of Formation The formation of the bilayer from a lipid/alkane droplet occurs when the lipid molecules align in monolayer aggregates at each oil-water interface. The aggregation occurs spontaneously to minimise the interfacial energy which arises from the Born repulsive forces between the hydrophobic acyl chains of the lipids and the water molecules and the charged groups in the polar heads of adjacent lipids. However, depending on the size of the aggregates and the viscosity of the hydrocarbon, and also on whether the phospholipid is above or below its transition temperature, the formation of the monolayers may take considerable time. Chapter 5: Method and Materials page 5.11 Karalis; Thesis: THE DIELECTRIC CHARACTERIZATION OF LIPID BILAYERS 1 2 3 4 5 6 FIGURE 5.4 LIPID BILA YER FORMATION The various stages of lipid bilayer formation are shown in a sequence of six of photographs. A full description of the processes is provided in the text. The experimental arrangement was that described in The Viewing System (paragraph 4.2.2). The torus is clearly visible surrounding a region of lipid that is thinning from the bottom upwards. A bimolecular region, (bilayer filled with solvent), appeared spontaneously at the bottom of the hole in the septum. This black region grew in size until it filled between 80-90% of the hole. The bilayer, formed in less than 1 0 minutes but continued to sequester solvent for a period of 1 hour. The lipid mixture was lecithin and cholesterol disolved in n-hexadecane. The aqueous medium was 1 mM KCI and the temperature 25°C. Chapter 5: Method and Materials Figure Karolis; Thesis: THE DIEU:CTRJC CHARACTERIZATION OF LJPID BILAYERS 81 During monolayer formation (refer to Figure 5.4), the hydrocarbon solvent drained upwards over the surface of the septum. When a large proportion of the droplet had drained away a pool of solvent could be seen spreading across the hole like a stretched greyish sheet which was highly reflective under white light illumination. Swirling in the oily sheet were usually small air bubbles and aggregates of phospholipid. As the solvent drained further, a thin film began to form, usually from the bottom of the hole. The thin film was over 100 µm thick and appeared as a band of colours. There was a distinct physical transition between the thin film and the oily sheet (picture No. 1 of Figure 5.4), which was seen to move upwards like a curtain to disclose a sequence of chromatic bands of reflected light and a thick oily torus around the hole. The colour bands, which were best seen against a black background, are interference fringes resulting from constructive and destructive interference when the thin film was illuminated by white light . The repeating sequence of colour fringes which at first were horizontal suggest that the film was wedge shaped with toe at the bottom of the hole. The distance between the repeating patterns could be used to estimate the thickness of the film which in this case was about 1ff 7 m. As the film thinned further under the influence of diffusion and drainage, London-van der Waals forces begin to act between the two monolayers. The colour bands became diffuse and wider and fewer in number (No.2 of Figure 5.4). When the film had thinned sufficiently, transparent very thin circular regions could be observed to suddenly appear at the bottom of the hole which appeared black against a dark background and had almost no reflectance (No.3, Figure 5.4). The membrane in this region was less than 0.25 x wavelength of light where as a consequence only destructive interference between reflected wave fronts (180° out of phase) took place. At this juncture the membrane was nearly bimolecular and strong van der Waals forces were in play. Border suction at the welt (the border between the coloured and black regions of the film) gave rise to a zipper like mechanism which led to a rapid growth of the black film after the appearance of the first black spots. Chapter 5: Method and Materials page 5.12 Karolis; Thesis: THE DIEUCTRJC CHARACTERIZATION OF LJPID BILAYERS 82 Thus for some considerable period of time there existed five quite distinct regions of lipid structure. There was a bulk reservoir region at the top of the hole. This pool of lipid/solvent, which resembled the bulk solution administered to the hole initially existed for nearly the life of the membrane. Its volume decreased rapidly initially but finally assumed the same proportions as another region called the torus. The torus was a bulky reservoir of lipid/solvent which formed the physical link between the growing membrane and the septum. This region, called the Plateau-Gibbs border, was the site of low pressure with respect to the planar membrane. Initially its physical dimensions would represent a significant proportion of the hole. Like the bulk reservoir region just described, however, it decreased in volume rapidly initially. The low pressure at the welt caused excess lipid/solvent to drain away from the forming membrane. The Plateau-Gibbs border remained for the life of the membrane. A third distinguishable region existed just below the bulk reservoir. This region reflected the Newton colours in a swirling paisley pattern and represents the first stages of film formation which occurred prior to bilayer formation. The paisley pattern which was constantly changing suggests that the film in this region was of variable thickness. It was here that the unevenness of the drainage of the thick film could be seen to be taking place. A fourth region was depicted by the striated bands of colour. The film was thinner than the previous region and there was an ordered drainage. The film in this region was wedge-shaped. The increasing width of the coloured bands and their change in colour indicated that the film was thinning. The fifth region depicted by zero reflectance represented the first stage of bilayer formation. The film was about 10 nm thick which is slightly thicker than twice the length of a lip_id molecule. This suggests that there may have been solvent and other lipid molecules trapped in the bilayer structure. The contents of the bilayer were in contact with the torus and there was a continual exchange of molecules. The bilayer, however, appeared not to be in direct contact with the striated region just described. Clearly visible around the spherical edge of the black region could be seen a thick line representing a region of bulk lipid. Further evidence of this could be seen in the small paisley swirls developing around the growing black region boundary (see pictures No. 4 and 5, Figure 5.4). It thus appears that a torus had been created inside the pre-bilayer thin film region. Chapter 5: Method and Materials page 5.13 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UP/D BILAYERS 83 When viewed against a dark background a faint shimmer of specular reflection of light could be seen over the black regions of the membrane which often was the only visible evidence of the presence of the lipid bilayer. This specular reflectance was used to monitor the membrane bowing in response to hydrostatic pressure differences across the membrane. At the black stage the membrane may not have been bimolecular. All that could be inferred optically was that the total thickness was much less than the wavelength of light. 5.3.3 The Lipid Solvent Mixture The viscosity and homogeneity of the lipid-solvent mixture was important to successful membrane production. The viscosity was related to the lipid-solvent concentration and temperature. The melting point of n-hexadecane was 18.2 °c and therefore it was necessary to warm the solvent in order to encourage the mixing of the lipid in the alkane. Failure to do so resulted in membranes breaking before forming across the whole septum, probably due to an excessively low lipid to alkane concentration. It is further possible that the drainage of the alkane under such conditions was too rapid to allow sufficient lipid to remain in the torus to provide a reservoir. (Lower order alkanes were considerably easier to mix with the lipid, Laver 1984). On the other hand a well mixed sample would, at room temperature, be too viscous and would not spread over the hole until the lipid solution was warmed above 45 °c. It was also noted that if the mixture was warm (< 35 °C) and the salt solution concentration high (0.1 Molar) the viscosity would again be too high and the bulk lipid/solvent would not separate. Thus the viscosity of the lipid-alkane mixture, which increased with the molarity of the salt solution considerably affected the prospects of membrane production. For example, at room temperature, in 0.1 molar concentrations of KCl, membranes did not form while at .001 molar concentrations they did so but slowly, taking perhaps 10 to 30 minutes to reach the partially black stage. To promote solvent drainage and encourage membrane thinning the temperature of the water-filled chambers was increased to about 40 °c for studies in 0.1 M KCl and 30 oC for 0.001 M KCl studies. After the membranes had formed the temperature was lowered to the value required for the experiment. Chapter 5: Method and Materials page 5.14 Karolis; Thesis: THE DIELECTRIC CHARACTERfZATION OF UPID BILAYERS 2 R1 R2 Figure 5.5 The experimental arrangements used in the amplifier calibration procedure. At low frequencies the upper configuration was used. At frequencies> 3 kHz the lower arrangement was adopted. The input capacitance of each amplifier is represented by the capacitors connected across the amplifier input terminals. R1 and R2 were set at 1 k to ensure that the reactance of the input capacitance of each amplifier could be neglected. Chapter 5: Method and Materials Figure 55 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 84 5.4 CALIBRATION - PERFORMANCE of DATA ACQUISITION SYSTEM 5. 4 .1 Introduction Frequent testing of the measuring apparatus was conducted over the course of this work. The tests included measuring the differences in the gain and phase response of the two-channel amplifier assembly; measuring the stray capacitance at the amplifier inputs and calibrating the reference components in series with the membrane. 5.4.2 Amplifier Matching The frequency response of the amplifiers was essentially constant below 10 kHz for the gain employed. Above 10 kHz, however, the response decreased quickly. The response of both amplifiers was matched for a common input signal such that the ratio of the amplitudes from the two amplifiers was unity and the phase difference zero at the outputs. This was achieved by a combination of meticulous selection of components used in the two amplifier circuits and compensating for the small differences in software. The compensation necessary in software was measured using procedure divided into two parts: a test at frequencies below 1 kHz, and a test at frequencies above 1 kHz. The first test consisted of connecting the inputs of the two amplifiers in parallel across the same resistance, (not necessarily known with any accuracy), as depicted schematically in Figure 5.5. At low frequencies the amplifiers function independently. Any phase or amplitude difference between the output signals could then have arisen solely from differences in the phase and gain response of each amplifier. The differences in phase and gain were detected by using the microprocessor to measure the impedance of the known resistance at frequencies below 1 kHz. The ratio of the two amplitude signals measured at each frequency was stored as a correction factor at that frequency in the frequency file (see Appendix A, Table Al). The phase differences were compensated by a simple arithmetic calculation and stored in the same way. Chapter 5: Method and Materials page 5.15 Karolis; Thesis: THE DIELECTRIC CHARACTERll.ATION OF UPID BILAYERS 85 Above 1 kHz, the amplifiers are not entirely independent of one another when connected in parallel. In the second test the amplifiers were connected in series and with a known low resistance (1 k Q) across each input. (Low values of resistance were used to minimise the effects any stray capacitance would have on the phase at the amplifier inputs). Phase angle corrections were then measured directly from the signals at each amplifier ouput. Amplifier gain differences at the high frequencies were corrected in software using a trial and error method based on the results obtained at low frequencies. Estimates of the gain corrections were inserted in the frequency file until a frequency-independent amplitude and phase response at high frequencies was obtained. 5. 4. 3 Measurement of Stray Capacitance The stray capacitance at the input terminals of the current and voltage amplifiers (Cl and C2, respectively) arises from their construction and the dielectric properties of the material located between the input terminals. Unless compensated for (in software), its contribution to the measured impedance will be additive. Measurement of the stray capacitance (Laver, 1984) consisted of measuring the phase difference between the amplifier outputs. The inputs of each amplifier were connected across one of two series resistors (Rl=l kn and R2= 36 k Q). Any phase difference between the amplifier outputs must be a consequence of the reactive impedance of the stray capacitance at the input of each amplifier. The corrected phase difference ~ 1, between the two output signals was measured at selected frequencies and recorded. Rl was then replaced by a resistance R3 equal to R2 and the new phase difference dq>2 measured. The parallel stray capacitance at the input of each amplifier could then be derived by solving the following simultaneous equations: Chapter 5: Method and Materials page 5.16 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID Sil.AYERS 86 At a given angular frequency, co Aq,1 = co(ClRl - C2R2) (5.1) A Therefore, A 5.4.4 Calibration of Electrical Standards In order to determine the current passing through the membrane, the voltage developed across an R-C network, connected in series with the membrane, was measured. Precise values of the components used in the R-C network were required to derive precise measurements of the bilayer impedance. Low-loss frequency-independent (within 0.01 %) polystyrene capacitors were used as the capacitance standards. The high value resistance standards were obtained from Kiethley Inc., U.S.A, (Type-Kobra) and exhibited excellent long term stability. Capacitance standards were calibrated (at 1 kHz, 20 °C) with an accuracy of one part in lQS on a General Radio measuring system (Type 1621) incorporating a capacitance bridge (Type 1616) at the Australian Standards Laboratory (C.S.I.R.O., Division of Applied Physics). The resistance standards (10-1000 M ohm) were calibrated at the Australian Standards Laboratory (C.S.I.R.O, Division of Applied Physics) using a resistance measuring bridge Chapter 5: Method and Materials page 5.17 Karalis; Thesis: THE DIEUCTRJC CHARACTERIZAIION OF UPID 8/U.YERS 87 (Kiethley 515A) operated at 10 V. An alternative method used by Laver (1984), which used the impedance measuring system to determine the value of the standard resistance (operating at 10 mV), agreed with calibrations performed by the C.S.I.R.O. within the experimental error of 0.1%. 5. 4. S Performance of the Apparatus A careful choice in the selection of the components used in the two amplifier circuits resulted in only very small corrections to the gain (amplitude ratio; V/1 was typically 0.9999) and phase (0.0 below 100 Hz). The stray capacitance across the input of both amplifiers representing the voltage and current channels respectively was less than 5 pF, which represents a correction of less than 0.1 %. No corrections were necessary for stray capacitance. The capacitance of the septum was less than 50 pF and was neglected. The total noise/signal ratio was less than 0.1 %. Data influenced by random bursts of excessive noise (resulting in distortion of the amplifier output signals, greater than 0.1 % ), were readily detected in the sum of the least squares coefficients and could be eliminated in the data collection and final analysis. It was possible to measure impedance over the entire frequency range with a maximum error of less than 0.1 % and the phase angle better than 0.1 °. For frequencies in the range 0.1 to 100 Hz the maximum error in the impedance measurement was 0.03% in magnitude and 0.02°. Chapter 5: Method and Materials page 5.18 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UP/D BILAYERS 88 5.5 DAT A PRESENTATION, REDUCTION AND ANALYSIS 5. 5 .1 Data Presentation The data, which was stored on magnetic disk (impedance datafile), consisted of the sum of the normalised fit parameters derived from the least squares fitting of the voltage and current wave forms; the phase angle between the theoretically derived sinusoidal wave forms of the current and voltage signals and thirdly the ratio of those signals. The least squares fitting took place after corrections for amplifier differences (gain and phase - obtained from the frequency data file) were made to the unprocessed signals. (The form of presentation is described in Appendix A). The data stored after a single scan of the frequency range was the average result of a number of measurements taken at each frequency. The number of times the impedance was determined at each frequency was dependent on the frequency and specified in the frequency data file (see Table Al). Several scans of the frequency range were possible with long surviving membranes. It was possible to average the data after normalisation of membrane area. Individual frequency profiles as well as averaged profiles could be examined. 5. 5. 2 Data Reduction The reduction of the data collected during measurement and stored on magnetic disk as an 'impedance data file' consisted of calculating the total impedance (ZT) and phase ( (5.4) (5.5) Chapter 5: Method and Materials page 5.19 Karolis; Thesis: THE DIEU:CTRIC CHARACTERIZATION OF UPID BILAYERS 89 where Zs and Most of this variation was due to the frequency-dependent reactance of the membrane capacitance. Unfortunately, these parameters were not sensitive to the presence of small differences in the dielectric properties of the bilayer lipid membrane associated with polar head groups of the lipid molecules. Reducing the data to the real and imaginary components of admittance (Yr-=1/ZT), however, revealed small dispersions in the susceptive (imaginary) component C(ro). The dispersions in capacitance were attributed to the existence of dielectrically distinct layers in the lipid bilayer. The admittance of the membrane expressed as a the total equivalent parallel capacitance (CT) and conductance (GT) were derived from the following equations: C . An examination of the frequency dispersion in the capacitance and conductance (as well as the impedance, phase, amplitude ratio and phase difference) was possible on a graphics display. The software was initially written in Focal and compiled with machine language subroutines to run on a PDP 11/03 microprocessor (Laver, 1984). More recently, the software has been rewritten, with improvements, in Motley (Chilcott, 1988) to run on a DEC computer. Chapter 5: Method and Materials page 5.20 Karolis; Thesis: THE DIE/£CTRIC CHARACTERlZMION OF UPID BILAYERS 90 5.5.3 Data Analysis by Theoretical Modelling ("Fitting") The data, expressed as a function of capacitance with frequency, exhibited several discrete structures. The difficulty associated with determining a unique solution to the data have already been discussed (Chapter 3). Two methods were employed in the determination of a solution. The first, required manual selection of the elements of the electrical analogue (which were selected on an a priori basis as discussed in Chapter 3). The minimisation of the X2 index resulting from a least squares fitting routine setved to judge the correlation between the data and the electrical analogue. The second method, which also involved a least squares routine (Chilcott, 1988) also examined the confidence associated with rejection of the theoretical model (Wolfe, 1987). This was done by examination of all the expressions of impedance. The second procedure quantified the uniqueness of the solution but required an approximate solution on which to work to minimise computation time. 5.5.4 Performance of the Software The custom designed software was upgraded many times to enhance its 'user friendly' characteristics. In data acquisition mode the status of the forming membrane and the ageing membrane was continually monitored and recorded when instructed. In data analysis mode the least time consuming method was manually guided computer fitting. That this might introduce systematic errors in selection of a theoretical solution a self driven analysis was introduced, which greatly increased the time of analysis. It was found that the manually guided fitting closely followed the automated computer fitting. Chapter 5: Method and Materials page 5.21 Karolis; Thesis: THE DIELECTRIC CHARACTER!7.AT/ON OF UPID BILAYERS Gshunt Gsoln circuit 1 Che Csoln G1 ~In circuit 2 Csoln ~hunt G1 G2 ~oln circuit 3 Csoln Gshunt G1 G2 Gn ~oln circuit n-1 Csoln ~hunt Figure 5.6 Electrical (Maxwell-Wagner) model of the lipid bilayer Circuit 1 depicts the bilayer as a single sheet of dielectric bounded by an electrolyte (G soln). The capacitance (C he) is due exclusively to the hydrocarbon region. The conductance (G shunt) due to pathways through this low dielectric region. The other circuits assume that the bilayer consists of two or more dielectric distinct regions. Chapter 5: Method and Materials Figure 5.6 Karolis; Thesis: THE D/El.ECTRIC CHARACTERIZATION OF UPID BIUYERS TABLE 5.5 Component values used in the test of the fitting routine and confirmation of the Maxwell-Wagner description of the data. The figures appearing in italics are the model component values after allowing for a supposed bilayer area of 3.87 x 1o-6 m2. component circuit 1 circuit 2 circuit 3 circuit4 circuit 5 circuit 6 2-elements 3-elements 4-elements 5-elements 6-elements 7-elements Che 27.294 nF 27.294 nF 27.294 nF 27.294 nF 27.294 nF 27.294 nF 7.053 mFm-2 Gshunt 29.8MO 29.8MO 29.8MQ 29.8MQ 29.8MQ 29.8MQ ...... 8.67mS m-2 ...... Csoln 2.875 nF 2.875 nF 2.875 nF 2.875 nF 2.875 nF 2.875 nF 0.743 mFm-2 Gsoln 211 o 211 o 211 o 211 o 211 o 211 o ...... 1.19 kS.m-2 ...... C1 1.54 µF 1.54 µF 1.54 µF 1.54 µF 1.54 µF 0.398 F m-2 2.71 MO 2.71 MO 2.71 MO 2.71 MO 2.71 MO ...... 0.954 mS.m-2 ...... C2 2.85 µF 2.85 µF 2.85 µF 2.85 µF 0.736 F m-2 G2 103K.Q 103KO 103KO 103KO 2.50 S m-2 C3 3.58 µF 3.58 µF 3.58 µF 0.925 F m-2 G3 11.79 KO 11.79 KO 11.79 KO 23.1 S m-2 C4 3.53 µF 3.53 µF 0.912 F m-2 G4 1.469 KO 1.469 KO 176 S m-2 C5 2.15 µF 0.556 F m-2 G5 324.8Q 796 S m-2 Chapter 5: Method and Materials Table55 Karolis; Thesis: THE DIELECTRJC CHARACTERIZATION OF UPID BILAYERS 91 5.6 PERFORMANCE OF THE SYSTEM 5.6.1 Introduction The system refers to the apparatus used in the measurement of impedance and the software used in its analysis. The performance of the system refers to the accuracy, reproducibility and resolution in the determination of the low frequency capacitance and conductance of the lipid bilayer and the suitability of the Maxwell-Wagner circuit model (Hanai, Haydon and Taylor, 1965a) to explain the variation in admittance with frequency. The performance of the system was tested by substituting the lipid bilayer with a simple RC circuit, consisting of components having precisely known values, measured individually and separately using alternative methods. 5.6.2 Method and Materials The values of the high impedance resistors and low capacitance capacitors were measured at the Australian Standards Laboratory (see Section 5.4.4). All other components were measured on a Fluke multimeter. Nominal component values were selected to simulate representative data of lipid bilayers and are given in Table 5.5. The circuits were assembled on polystyrene boards, with the components mounted on polystyrene plugs.(The silver electrodes, bilayer lipid membrane chamber and lipid bilayer were essentially replaced by a Maxwell-Wagner circuit). The circuits are shown schematically in Figure 5.6. The most simple model of the lipid bilayer bounded on each side by an aqueous environment is that shown as circuit 1 . The capacitance of the hydrocarbon interior of the bilayer (Che), shunted by a resistance to represent the bilayer conductance (GshunV- In series with the bilayer is an element (Csoln - Gsoln) to represent the electrolyte impedance. This circuit was tested first by measuring the impedance spectrum over the frequency range 0.01 Hz to 45 kHz. The experiment was repeated 9 times resulting in 36 individual measurements at the lowest frequency to 135 individual measurements at frequencies greater than 1 Hz. Chapter 5: Method and Materials page 5.22 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 0.700 @" < E u:: 0.695 E -a, 0 C: ~ ·o 0.690 C1S a. C1S (.) C: C1S a, :E 0.685 0.680 2 1 o- 1 0 1 1 o3 Frequency (Hz) Figure 5.8d Capacitance spectrum of a 4-element hard-wired Maxwell-Wagner circuit. 4-element fit. 3 elements for bilayer and one for the electrolyte @" e: o.695 u:: -E ~ 0.690 C: ~ "ij ~ 0.685 (.) C: C1S a, :E 0.680 0.675 2 1 o- 1 0 1 1 o2 Frequency (Hz) Figure 5.8e Capacitance spectrum of a 5-element hard-wired Maxwell-Wagner circuit. 5-element fit. 4 elements for the bilayer and one for the electrolyte. Chapter 5: Method and Materials Figure 5.8 d and e Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 0.8 ------ @' ·----"'"'"'II < Iii E 1:1 Figure 5.8a Capacitance Spectrum u:: 0.6 ~ of a 2-element hard-wired E II Maxwell-Wagner circuit -Cl) (,) Iii C: 1-element fit ·o~ 0.4 - as 1:1 Q. 1 element for the bilayer as (.) and 1 for the electrolyte C:as Cl) 0.2 - Iii ~ ----· __. 0.0 2 1 -· ,o· 10· 1 o2 1 o4 Frequency (Hz) 0.8 @' 0.7 < E Figure 5.8b Capacitance spectrum u.-- 0.6 of a 2-element hard-wired .s Maxwell-Wagner circuit Cl) (,) 0.5 C: 2-element fit ·o~ 0.4 as Q.as 1 element for the bilayer (.) 0.3 and 1for the electrolyte C:as Cl) 0.2 ~ 0.1 0.0 2 , 0 - 1 0 - 1 1 0 1 10 2 1 o3 10 4 1 o5 Frequency (Hz) 0.704 @' 0.702 < E Figure 5.8c Capacitance spectrum u:: 0.700 of a 3-element hard-wired E Maxwell-Wagner circuit Cl) (,) 0.698 C: 3-element fit ·o~ 0.696 as Q.as 2 elements for the bilayer (.) 0.694 and 1for the electrolyte C:as Cl) 0.692 ~ 0.690 0.688 2 , 0 - 1 0 - 1 10° 1 0 1 1 o2 10 3 Frequency (Hz) Chapter 5: Method and Materials Figure 5 .8 a, b and c Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 0.8 0.7 N < E 0.6 u. --E • 2-elements 0.5 -Q) 0 • 3-elements C: • ·u~ 0.4 ro • 4-elements a. • ro 0.3 () o 5-elements C: ro 0.2 Q) •• ~ • 0.1 0.0 2 1 0. 1 0 2 1 0 3 1 0 4 1 0 5 Frequency (Hz) Figure 5. 7a The mean capacitance of hard-wired Maxwell-Wagner circuits plotted against frequency. 0.710 .------. N 0.705 < E 1:1 ~~1:11:11:11:11:11:11:11:11:11:11:11:11:11:11:11:11:11:11:11:11:11:1 u:: ~ a~~ 1:11:11:1 i 1:1 E 0.700 1:1 -Q) 0 •• -~ 0.695 ••••.,. ro0 g- 0.690 1 1:1 2-elements () ' 11:;······················ • • 3-elements ~ 0.685 al• Q) ' ••••••••••••••••• ~ • • • 4-elements 0.680 •• 0 •••••••••• ••• o 5-elements 0.675 2 1 0. 1 0 1 1 o2 1 o3 Frequency (Hz) Figure 5.7b Expanded view of data shown above to show structure as the number of elements increases. Chapter 5: Method and Materials Figure 5.7 a and b Karolis; Thesis: THE DIELECTRIC CHARACTERlZAT/ON OF UPID BILAYERS 92 The measurements were averaged in software with the area of the bilayer arbitrarily set at unity. Following circuit 1, circuit 2 was tested in the same way, and so on. The averaged data were fitted as described and the values of the electrical components derived by the theoretical model compared with the measured values. 5.6.3 Results The variation of capacitance with frequency (including error bars) for each circuit is shown in Figure 5.7a. The structure in the capacitance spectrum is more clearly seen in an expanded view shown in Figure 5.7b. The values of the components derived from a manually driven fit of the data (Figure 5.8) were found to be essentially in agreement with the values used in the circuits. The results of a least squares fitting program, used to determine the number of elements in the model and the individual values, can be seen in the example in Table 5.6 below. The accuracy to which the value of a component in the model could be estimated depended upon its contribution to the total admittance. The contribution of element 4 to the total admittance (largest conductance) was small, and the estimation of component values for that element were - 25% from the actual values. The comparison was more favourable for values of other elements some of which were within 0.05% of the actual values used in the circuit. Chapter 5: Method and Materials page 5.23 Karolis; Thesis: THE DIELECTRIC CHARACTERfZAT/ON OF UPID BILAYERS 93 TABLE 5.6 A comparison of Maxwell-Wagner model component values, estimated from admittance measurements of an hard-wired circuit over the frequency range 0.01 to 104 Hz, with those values actually used in the hard-wired circuit. Element Model Component Values Actual Component Values Che 27.28 nF 27.30 nF Gshunt 100.IOMn 100.00Mn Ct 2.231 µF 2.260 µF G1 1.084 Mn 1.024 Mn C2 5.865 µF 5.780 µF G2 24.98 kn 26.90 kn C3 7.268 µF 9.099 µF G3 250.6 kn 324.o kn C4 0.0 0.0 G4 3.268 kn 3.268 kn 5.6.4 Discussion A dispersion of 2% in the capacitance represented a 3 fold change in the time constant between elements. This was readily detectable by the measuring system and successfully resolved by the theoretical fitting procedures (manually and software driven). The accuracy of the capacitance measurement at the highest time constant (lowest frequency) was found to be better than 0.1 %. The values of the individual components at higher frequencies was better than 2%. Chapter 5: Method and Malerials page 5.24 Karolis; Thesis: THE DIEIECTRIC CHARACTER/ZITJON OF UPID BILAYERS 94 S. 7 SUMMARY A detailed description of the materials used in this work has been presented. The manner in which bilayers were prepared for examination was also described. The appearance of the forming bilayer when viewed with a low powered microscope revealed that several phases existed and that all phases were necessary for long term stability. The electrical apparatus was also described in detail as was its calibration and performance. The manner in which the data was presented and analysed was shown to adequately describe the dielectric behaviour of the bilayers over the frequency range 10-2 to 104 Hz. Chapter 5: Method and Materials page 5.25 Karalis; Thesis: THE DIELECTRIC CHARACTERfZATION OF UPID BILAYERS 95 CHAPTER 6 THE LOW FREQUENCY CAPACITANCE OF BILAYERS AND ITS RELATION TO THE HYDROCARBON REGION 6.1 INTRODUCTION 96 Electrical Double Layers ...... 96 Frequency of Measurement ...... 91 Area ...... 91 Temperature ...... 98 Dielectric Constant ...... 98 Measurement ofCapacitance ...... 100 Egg Lecithin - Cholesterol Bilayers ...... 101 6.2 THEORY 102 6.2.1 The Capacitance Equation ...... 102 Ignoring the Gouy-Chapman diffuse double layer and surface charge ejfects ...... 102 6.2.2 Double Layer Capacitance ...... 103 Ignoring swface charge effects ...... 103 Constant surface charge ...... 104 6.2.3 The Dielectric Constant of the Hydrocarbon Interior ...... 105 6.2.4 Temperature Dependence of the Dielectric Constant...... 106 6.2.5 The Interactive Volume ...... 107 6.3 METHOD 109 6.4 RESULTS 110 6.4.1 The Age and Stability of the Bilayers ...... 110 6.4.2 The low frequency, area specific, measured capacitance (Cm) ...... 111 6.4.3 Double layer correction of the measured capacitance (Cg) ...... 112 6.5 DISCUSSION 114 6.5.1 Removal of the double layer capacitance...... 115 6.5.2 The Thickness of the Hydrocarbon Region ...... 117 6.6 SUMMARY 118 Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page6.l Karolis; Thesis: THE DIEUCI'RJC CHARACTERIZATION OF UPID BILAYERS 96 6.1 INTRODUCTION The measurement of capacitance has long been regarded as an important physical parameter to the understanding of the structure of biological membranes (Fricke and Morse, 1923). The interpretation of such measurements, however, has been complicated by the uncertainties in composition and conformation of the molecular constituents as well as the electrical pathways. The planar lipid bilayer is a simple model of the biological membrane and has been used widely to evaluate the significance of these variables (Tien, 1974; Jain, 1972). The capacitance of a planar bilayer can reveal important structural information about the hydrocarbon region of the bilayer if the dielectric constant of this region is known. The interpretation of the measured capacitance, however, requires considerable care. Electrical Double Layers Certain electrochemical phenomena associated with the measurement of capacitance such as electrical double layers at the lipid-water and electrode-water interfaces may seriously understate the true value of the capacitance (Lauger, Lesslauer, Marti and Richter, 1967; Everitt and Haydon, 1968; Smith, 1977). For example, the measured capacitance for a bilayer with a neutral surface charge in a 10-3 mole per litre uni-valent electrolyte solution, could be understated by as much as 22% while in 1 molar solutions the discrepancy is less than 1% (see Table 6.2). The corrections for bilayers with a net surface charge were considered by Everitt and Haydon (1968). They concluded that the surface charge might go some way to neutralising the polarised charge in the double layer and so reduce the effect of the double layer capacitance even at very low salt concentrations. The effect of the electrostatic dipoles in the polar heads of neutral phospholipids, such as egg-lecithin, on the double layer have not been evaluated. Smith (1977) considered the magnitude of the electrode-water double layer capacitance at low frequencies for a 2-terminal system and found it to be similar to the bilayer capacitance. By separating the voltage and current signals with a 4-terminal system, however, the double layer Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page62 Karolis; Thesis: THE DIEI.ECTRIC CHARACTERIZATION OF LJPID BILAYERS 97 capacitance at the electrode-solution interface was effectively eliminated from the measured bilayer capacitance. Frequency ofMeasurement It has been suggested that the capacitance of the bilayer is independent of the measuring frequency (Hanai, Haydon and Taylor, 1964; Hanai, Haydon and Taylor, 1965c; Everitt and Haydon, 1968). Careful consideration of the resolution and precision required for such measurements by Coster and Smith (1974) demonstrated that the bilayer capacitance exhibits a dispersion with frequency which could only result in an underestimate of the capacitance if the measurement were performed at frequencies greater than lHz. The results of Clowes, Cherry and Chapman (1971), Ashcroft, Coster and Smith (1981) and Ashcroft, Coster, Laver and Smith (1983) have shown that the capacitance of the hydrocarbon region of the bilayer might be understated by as much as 13% when measured at frequencies >100 Hz. It appears that measurements of capacitance performed at frequencies greater than 1 Hz result from regions in the polar head group of atoms (Clowes, Cherry and Chapman, 1971; Coster and Smith, 1974). Area The age and stability of the bilayer, as well as precise knowledge of its planar area, are important considerations in the accurate assessment of capacitance. A common problem associated with the study of the properties of bilayers is the time required for them to reach a stable equilibrium and the unpredictability of their life-time. The choice of alkane solvent, for example, may result in fairly rapid bilayer formation but the bilayer may suffer long term instability. The capacitance of phospholipid bilayers formed with small acyl chain solvents such as n-decane, for example, have been observed to drift with time. The drift could not be explained by changes in the area and was thought to be a slow sequestering of solvent retained in the bilayer (White, 1970a; White and Thompson, 1973; Ashcroft, Coster and Smith, 198; Coster and Laver, 1986a,b). Stability is reflected by longevity, while changes in the capacitance with time may be due to area changes. Small changes in area which affect the magnitude of the measured capacitance are difficult to estimate with a microscope eye piece. An accuracy of -5% Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page63 Karolis; Thesis: THE DIEUCTRJC CHARACTERIZATION OF UPID BILAYERS 98 has been suggested (Chemomordik, Melikyan, Dubrovina, Agibor and Chizmadzhev, 1984). The best estimates of area measured with a graticule were no better than 4% (White, 1970a). The authors own visual estimates have invariably over estimated the area. For bilayers occupying at least 90% of the annulus, the discrepancies were as much as +5%. Most bilayers occupied areas around 80% of the annulus and formed with an irregular shaped torus. The over estimates of the area using visual techniques for these bilayers, were often in excess of 10%. Temperature The role of temperature in capacitance measurement has only seriously been considered by White (1970a and b, 1974, 1975 and 1976) and Coster and Laver (1986). Experiments with oxidised-cholesteroVn-decane and glycerol monooleate/n-hexadecane systems by White suggest that the capacitance was strongly dependent on temperature because both the bilayer concentration of alkane solvent and density of the solvent was temperature dependent. In each case the capacitance was seen to increase linearly with decreasing temperature, at least as far as the freezing point of the alkane. Similar experiments with bilayers formed from egg phosphatidylcholine and alkanes ranging from C-12 to C-16 by Coster and Laver (1986) supported White's findings. They were able to show that for the long chain alkanes, in lecithin at least, a temperature can be reached above the freezing point of the alkane, and below which the capacitance remains constant. Experiments by Fettiplace, Andrews and Haydon (1971) with lecithin/hexadecane and cholesterol systems support this result. Dielectric Constant The solubility of the alkane in the acyl chains of the bilayer and the effect of this on the value of the dielectric constant of the hydrocarbon region of the bilayer has been a constant source of uncertainty in the interpretation of the capacitance measurement. Although it has been possible to produce planar bilayers with many different natural and synthetic lipids (Tien,1974) it is not possible to produce a bilayer of egg-lecithin or any other phospholipid or monoglyceride without the use of a solvent such as an n-alkane, to disperse the lipid. Initially, it was thought (Hanai, Haydon and Taylor, 1964; Taylor and Haydon, 1966) that the length of the acyl chain Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page 6.4 Karolis; Thesis: THE DIELE.CTRIC CHARACTERl'ZATION OF UPID BILAYERS TABLE 6.la THE CAPACITANCE OF EGG LECITHIN* BILAYERS *unless otherwise stated AUTHOR alkane temp electrolyte frequency capacitance (n) oc (mol m-3) (Hz) (mF m-2) Hanai, Haydon & Taylor (1964) ...... 7 20 102 NaCl, CaCl2 50 - 107 3.8 10 20 10 NaCl, CaCl2 16 20 4x103 KCl Uiuger, Lesslauer, Marti & Richter (1967) ...... 10 35 lo2 KCl 102 - 1<>4 3.3 Rosen & Sutton (1968) ...... 7 22 not specified ns 3.8 Ohki (1969) ...... 10 25 102 NaCl 1<>4 3.6 - 4.7 Fettiplace, Andrews & Haydon (1971) ...... 10 21 102 NaCl 550 3.85 12 4.43 14 5.15 16 6.03 Clowes, Cherry & Chapman (1971) ...... 10 ns 10-1-102 KCl 2.4 - 3.8 Redwood, Pfeiffer, Weisbach & Thompson (1971)1.. 10 24 10 KCl 3.8 - 4.3 Montal & Mueller (1972)2...... monolayer vd3 9.0 Coster & Smith (1974) ...... 14 22 103 KCl 0.1 - 100 5.0 102 10 10-l Benz, Frohlich, Uiuger & Montal (1975)2.4 C-18 10 25 10 KCl 2 X 106 7.21 C-20 5.69 C-22 4.81 Bamberg & Benz (1976)5 ...... 10 40 103 NaCl 2 X 106 3.50 Benz & Janka (1976) ...... 10 25 102 NaCl \0 3.39 dioleolyl 8 25 102 NaCl \0 3.77 10 3.74 12 4.22 14 4.36 16 6.24 monolayer 7.28 Ashcroft, Coster & Smith (1977) ...... 14 18 102 KCl 10-2 -102 5.10 Ashcroft, Coster & Smith (1981) ...... 14 20 1 KCl 10-2_ 220 5.35 10 KCl 5.43 102 KCl 5.50 103 KCl 5.80 10 20 1 KCl 4.106 Coster, Laver & Schoenborn (1982) ...... 16 30 1 KCl 0.1 6.40 Fettiplace (1978)2 ...... 22 102 KCl 550 7.60 Laver (1984) ...... 16 20- 1 KCl 0.01 6.35 30 10 KCl 6.70 lo2 KCl 7.00 Coster & Laver (1986) ...... 16 25 lo2 KCI 1 6.80 Niles, Levis and Cohen (1988)2 monolayerDPC 25 \0 7.80 monolayerTPE 8.70 1 Synthetic lecithin 2 Monolayer studies 3 Voltage drop 4 Synthetic lecithin, Chains: C-18, C-22, C-24 5 Synthetic lecithin, Dioleoyl 6 Capacitance not stable. Increased with time. Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness Table 6.la Karolis; Thesis: THE DIELECTRIC CHARACTERfZAT/ON OF UPID BILAYERS 99 of the alkane solvent did not influence the measurement of capacitance. As a result many early experiments with bilayers were conducted with n-decane (Table 6. la), simply because they were relatively easy to produce and formed very quickly at room temperature. The results of Andrews, Manev and Haydon (1970), Fettiplace, Andrews and Haydon (1971), Benz and Janko (1976), White (1975, 1977) and Coster and Laver (1986), however, have refuted this suggestion. The effect of solvent on the measured capacitance appears to be one of space occupation in the interactive volume, i.e. the space available in the central region of the bilayer (White, 1977), and therefore a thickening of this region. Small chain n-alkanes (C-8 to C-14) appear to have no difficulty in occupying this region, (Andrews, Manev and Haydon, 1970; Requena and Haydon, 1975; White, 1977; McIntosh, Simon and MacDonald, 1980; White, King and Cain, 1981). Hexadecane, however, is only slightly soluble in the acyl chains of the phospholipid or monoglyceride bilayer (Fettiplace, Andrews and Haydon, 1971; White, 1975; Coster and Laver, 1986). Large solvent molecules such as squalene, on the other hand appear to be physically too large to occupy the fluid central region of the bilayer (White, 1977) and are totally excluded from the bilayer ((White, 1978; Simon, Lis, MacDonald and Kauffman, 1977; Chernomordik, Melikyan, Dubrovina, Agibor and Chizmadzhev, 1984). Coster and Laver (1986b) showed that benzyl alcohol causes bilayers to thicken in n-hexadecane at low temperatures. The alkanes have a profound influence on the action potential of the squid giant axion (Haydon, Hendry, Levinson and Requena, 1977). Bilayers formed with and without retained alkane solvent respond differently to the anaesthetic, benzyl alcohol (Ebihara, Hall, MacDonald, McIntosh and Simon, 1979). Bilayers containing n-decane, for example were observed to decrease in thickness, supporting an earlier observation by Ashcroft, Coster and Smith (1977a,b), who used tetradecane. Solvent-free bilayers, on the other hand, were observed to thicken. The partial molar volume of solvent with respect to the acyl chain volume will affect the average dielectric constant, (Fettiplace, Andrews and Haydon, 1971) which has been shown to depend Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page 6.5 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF LJPID BILAYERS 100 on the thickness of the bilayer as well as the spacing between the acyl chains (Huang and Levitt. 1977). Several attempts have been made to estimate the partial molar volume of alkane chains in the bilayer (Fettiplace, Andrews and Haydon, 1971; Requena and Haydon, 1975; White, 1977; Coster and Laver, 1986) with the result that the dielectric constant has been taken to be 2.1. Measurement ofCapacitance The first measurements of capacitance of egg-lecithin bilayers were reported by Hanai, Haydon and Taylor (1964). The capacitance was measured to be 0.38 mF m-2 , and they reported the capacitance to be independent of the frequency of measurement, the external electrolyte concentration and the chain length of the alkane solvent. Almost identical values of capacitance were reported by others (Lauger, Lesslauer, Marti and Richter, 1967; Ohki, 1969; Clowes, Cherry and Chapman, 1971), who used n-decane as the solvent (Table 6.la). Rosen and Sutton (1968) claim to have reproduced the results of Hanai et al using n-heptane but did not quote their values. Redwood, Pfeiffer, Weisbach and Thompson (1971), using a synthetic lecithin in n-decane reported a similar value of capacitance and observed a significant pH dependence also. Fettiplace, Andrews and Haydon (1971) in contrast to Hanai, Haydon and Taylor (1964), were the first to demonstrate the dependence of capacitance on the chain length of the n-alkane solvent. Their results, which were supported by Benz and Janko (1976) demonstrated that short chain alkanes were retained in the lecithin bilayer thereby distorting its physical properties such as its thickness, molecular conformation and conductivity. Since then a number of different approaches have been used to obtain lecithin bilayers essentially free of trapped solvent. The monolayer apposition technique used by Montal and Mueller ( 1972) resulted in a capacitance measurement of 9.0 mF m-2, for a number of different lipids. Benz, Frohlich, Lliuger and Montal (1975), using a similar method found the capacitance to depend on the acyl chain length. The largest capacitance was measured to be 7.21 mF m-2 for 18-carbon chains and 4.81 mF m-2 for 24-carbon chains, consistent with an earlier observation by Taylor and Haydon (1966). Benz and Janko (1976) also used monolayer apposition techniques with Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page6.6 Karolis; Thesis: THE DIEUCI'R/C CHARACTERIZATION OF UP/D 8/U.YERS TABLE 6.lb THE CAPACITANCE OF EGG LECITHIN-CHOLESTEROL BILAYERS AUTHOR alkane temp. electrolyte frequency capacitance (n) (QC) (mol m-3) (Hz) (mF m-2) Hanai, Haydon & Taylor (1965a) ...... lO 20 ns 4.0 - 6.0 Simmons (1968) ...... 14 5-46 10-2 - 4xl<>5 NaCl 6.0 Ohki (1969) ...... lO 25 102 NaCl 1<>4 5.0 - 5.8 Redwood and Haydon (1969) ...... lO 20 102 KCl 104 5.9 30 5.3 40 3.8 White ( 1970) - oxidised cholesterol...... lO 27.5 3.8 - 4.6 Fettiplace, Andrews & Haydon (1971) ...... 16 24 102 NaCl 550 5.93 40 5.99 Ashcroft (1979) ...... 14 20 1 KCl 10-2- 220 5.80 lO KCl 6.20 102 KCl 6.80 1o3 KCI 6.10 Ashcroft, Thulborn, Smith, Coster & Sawyer ( 1980) 10 18-22 1 KCI 4.6 14 20 5.7 Laver (1984) ...... 16 22 1 KCI 0.01 6.6 lO KCl 6.8 102 KCl 7.0 Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness Table 6.1 b Karolis; Thesis: THE DJEUCI'RIC CHARACTERIZATION OF UPJD Bll.AYERS 101 dioleol-PC (dioleol phosphatidylcholine) and measured the solvent free capacitance to be 7.28 mF m-2. The bilayers they produced by the Mueller, Rudin brush technique with n-hexadecane, however, were found to have a capacitance of only 6.24 mF m-2 . The results of monolayer studies on egg lecithin by Fettiplace (1978) essentially confirmed the results of others (see Table 6.la). Solvent free bilayers of glycerol monoleate (GMO) were produced by White (1973) using a freeze-out method. By this method, Coster and Laver (1986) were able to show that egg lecithin bilayers produced with n-hexadecane solvent are essentially free of solvent below 30't and have a capacitance of 6.8 mF m-2 at 1 Hz. Egg Lecithin - Cholesterol Bilayers The study of egg lecithin - cholesterol bilayers by impedance measurement, has received very little attention over the last 30 years (Table 6.lb). Most studies were performed with short chain alkanes with the inevitable result that low values of capacitance were recorded (< 6 mF m-2 ). In this chapter the low frequency capacitance of egg lecithin bilayers is examined. Derived from such measurements are estimates of the thickness of the hydrocarbon region of the bilayer. Similar measurements performed at different electrolyte concentrations are used to examine the effects of the Gouy-Chapman diffuse double layer on the measured capacitance and therefore the apparent thickness of the hydrocarbon region. The effects due to surface charge are also examined with the introduction of cholesterol and oxidised cholesterol in the lipid mixture. Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page6.7 Karolis; Thesis: THE DIELECTRIC CHARACTERfZATION OF UPID Bll.AYERS 102 6.2 THEORY 6. 2 .1 The Capacitance Equation The relationship between the thickness of the bilayer and the measured capacitance has been considered by Hanai, Haydon and Taylor (1964), White (1970a) and Coster and Smith (1974). All agree that the presence of water and ions in the polar group regions of the bilayer would result in a relatively large capacitance associated with that region (more than 50 times the actual measured values of the bilayer capacitance). As a consequence, the measured value of bilayer capacitance is taken to be that of the hydrocarbon moiety ( or that region bounded by the two carboxyl carbon atoms at each face of the bilayer), subject to some corrections related to double layer and surface charge effects. Ignoring the Gouy-Chapman diffuse double layer and surface charge effects The capacitance (CT) of the bilayer, if treated like a parallel plate capacitor, will be given by: (6.1) where, Eo = 8.854x10-12 F m- 1, is the permittivity of free space, Ebe is the dielectric constant of the hydrocarbon region of the bilayer. 8hc is the thickness of the hydrocarbon region, Am is the area of the planar bilayer. The area specific capacitance, Cg, (the value quoted in Tables 6. la and 6. lb) is related to capacitance of the bilayer as follows: (6.2) Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page6.8 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 103 6.2.2 Double Layer Capacitance Ignoring surface charge effects If the bilayer has net zero surface charge, but is bounded on each side by a diffuse double layer, the capacitance associated with the double layer, Cd, will be present as two series elements during measurement (Uiuger, Lesslauer, Marti and Richter, 1967) and the measured capacitance, Cm, will be given by: 1 1 2 + (6.3) Cm = Cg cd 8hc 2 = + (6.4) EoEhc EofwK where, K is the reciprocal Debye-Hi.ickel length, given by: (6.5) where, R is the Universal Gas Constant (8.31 J K- 1 Mol-l) T is the absolute temperature (°K) ~ is the dielectric constant of the aqueous medium, which is temperature and electrolyte concentration dependent (Bockris and Reddy, 1970) F is the Faraday Constant (9.65x104 Mol- 1) c is the electrolyte concentration. (If the electrolyte concentration is expressed in moles litre-1, i.e. molarity. The conversion is as follows: molarity x NA x 103 m-3 , where NA is Avogadro's number). Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page6.9 Karolis; Thesis: THE DIEUCTR/C CHARACTERIZATION OF UPID 8/IAYERS TABLE 6.2 THE DOUBLE LAYER CAPACITANCE AND ITS CONTRIBUTION TO THE MEASURED CAPACITANCE The correction to the measured capacitance, Cm, due to a Helmholtz-Perrin parallel plate capacitor model of the double layer in monovalent electrolyte solution determined for two hypothetical bilayers with hydrocarbon regions of thickness, Ohc = 3.9 nm and 2.8 nm (corresponding to geometrical capacitances of 5 mF m-2 and 7 mF m-2 respectively) and dielectric constant 2.2. The dielectric constant of the aqueous medium, Ew, was taken to be 78 except for 1 molar concentration where 70 was used. electrolyte dielectric Debye-length double layer % correction to Cm concentration constant (rl) capacitance (~t Ohc= (nm) (mole litre-1) Ew (mFm-2) 3.9 nm 2.8 nm 1 70 0.288 2152 -0.4 -0.6 10-1 78 0.960 719 -1.1 -2.0 10-2 78 3.040 228 -3.4 -6.9 10-3 78 9.600 72 -11.1 -22.2 lQ-4 78 30.400 23 -37.0 -74.2 Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness Table 6.2 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UP/D BILAYERS 104 Rearranging Equation 6.3, (6.6) = (6.7) (6.8) One can see from Table 6.2 that at high electrolyte concentrations the effects due to the diffuse double layer may be neglected. Constant surface charge If the bilayer surface charge is denoted by crB and the diffuse charge in the solution by crd, we have from before (Equation 3.75) (6.9) where, '1'0 is the potential at distance x=O relative to the potential at a distance x=~1 where it is zero. If 'l'B is the bilayer surface potential and only point charges are considered, 'l'B = 'I'0 is a reasonable approximation and it follows that the differential capacity of the double layer will be given by; (6.10) Chapter 6: The low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page 6.10 Karolis; Thesis: THE DIELECTRIC CHARACTERlZATION OF UPID BILAYERS 105 6.2.3 The Dielectric Constant of the Hydrocarbon Interior To a reasonable approximation the dielectric constant of a mixture of hydrocarbons is a quantity that may be obtained by summation of the dielectric constants of the component hydrocarbons on a volume fraction basis if the differences between the dielectric constants and molecular volumes of the components are relatively small. (The physical properties of bulk solutions are assumed to apply to microscopic quantities found in the bilayer). Thus (6.11) where, Xi is the volume fraction of the hydrocarbon moiety i. Ei is the dielectric constant of the hydrocarbon moiety i. The hydrocarbon chains of lipids, however, usually consist of an odd number of carbon atoms (the atom linked to the polar group oxygen not being counted) and are frequently unsaturated. They also possess a single terminal methyl group and as such there are no data in the literature on the dielectric constants of such residues. From the polarizabilities (expressed as a function of the dielectric constant by means of the Clausius-Mossotti relation) and molecular volumes of the component groups it is possible to determine the dielectric constant of the whole residue from the following relation, (6.12) where, Ei, Yi and Xi are respectively the dielectric constant, molecular volume and mole fraction of the component groups and v is the molecular volume of the whole residue. The values of Vi can be derived from the densities and molecular weights of the liquid hydrocarbons and the Ei Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page 6.1 J Karolis; Thesis: THE DIELECTRIC CHARACTERlZ.ATJON OF UPID BILAYERS 106 from the refractive indices (Handbook Chemistry and Physics, 64th Ed.). The result for egg lecithin was found in this way to be 2.202 (Requena and Haydon, 1975). Bilayers containing alkane solvent are thicker than those that are solvent-free. Provided the difference in thickness, ~o, between the solvent-free and solvent-containing bilayer arises entirely from the partial molar volume of the alkane in the bilayer without affecting the area density of the lipids at the interface, one can calculate the molar concentration of the alkane per unit area in the bilayer, Xa, using the expression, Xa = ~Ova (6.13) where, Va, is the alkane molar volume. Alternatively, if the area occupied by each lipid molecule at the interface is known (A), the average dielectric constant of the bilayer (Ebe) containing solvent will be given by, (6.14) where £1 and £2 are the dielectric constants of two hydrocarbon components and V2 is the molecular volume of species 2, and for which A is known. 6.2.4 Temperature Dependence of the Dielectric Constant The density of the hydrocarbon solvent has been shown to be linearly dependent on the temperature (Aveyard and Haydon, 1965; White, 1974), (6.15) The dielectric constant is related to the density by: Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page 6.12 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 107 1 + 2(p~cm + Phcbhc)/M (6.16) 1 - (p~cm + Phcbhc)/M and ghc is a constant = 786.4 kg m-3 for n-hexadecane hhc is a constant= -0.6402 kg m· 3 for n-hexadecane Ebe , Phc denote the dielectric constant and density of the hydrocarbon region of the bilayer at 20°c m is a constant= -3000 m3 kg-lmol-1 M is the molecular weight T is the temperature 0 c 6.2.5 The Interactive Volume Thickness, determined from Equation 6.1, is a direct measure of bilayer composition. The volume of a planar bilayer of thickness Ohc and area A is simply A8hc. If the bilayer were to consist only of lipid and solvent molecules, then NaMa N1M1 --+- (6.18) NAPa NAPI where, NA is Avogadro's number, Pa and PI are the densities of the alkane solvent and lipid acyl chains (or their equivalent to be more precise) respectively. Na and N1 are the total number of alkane molecules and lipid acyl chains respectively. Ma and M1 are the molecular weights of the alkane solvent and lipid acyl chains respectively. Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page 6.13 Karolis; Thesis: THE DIE/£CTRJC CHARACTERIZATION OF UPID BllJ\YERS 108 It follows that the volume fraction of the alkane solvent in the bilayer per unit bilayer area will be given by: (6.19) which reduces to: 1 (6.20) Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page 6.14 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 109 6.3 METHOD Egg-lecithin bilayers were produced by the method described in sections 5.2 and 5.3 . The procedure consisted of dispersing 5x10-6 mole egg lecithin in 1.365x10-3 mole n-hexadecane (-5x10-3 ratio) while gently heating to facilitate mixing. The lipid mixture was wiped across a small hole in a septum which was initially preheated to 40°C, (see sections 4.3.2 and 4.3.3). The septum was immersed in KCl solutions, buffered to a pH of 7 with either HCl or KOH, and having concentrations 1 Molar, 100 mM and 1 mM. Egg-lecithin/cholesterol and egg-lecithin/oxidised cholesterol mixtures, produced by the method outlined in Section 5.2, were dispersed in n-hexadecane such that the mole ratio of lecithin:cholesterol:hexadecane was 2:1:3000. The mixture was gently heated just prior to wiping a small aliquot across the septum, usually at temperatures in the range 35° - 40°C in KCl solutions of 100 mM, 10 mM, 1 mM and 0.1 mM (pH of 7), and also Ringer solution. The capacitance was monitored at 1 Hz while the bilayer formed and underwent a growth in area. Frequent monitoring of the progress of the bilayer visually with the aid of a low powered microscope was accompanied by hydrostatic pressure adjustment to keep the thin film flat. When the bilayer area growth appeared to have slowed, as evidenced by a slowly changing measurement of capacitance, the temperature was brought down to 35°C, in the case of the pure lecithin membranes and room temperature (22°C) in the mixed lipid studies. When the 1 Hz capacitance had stabilised, the bilayer and septum were photographed (section 4.3.6) and an admittance spectral run, lasting 30 minutes was commenced. The lowest frequency used was 0.04 Hz and the highest 44.4 kHz (in steps of xl.41). Admittance measurements at frequencies as low as 0.01 Hz were performed on stable bilayers that had lasted longer than 3.6 ks. The bilayer was also photographed at the end of each frequency scan. At least 3 runs of the frequency profile were performed on each bilayer. Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page 6.15 Karolis; Thesis: THE DIELE.CTRIC CHARACTERIZATION OF UPJD BILAYERS 110 6.4 RESULTS 6. 4 .1 The Age and Stability of the Bilayers Bilayers formed quickly in low salt concentrations and at temperatures > 30°C. It was quite common to commence measurement within 1.8 ks of painting. At high salt concentrations and in Ringer, bilayer formation was typically very slow, often taking 3.6 ks to establish a sufficiently slowly expanding area as not to change significantly during a cycle of measurement.. The 'age' of the bilayers was arbitrarily recorded as the time usefully engaged in measurement. Some bilayers were intact many hours after a cycle of measurement had been completed. The age of the pure egg-lecithin bilayers ranged from 1.8 ks to 21.6 ks. The average age was 9 ks (5 bilayers). The age of the egg-lecithin/cholesterol bilayers ranged from 1.8 ks to 50.4 ks. The average age was 10.8 ks (23 bilayers). The egg lecithin membranes were the least stable of the bilayers. Egg-lecithin/cholesterol and egg-lecithin/oxidised cholesterol bilayers were more stable and easier to produce. Formation of bilayers was easier at high salt concentrations but only when the temperature exceeded 30°C. Cooling to room temperature proved to be hazardous with many apparently stable bilayers rupturing just below 30°C. This was particularly so for egg-lecithin bilayers. Bilayer formation progressed far more quickly at low concentrations often with a smooth fluid torus. At high salt concentrations the torus was coarse and accompanied by islands of aggregated lipid that made estimation of the bilayer area difficult. The area of the bilayer varied from as low as 60% of the total septum area to as high as 90%. At no time was the bilayer observed to occupy the whole of the septum area. All attempts to visually estimate the area occupied by the bilayer resulted in an over estimate - usually by as much as 10-15%. Photographing the bilayer at frequent intervals and comparing the capacitance with the area of the measured "black" regions permitted a careful check on the area determinations. Agreement was generally better than 5%. The error in the determination of the area was estimated to be better than 5% for these bilayers. Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page 6.16 Karolis; Thesis: THE DIELECI'RJC CHARACTERfZATJON OF UPID Sil.AYERS TABLE 6.3 THE LOW FREQUENCY MEASURED CAPACITANCE (Cm) OF BILAYERS FORMED WITH n-HEXADECANE IN DIFFERENT CONCENTRATIONS OF KCI Bilayer Electrolyte Measured Corresponding Type Concentration Capacitance thickness of the (Cm) hydrocarbon region (mole litre- 1) (mF m-2) (nm) (nm) Ehc=2.14 Ehc=2.20 Egg Lecithin 1 7.65 ± 0.3 2.48 2.55 10-1 7.60±0.1 2.50 2.58 10-3 6.20 ± 0.2 Egg lecithin/cholesterol Ringer 7.2 ± 0.2 2.65 2.71 10-1 7.0 ± 0.1 2.71 2.78 10-2 6.6 ± 0.1 10-3 6.4 ± 0.3 lQ-4 6.2 ± 0.2 Egg lecithin/Ox. Cholest. 10-1 7.1 ± 0.1 2.67 2.74 10-2 6.8 ± 0.1 10-3 6.3 ± 0.2 Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation 10 Hydrocarbon Region Thickness Table 63 Karolis; Thesis: THE DIEU:CTRIC CHARACTERflATION OF UPID BILAYERS 111 At temperatures > 30°C the bilayer appeared fluid and elastic. It could withstand shock from vibration and considerable extension under hydrostatic pressure stress. At lower temperatures, particularly near the freezing point of hexadecane the bilayer appeared rather more brittle and sensitive to vibrations. If the membrane was allowed to distend slowly over a few hours, it could be flattened only with considerable care. When flattened the bilayer resembled a loose flapping sheet for a few seconds before becoming taut. 6.4.2 The low frequency, area specific, measured capacitance (Cm) The low frequency, area specific, measured capacitance was calculated directly from data recorded during measurement at frequencies below 0.1 Hz, using Equation 5.3 and normalised to unit area after the bilayer area had been determined photographically (section 4.3.6). The results are summarised in Table 6.3. Thus: (6.21) The measured capacitance decreased with decreasing electrolyte concentration for all types of bilayers. The highest value recorded was 7 .65 mF m- 2 for pure egg lecithin in 1 molar solutions. The corresponding thickness of the hydrocarbon region was determined at the highest salt concentrations using Equation 6.2 for two different values of dielectric constant (2.14 and 2.20) and assumes Cm=Cg. The influence of the double layer capacitance was neglected so that the results may be compared directly with others given in Table 6. la. The hydrocarbon region thickness varied between 2.55 nm when solvent free and without cholesterol (2.48 nm if partially filled with solvent) to 2.78 nm when cholesterol was present. The result for oxidised cholesterol was 2.74 nm. Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page 6.17 Karolis; Thesis: THE DIEUCI'RJC CHARACTERfZATJON OF UPID BILAYERS TABLE 6.4 THE LOW FREQUENCY AREA SPECIFIC CAPACITANCE (Cg) OF BILAYERS FORMED WITH n-HEXADECANE IN DIFFERENT CONCENTRATIONS OF KCI CORRECTED FOR THE SERIES DOUBLE LAYER Bilayer Electrolyte Area Specific Corresponding Type Concentration Capacitance thickness of the (Cg) hydrocarbon region (mole litre-1) (mF m-2) (nm) (nm) £hc=2.14 £hc=2.20 Egg Lecithin 1 7.70±0.3 2.42 2.53 10-1 7.76±0.1 2.44 2.51 10-3 7.49±0.2 2.53 2.60 Egg lecithin/cholesterol Ringer 7.32±0.2 2.59 2.66 10-1 7.14±0.1 2.65 2.73 10-2 7.01±0.1 2.70 2.78 10-3 7.79±0.3 2.43 2.50 10-4 13.43±0.2 1.41 1.45 Egg lecithin/Ox.cholest. 10-1 7.24±0.1 2.62 2.69 10-2 7.24±0.1 2.62 2.69 10-3 7.64±0.2 2.48 2.55 Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness Table 6.4 Karolis; Thesis: THE DIEI.£Cl'RIC CHARACTERIZATION OF UPID BILAYERS 112 6.4.3 Double layer correction of the measured capacitance (Cg) The contribution of the series double layers to the measured capacitance was examined by performing low frequency capacitance measurements at low electrolyte concentrations. The results appear in Table 6.3. The capacitance due to the double layers was eliminated from the measured capacitance using the procedure outlined in the first part of Section 6.2.2 (after Lliuger, Lesslauer, Marti and Richter, 1967). The results of these corrections are presented in Table 6.4 with the corresponding thicknesst of the hydrocarbon region. The corrections to the measured capacitance of egg lecithin were essentially in accord with the predictions of Table 6.2. The thickness of the hydrocarbon region of egg lecithin was thereby estimated to be 2.5±0.1 nm, corresponding to an area specific geometric capacitance of 7.8 mF m-2. The corrections to the measured capacitance of egg lecithin/cholesterol bilayers deviate from the predictions of Table 6.2 at concentrations::;; 1 mol m-3, although there is good agreement at much higher concentrations and in Ringer solution. (The thickness of the hydrocarbon region appears to get smaller by nearly 50% when the solution concentration changes by a factor of J0-3). The thickness of the hydrocarbon region of egg lecithin bilayers containing cholesterol t The corrected thickness was derived from Equations 6.3 and 6.4. We have:- 1 1 2 =--- therefore, Ohc = eh{ ~: - ~w] where the symbols have the same meaning as in the text Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page 6.18 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF LIPID BILAYERS 113 appears to be 2.65 ± 0.05 nm, which corresponds to an area specific capacitance of 7.16 ± 0.10 mF m-2. The corrections to the measured capacitance of egg lecithin/oxidised cholesterol bilayers result in a hydrocarbon region thickness of 2.62 ± 0.05 nm corresponding to an area specific capacitance of 7.24 mF m-2. Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page 6.19 Karolis; Thesis: THE DIEUCTRIC CHARACTERll.ATION OF LJPID BILAYERS 114 6.5 DISCUSSION The low frequency, area specific, measured capacitance of bilayers formed in high electrolyte concentrations (~ 100 mol m-3), summarised in Table 6.3, are in good agreement with the results obtained from monolayer apposition experiments by Fettiplace (1978), Benz and Janko (1976), Benz, Frohlich, Lauger and Montal, (1975) and Niles, Levis and Cohen, (1988). The capacitance is substantially higher than those experiments performed with shorter chain alkanes (see Table 6. la), where equilibrium was thought to be established with solvent retained in the bilayer interior. The capacitance measured in this work is also significantly higher than others who used n-hexadecane such as Fettiplace, Andrews and Haydon (1971), Benz and Janko (1976), Ashcroft, Coster, Laver and Smith (1983) and Coster and Laver (1986). The reason for this may be due to several factors which were alluded to earlier (Section 6.1 ); such as the age of the bilayer; the temperature at which the measurement was performed; the frequency of measurement and the estimation of the bilayer area. Bilayers formed with n-hexadecane can take longer than 7.2 ks to form stable structures at room temperature. Any attempt to measure capacitance before the bilayer had reached equilibrium and therefore free of trapped solvent, would result in a low measured capacitance (Ashcroft, Coster, Laver and Smith, 1983). Capacitance measurements above 30°C, are influenced by retained alkane solvent and would also result in a low measured value (Coster and Laver, 1986). It has been shown by Coster and Smith (1974), and Clowes, Cherry and Chapman (1971) that the capacitance can be understated by as much as 13% if the measurement is performed at high frequencies. Apart from the work of Coster and Smith (1974), Ashcroft, Coster and Smith (1977a,b, 1981) and Coster and Laver (1986), the measurements performed by others were done so at frequencies higher than 100 Hz. Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page 6.20 Karolis; Thesis: THE DIELECTRIC CHARACI'ER/7.ATJON OF UPJD BILAYERS a-.------. 7 Q) 0 C: -O;t::ea 6 E ~ .i= a. ·.: ea - 0 eaO> .... 0 Q) 5 - ea>, ....ea -Q) --e-- lnCd ::, - - ..0 N In Cd(L) zoea ::, "O 4 + In Cd(L-C) Q) .i=- o In Cd(L-O-C) 3 · 1 o· 4 Electrolyte molarity Figure 6.1 Natural Logarithm of the double layer capacitance vs the molarity of the electrolyte for different bilayer systems. Qj refers to electrolyte onlyt Cd(L) refers to lecithin bilayers Cd(L-C) refers to lecithin/cholesterol bilayers Cd(L-O-C) refers to lecithin/oxidised cholesterol bilayers t The double layer capacitance was detennined by the method of Uuger, Lesslauer, Marti and Richter, (1967), and assumes no surface charge on the bilayer. Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness Figure6.l Karolis; Thesis: THE DIEU'.CTRJC CHARACTERlZAT/ON OF UPID BILAYERS 115 6.5.2 Removal of the double layer capacitance Associated with the bilayer-electrolyte interface is a diffuse electric double layer. The capacitance of this region, in series with the bilayer is dependent on the potential across the interface as well as the ion concentration. According to Lliuger, Lesslauer, Marti and Richter (1967), for bilayers with no surface charge and in small electrical fields, at high concentrations (~100 mol m-3), the capacitance is so much larger than that of the bilayer that it has a negligible effect on the measurement of the bilayer capacitance. This is true for bilayers that are greater than 5 nm thick. However, for the thin bilayers examined in this work, the double layer capacitance can have a measurable effect. For example, according to Table 6.2, the measured capacitance may understate the true capacitance of the bilayer by as much as 2% at 100 mol m-3 concentration for bilayers < 3 nm thick. Measurements performed at low salt concentrations could result in a 75% error for the same thickness bilayer. If the double layer is regarded as a Gouy-Chapman diffuse type which reduces to a Helmholtz-Perrin double layer at small potentials a simple arithmetic subtraction would be sufficient to correct the measured capacitances at low electrolyte concentrations (~ 10 mol m-3). The result of such corrections, shown in Table 6.4, suggest that for egg lecithin bilayers this model of the electric interface is sufficient. In Figure 6.1 the behaviour of the double layer capacitance with electrolyte concentration is examined for the different bilayers. The double layer capacitance was determined from Equation 6.3 and assumed that the geometric capacitance determined at concentrations ~ 100 mol m-3 was the dielectric capacitance of the bilayer and was independent of electrolyte concentration. The bold line represents data from Table 6.2 which is what would be expected at a charge-free surface interface. One can see that there is good agreement between this model of the interface supports the notion that the bilayers were free of a net surface charge. The results for added cholesterol deviate from this model at concentrations ~ 10 mol m-3. After removal of the double layer the capacitance of the bilayer increases to 13.4 µF m-2 at 0.1 mol m-3. One reason for this may be due to an underestimate of the dielectric constant of the Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation lo Hydrocarbon Region Thickness page 6.21 Karalis; Thesis: THE DIEUCI'RJC CHARACTERIZATION OF UPID BILAYERS 8 Q) -0 C: CU 7 ·c:;- a.CU CU ....0 6 Q) >- !2 Q) 5 j5 ::, 0 ,::, -0-- In Ccf 4 0 -C: In Cd(+) + In Cd(L-C) 3 1 o- 4 1 o- 3 1 o- 2 1 o- 1 1 o0 Electrolyte concentration (moles/litre) Figure 6.2 Natural Logarithm of the double layer capacitance vs the molarity of the electrolyte for lecithin-cholesterol bilayers (Cd(L-C)); charged membrane (Cd(+)/5.8x1 o-3 C m-2); and electrolyte only ( Cd) Chapter 6: The Low Frequency Capacitance of Bilayers and its RelaJion to Hydrocarbon Region Thickness Figure6.2 Karolis; Thesis: THE DIELECTRIC CHARACTERll.AT/ON OF UPID BILAYERS 116 of the aqueous phase would need to be 320 at distances up to 30 nm from the interface (Laver 1984). Rather, the reorienting of the water near the lipid polar moieties of lecithin should tend to reduce the dielectric constant of the electrolyte in the immediate vicinity of the interface. Alternatively, the presence of a net electrostatic dipole field at the interface would produce a double layer capacitance given by Equation 6.10. In Figure 6.2 the double layer capacitance determined for cholesterol/lecithin bilayers is presented. The fitted curve describes a Stern model of the bilayer interface. A least squares best fit to the cholesterol data resulted in a surface charge density of 5.8 x lQ-3 C m-2. Surface charge estimates by Chernomordik, Melikyan, Dubrovina, Abidor, Chizmadzhev and Yu (1984) on PE solvent free bilayers were found to be 5 ± 3 x lQ-3 C m-2. It is interesting to note that differences between head groups of different lipids such as glycerol monooleate (having no charged head group) and phosphatidylcholine (electrostatic dipole in head group, -0.4 nm), have little effect on the double layer capacitance (Laver 1984). The effect of the electrostatic dipole should only be important when the Debye length in the electrolyte is similar to the separation of the discrete charges (Cole 1969). At low electrolyte concentrations, when the ionic double layers contribute significantly to the bilayer capacitance, the Debye length is -10 nm, which is much greater than the discrete charge separation. However, at concentrations where the Debye length is similar to the charge separation in the choline-phosphate groups (i.e. when the effect of the electrostatic dipoles can be ignored) the capacitance of the ionic double layers was large enough not to contribute to the total bilayer capacitance. Thus if a deviation from Gouy-Chapman theory did occur at high salt concentrations as a result of electrostatic dipoles at the bilayer surface, it would not have been detectable in this work. Therefore, we must conclude that the capacitance data reported here for egg lecithin bilayers is consistent with the notion that no net surface charge exists on them and that the double layer capacitance, as predicted by the Gouy-Chapman theory is sufficient to explain the behaviour of the measured capacitance down to at least 1 mol m-3. The orientation of the polar head group of the lecithin molecules may thus be in the same plane parallel to the interface. Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page 6.22 Karolis; Thesis: THE DIELECTRIC CHARACTERflATION OF UPID Bll.AYERS 117 The Stem model of the double layer is also sufficient to explain the behaviour of the capacitance data for lecithin/cholesterol bilayers assuming a residual net surface charge of 5.8 x IQ-3 C m-2. The net surface charge may arise from a realignment of the polar head group of the lecithin molecules from the plane of the interface into the aqueous phase as a result of the condensing effect of cholesterol (discussed more fully in Chapter 8). The data for oxidised cholesterol is unclear. It would appear that the surface of the bilayer is without a net charge. Measurements down to lQ-3 mol m-3 support this view. 6. 5. 2 The Thickness of the Hydrocarbon Region The geometric capacitance given in Table 6.4, suggests that there may be very little solvent retained in the bilayers. As a consequence, the thickness of the hydrocarbon region was determined using a dielectric constant of 2.2, which was the value determined by Requena and Haydon (1975), for the lipid acyl residues of egg lecithint. For egg lecithin bilayers the thickness of the hydrocarbon region was found to be 2.5±0.3 nm and for egg lecithin-cholesterol bilayers, 2.72 ± 0.3 nm. For bilayers containing oxidised cholesterol the thickness decreased slightly to 2.69 ± 0.3 nm. The thickness of the hydrocarbon region of the bilayer is, therefore, only slightly greater than the length of a single acyl chain. The length of palmitic acid is -2.4 nm and the length of oleic acid is -2.5 nm. If one excludes the carboxylic acid group from these organic acids, their respective lengths reduce to 2.1 nm and 2.2 nm. Quite clearly, with these dimensions it is impossible for the acyl chains to be aligned perpendicular to the biface without a significant degree of interdigitation and folding. NMR studies have shown that the bilayer centre is occupied by metheline groups (-CH2-), close to the terminal methyl group (-CH3), which are considerably more fluid than those near the polar head group. t The dielectric constant most often used for this region, 2.14, assumes a significant n-hexadecane presence in the bilayer interior and was used to detennine the thickness of this region for comparison purposes. The change makes only - 3% difference to the calculation of the thickness. Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page 6.23 Karolis; Thesis: THE D/EU',CTRJC CHARACTERfZAT/ON OF UPID BILAYERS 118 6.6 SUMMARY The low frequency capacitance of lecithin and lecithin-cholesterol bilayers was determined. It was shown that the bilayers were essentially free of solvent and that the capacitance could be used to estimate the thickness of the hydrocarbon region of the bilayer. The thickness of the bilayer was estimated to be 2.5 nm. The influence of the double layer capacitance was examined repeating the measurements at low electrolyte concentrations. It was shown that bilayers containing cholesterol had a residual surface charge of the order of 5.8 x 10-3 C m2. Chapter 6: The Low Frequency Capacitance of Bilayers and its Relation to Hydrocarbon Region Thickness page 624 Karolis; Thesis: THE D/El£CTRJC CHARACTERfZATION OF UPID 8/UYERS 119 CHAPTER 7 THE CONDUCTANCE OF LIPID BILAYERS 7 .1 INTRODUCTION 120 7.2 11-IEORY 123 Naked Ion Trans/ocation ...... 123 Hydrated Ion Trans location ...... 123 Trans location via formation of a transmembrane pore ...... 125 Trans/ocation via existing transmembrane pore ...... 126 7. 3 MEIBOD AND MATERIALS 128 7.4 RESULTS 128 7 .5 DISCUSSION 129 7.6 SUMMARY 131 Chapter 7: The Conductance of Lipid Bilayers page 7.1 Karolis; Thesis: THE DIEU.CTRJC CHARACTERIZAIJON OF UPID BILAYERS 120 7 .1 INTRODUCTION The mechanism by which water, ions and non-polar molecules traverse the hydrocarbon region of a lipid bilayer is of fundamental importance to the understanding of the behaviour of biological cellular systems. Although the permeation of water and nonelectrolytes through unmodified lipid bilayers can be predicted from their bulk solubility and diffusion data in liquid hydrocarbons (Black, Joris and Taylor, 1948; Schatzberg, 1963, 1965) and olive oil (Overton, 1899)t , ion conductivity can not. Lipid bilayers have generally exhibited a varied, often unpredictable, conductance, the reasons for which have eluded plausible explanation (Hanai, Haydon and Taylor, 1964; Tien, 1974; Smith, Coster and Laver, 1985). The resistance of bilayers made from the same materials for example, has been observed to vary as much as 100 fold (Hanai, Haydon and Taylor,1964; Ui.uger, Marti and Richter, 1967; Ashcroft, Coster and Smith,1981) with no obvious correlation with the type of solvent, electrolyte concentration, valency or temperature. A discussion of the mechanics of electric charge transfer must involve a discussion of the possible pathways (Miyamoto and Thompson, 1967). For example, Hanai, Haydon and Taylor, (1965c) have suggested that the variations in conductance may be due to changes in the size of leakage channels formed at the border of the support. They argued that lipid bilayers formed from phosphatidylcholine/n-decane solutions should have an intrinsically low conductance (about lQ-5 S m-2) and that the variations in the magnitude of the conductance are due to stochastic changes in the size of leakage channels which simply swamp the intrinsic bilayer conductance. This conclusion was reached from an observed linear relationship between conductance and bilayer area tt which only occurred with bilayers of very low conductance. t In the case of water permeability in liquid hydrocarbon, for example, a value of 35x10-6 m s -I can be predicted from solubility and diffusion data, which is in good agreement with experimentally derived values (Hanai and Haydon, 1966; Cass and Finkelstein, 1967; Redwood and Haydon, 1969; Price and Thompson, 1969). tt The bilayer area was altered physically by introducing a controlled hydrostatic pressure difference across the lipid bilayer thus causing it to bow. Chapter 7: The Conductance of Lipid Bilayers page 7.2 Karolis; Thesis: THE DIEU:CTRJC CHARACTERIZAI/ON OF UPID BILAYERS 121 The Hanai et al hypothesis was consistent with an intrinsic minimum border leak of 0.6 x 10-11 S. Tien (1974) pointed out that this would account for about one third of the total measured conductance of a 1 mm2 bilayer and therefore appears unlikely. The hypothesis was also rejected by Andreoli, Bangham and Tosteson, (1967) who attributed the linearity observed by Hanai et al, to a reversible change in the molecular organisation of the bilayer under tension. Miyamoto and Thompson (1967) found that the conductance of phosphatidylcholine/n tetradecane lipid bilayers was higher than that observed by Hanai et al, and varied approximately linearly with membrane area when the membranes were formed on septa with holes of different areas. They concluded that the conductance was primarily attributable to the bilayer phase. Measurements by Smith, Laver and Coster (1984) on the temperature dependence of phosphatidylcholine/n-hexadecane membranes and Smith, Coster and Laver (1985) on the concentration and composition of the external electrolyte, appear to support this view. The mechanism for current transfer across the bilayer is still largely unresolved. Water permeability experiments suggest that sufficient ions might be transferred with the known water flux (Huang and Thompson, 1966; Miyamoto and Thompson, 1967; Price and Thompson, 1969). The activation energy for osmotic permeability has been measured to be around 5 kJ mol- 1 (Redwood and Haydon, 1969; Price and Thompson, 1969). However, the variability in ion selectivity due to surface charge effects (Hopfer, Lehninger and Lennarz, 1970); the influence of bilayer composition such as the inclusion of cholesterol on water permeability (Finkelstein and Cass, 1967; Fettiplace, 1978); the change in conductance with ionic strength and charge carriers (Smith, Coster and Laver, 1985) as well as temperature (Smith, Laver and Coster, 1984), and the effects of 'carriers' and 'pore' inducers (Holtz and Finkelstein, 1970; Stark, Benz, Pohl and Janko, 1972; Ginsberg and Noble, 1974; Bamberg and Benz, 1976) as well as the very small effect associated with pH changes clearly indicate a more complicated process for ionic transfer. Chapter 7: The Conductance of Lipid Bilayers page 7.3 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF LJPID BILAYERS : : : : :ir.iduced:char ·e:due:to:iori i:ri: pore: bilayer .. C" ...... ·e· ...... C; ...... ·C.,· . t ...... water: ...... wa er ...... ------. •·•r2b ••• •:· ···· ...... ------...... : : : : : : : : : '?'?~er : bilayer -~ . ),, . -~- .. . ·u · · ·· ··he··...... FIGURE 7.1 Transmembrane pore. The dielectric constant of the pore is the same as the water. The symbols have the same meaning used in the text. Chapter 7: The Conductance of Lipid Bilayers Figure 7.1 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 122 Two possible simple mechanisms by which ions may be transported across the lipid phase are the formation of water filled cylindrical pores and charge carriers (Parsegian,1969). Using the Parsegian model, depicted in Fig 7 .1, Smith, Laver and Coster (1984) examined the temperature dependence of the area specific conductance of egg-lecithin/cholesterol bilayers formed with n-hexadecane in 1 mM KCl and deduced the activation energy for conduction to be 35 kJ mol- 1 from Arrhenius plots. Several possibilities were explored which are described in paragraph 7 .2 of this chapter. An alternative method for testing this model might be to examine the conductance of similar bilayers at different electrolyte concentrations. This would require measurements on stable long lived bilayers in order to be confident that the dominant pathways for conduction had been established and were in equilibrium. The data obtained from admittance measurements used for the determination of the capacitance described in Chapter 6 could be used for this purpose. The following work describes the results of conductance measurements on long surviving, stable lecithin and lecithin-cholesterol bilayers and compares the results with the predictions of the Parsegian model of the transmembrane pore. Chapter 7: The Conductance of Lipid Bilayers page 7.4 Karolis; Thesis: THE DIELECTRIC CHARACTERfZATION OF UP/D 8/1.AYERS 123 7.2 THEORY Naked Ion Trans location For the translocation of an ion between an external aqueous phase of dielectric constant Ew and a hydrophobic phase with dielectric constant Ebe, the difference in electrostatic self energy L\UE is given by (7.1) L\UE will decrease with increasing ionic radius but even for the chloride ion (Ri = 0.18 run), the energy will be - 180 kJ mol-1 (for Ebe= 2.1, Ew= 80) which is unrealistically high and would predict conductances for the bilayer some 10 12 orders of magnitude lower than those reported in this thesis and elsewhere. Hydrated Ion Translocation The electrostatic energy difference L\UE will be reduced as the ionic radius increases and will thus be lower for hydrated rather than naked ions. However, for the partitioning of hydrated ions into the hydrophobic interior, the interfacial free energy of the associated bubble of water surrounding the ion must be considered (Macdonald, 1976). If one ignores possible changes in the hydration number on translocation, the energy L\U s involved in the creation of this additional interfacial area will be given by (7.2) where y is the interfacial tension between the hydrophobic region and the external electrolyte (assumed to be independent of temperature as a first approximation) and Bis the radius of the hydration bubble. The electrostatic difference will therefore be given by Chapter 7: The Conductance of Lipid Bilayers page 7.5 Karolis; Thesis: THE DIELECTRIC CHARACTERlZATION OF UPID BILAYERS 124 (7.3) The total energy difference LiUT is simply (7.4) Now, LiUTwill undergo a minimum (Macdonald, 1976) when (7.5) at a radius given by (7.6) If y = 0.05 J m-2 and B - 0.34 nm, LiUT - 140 kJ mol-1 which is still too high to be consistent with the activation energy measured by Smith, Coster and Laver (1984). Ashcroft and Coster (1978) have dismissed the effect of hydration number on Bmin having found that typical values of 3-4 are of little significance. Chapter 7: The Conductance of lipid Bilayers page 7.6 Karolis; Thesis: THE DIEU:CTRIC CHARACTERIZATION OF UPID BILAYERS 125 Translocation via formation of a transmembrane pore The electrostatic energy difference for ion translocation through the hydrophobic interior would be considerably reduced if the ion could traverse through a region of high polarizability such as a pore (see Figure 7.1). The self energy of an ion in a pore will be increased from that in the bulk phase by a term due to the induced charges formed at the bilayer surface of the pore. Consider a cylindrical pore filled with water (Ew), and radius b << <>he (the thickness of the bilayer). The total self energy of an ion situated in a pore will be given by wpore = (7.7) where, ~ is a constant which depends upon the shape of the pore and the ratio of the dielectric constants of the bilayer (Ebe) and pore (Ew). Riis the ionic radius, and £0 is the permittivity of free space. (The first term represents the ion self energy when in the bulk aqueous phase. The second term is the ion self energy (say LiUE) arising from the charge induced around the pore boundary due to the presence of the ion. It is assumed that this component is independent of the position of the ion in the pore and, if the dielectric constants of the pore and bilayer are known, will depend only on the pore radius). Thus (7.8) However, there is an additional interfacial energy involved in the creation of the pore which is given by (7.9) Chapter 7: The Conductance of Lipid Bilayers page 7.7 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID B/1.AYERS 126 Since LlU s increases as LlUE decreases with the pore radius b, a minimum energy will exist at a radius given by (7.10) For a hydrophobic region of thickness Ohc = 3 nm, the optimum pore radius will be -0.14 nm and the minimum total energy difference -160 kJ mol-1 which exceeds the measured value. Furthermore, the pore radius is comparable to the crystal radii of many ions. Larger ions would require the pore to be larger with a consequent increase in Wpore. In some cases additional energy would be required to remove a hydration shell to permit passage through such a narrow pore. Translocation via existing transmembrane pore If the pore were formed by an independent process the activation energy would need to be equated to only the electrostatic energy difference given in Equation 7.8. We now examine the value of this term as a function of pore radius and assume Ehc= 2.1, Ewater = 80, ~ = 0.15 and consider its effect on the ion concentrations in the pore. From Boltzman statistics, the equilibrium ion and counter ion concentrations will be given by (7.11) (7.12) respectively, where Chapter 7: The Conductance of lipid Bilayers page 7.8 Karolis; Thesis: THE DIELECTRIC CHARACTERTZATION OF UPID 8/1.AYERS 127 are the concentration of the positive and negative ions in the pore is the concentration of each ion species in the bulk phase, either side of the bilayer 'I' is the surface potential on the bilayer LiUp, LiUn are the induced energies for a positive and negative ion respectively when located in a pore. (LiUp=LiUn=LiU) eo is the electronic charge z the ion valency k Boltzmann constant T the absolute temperature R Universal Gas constant The conductance of a single pore, Gpore, is related to the ion concentration in the pore by : (7.13) where, D is the diffusion coefficient for the positive and negative ions (assumed equal), L is the length of a typical pore (3 nm) and b the radius. Chapter 7: The Conductance of Lipid Bilayers page 7.9 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF LJPID BILAYERS TABLE 7.1 The low frequency area specific CONDUCTANCE (Gg) of bilayers formed with n-hexadecane in KCI solutions of different concentration electrolyte egg lecithin egg lecithin- egg lecithin - concentration cholesterol oxidised cholesterol (mole litre-1) (mS m-2) (mS m-2) (mS m-2) Ringer not measured 7.20 ± 0.20 not measured 100 9.6 ± 4.8 not measured not measured 10-1 4.8 ± 1.4 2.30 ± 2.00 3.0 ± 2.0 10-2 not measured 0.45 ± 0.45 1.8 ± 1.2 10-3 1.6 ± 1.3 0.50 ± 0.20 1.3 ± 1.1 lQ-4 not measured 0.37 ± 0.18 not measured Chapter 7: The Conductance of Lipid Bilayers Table 7.1 Karolis; Thesis: THE DIEL£CTRJC CHARACTERIZATION OF UPID Bit.AYERS 128 7.3 METHOD AND MATERIALS Egg lecithin, egg lecithin/cholesterol and egg lecithin/oxidised cholesterol bilayers were produced in the manner described in Chapter 6. The area specific conductance was obtained by the method described in Chapter 5 from admittance measurements at frequencies below 0.04 Hz. The measurements were obtained simultaneously with those of capacitance described in the previous chapter. The only assumption made in the analysis of the data was that the measured conductance was attributable to a single type of pathway across the bilayer. 7 .4 RESULTS The results for lecithin bilayers appear in Table 7 .1 where it can be seen that the conductance was measured to be 1.6 ± 1.3 mS m-2 at 1 mM KCl, 4.8 ± 1.4 mS m-2 at 100 mM and 9.6 ± 4.8 mS m-2 at 1 M KCl. The conductances observed with lecithin-cholesterol bilayers and lecithin-oxidised cholesterol bilayers also appear in Table 7 .1. The conductances are all of the same magnitude but exhibit an unusual behaviour in so far as the conductance is not proportional to the concentration of ions. Of interest is the decrease in conductance shown by the addition of cholesterol to the lipid mixture. Chapter 7: The Conductance of Lipid Bilayers page 7.10 Karolis; Thesis: THE DIEU:.CTRJC CHARACTERfZATJON OF UPID BILAYERS TABLE 7.4 Calculated ion concentrations in pores of different radii spanning a bilayer with a net surface charge of 5.8 x I0-3 C m·2 Co 'I' pore radius Cp Cn Cp + Cn (moles litre·l) (volts) oo-9 m) (moles litre·O (moles litre·l) (moles litre·l) 1 0.0025 0.133 < 10-8 < 10-8 < 10-8 0.399 2.5x10·5 3.0x10·5 5.5x10·5 0.665 l.7x10·3 2.0x10·3 3.1x10-3 1.330 3.7x10·2 4.5x10·2 8.2x10·2 10-l 0.0081 0.133 < 10-8 < 10-8 < 10-8 0.399 2.ox10-6 3.8x10·6 5.8x10·6 0.665 l.3x104 2.5x10·4 3.8x10·4 1.330 3.0x10·3 5.6x10·3 8.6x10·3 10-2 0.0246 0.133 < 10-8 < 10-8 < 10-8 0.399 l.lx10·7 7.2x10·7 8.3x10·7 0.665 7 .lx10·6 4.8x10-5 5.5x10·5 1.330 l.6x104 1.lx10·3 l.2x10·3 10-3 0.063 0.133 < 10-8 < 10-8 < 10-8 0.399 2.4x10·9 3.2x10·7 3.2x10·7 0.665 l.6x10·7 2.lx10·5 2.lx10·5 1.330 3.5x10·6 4.7x10·4 4.7x10·4 10-4 .118 0.133 < 10-8 < 10-8 < 10-8 0.399 2.8x10· 11 2.7x10·7 2.7x10·7 0.665 l.9x10·9 l.8x10·5 l.8x10·5 1.330 4.lx10·7 4.0x10·4 4.0x10·4 Chapter 7: The Conductance of Lipid Bilayers Table 7.4 Karolis; Thesis: THE DIEL.£CTRJC CHARACTERIZATION OF LJPID BILAYERS TABLE 7.2 The additional energy LiU required by an ion to place in a pore spanning a lipid bilayer b LiU = l~.4 LiU (pore radius) RT (nm) (kJ mole-1) 0.133t 78.2 31.6 0.399 26.1 10.5 0.665 6.3 6.3 1.330 3.2 3.2 TABLE 7.3 The anion and cation concentrations of a univalent electrolyte in the region of a charged bilayer surface Cp Cp+Cn (volts) (mole litre-I) (mole litre-1) (mole litre-1) 1 0.0025 0.91 1.100 2.00 10-1 0.0081 7.3x10-2 0.137 0.20 10-2 0.0246 3.8x10-3 0.026 0.03 10-3 0.0630 8.6x10-5 0.012 0.01 10-4 0.1180 l.0xl0-6 0.010 0.01 t K+ ion radius Chapter 7: The Conductance ofLipid Bilayers Table 7.2 and 73 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF LJPID Bll.AYERS 129 7 .5 DISCUSSION According to Equation 7.4 the conductance is proportional to the ion concentration. This is indeed the case for bulk electrolyte solutions. However, the 1000 fold change in the bulk solution concentration used in this study is not reflected in the bilayer conductance. Rather the conductance is fairly constant between lQ-4 and 10-2 molar KCl before rising sharply at 10-1 and higher concentrations. In Table 7.2 the induced energy arising from the pore geometry has been calculated for different radii expressed as multiples of the K+ ion where it can be seen that for a realistic pore size of 1 nm, the activation energy was about 3 kJ mol· 1. (The ion self energy in the bulk solution is 6.5 kJ mol-1). The effect on the anion and cation concentrations in a pore bounded with a net surface charge density of 5.8 x 10-3 C m·2, was determined in Table 7.3. (The activation energy (LiU) was set to zero and 'I' was determined from Equation 6.9). In Table 7.4, the influence of pore has been included where it can be seen that the anion and cation concentrations have been reduced by a factor of 25. The total anion-cation concentration for a pore radius of l.33x10·9 m (10 x K+ ion radius) has been plotted against the electrolyte molarity in Figure 7 .2. The net surface charge of the pore was assumed to be 5.8 x 10-3 C m2 (to be consistent with the earlier discussion of capacitance vs concentration). On the same graph the conductance variation with concentration has also been presented. The agreement at low concentrations appears excellent. At higher concentrations the results diverge. The divergence, however, is considerably less than if the bilayer surface charge was assumed to be zero. Chapter 7: The Conducrance of lipid Bilayers page 7.11 Karolis; Thesis: THE DIEU!.CIRIC CHARACTERIZATION OF u PID BILAYERS 10· 1 ""T"'""------10. 1 C\I -< 10· 2 ..§ Cl) -Q) 0 C: CU 0 -::, 10· 3 -g 0 0 c:: -o-- charged pore 0 -~ ~ conductance 10· 4 --_,...... ,....,....,...,..,.,..,.,....----,.....,....,...,...... ,..,.,....__,._,.....,...... ,..,.,...,---,,..__ ...... - ...... _,...... ,,_10· 4 10· 4 10· 3 10· 2 10· 1 10° 10 1 molarity FIGURE 7.2 Conductance of lecithin/cholesterol bilayers and the sum of the anion and cation concentrations in transmembrane pores. The charged pores were assumed arbitrarily to have a surface charge concentration of 5.8 x 1o-3 C m2 and the pore radius was assumed to be 1.33 X 1Q-9 m. Chapter 7: The Conductance ofLipid Bilayers Figure 7.2 Karolis; Thesis: THE DIELECTRIC CHARACTERfZATION OF UPID BILAYERS 130 Smith, Coster and Laver (1984), have argued that the small activation energy (35 kJ mol-1) determined for lecithin/cholesterol bilayers in solutions of 1 mM KCI, is indicative of the existence of transmembrane pores. If one assumes that the ionic diffusion constant inside the pore is similar to the free solution value (2 x 10-9 m2 s-1), there is a contribution to the measured activation energy due to ionic transport - 17 kJ mol-1. If'¥ is zero, equations 7.11 and 7.12 reduce to: (7.14) Substituting the following, and converting where necessary from moles to m-3 : quantity symbol value unit electronic charge eo 1.6 X lQ-l9 C diffusion coefficient D 2 X lQ-9 m2 s-1 pore radius b 1 X 10-9 m length of pore L 3x 10-9 m concentration of ions in Cp moles the pore concentration of ions in the bulk solution Co 1 X lQ-3 moles temperature T 298 K activation energy ~u 18 X lQ3 J moI-1 gas constant R 8.3 J K- 1mol-l Avogadro's number NA 6.02 X lQ-26 m-3 It follows that Cp is -10-6 molar or 6 x 1020 ions m-3, and the conductance Gp= 0.8 x 10-14 S The measured conductance for lecithin/cholesterol bilayers formed in 1 mM solutions was, from Table 7.1, 0.5 x 10-3 S m-2. Thus, - 6 x 1010 pores m-2 would be necessary. Chapter 7: The Conductance of Lipid Bilayers page 7.12 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 131 7.6 SUMMARY The conductance of lipid bilayers was determined using low frequency impedence spectroscopy. In 100 mM KCl, the conductance was determined to be 4.8 mS m-2 for lecithin bilayers and 2.3 mS m-2 for lecithin bilayers containing cholesterol. The reduced conductance of the latter was attributed to the increased stability of pore formation. Measurements at different electrolyte concentrations showed that the ion concentration and conductance could not be explained by a simple analogy. Rather the conductance could be explained by the presence of pores and that in the case of bilayers containing cholesterol, the pores had a surface charge of 5.8 x 10-3 C m-2. Chapter 7: The Conductance of Lipid Bilayers page 7.13 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID Bll.AYERS 132 CHAPTER 8 CHOLESTEROL INCLUSION IN EGG-LECITHIN BILAYERS (THE DIELECTRIC PICTURE OF STRUCTURE) 8.1 INTRODUCTION 133 8.2 METI-IOD AND MATERIALS 136 Materials ...... 136 Frequency dependence of bilayer impedance ...... 136 8.3 RESULTS 138 8.4 DISCUSSION 140 8.5 SUMMARY 144 Chapter 8: Cholesterol Inclusion in Egg Lecithin Bilayers page 8.1 Karolis; Thesis: THE DIELECTRIC CHARACTERlZAT/ON OF UPID 8/I.AYERS -133 8.1 INTRODUCTION Since its isolation and recognition by Chevreul in 1816, the biochemistry of cholesterol has been studied extensively, (Sabine, 1977; Kritchevsky, 1958; Myant, 1981). It is one of the most widely disseminated organic compounds in the animal kingdom and has been found to vary extensively in proportion with phospholipids in cellular bilayers. Despite this and a wealth of knowledge of the biosynthesis and metabolism of cholesterol its function and conformation in cell membranes is not clear. Phospholipid membrane models such as monolayers, vesicles and planar lipid bilayers have provided insights into the internal organisation of bilayers and the effects of the incorporation of specific molecules into bilayers. X-ray diffraction studies (Rand and Luzzati, 1968; Lecuyer and Dervichian, 1969 ) and ESR studies ( Hsia, Schneider and Smith, 1971 ) of aqueous mixtures of lecithin and cholesterol suggest that the presence of cholesterol leads to an increase in thickness of the membrane hydrocarbon region and a reduction in the mean molecular area of the lecithin molecules. This condensing effect was first observed by Leathes (1925) and has since been confirmed by NMR and ESR studies (Darke, Finer, Flook and Phillips, 1972; Stockton and Smith, 1976; Marsh and Smith, 1973). The change in molecular area is associated with an ordering of the acyl chains due to the position of the rigid sterol nucleus. In bilayer lipid bilayers, this ordering is manifested in changes in viscosity and permeability (Finkelstein and Cass, 1967). Two extreme models have been proposed to explain the molecular mechanism of the condensation effect. The Cavity Model proposed by Shah and Schulman (1967) assumes that the effective area of the lecithin molecule is unchanged from a monolayer of pure lecithin while the effective area of the cholesterol molecule is reduced by its incorporation into molecular cavities which exist within the loosely packed hydrocarbon chains of lecithin. In its simplest form the cavity model implies that molecular separation would remain unchanged with increasing cholesterol composition. The measurements of Butler, Smith and Schneider (1970), Hsia, Schneider and Smith, (1971) and Oldfield and Chapman (1972), however, do not Chapter 8: Cholesterol Inclusion in Egg Lecithin Bilayers page8.2 Karolis; Thesis: THE DIELECTRIC CHARACTERIZ.ATION OF LJPID BILAYERS 134 support this. The Interaction Model proposed by Weiner and Felmeister, (1970) assens that the effective area of cholesterol is the same as in a monolayer of pure cholesterol and the effective area of the lecithin molecule is reduced by the interaction of cholesterol with its hydrocarbon chains (Stockton and Smith, 1976). The behaviour of cholesterol in monolayer studies appears to support this view, ( Demel and de Kruyff, 1976 ). The change in fluidity of lecithin-cholesterol mixtures is related to the saturation of the fatty acid chains and the homogeneity of the lipid content of the membrane. Experiments performed with different phospholipids containing various proportions of cholesterol ( Oldfield and Chapman, 1971; Marsh and Smith, 1973; Schrieier-Muccillo, Marsh, Dugas, Schneider and Smith, 1973) show widely varying effects. For example, increasing the cholesterol content of egg lecithin bilayers results in an extension of the fatty acid chains and a decreased amplitude of motion of the long axis. Cholesterol increases the chain order and this also reduces the solubility of short chain hydrocarbons in the lipid bilayer (Coster and Laver, 1986). The latter may be responsible for the conflicting reports on the effects of cholesterol on the thickness of artificial lipid bilayers. Increasing the cholesterol content of dipalmitoyllecithin bilayers, on the other hand, results in an increase in mobility and amplitude of motion of the fatty acid side chains. The condensing and liquefying effect of cholesterol on phospholipid bilayers is thought to be intimately related to the long term stability requirements (tum over of lipid) of different bilayers. For example, in myelin in which there is generally a high concentration of dipalmitoyl phosphatidyl choline, the presence of cholesterol might stabilise the membrane by fluidising the matrix. On the other hand in plasma bilayers the lipids are more labile. The presence of cholesterol therefore may play an important role by decreasing the fluidity of the bilayers which have a greater predominance of phosphatidyl choline lipids than in myelin. The osmotic permeability of phospholipid bilayers also appears to be influenced by the presence of cholesterol (Finkelstein and Cass, 1967; Deuticke and Ruska, 1976; Kroes and Ostwald, 1971). The position of the cholesterol hydroxyl group in the bilayer and the influence, if any, of hydrogen bonding is largely unresolved ( Darke, Finer, Flook and Phillips 1972; Huang, 1976; Ashcroft, Coster, Laver and Smith, 1983 ). Chapter 8: Cholesterol Inclusion in Egg Lecithin Bilayers page83 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 135 The autoxidation of cholesterol dispersed in aqueous solution has been thoroughly investigated (Smith et al 1973). The initial products are mainly 7a- and 7b- hydoperoxides which decompose to the common impurities in commercial cholesterol, 3b-hydroxycholest-5-ene-7- one and cholesta-3,5-diene-7-one. Radical autoxidation can occur in the solid state and similar products are formed. The great ease with which cholesterol can be oxidised in air means that a highly purified sample of cholesterol must be stored under an inert atmosphere in the absence of light and preferably at low temperature. Oxidation products of cholesterol, such as 7- dehydrocholesterol, are known to play a vital role in some membrane functions (Tien et al, 1966). Planar bilayer lipid bilayers have been produced from oxidised cholesterol alone (fien et al, 1966), and in association with phospholipids, (Ashcroft , Coster, Laver and Smith, 1983). No structural information was obtained from these studies other than membrane thickness, permeability and a subjective analysis of their fluidity. In the present study admittance dispersion spectra have been used to determine the effects of cholesterol on the dielectric structure of lecithin bilayers and the differential effects and location of oxidised and unoxidised cholesterol on the bilayer structure. Chapter 8: Cholesterol Inclusion in Egg Lecithin Bilayers pageB.4 Karolis; Thesis: THE DIELECTRIC CHARACTERfZATION OF UP/D BILAYERS 136 8.2 METHOD AND MATERIALS Materials Egg lecithin (phosphatidylcholine) was obtained from Sigma and used as supplied. Cholesterol was purified by formation of the dibromide and regenerating the double bond with zinc/acetic acid. It was recrystallised to constant melting point and optical rotation from aqueous methanol. Cholesterol was obtained as large colourless needles. 1H NMR, 13C NMR and infra-red spectra were consistent with a very high degree of purity. The sample was stored under nitrogen in glass tubes wrapped in foil at -20°C. Examination by TLC (Smith, Teng, Kulig and Hill, 1973) confirmed that hydroperoxides were absent. A purified sample weighing 0.25 g was dissolved in a 10 ml solution of a 3: 1 chloroform:methanol mixture (v:v) and stored at -4°C in a light free container. Oxidised cholesterol was produced by bubbling oxygen through a cholesterol/chloroform solution for 4 hours (see Chapter 5). Bilayers were produced from lipid mixtures of either egg lecithin alone; egg lecithin/cholesterol (mole ratio 2: 1) or egg lecithin/oxidised cholesterol (mole ratio 2: 1). The mixture was dried at 40°C for 3 hours. Subsequently, n-hexadecane was added and the preparation was painted with a syringe over a small hole in a polycarbonate septum. The bilayers were painted in 100 mol m-3 KCl at pH 7.2. In order to facilitate thinning of the bulk painted material, particularly at high salt concentrations, it was necessary to warm the electrolyte to 35°C. As soon as the bilayer appeared and began to spread across the septum, the temperature was slowly adjusted to 2s 0 c. Frequency dependence of bilayer impedance The progress of bilayer formation was monitored visually with a low powered microscope and electrically by monitoring the capacitance at a frequency of 1 Hz. The area of the membrane was determined from photographs taken through a low powered microscope. Admittance measurements were carried out usually at 25°C and 35°C, and KCl concentrations of 1, 10, 100 mM and 1 Molar. Chapter 8: Cholesterol Inclusion in Egg Lecithin Bilayers page8.5 Karolis; Thesis: THE DIELECTRIC CHARACTERfZAT/ON OF UPID BILAYERS 137 The computer based high resolution, ultra low frequency impedance spectrometer, described in Chapter 4, was used to analyse the structure of the bilayers. A measurable frequency dependence in the impedance was observed in each case which suggested that the bilayer contained regions of different dielectric constant. The dispersion in the capacitance and conductance associated with a multi-dielectric structure could be understood in terms of an equivalent electrical circuit in the manner described Chapter 5. Chapter 8: Cholesterol Inclusion in Egg Lecithin Bilayers page 8.6 Karolis; Thesis: THE DIELECTRIC CHARACTERIZ4TION OF LJP/D 8/l.AYERS 0.76 i!i.I.. N 0.74 0 < ' 2 Lecithin E 2 2 a LedChol LL 2 E 0.72 li2u22 Q) (.) 2222 C !2 0.70 Cl T T ·c3 f Cl T TT .J. f Cl a ctl .I.. .I.. T a. Cl T T ctl .L. Cl f T .L. a 0 0.68 ~ T ... .J. Cl T T ..&.. ~ D TT ci ... .J. ...a 0.66 0.64 2 1 0. 1 0. 1 1 0 o 1 0 1 1 o2 Frequency (Hz) FIGURE 8.3 Expanded view of the capacitance spectra for a lecithin and lecithin·cholesterol bilayer formed in 100 mM KCI at 25°C. 0.76 .... C\I - 0.74 \ 0 LedChol < ' E \ ...... -1 LL ..... • Lecithin E 0.72 ···············...... ····························----·-· Q) ...... -- 1element (.) ...... C -.------...• !2 0.70 2 elements ·c3 ••• ...• a.ctl ...... ·- ·-· ctl •• 3 elements 0 0.68 4 elements 0.66 - · - ·- 5 elements 0.64 2 1 0 . 1 0 1 1 o2 1 o3 Frequency (Hz) FIGURE 8.4 Manual sequential fitting of different parts of the capacitance spectra of the lecithin data. Chapter 8: Cholesterol Inclusion in Egg Lecithin Bilayers Figure 83 and 8.4 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 0.8 10 5 0.7 10 4 0.6 N N -I -I < 10 3 < E 0.5 E u. en E El lectthin-capacttance E 0.4 10 2 -(I) -(I) 0 0 C: lectthin-conductance C: ea 0.3 ea ·o 1 0 -ea 10 -:::, a. "O ea 0.2 C: 0 0 10 o 0 0.1 0.0 10 - 1 1 0 - 2 1 0 - 1 1 o0 1 0 1 10 2 1 o3 1 o4 1 o5 Frequency (Hz) FIGURE 8.1 Capacitance and conductance spectra for an egg lecithin bilayer formed in 1oo mM KCI at 25°C. 0.8 10 5 10 4 0.7 .... N N -I 10 3 -I < < E E u. 0.6 en E Ill lec/chol-capacttance 10 2 E -(I) -(I) 0 lec/chol-conductance 0 C: 10 1 C: ea 0.5 ea ·o- u:::, ea "O a. 10 o C: ea 0 0 0 0.4 10 - 1 0.3 10 - 2 1 o· 2 1 0 - 1 1 o0 1 0 1 1 o2 1 o3 1 o4 10 5 Frequency (Hz) FIGURE 8.2 Capacitance and conductance spectra for an egg lecithin cholesterol bilayer formed in 100 mM KCI at 25°C. Chapter 8: Cholesterol inclusion in egg lecithin bilayers Figure 8.1 and 8.2 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF llPID BILAYERS 138 8.3 RESULTS A plot of the capacitance and conductance frequency spectrum for lecithin and lecithin/cholesterol bilayers is shown in Figure 8.1 and Figure 8.2, respectively. On this scale the error bars lie mostly within the area of the dots. There is clearly a change in capacitance with frequency which confirmed earlier predictions that unless the measurements are performed at sufficiently low frequencies the capacitance would be underestimated by as much as 9% (at 1Q3 Hz). In Figure 8.3, the ordinate has been expanded to reveal the structure in the capacitance spectra and the differences between the spectra of lecithin bilayers and lecithin-cholesterol bilayers. (The temperature was 25°C and the electrolyte (KCl) concentration was 100 mM). The major difference between the two spectra arises from the hydrocarbon capacitance. The capacitance of the hydrocarbon region for lecithin, lecithin-cholesterol and lecithin-oxidised cholesterol bilayers is represented in the histogram of Figure 8.5a as the acyl chains. As pointed out in Chapter 6 the low frequency capacitance measurement of lecithin bilayers was in excellent agreement with results obtained by others from bilayers formed from monolayers. The bilayers reported in this work may be regarded as essentially free from solvent inclusion in the hydrocarbon region of the bilayer. The capacitance measurement for lecithin bilayers corresponds to a width of the hydrocarbon interior of approximately 2.47 nm (e=2.2). The hydrocarbon region of bilayers formed from lecithin/cholesterol and lecithin/oxidised cholesterol mixtures appear to be thicker by about 9% or 0.2 nm. The conductance (shunt conductance) of the bilayers formed from lecithin, lecithin-cholesterol and lecithin oxidised-cholesterol is presented in the histogram of Figure 8.5b for the acyl chains. The data was presented in a different form in Chapter 7. Unlike capacitance which is very reproducible between like bilayers, the conductance was found to be vary considerably resulting in large errors. A significant reduction in the conductance was nevertheless recorded with the addition of cholesterol to the bilayer mixture. Chapter 8: Cholesterol Inclusion in Egg Lecithin Bilayers page 8.7 Karolis; Thesis: THE DIEI.ECTR/C CHARACTERfZAT/ON OF LJPID BILAYERS 80 Lee •fa Lee/Chol 60 Lec/0xChol N BI <' E LL E 40 CJ) u C ·~u ea 20 a.ea 0 0 Acyl chains Acetyl Region Glycerol bridge Phosphatidylcholine Group FIGURE 8.Sa The capacitance of the different regions of bilayers consisting lecithin; lecithin-cholesterol; lecithin-oxidised cholesterol in 1oo mM KCI at 2s0 c. 105 Lee • Lee/Chol 104 m C;J BI Lee/OxChol < E (/) E 103 CJ) u C ea 102 u::, "O C 0 0 10 1 100 Acyl chains Acetyl region Glycerol bridge Phosphatidylcholine Group FIGURE 8.Sb The conductance of the different regions of bilayers consisting lecithin ; lecithin-cholesterol; lecithin-oxidised cholesterol in 1oo mM KCI at 2s0 c. Chapter 8: Cholesterol Inclusion in Egg Lecithin Bilayers Figure 85 Karolis; Thesis: THE DIEI.ECI'RJC CHARACTERIZATION OF UPID BILAYERS TABLES.I THE LOW FREQUENCY AREA SPECIFIC CAPACITANCE (Cg) OF BILAYERS FORMED WITH n-HEXADECANE IN lOOmMKCI CORRECTED FOR THE SERIES DOUBLE LAYER Bilayer Electrolyte Area Specific Corresponding Type Concentration Capacitance thickness of the (Cg) hydrocarbon region (mole litre-I) (mF m-2) (nm) (nm) Ehc=2.14 Ehc=2.20 Egg Lecithin 10-1 7.76±0.1 2.44 2.51 Egg lecithin/cholesterol 10-1 7.14±0.1 2.65 2.73 Egg lecithin/Ox. cholest. 10-1 7.24±0.1 2.62 2.69 Chapter 8: Cholesterol Inclusion in Egg lecithin Bilayers Table8.l Karolis; Thesis: THE DIEI.ECTRIC CHARACTERIZATION OF UPID BILAYERS 139 The results of Maxwell-Wagner fitting of the admittance data (as described in Chapter 5) are presented in bar form in Figure 8.5 for 100 mM KCl solutions. The results for different electrolyte concentrations are presented in Table 8.1 Chapter 8: Cholesterol Inclusion in Egg Lecithin Bilayers page 8.8 Karolis; Thesis: THE DIEUCTRJC CHARACTERfZAT/ON OF LIPID BILAYERS 140 8.4 DISCUSSION The division of the capacitance frequency spectrum into regions characterised by different time constants suggests that the bilayer is composed of dielectrically resolvable sections. The predominant feature was that due to the hydrocarbon moiety of the interior. The low frequency capacitance suggests that the thickness of this region was significantly affected by the presence of cholesterol in the bilayer. It can be argued that because the capacitance of lecithin bilayers formed from n-hexadecane is similar to bilayers formed from monolayer apposition, there was almost no solvent retained in the bilayer. A dielectric constant of 2.2 (Requena and Haydon, 1975), for this region would therefore seem to be appropriate. Thickness calculations, summarised in Table 8.1, indicate that the hydrocarbon region of bilayers containing cholesterol are about 9% thicker than lecithin-only bilayers. This could come about from the increased space made available by the cholesterol molecule, perhaps allowing a greater retention of n hexadecane molecules. This argument is supported by conductance measurements of this region where the inclusion of cholesterol reduced the electrical conductivity of the lecithin bilayer by 50% while the substitution of cholesterol with oxidised-cholesterol increased the conductance only slightly. These measurable effects plus the observation that lecithin bilayers become more stable physically, with the inclusion of cholesterol can be expected from energetic considerations (Coster, 1989). The energetics of pore formation has been discussed by Taupin, Dvolaitzky and Sauterey ( 197 5), Abidor, Arakelyan, Chernomordik, Chizmadzhev, Patushenko and Tarasevich (1979) and Petrov, Mitor and Derzhanski (1980). Basically, the energy to form a pore, Ep of radius R is given by: 2 v2 E = 2rcW - rcR (y+ E F._-) (8.1) p o-H 2 Chapter 8: Cholesterol Inclusion in Egg Lecithin Bilayers page8.9 Karolis; Thesis: THE DIEUCTRIC CHARACTERIZATION OF UPID BILAYERS ~ zw w w a: ~ Re RADIUS Figure 8.6 A sketch of the total energy required to form a pore, as a function of pore radius (Equation 8.1). For small pores the energy cost associated with the curved perimeter of the pore increases with the pore radius faster than the energy saving associated with the decreased area of the planar portions of bilayer - water interface. For large pores the reverse is true; the total energy required to form a pore reaches a maximum at a critical radius R c A pore of this radius would grow spontaneously and would lead to lysis. (Coster, 1990). Chapter 8: Cholesterol Inclusion in Egg lecithin Bilayers Figure 8.6 Karalis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID Bll.AYERS 141 where W is the perimeter energy per unit perimeter length and y is the interfacial free energy of the bilayer (see Figure 8.6). The first term represents the cost of making the new edgewhere entropic and energy items are unfavourable for the packing of lipid molecules into a highly curved surface. The second term represents the energy of the area of bilayer now occupied by the pore (i.e. energy saved). For small pores the energy cost to form the perimeter is larger than the energy saved by a reduction in area of the planar bilayer. Eventually the differential increase in the perimeter energy required equals the differential decrease in surface energy. At that point the bilayer would be unstable: a pore of this radius would grow uncontrollably leading to bilayer rupture. The distribution of the pore sizes can now be obtained via the Boltzmann distribution function. A molecule such as cholesterol, which has a small polar head and a large hydrophobic region will not pack well into the highly (negatively) curved pore region. The presence of such a molecule in the bilayer would therefore tend to increase in the perimeter energy and shift the distiibution of pore radii towards smaller radii (Coster 1989). The critical pore radius (at which the bilayer would rupture) is also increased (statistically a rarer event) and this would be reflected in greater bilayer stability. It has been found that cholesterol stabilises lecithin bilayers and reduces the electrical conductance. The first dispersion in capacitance which took place at about 0.02 Hz can be described in terms of a theoretical 2-layer model (see Chapter 5). The bilayer region under consideration is the interface defined by the C-1 and C-2 carbon atoms of the acyl chains. Huang (1976) has suggested that hydrogen bonding is a dominant factor in positioning of the 3(3-OH group of cholesterol. The time constant of this region was noticeably different for the three types of bilayers, ranging from approximately 1 for lecithin only bilayers to more than 4 for lecithin/oxidised cholesterol bilayers. The capacitance of this region was nearly three times less in lecithin bilayers than in those containing cholesterol. There was, therefore, a marked difference in the thickness of this region or the dielectric constant was three times larger with cholesterol in the membrane, or perhaps a combination of these. Chapter 8: Cholesterol Inclusion in Egg Lecithin Bilayers page 8.10 Karolis; Thesis: THE DIELECTRIC CHARACTERfZAT/ON OF UPID BILAYERS 142 A plausible explanation for an increase in the dielectric constant of this region lies in the presence of the 3P-OH group of cholesterol. The slightly higher conductance observed in lecithin/cholesterol bilayers supports this view. When the dielectric constant increases the concentration of charge carriers would also increase and this would result in an increase in the conductance. The lower conductance observed in the lecithin/oxidised-cholesterol bilayers was significant because it would imply that this region was thicker than in lecithin/cholesterol bilayers, or that the dielectric constant was reduced in some way. Observations of very long lived bilayers(> 10 hours) made from lecithin/cholesterol indicate a lowering of the conductance in this region with time. The cholesterol molecule may oxidise in situ and moves out of the bilayer interior, albeit only slightly. If the oxidised portions of the cholesterol molecule are sufficiently polar one might expect them to be located at the hydrophobic-hydrophilic interface; i.e. in the glycerol bridge region. The cholesterol molecule, on oxidation would thus be drawn further out of the membrane interior. If part of the ring structure now occupies the acetyl region the dielectric constant will be reduced which would account for the drop in capacitance and conductance. The second dispersion took place around 0.1 Hz and appeared to be associated with the glycerol bridge. The change in the packing density resulting from the inclusion of cholesterol would allow a greater concentration of water to occupy this region. This was evidenced by the relatively large increase in conductance observed in going from lecithin to lecithin/cholesterol bilayers. If the notion of oxidised cholesterol is correct it would place the 3-P-OH group in the region of the glycerol bridge and therefore restrict the number of water molecules. This would have the effect of lowering the conductance of the region as was indeed observed. The third dispersion occurred at 1 Hz, and was much less pronounced in all the bilayers. There were also smaller differences between bilayers. The conductance of this region was fairly high but it was still lower than the external solution and may be associated with the Chapter 8: Cholesterol Inclusion in Egg lecithin Bilayers page 8.11 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF LJPID BILAYERS 143 phosphatidylcholine group, and the next dispersion, not shown in the figure could thus be due to the choline group. Chapter 8: Cholesterol Inclusion in Egg Lecithin Bilayers page 8.12 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 144 8.5 SUMMARY 1) The low frequency impedance spectrometry is capable of resolving as many as 7 separate elements in lipid bilayer membrane/electrolyte systems. Using this technique the structure of lecithin, lecithin/cholesterol and lecithin/oxidised cholesterol was characterised. 2) Lecithin bilayers appear to have a low dielectric constant region at the hydrophobic/hydrophilic interface. 3) The addition of cholesterol to lecithin bilayers resulted in an increase in polar nature of the hydrophobic - hydrophilic interface possibly due to an increase in water penetration into this region on addition of cholesterol. The effect is greatest for unoxidised cholesterol. 4) The cholesterol molecules were located in the hydrocarbon interior of the bilayer with their hydroxyl groups spanning the acetyl-interface. 5) Oxidised-cholesterol molecules were located just slightly out of the hydrocarbon interior, with their polar regions spanning the glycerol bridge; this could be inferred fromthe change in capacitance and conductance of the acetyl and glycerol regions of the bilayer on substituting oxidised for unoxidised cholesterol. Chapter 8: Cholesterol Inclusion in Egg Lecithin Bilayers page 8.13 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 145 This page left blank intentionally Chapter 8: Cholesterol Inclusion in Egg Lecithin Bilayers page 8.14 Karolis; Thesis: THE DIEUCTRJC CHARACTERfZATION OF UPID BILAYERS 146 CHAPTER 9 THE INCLUSION OF CYCLOSPORIN A (CsA) IN EGG LECITHIN BILAYERS (A DIELECTRIC PICTURE OF STRUCTURE) 9.1 INTRODUCTION 147 9 .1.1 Physiochemical Properties ...... 147 9.2 METHOD and MATERIALS 149 9.3 RESULTS 150 Frequency dependence of the capacitance ...... 150 Frequency dependence of the conductance ...... 150 9.4 DISCUSSION 151 9.5 SUMMARY 153 Chapter 9: The inclusion of CsA in egg lecithin bilayers page 9.1 Karolis; Thesis: THE DIELECTRIC CHARACTERfZATION OF UPID BILAYERS CH 3 H \ I C II C I \ CH 3 CH3 H C~ \ I I /H CH CH3 CH3 OH C I \ / \ / 't'cH3 /CH3 CH2 CH 3 CH CH 3 CH CH2 CH 3 H,.... I ....,,H I 1,,H H,.... I CH - N - C - CO - N- C - C - N - C - CO- N - C - C - N - CH2 3 I II I 11 I Hco O H O co CH3 \ I I I I I "cH-CH ~c 1 3 1 2 1 1 / 2 I I N-CH CH I 3 3 CH 3 - N H O H I I II I I QC - C - N - CO - C - N - C - C - N - C - C - N- CO -CH I ..H I •'H II •'HI •'H .. CH 3 H CH 3 O CH2 CH 3 CH CH2 I I I / \ I CH CH3 CH3 CH ... - - - -4 - - - - • / \ / \ CH 3 CH 3 CH 3 CH 3 10 11 2 3 Meleu - MeVal MeBmt -- Abu -Sar I 9 Meleu I p·Ala -Ala Meleu -Val -Meleu 8 7 6 5 4 FIGURE 9.1 Structural formula of cyclosporin A (CsA) Chapter 9: The inclusion of CsA in egg lecithin bilayers Figure 9.1 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF LIPID BIUYERS 147 9 .1 INTRODUCTION Cyclosporin A (CsA) is a neutral cyclic undecapeptide fungal metabolite of Trichoderma polysporum Rifai (Petcher, Weber and Ruegger, 1976) and is used as a selective immunosuppressant drug in solid organ and bone marrow transplantation. Based on the observation that the binding affinities of CsA to T-lymphocytes and phospholipids are approximately the same, Le Grue, Friedman and Kahan, (1983) suggested that CsA may exert its immunosuppressive effect through a non specific membrane-mediated mechanism. To investigate this proposal, the interaction between CsA and dimyristoylphosphatydalcholine (DMPC) multilamellar dispersions was quantified using scanning calorimetry, and infrared Raman spectroscopy (O'Leary, Ross, Lieber and Levin, 1986). It was found that the temperature and maximum heat capacity of the lipid bilayer gel-to-liquid crystalline phase transition were reduced. Raman spectroscopy indicated that the effects induced by CsA on the phase transition were not accompanied by major structural rearrangements of the lipid headgroup or hydrocarbon chain regions at temperatures remote from the transition temperature. Further, whilst CsA had demonstrable effects on certain aspects of model membrane behaviour, it had no effect on erythrocyte haemolysis in contrast to many compounds that act through membrane-mediated pathways. In the light of a recent study of the structure-function relationships for CsA and nine derivatives (Borel 1986) a non-specific membrane mechanism is difficult to formulate. The role of membranes in the expression of CsA activity is an intriguing problem that requires further investigation. 9 .1.1 PHYSIOCHEMICAL PROPERTIES The cyclic peptide CsA (C62H111N 11012) consists of eleven amino acids, seven of which are N-methylated (Figure 9.1). Ten are known aliphatic amino acids. These are A-aminobutyric acid (Abu) in position 2, sarcosine (Sar) in position 3, N-methylleucine (MeLeu) in positions 4, 6, 9 and 10, valine (Val) in position 5, alanine (ala) in position&, D-alanine (D-Ala) in position 8 and N-methylvaline (MeVal) in position 11. The novel amino acid in position 1 is (4R)-4- [(E)-2-butenyl]-4,N-dimethyl-L-threonine (MeBmt). Chapter 9: The inclusion of CsA in egg lecithin bilayers page 9.2 Karolis; Thesis: THE DIEUCTRJC CHARACTERl7.ATJON OF UPID BILAYERS TABLE 9.1 PHYSIOCHEMICAL PROPERTIES OF CYCLOSPORIN-A Formula C62HN11012 Elemental analysis C 61.9; H 9.5; N 12.6; 0 15.8 % Molar mass 1201.842±0.003 (mass spectrum) Molecular weight 1202.635 Solubility (mg/ml) water 0.04 ethanol > 100 acetone > 50 chloroform > 100 n-hexane 5. 5 Functional groups 1 double bond 1 secondary hydroxy 11 amidecarbonyl 4 amidehydroxy Chapter 9: The inclusion of CsA in egg lecithin bilayers Table 9.1 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID Bll.AYERS 148 From structure determined by X-ray diffraction (Petcher, Weber and Ruegger 1976; Loosli, Kessler, Oschkinat, Weber Pecther and Widmer 1985) and from NMR studies (Loosli et al 1985) it is known that the molecular backbone of CsA assumes a rigid structure and four hydrogen bonds hold the backbone in its folded configuration (see Figure 9.1 and Figure 5.3). Some relevant physiochemical properties have been listed in Table 9.1. The purpose of this study was to examine the effects, if any, on the dielectric properties of lecithin-cholesterol bilayers by the inclusion of CsA molecules. Such structural information may give insight into the highly specific pharmacological activity associated with this substance. CsA is a compact structure if the MeBmt-1 side chain remains in the ~-sheet segment The low resolution structure of CsA resembles an ellipsoid of half axes of -0.5 nm by -0.5 nm by -1 nm. This compares with -1.5 nm for the length of a phospholipid hydrocarbon chain and therefore ideally suited, atleast geometrically, to slipping in the lipid bilayer with its long axis parallel to the hydrocarbon chains. Chapter 9: The inclusion of CsA in egg lecithin bilayers page 9.3 Karolis; Thesis: THE DIELECTRIC CHARACTERflATION OF UPID Bll~YERS 0.8 ...,._------~ ~ 0.7 < E LL E 0.6 -Q) (.) c:: 0.5 -~(.) a.ctl ctl (.) 0.4 0.3 0.2--t--,-,...,....,..,...,-T"""T"TTTrm---,-..,...,.,.,.,.,,,.---r-,-"TT"r...... ---,-...,...... ,...--~r-TT...... ,---,.....,...... ,..,"ffl 10- 2 10- 1 10° 10 1 10 2 103 104 10 5 Frequency (Hz) FIGURE 9.2a Mean capacitance spectra for an egg lecithin/cholesterol bilayer containing cyclosporin A, formed in 100 mM KCI at 2s0 c. The error bars lie within the plot symbol. 0. 7 6 -r--.--,-,-TTT,..,...-..,.-.,....,.,..,."""",----,---,-T""T"T"T"T'l,...... """'T""'T"'l...... ,""""-.--r-,-.,.....rm • m Lee/Chol -N 0.74 < ' • E •• • Lecithin LL •• E 0.72 • • • ••• • CsA -Q) •• (.) c:: • • ctl 0.70 •• .'!::: •• (.) • a.ctl ••• ctl •••••••• (.) 0.68 •• 0.66 0.64 2 1 0 - 1 0 o 1 0 1 1 o2 103 Frequency (Hz) FIGURE 9.2b Expanded view of the capacitance spectra for an egg lecithin/cholesterol bilayer containing cyclosporin A; lecithin bilayer and a lecithin bilayer containing cholesterol, formed in 100 mM KCI at 2s0 c . Chapter 9: The inclusion of CsA in egg lecithin bilayers Figure 9.2 Karolis; Thesis: THE DIEI.ECTRIC CHARACTERIZATION OF UPID BILAYERS 149 9.2 METHOD AND MATERIALS Two preparations of the drug were available for study. An intramuscular (i.m.) solution with 200 mg CsA dissolved in an oiValcohol solution (20 mg ethanol, 10 mg benzyl alcohol, 1912 mg 812-a neutral oil to make up a 2 ml ampoule), and a pure powder crystalline sample. CsA is highly insoluble in water. In the preparation of the lecithin-cholesterol- i.m. CsA mixture, the CsA was dispersed in the solvent, n-hexadecane in the proportion 10 ml of i.m. CsA in 5 ml n-hexadecane. Thus 0.5 ml aliquots of solvent contained 1 ml of i.m. CsA (or 0.1 mg CsA). This was the quantity of solvent used to disperselO mg lecithin/2.5 mg cholesterol. The ratio by weights of lecithin:cholesterol:CsA were 100:25:1. 10% by weight of CsA were also investigated. The powder form of the drug was dissolved in chloroform and added to the lecithin and cholesterol mixture prior to evaporation of the chloroform. Bilayers were produced in 1, 10, 100 mol m-3 KCl solutions by ejecting a small quantity of the lipid/solvent mixture from a syringe while wiping the syringe tip across a small hole in a polycarbonate septum. The technique was described in Chapter 5. The capacitance was monitored at 1 Hz until the it had stabilised before admittance measurements were commenced over the frequency range 0.0lHz to 44.4 kHz. Chapter 9: The inclusion of CsA in egg lecithin bilayers page 9.4 Karolis; Thesis: THE DIELECTRIC CHARACTER!ZATION OF UPID Bll.AYERS TABLE 9.2 THE LOW FREQUENCY AREA SPECIFIC CAPACITANCE (Cg) OF EGG LECITHIN/CHOLESTEROL BILAYERS CONTAINING CsA (formed with n-hexadecane) in KCI solutions of different concentration The thickness of the hydrocarbon region of the bilayer was determined for two values of the dielectric constant (Ehc). For a bilayer with a negligible amount of solvent, the dielectric constant was taken to be 2.2, which is the volume averaged value of the dielectric constant of lecithin and cholesterol. For a bilayer containing an appreciable quantity of solvent the dielectric constant was taken to be 2 .14. Electrolyte Area Specific Corrected Thickness Concentration Capacitance of (Cg) Hydrocarbon Region (moles litre-1) (mF m-2) (nm) Ebe= 2.14 Ebe= 2.2 10-l 7.24±0.1 2.62 2.69 10-2 7.35±0.2 2.58 2.65 10-3 7.49±0.2 2.53 2.60 Chapter 9: The inclusion of CsA in egg lecithin bilayers Table 9.2 Karolis; Thesis: THE DIELECTRIC CHARACTERfZATJON OF LJPID BILAYERS 150 9.3 RESULTS The inclusion of CsA in the bilayer mixture resulted in bilayers that were easy to produce and consistently stable after formation. Typical life-times were in excess of 14.4 ks (4 hours), with one bilayer surviving as long as 64.8 ks (18 hours). It was thus possible to perform repeated measurements of the frequency dependence of the capacitance for each bilayer. Impedance measurements were usually made at 25 °C. At higher temperatures (-35 °C) the low frequency capacitance was about 1% lower than at 25 °C. Frequency dependence of the capacitance Figure 9.2 shows the frequency dependence of the capacitance of bilayers made from egg lecithin, cholesterol and pure CsA. The plot is the average of 6 spectra on the same bilayer and was typical of the different bilayers produced under similar conditions. The measurements were taken at 25°C, in 100 mM KCI. The error bars show the standard error. The variation was due to small changes in the bilayer with age; repeated measurements were taken over the course of 6 hours. The capacitance of Lecithin/cholesterol bilayers containing CsA was found to be 7.1±0.1 mF m-2 (in 100 mM KCl) at 0.01 Hz and decreased with frequency by about 0.1 mF m-2 per decade between 0.01 Hz and 1 kHz. Above 1 kHz the capacitance decreased rapidly with frequency. The low frequency area specific capacitance (measured capacitance corrected for the double layer capacitance) at lower salt concentrations was 6.9 ± 0.2 mF m-2 at 10-2 molar KCl and 6.2 ± 0.2 mF m-2 at 10-3 molar KCl (Table 9.2). Frequency dependence of the conductance The frequency dependence of conductance was typical of bilayers examined in this work. Interestingly, however, the low frequency conductance was remarkably consistent among different stable bilayers. The variation was within a factor of 3 and was unchanged for a 10 fold change in electrolyte concentration from 10- 1 andlQ-2 molar KCI. (Table 9.3). The average value of the low frequency limit of the conductance was 1.3 ± 0.3 mS m-2 for the former and Chapter 9: The inclusion of CsA in egg lecithin bilayers page 9.5 Karolis; Thesis: THE DIEU:CTRIC CHARACTERIZATION OF UPID BILAYERS TABLE 9.3 THE LOW FREQUENCY AREA SPECIFIC CONDUCTANCE (Gg) OF EGG LECITHIN/ CHOLESTEROL BILAYERS CONTAINING CsA (formed with n-hexadecane) in KCI solutions of different concentration Electrolyte Area Specific Area Specific Concentration Conductance Conductance (crystalline) (i.m.) (mS m-2) (mS m-2) 1.3 ± 0.3 4.0 ± 1.5 1.9 ± 0.5 2.7 ± 0.5 0.2 ± 0.1 0.8 ± 0.05 Chapter 9: The inclusion of CsA in egg lecithin bilayers Table 9.3 Karolis; Thesis: THE DIELECI'RJC CHARACTERIZATION OF UPID BILAYERS 151 1.9 ± 0.5 mS m-2 for the latter. At 10-3 molar KCl, the conductance fell approximately 10 fold to 0.2 ± 0.1 mS m-2. 9.4 DISCUSSION The magnitude of the capacitance of bilayers containing CsA is similar to bilayers formed from egg lecithin/cholesterol mixtures. The thickness of the hydrocarbon region, therefore, was largely unaffected by the inclusion of CsA molecules. The absence of a temperature dependence of the measured capacitance suggests that the hydrophobic interior was also free of solvent and CsA. The dispersion of the capacitance was affected only slightly by the presence of CsA as indicated by similar dispersion gradients to egg lecithin bilayers and those containing cholesterol, shown in Figure 9.2b. The presence of cholesterol, thus appears to have a dominant role in the capacitative dielectric behaviour of these bilayers or there has been a substitution of cholesterol molecules by CsA molecules. To elucidate the effects of CsA on the bilayer structure, a Maxwell-Wagner analysis was made of the impedance dispersion and compared, in Chapter 10, with the results obtained from bilayers not containing CsA. The effect on the conductance was more obvious. The introduction of pure CsA produced a dramatic fall in the bilayer conductance (Figures 9.3 a and b). Bilayers formed from the intramuscular preparation were 2-3 times more conducting, perhaps reflecting the presence of benzyl alcohol. A drop in the conductance was not expected. Neither was the increased stability of the bilayer. CsA molecules were expected to stack against one another in the plane of the cyclic ring to span the bilayer. Such a structure would create water channels across the bilayer with a consequent increase in conductivity and reduced stability. Measurements by Knott (1989) show a fairly compact structure of CsA in the bilayer with no evidence of molecules spanning the two halves of the bilayer. The 50% drop in conductance is not likely to be a spurious effect related to phase boundary effects associated with the membrane-torus system (Perez and Wolfe, 1988). Such phenomena lead to unstable structures with short lives. Measurements of capacitance and conductance at lower salt concentrations, used previously to examine the effects of the double layer and test the Stem model of the electrical double layer, Chapter 9: The inclusion of CsA in egg lecithin bilayers page 9.6 Karolis; Thesis: THE DIEU:CTRIC CHARACTERfZATION OF UPID BILAYERS 8 • Egg Lecithin N Ill Lec JChol. <' 6 E LL Ill Lee JChol.-CsA E Q) (.) C 4 ~ ·c::; ell 0. ell (.) 2 co CD CD Acyl chains Acetyl region Glycerol bridge Phosphatidylcholine Group FIGURE 9.3a The capacitance of the different regions of bilayers consisting of lecithin; lecithin-cholesterol; lecithin-cholesterol- cyclosporin A in 100 mM KCI at 2s0 c. 10 • Egg Lecnhin 111 Lec.!Chol. 10 q < ml Lec./Chol.-CsA E (/) E 10 Q) (.) C ell ti :::, -g 10 0 (.) 10 10 Acyl chains Acetyl region Glycerol bridge Phosphatidylcholine Group FIGURE 9.3b The conductance of the different regions of bilayers consisting of lecithin; lecithin-cholesterol; lecithin-cholesterol- cyclosporin A in 1oo mM KCI at 2s0 c. Chapter 9: The inclusion of CsA in egg lecithin bilayers Figure 9.4 Karolis; Thesis: THE DIEUCTRJC CHARACTERfZAT/ON OF UPID BILAYERS 152 suggest that a small change in the surface charge has taken place with the introduction of CsA (see Table 9.3). The possibility of a reduction in the concentration of cholesterol by the substitution of CsA therefore appears quite likely. Chapter 9: The inclusion of CsA in egg lecithin bilayers page 9.7 Karolis; Thesis: THE DIELECl'RJC CHARACTERfZATION OF UPID BILAYERS 153 9.5 SUMMARY 1. The presence of cyclosporin A in lecithin-cholesterol bilayers was detected using low frequency impedance spectrometry. 2. The thickness of solvent free bilayers containing cyclosporin A was 2.7 nm. which was similar to lecithin-cholesterol bilayers. 3. The conductance of solvent free bilayers containing cyclosporin A was nearly four times lower than lecithin bilayers and nearly half that measured for lecithin cholesterol bilayers. 4. Bilayers containing cyclosporin A were found to be the most stable of those produced in this work with many lasting several hours. The stability and low conductance measured for these bilayers suggests that spontaneous pore formation may be less easily achievable with the presence of cyclosporin A or the pore radii are significantly smaller. 5. Cyclosporin A appears to occupy space in the polar head region of the bilayer similar to cholesterol. 6. There may be a suggestion that the surface charge of bilayers containing cyclosporin A is less than that for bilayers containing cholesterol, which may indicate some substitution of cholesterol with cyclosporin A or an expansion of the head group area to accommodate the cyclic ring. Chapter 9: The inclusion of CsA in egg lecithin bilayers page 9.8 Karolis; Thesis: THE DIELECTRIC CHARACTER!ZAT/ON OF UPID BILAYERS 154 CHAPTER 10 THE MULTILAYER DIELECTRIC MODEL OF EGG LECITHIN BILAYERS 10.1 INfRODUCTION 155 10.2 IBEORY 156 10.2.1 Model for the frequency dependence of bilayer impedance ...... 156 10.2.2 Least Squares Fitting Algorithm ...... 158 10.2.2 Correlation Index ...... 160 10.2.3 J-Parameters and Confidence Levels for Rejecting a Model ...... 161 10.3 MEIBOD AND MATERIALS 162 10.4 RESULTS 163 10.5 DISCUSSION 164 10.5.1 Features of the Multilayer Dielectric Model of the Bilayer ...... 164 The hydrocarbon region (he) ...... 164 Polar-head regions (Pi) ...... 164 ucithin bilayers ...... 165 The effect of cholesterol ...... 165 Effect of substituting cholesterol with oxidised cholesterol ...... 166 Effect of including CsA ...... 166 10.6 SUMMARY 167 Chapter 10: The Multilayer Dielectric Model of Egg lecithin Bilayers page JO.I Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 155 10.1 INTRODUCTION In previous chapters we have alluded to the multilayer dielectric behaviour of the bilayer but have restricted discussions to 'macro' physical properties, such overall thickness (and its relation to capacitance) and conductivity. We now draw attention to the substructure of the bilayer which relates to the molecular conformation and the division of the bilayer into dielectrically distinct regions. Hanai, Haydon and Taylor (1965a) were the first to point out that differences in the dielectric behaviour of different regions of the bilayer might result in Maxwell -Wagner dispersions. For reasons that have already been mentioned (Chapter 1; 1.3.6), however, they were unable to detect such dispersions. It was left to Coster and Smith (1974) to explain why the dispersions were difficult to detect: they took place< 1 Hz and could only be detected with instrumentation having a phase angle resolution - 0.04°. These authors proceeded to measure the polar head-hydrocarbon region dispersions in certain bilayers (Ashcroft, Coster and Smith 1977) with a high resolution impedance spectrometer (Bell, Coster and Smith 1975). The main features of the impedance spectrometer were its ability to digitally synthesise the current and voltage response from two matched differential amplifiers recording the current and voltage signals from a four terminal measuring system (see Chapter 4; 4.3.9). With improvements in the spectrometer (Chilcott 1988) the number of dispersions that could be detected increased to about 5 (Ashcroft, Coster, Laver and Smith 1983). The dispersions were attributed to the hydrophobic region, the acetyl region and three regions in the polar head. An analysis of the substructure, in dielectric terms, of any one type of bilayer has a limited meaning, however, because of the gross uncertainties in the magnitude of the dielectric constant of the different regions in the bilayer (except, perhaps, for some dimensional features associated with the polar and non-polar regions of the bilayer). Nevertheless, a comparison of the dielectric substructure of bilayers formed from different systems can, be quite informative. For example this approach has been useful in ascertaining the position of large molecules such as the sterol cholesterol (Ashcroft, Coster, Laver and Smith 1983) and the hormone oestradiol (Perez and Wolfe 1988) in egg lecithin bilayers. Chapter 10: The Multilayer Dielectric Model of Egg Lecithin Bilayers page 10.2 Karolis; Thesis: THE DIEI.ECTRIC CHARACTERIZATION OF UPID BILAYERS 156 In this work Maxwell-Wagner dispersions were fitted to averaged impedance spectra obtained from egg lecithin bilayers and compared with the results obtained from bilayers made from egg lecithin with the inclusion of cholesterol, oxidised cholesterol and cyclosporin A. In this way the location of the inclusive molecules could be determined. 10.2 THEORY 10. 2 .1 Model for the frequency dependence of bilayer impedance The electrical model of the bilayer consists of a series of electrically distinct layers to each of which is attributed an area specific conductance G and capacitance C (Coster and Smith 1974; Smith 1977). The equivalent circuit of such a model is a series combination of capacitors, each shunted by a conductor (see Figure 5.6). Dispersions of impedance with frequency arise from such admittances in series when the time constants CIG of different layers are unequal and are called Maxwell-Wagner dispersions. For a circuit comprising II elements, each of which is the parallel combination of a conductor G; and a capacitor C;, the admittance, Y, is 1 v =[i Examples of such circuits were presented in Chapter 5 (5.6.2). The admittance of a two element circuit can be calculated from Equation 10.1, by expanding and rationalising the denominator the total capacitance and conductance of the circuit will be given by: Chapter 10: The Multilayer Dielectric Model of Egg Lecithin Bilayers pagel03 Karolis; Thesis: THE DIELECTRIC CHARACTERTZATION OF UPID BILAYERS 157 C= (10.2) 0 1 0 2 (01 + 0 2) + cl(01C~ + 0 2C~ 0= (10.3) 2 2 2 (01 + 0~ + ro (C1 + C2) In the low frequency limit of a two element circuit (f « l/1:1, where 7:J = C1 IG1 ), the capacitance is (C2G~ + C1G~J/(G1+G2)2. In the high frequency limit, (f » 111:2), the capacitance is C1C2l(C1+C2). The effect of adding additional series elements with time constant 7:, (1:1<1:<1:2) is to introduce an additional dispersion around the frequency 1/t with the result that the capacitance is reduced at higher frequencies. By careful selection of the C;, G; values it is possible to generate a set of parameters that describes the frequency dispersion in impedance. For bilayers, the time constant of successive layers is thought to increase towards the centre of the bilayer (Ashcroft, Coster, Laver and Smith 1983; Laver, Smith and Coster 1984) which implies that the dielectric constant and conductivity both decrease towards the centre. At frequencies well below the reciprocal of the time constant of the electrolyte, the admittance approaches its conductance and so the total capacitance of the system is increased. At successively lower frequencies, a further increase in C is observed near the characteristic frequency (GIC) of each layer. A general one-dimensional model of a bilayer would have a local conductivity and dielectric constant which would be continuous functions of position along the bilayer normal, and would thus require an infinite number of series elements to represent it precisely. The finite precision of impedance measurements limits analysis to a small number of discrete layers, identified for instance with the hydrophobic interior, the polar head region, the acetyl region between the two, and various subdivisions of these. Chapter 10: The Multilayer Dielectric Model of Egg Lecithin Bilayers page 10.4 Karolis; Thesis: THE DIELECTRIC CHARACTERfZATION OF UPID BILAYERS 158 10.2.2 Least Squares Fitting Algorithm Least squares fitting attempts to minimise the sum of the squares (S) of the difference between a certain theoretical function T(f), described by parameters Pi, and the data D(f). Thus: S = L [T(f) - D(f)]2 (10.4) Minimisation of S occurs when the partial derivatives of S with respect to the parameters Pi are all zero. i.e. as _0 i)p. - (10.5) 1 Differentiating equation 10.4 with respect to the parameters and substituting in equation 10.5 gives 21 equations of the general form: (10.6) If the P0 i are the initial approximations to the parameters, they are related to Pi by p?1 = P- 1 + dP- 1 (10.7) Using a Taylor expansion about the initial approximation of the parameters and provided the dPi are small, 21 aT°(P?) T(P) = T°(Pf) + I c)P I dPn (10.8) n=O n Chapter 10: The Multilayer Dielectric Model of Egg Lecithin Bilayers pagel05 Karolis; Thesis: THE DIELECTRIC CHARACTERlZATION OF UPID BILAYERS 159 It can be shown that equation 10.6 gives a set of 21 equations in terms of the initial approximations of parameters and their partial differentials: (10.9) where, (10.10) These equations can be solved for the dPi and substitution into equation 10.7 will give a closer approximation to the set of parameters. The new approximations to the parameters and their partial derivatives can then be substituted into equations 10.9 and 10.10 to produce even better approximations. By repeating this procedure, a minimum in Smay be reached. Chapter IO: The Multilayer Dielectric Model of Egg Lecithin Bilayers page 10.6 Karolis; Thesis: THE DIEIECTRJC CHARACTERIZATION OF UPID BILAYERS 160 10.2.2 Correlation Index The parameters that were used to determine the closeness of the theoretical curve to the data were the sum of the least squares error (Etheory), sum of the experimental error (Eexperiment), and the correlation index (Kindex), If T(f) is the theoretical cutve, Di are the data with standard errors ei at frequencies fi respectively, then: N [T(f.) - ,L.J~ 1 o.J2 1 i=l Etheory = (10.3) N L[e)2 i=l Eexperiment = N (10.4) L[oif i=l l _ Etheory ] Kindex = [ (10.5) Eexperimen/S-1) where S is the number of spectra used to compute the standard error and N is the size of the data set. Chapter 10: The Multilayer Dielectric Model of Egg Lecithin Bilayers page 10.7 Karolis; Thesis: THE DJEUCTRIC CHARACTERlZATJON OF UPID BILAYERS 161 10.2.3 ]-Parameters and Confidence Levels for Rejecting a Model When an analytical function with several adjustable parameters is fitted to a set of pairs of data, a small residual sum of least squares error (i.e. Etheory) need not imply that the fitted function has a physical significance; several formally different functions may all give small residual values for Etheory· By analysing systematic displacement of points from the fitted function, it is often possible to decide between different functions fitted to the data (Wolfe, priv. comm.). The I-parameter for a theoretical curve is the number of times the residual error (T(fi) - Di) at consecutive data points changes sign. This with the number of data points, N, defines confidence levels for rejecting the hypothesis that the residual errors are randomly distributed. Rejection of this hypothesis means that the theory is inadequate or inappropriate, or that there is a systematic error. A table of confidence levels is listed below. TABLE 10.1 For a given N and confidence level, if J lies outside the (inclusive) range listed in the table, the hypothesis that the fitted function is an underlying function of the data may be rejected Limits of J at the indicated confidence level N 99% confidence 98% confidence 95% confidence 20 6 - 13 5 - 14 4- 15 21 6 - 14 6 - 15 5 - 15 22 6 - 15 6 - 15 5 - 16 23 7 - 15 6- 16 5 - 17 24 7 - 16 6- 17 6 - 17 25 8 - 16 7 - 17 6 - 18 26 8 - 17 7 - 18 7 - 18 27 8 - 18 8 - 18 7 - 19 28 9 - 18 8 - 18 7 - 20 29 9 - 19 8 -20 8 -20 30 10-19 9- 20 8 - 21 Chapter 10: The Multilayer Dielectric Model of Egg Lecithin Bilayers page 10.8 Karolis; Thesis: THE DIEI.ECTR/C CHARACTERIZATION OF UPID BIIJ\YERS TABLE 10.2 BILA YER STATISTICS Lecithin Lee/Chol Lec/CholO Lec/ChoVCsA 100 mol m-3 KCI No. of bilayers 3 9 5 5 Mean Life (hrs) 4.0±2.0 3.6±4.4 4.0±3.5 3.2±1.3 JO mol m-3 KCI No. of bilayers 6 4 4 Mean Life (hrs) 3.0±1.0 2.7±3.0 5.2±0.9 I mol m-3 KCI No. of bilayers 2 4 4 4 Mean Life (hrs) 1.0±1.0 4.5±4.0 4.8±3.6 4.0±3.0 Chapter 10: The multilayer dielectric model of egg lecithin bilayers Table 10.1 Karolis; Thesis: THE DJEU'.CTRJC CHARACTER!Z.ATJON OF UPID BILAYERS 162 10.3 METHOD AND MATERIALS The bilayers were produced from lipid mixtures consisting of egg lecithin; egg lecithin cholesterol; egg lecithin-oxidised cholesterol; egg lecithin-cholesterol-cyclosporin A. Detailed descriptions of the preparation of these bilayer materials has been given in Chapter 5 (5.2), Chapter 6, 8 and 9. The bilayers were painted in 100 mol m-3 KCl on a polycarbonate septum. The aqueous solution was pre heated to 35°C in order to facilitate bilayer formation. As the bilayer began to form ( observation via low powered microscope, and capacitance measurement at 1 Hz), the temperature was gradually lowered. Measurements were performed at 30°C and room temperature (20°C - 25°C). Photographic negatives of the bilayers and septum were obtained at the commencement of measurement and periodically during data collection. A description of the measuring system has been given in Chapter 4. Suffice it to say that measurements of bilayer impedance at ultra-low frequencies ( <1 Hz) are commonly subject to two difficulties. First, bridge techniques are inaccurate and impractical at such frequencies. Second, two-terminal measurements necessarily include the potential across the solution electrode interface in the measurement of the trans-bilayer potential. The electrical measurements in this study were made using a four terminal system (Bell, Coster and Smith 1975; Chilcott 1988) described in Chapter 4 (4.3.9). With this apparatus the amplitude of the impedance was determined within ±0.1 % and the phase angle to within 0.01 °. The measurements were recorded over a frequency range of 0.01 to 44.4 kHz. As many as 9 scans of this frequency range were possible for each bilayer. The average of the 9 scans, corrected for changes in area, was stored for fitting. The conductance and capacitance parameters of the model were determined by fitting the finite element model [Equation ( 10.1)] to the measured data of the impedance (magnitude and phase angle at each frequency). Chapter 10: The Multilayer Dielectric Model of Egg Lecithin Bilayers page 10.9 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS TABLE 10.3 MULTILAYER DIELECTRIC MODEL OF THE BILAYER in 100 mol m·3 KCI The symbols in italics refer to the different regions of the bilayer as they are presented in the histograms of Figure 10.1 CAPACITANCE (mF m·2) Cm C1 C2 C3 C4 Cs (he) (Pl) (P2) (PJ) (P4) (P5) BILAYER acyl chains acetyl region glycerol phosphatydilcholine group electrolyte bridge Lecithin 7 .65±0.3 180±50 280±130 410±250 100±50 0 L-Chol 7.00±0.1 420±40 430±90 630±180 835±280 820 L-CholO 7.10±0.1 410±80 360±140 350±130 330±110 750 L-Chol-CsA 7 .24±0.1 275±50 425±140 425±180 450±150 650 CONDUCTANCE (mS m·2) Shunt G1x10 1 G2x103 G3xlo4 G4xl05 G5xl06 (he) (P1) (P2) (P3) (P4) (P5) BILAYER acyl chains acetyl region glycerol phosphatydilcholine group electrolyte bridge Lecithin 4.8±1.4 5±3 12.7±3.l 2.5±2.0 6±3 1.0±0.5 L-Chol 2.3±2.0 19±6 3.9±2.0 2.8±2.6 4±2 2.7±1.6 L-CholO 3.0±2.0 9±4 20.0±10 2±1 3±1 5±1 L-Chol-CsA 1.3±0.3 8±3 2.6±1.9 3±3 4±1 6±1 Chapter 10: The multilayer dielectric model of egg lecithin bilayers Table 103 Karolis; Thesis: THE DIEIECI'RJC CHARACTERfZATJON OF LJPID B11.AYERS 163 10.4 RESULTS The dynamic features of bilayer formation have been described in Chapter 5. The stability of the bilayers formed in this work, as measured by their mean life, was similar although the variability in stability was significantly less with CsA in the bilayer (see Table 10.2, which also presents data for 10 and 1 mol m-3 KCl solutions). Although many bilayers were produced with mean lives less than 1 hour, the data collected with these were rejected on the basis that the bilayers had insufficient time to stabilise for the low frequency measurements. The results of the least squares fitting of the electrical model for bilayers produced in 100 mol m-3 KCl appear in Table 10.3 (capacitance and conductance values). The data is schematically presented in Figure 10.1. The fitting procedure has been described in detail in Chapter 5 with hard-wired circuits and in Chapter 8 for lecithin and lecithin/cholesterol bilayers. The capacitance and conductance spectra for lecithin bilayers over the whole frequency range was presented in Figure 8.1. In Figures 8.3 and 8.4 the structure in the capacitance spectra was demonstrated with a considerably expanded capacitance scale. Figure 8.4 shows that at least five distinct admittance elements (i.e. 10 parameters) were needed to describe the dispersions with frequency. The time constants of these elements are presented, (for lecithin, L) in Table 10.4 and schematically in Figure 10.2. Tests of the Maxwell-Wagner model using hard-wired electrical elements in Chapter 5 indicated that the accuracy to which the value of the components of the electrical analogue could be determined depended on its contribution to the total admittance. The variation of the derived component values from the actual values ranged from less than 0.05% (element which made the largest contribution) to 25% (element which made the least contribution). The data presented in Table 10.3 suggest some deterioration in the accuracy of the elemental values. The correlation index was typically better than 0.90 for conductance and capacitance for most bilayers. The values appear to indicate that all parameters make a significant contribution to the total admittance spectra. Chapter 10: The Multilayer Dielectric Model of Egg Lecithin Bilayers page JO.JO Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID Sil.AYERS FIGURE 10.1 CAPACITANCE (mF m·2) OF THE BILAYER REGIONS 1000 L 800 C\I • L-Chol < II E u::: Ill L-CholO E 600 rzl L-CholCsA Q) (J C !:! (J 400 ctl a. ctl 0 200 0 he P1 P2 P3 P4 PS Region in the bilayer CONDUCTANCE (mS m·2) OF THE BILAYER REGIONS 8 C\I < L (log) E •Fd L-Chol (log) Cl)--- 6 E 1111 L-CholO(log) Q) (J f?:a L-Chol-CsA (log) C ctl u 4 :J "'C C 0 0 0) 0 __J 2 0 he P1 P2 P3 P4 PS Region in the bilayer Chapter 10: The multilayer dielectric model of egg lecithin bilayers Figure JO.I Karolis; Thesis: THE DIEU:CIRJC CHARACTERIZATION OF UPID BILAYERS 164 10.5 DISCUSSION 10.5.1 Features of the Multilayer Dielectric Model of the Bilayer The dielectric sandwich model of the lecithin bilayer consisted of two principle regions: the hydrophobic region and the polar-head region. The polar-head region was found to consist of several sub-structural regions which will be discussed below. The hydrocarbon region (he) The dominant feature of the multilayer dielectric model of the bilayer was that due to the central region (he) of the bilayer occupied by the acyl chains of the fatty acid component of lecithin. The small capacitance of this region was found to be associated with a very low conductance (shunt) and its detection was observed at frequencies - 0.01 Hz. In Chapter 6 and Chapter 7 we alluded to the importance of this region to the physical properties of the bilayer such as its thickness and pore dimensions. It has been established that this region was relatively free of alkane solvent and represented to major part of the physical thickness of the bilayer. Polar-head regions (P;) The polar-head region consists of the acetyl bonds of the fatty acids, the glycerol bridge and the cholinephosphate dipole. The latter possesses rotation freedom and flexibility around the phosphate group. Several sub-structural regions (P1_4) were assigned to the polar-head. Evidence for the existence of the first region first appeared between 0.01 Hz and 0.1 Hz with a dispersion characterised by a high capacitance and fairly low conductance. Others occurred around 1 Hz, 10 Hz and 100 Hz with steadily increasing conductance and fairly constant capacitance. Dispersions at higher frequencies were attributed to the electrolyte boundary and were more pronounced at high salt concentrations. Chapter 10: The Multilayer Dielectric Model of Egg Lecithin Bilayers page 10.11 Karolis; Thesis: THE DIELE.CTR/C CHARACTERrz.ATION OF UPID BILAYERS TABLE 10.4 Time constant ('ti=Ci/Gi) of the different regions of the bilayer in 100 mol m·3 KCI BILAYER Region L L-Ch L-ChO L-Ch-CsA hydrocarbon 1.59 3.04 2.36 6.45 Polar 1 3.60 2.21 4.56 3.44 Polar 2 0.220 1.100 0.16 1.63 Polar 3 0.164 0.225 0.175 0.140 Polar 4 0.001 0.021 0.001 0.011 Polar 5 0 0.003 0.002 0.001 FIGURE 10.2 Time constant (C/G) for different regions in lipid bilayers in histogram form 0 ,...... _ -1 u0 ---bl) -2 L 0 ..J •Ill L-Ch -3 II L-ChO ~ L-Ch-CsA -4 he P1 P2 P3 P4 PS Region in the Bilayer Chapter 10:The multilayer dielectric model of egg lecithin bilayers Table 10.4 and Figure 10.2 Figure 10.2 Karolis; Thesis: THE DIEU:.CTR/C CHARACTERflAT/ON OF LJPID BILAYERS 165 The degree of water penetration in these regions and the orientation of the cholinephosphate dipole profoundly influence the dielectric nature of the region. The inclusion of new molecules in the lecithin bilayer such as cholesterol and CsA might also influence the dielectric behaviour in these regions. Lecithin bilayers The results for lecithin bilayers in 100 mole m-3 KCl, may be considered to represent the most simple of bilayers, having almost no alkane solvent retained in hydrocarbon centre. This region was characterised by a capacitance of 7.65 mF m-2, (which is consistent with monolayer studies, see Chapter 6), and a very low conductance of 4.8 mS m-2 at very low frequencies (around 0.01 Hz). The first dispersion occurred near 0.1 Hz and resulted from a region having a time constant of 3.6 (see Table 10.4). The conductance of this region was about 10 times greater than determined in the hydrocarbon region, but the capacitance was 20 times greater. The next dispersion occurred at 1 Hz and arose from a region having a time constant of 0.22. The conductance of this region was 200 times greater than the previous region and was associated with a capacitance of 280 mF m-2. The dispersion thought to arise from the cholinephosphate group occurred at 10 - 100 Hz. This region was characterised by very high conductances, (in the region of 104 - 105 mS m-2), while the capacitance was in the order of 100 - 410 mF m-2. The effect of cholesterol The addition of cholesterol to the lecithin bilayer resulted in: a) 9.5% increase in the capacitance of the hydrocarbon region. Assuming no change in the dielectric constant of this region the change corresponds to 9.5% reduction in thickness. b) 50% decrease in the bilayer conductance. c) 230% increase in the capacitance of the acetyl region ( P 1 ). d) 400% increase in the conductance of the acetyl region (P 1 ). Chapter 10: The Multilayer Dielectric Model of Egg Lecithin Bilayers page 10.12 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 166 e) 150% increase in the capacitance of the polar head 2 region (P2) and polar head 3 region (P3). f) 400% decrease in the conductance of the polar head 2 region (P2) but essentially no change in other polar head regions. Effect of substituting cholesterol with oxidised cholesterol a) essentially no change in the capacitance of the hydrocarbon region, acetyl region or polar head 2 region. b) 30% increase in the bilayer conductance, 50% reduction in conductance of the acetyl region and a 400% increase in the polar head 2 region conductance. Effect of including CsA a) essentially no change in the capacitance of the hydrocarbon region but a 35% reduction in the capacitance of the acetyl region. The capacitance of the other polar head regions was not significantly different b) 50% decrease in the bilayer conductance (500% less than pure lecithin alone), and a 50% decrease in the conductance of the acetyl region. Other regions were found to have similar conductances. These alterations in the substructural parameters show that cholesterol and its oxidative product assemble in the bilayer. The results also suggest that Cyclosporin A also assembles in the bilayer and may substitute molecules of cholesterol (see Chapter 9). Chapter 10: The Multilayer Dielectric Model of Egg Lecithin Bilayers page 10.13 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID Bll.AYERS 167 10.6 SUMMARY The impedance dispersions of a wide range of bilayers of different composition are qualitatively similar, and share the following features: i) The low frequency (< O.OlHz) capacitance is nearly equal to that of the hydrophobic interior. ii) The outer regions of the bilayer (acetyl and polar head regions) contribute to dispersions over the frequency range 0.1 to 1,000 Hz. The smaller the admittance of these regions, the larger the change in the total capacitance over this range. iii) The dispersion due to the electrolyte solution occurs at frequencies of about 1 kHz. This layer is relatively thick and therefore has a small capacitance. As a result, the total capacitance decreases substantially, and at high frequencies the capacitance of the system approaches that of the bulk solution and the double layer. From the data presented in this work, the model values can be interpreted as arising from electrically distinct substructures within the bilayer. The bilayer was thinnest when lecithin was not mixed with other membrane molecules. With dimensions of the order of 2.5 nm it is difficult to see how any alkane molecules were retained in the bilayer. The thickness of the hydrocarbon region of the bilayer has been discussed in Chapter 6. This region, for all bilayers, was associated with a small conductance. It is interesting to note that the shunt conductance was lowest when additional molecules were mixed with lecithin. Since the thickness of the hydrocarbon region changes only slightly with added molecules, the changes in conductance of this region may be due to a reduction in the pore size rather than retention of the alkane solvent molecules. Bilayers formed with CsA were noticeably more stable than others. Lecithin bilayers alone were least stable. Chapter 10: The Multilayer Dielectric Model of Egg Lecithin Bilayers page 10.14 Karolis; Thesis: THE DIEUCTRJC CHARACTERIZKIION OF UPID BILAYERS 168 Moving away from the central region of the bilayer, but adjacent to it is a region characterised by oxygen atoms and double bonds. The capacitance of this region was about 50 times greater than the hydrocarbon region and the conductance 10 times greater. It would appear that water and some ionic penetration in this region has increased the dielectric constant to about 20. This region is either thicker when cholesterol is added or the presence of cholesterol has raised the dielectric constant to about 40. This region was thinnest when lecithin was used on its own or there was significantly less ionic penetration. Chapter 10: The Multilayer Dielectric Model of Egg Lecithin Bilayers page 10.15 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 169 CHAPTER 11 A STUDY OF BILAYERS FORMED FROM THE LIPIDS OF MAMMALIAN ERYTHROCYTE MEMBRANES 11.1 INTRODUCTION 170 11.2 METHOD 171 11.3 RESULTS 172 11.4 DISCUSSION 173 11.5 SUMMARY 175 Chapter 11: A Study of Lipid Bilayers Formed from the Lipids of Mammalian Erythrocyte Membranes page 11.1 Karolis; Thesis: THE DIEUCTRJC CHARACTERfZATION OF UP/D BILAYERS 170 11.1 INTRODUCTION The characterization of the mammalian erythrocyte membrane represents a challenging and multifaceted problem that demands many different approaches for a complete understanding. Even an incomplete listing of the various components of this membrane (such as simple and complex lipids, proteins with and without enzymatic activity, glycoproteins, metal ions, etc) serves only to indicate the magnitude of the problem associated with their definitive characterization and location in the membrane. The main function of the red cell is to transport oxygen to various tissues. In order to sustain this function, the erythrocyte retains an impressive array of enzymes, proteins, carbohydrates and lipids, many of which have been demonstrated to participate in an active and essential metabolic process. The lipid composition of the membrane has been carefully studied many times (eg Sweeley and Dawson, 1969; Cooper, 1970; Beutler and Srivastava, 1977), since it is thought that membrane anomalies may be responsible for numerous disease processes (Cooper, 1970; Tao,1982). Lipids account for approximately one half the dry weight of the human erythrocyte membrane. Over 95% of this consists of phospholipids and cholesterol. The molar ratio of cholesterol to phospholipid has been estimated to be about 0.82 (Hanahan, 1969). The interaction between these two major lipid classes within the membrane appears to be important for maintaining a stable and functional bimolecular leaflet. The phospholipids of the red cell are disposed asymmetrically across the lipid bilayer (Bretscher, 1972; Op den Kamp, 1979) with sphingomyelin and phosphatidylcholine located mainly at the external surface and phosphatidylethanolamine and phosphatidylserine at the cytoplasmic surface. Thus the outer surface is mostly zwitterionic whereas the inner leaflet is largely anionic in character. Counterions, such as Ca2+ and Mg2+, may play an important role in neutralizing the repulsive forces of and linking in other molecules such as proteins, to the anionic headgroups of the inner membrane phospholipids. Chapter 11: A Study of Lipid Bilayers Formed from the Lipids of Mammalian Erythrocyte Membranes page 11.2 Karolis; Thesis: THE DIELECTRIC CHARACTERlZATION OF UPID BILAYERS 171 lnformation on the distribution of cholesterol within the lipid bilayer is limited. Cholesterol is unreactive and no suitable chemical probe is available to undertake appropriate studies. Higgens, Florendo and Barnett (1973) used osmium-cholesterol in electron microscope studies of erythrocyte ghosts and deduced that cholesterol was dispersed in clusters and that these clusters were distributed throughout the thickness of the red cell. Such experiments, however, are plagued by possible artefacts produced during fixation and therefore may be unreliable. Murphy (1965), using autoradiography, made the obseivation that cholesterol was concentrated around the outer edge of the biconcave disc and more specifically localised to the convex surface of the cell. Such asymmetry was confirmed by Fisher (1976) using a freeze-fracture technique. The X-ray diffraction data obtained by Caspar and Kirschner (1971) on the outer layer of the myelin membrane indicated a higher ratio of cholesterol to phospholipid. The role of phospholipids and cholesterol in the red cell membrane is mainly structural, although the functional significance of the asymmetric distribution of these lipids is not clear. In this chapter, the lipid elements of the red cell were isolated and used to produce bilayers with n-hexadecane solvent in solutions of Ringer and KCl to ascertain the variations in lipid structure arising from the reconstitution of blood lipids into a planar bilayer. 11.2 METHOD Blood samples were obtained from two people. The lipids were extracted from 450 ml samples of whole blood by a combination of the methods of Reed, Swisher, Marinetti and Eden (1960) and Dodge, Mitchell and Hanahan (1963). A detailed description has been given in Chapter 5 (5.2.5). Bulk quantities of the lipid extracts were dissolved in chloroform in the proportion 10-1 Kg of lipid per litre of chloroform and were kept at -4°C in specially cleaned test tubes and free from light. The resultant mixture was painted across a small hole (diameter varied between 1.7 mm to . 111"1. 1~ tt pclycei1b,mcde. 5(•ph.Jn,1 >l'p_eital,,.1 I-we e.qilt>o~·~ ff5f>liloi.,s ,,. ../it;_ /i,tl J;,,/cty«cl.aa 2.7t11e preparation of the lipid extract for bilayer productlon was similar to the preparation 6f bilayers made from lecithin. A small aliquot of the bulk sample (200 µ1) was placed a clean test Chapter 11: A Study of lipid Bilayers Formed from the lipids of Mammalian Erythrocyte Membranes page 11.3 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 172 tube. The chloroform was evaporated under vacuum for 3 hours in a warming oven. The lipid appeared as a smear of grease at the bottom of the test tube. 500 µl of n-hexadecane was added to the test tube. The mixture was stirred with the tip of a 23 gauge syringe whilst warmed gently. fflRl) ia a polyearbonaw septum sepamring two aqueeus resen oil's in the lipid bilayct chambe1. The aqueous reservoir was pre-heated to 35°C. The formation of the bilayer was observed through a low powered microscope while the capacitance and conductance was monitored at 1 Hz. When the capacitance had stabilised admittance spectral scans were commenced in the frequency range .04 Hz to 44.4 kHz. After three scans (1 hour), the temperature was lowered to room temperature and the same series of scans repeated. After a further 1 hour of measurement, if the bilayer conductance was seen to be reasonably stable, the frequency range was extended down to 0.01 Hz, where a further series of admittance measurements were performed. If the bilayer appeared to be stable after this 4 hour series of measurements, a further 6 hours of measurements was begun. At several stages during measurement the bilayer and septum were photographed to determine the area of the bilayer. At the conclusion of measurement the data was normalised to the bilayer area and the capacitance and conductance recalculated. Maxwell-Wagner models were obtained from the average of 3 early scans. Bilayers that lasted for sufficiently long periods it was possible to average several hours of measurement. Experiments were performed in Ringer, 10-1 and 10-2 mole litre-I solutions of KCl. 11. 3 RESULTS Considerable difficulty was encountered in producing stable bilayers in all types of aqueous solutions. It was not possible to produce bilayers without raising the temperature of the aqueous phase to 36°C and greater. The lipid appeared viscous and encountered difficulty in thinning to a bilayer. The pre-bilayer stage was characterised by a mosaic of thinned areas separated by thick regions of aggregated lipid. Attempts to reduce the concentration of lipid Chapter 11: A Study of Lipid Bilayers Formed from the Lipids of Mammalian Erythrocyte Membranes page 11.4 Karol is; Thesis: THE DIELECTRIC CHARACTERIZATION OF LJPID BILAYERS FIGURE 11.1 FORMATIONOFBLOODLIPIDBILAYERIN100MMKCL The left photo was taken soon after wiping the lipid solvent mixture across the septum. The tip of a b1ight illuminating source appears to the left . Faint vertical shadows of the cunent electrodes may be seen above the forming bilayer. The torus can be seen to consist of lipid aggregates as the bulk solvent drained upwards. In the 1ight photo, the bulk solvent has drained away leaving a stable bilayer and torus on the septum. TABLE 11.1 THE LOW FREQUENCY MEASURED CAPACITANCE (Cm) OF BILA YEAS FORMED WITH n-HEXADECANE IN DIFFERENT CONCENTRATIONS OF KCI AND RINGER SOLUTION Bilayer Electrolyte Measured Corresponding Type Concentration Capacitance thickness of the (Cm) hydrocarbon region (mole litre-1) (mF m-2) (nm) (nm) ehc=2.14 ehc=2.20 Egg Lecithin 1 7.65±0.3 2.48 2 .55 1 o-1 7.60±0 .1, 2 .50 2 .58 Egg lecithin/cholesterol Ringer 7 .2±0.2 2.65 2.71 1 o-1 7.0±0.1 2 .71 2 . 78 1 o-2 6 .6±0.1 Blood lipid S1 4 Ringer 6 .0±0 .1 3 . 16 3 .24 4 1 o-1 7 .5± 1 .6 2.53 2 .60 4 1 o-2 6.6±0.3 Chapter 11: A study of lipid bilayers formed from the lipids of mammalian erythrocyte membranes Figure 11 .1 & Table 11.1 Karolis; Thesis: THE DJEI.ECI'RJC CHARACTERfZATJON OF LJPJD BILAYERS 173 molecules to solvent were not immediately successful. Altering the pH from 5.6 to 7.2 did not affect the process of thinning which often took several hours. Estimates of the area of the thin regions were complicated by the appearance of many small thinned regions rather than one large area (see Figure 11.1). The torus was often quite pronounced and occupied a large part of the hole in the septum; the area of the bilayer was measured to be in the range 30 to 80% of the area of the hole and was typically around 50%. The estimated uncertainty in the determination of the area of the bilayer region was 10%. This was the largest source of uncertainty. The length of time usefully engaged in measurement varied between 5.4 ks and 5 Ms. Typical times were 14.4 ks. The low frequency capacitance of the bilayers formed from blood lipid appears in Table 1 1. 1. In Ringer solution the capacitance was found to be 6.0±0.1 mF m-2 in Ringer solution; 7 .5±1.6 mF m-2 in 100 mM KCl and 6.6±0.3 mF m-2 in 10 mM KCL The shunt conductance for each system is presented in Table 11.2 where it can be seen that the conductance was 10.9±4.0 mS m-2 in Ringer solution; 12.5±9.3 mS m-2 in 100 mM KCl and 4.7±2.6 mS m-2 in 10 mM KCL 11.4 DISCUSSION The fragmented appearance of the bilayers formed with blood lipids resulted in a 20% uncertainty in estimates of the bilayer area when the bilayer was formed in Ringer solution, (see Figure 11.1) and about 5% in 100 mM and 10 mM KCL In Table 11.1 the results of capacitance measurements of lecithin and lecithin-cholesterol bilayers are compared with blood lipid bilayers. Unless there is a significant difference in the dielectric constant of the blood lipid bilayers, which is highly unlikely, the data suggest that the hydrocarbon regions are of similar proportions. This is consistent with the fatty acid compositions of the lecithin bilayers and Chapter 11: A Study of Lipid Bilayers Formed from the Lipids of Mammalian Erythrocyte Membranes page 115 Karolis; Thesis: THE DIELECTRIC CHARACTERfZAT/ON OF LIPID BILAYERS 10-1 1 Q) 10 - -~-:::::: CD 0 -E C: .Q molarity FIGURE 11.3 Conductance of blood lipid bilayers and the sum of the anion and cation concentrations in transmembrane pores. The charged pores were assumed to have a surface charge concentration of 5.8 x 10-3 C m-2 and the pore radius was assumed to be 1.33 x 1o- 9 m. Chapter 11: A Study of Lipid Bilayers Formed from the lipids of Mammalian Erythrocyte Membranes Figure 113 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS TABLE 11.2 THE LOW FREQUENCY AREA SPECIFIC CONDUCTANCE (Gg) OF BILAYERS FORMED WITH n-HEXADECANE IN DIFFERENT CONCENTRATIONS OF KCL AND RINGER SOLUTION Bilayer Electrolyte Area specific Type Concentration Conductance (Gg) mole litre-1 ms m-2 Egg Lecithin 1 9.6±4.8 1 o- 1 4.8±1 .4 Egg lecithin/cholesterol Ringer 7.2±0.2 1 o- 1 2.3±2.0 1 o- 2 0.45±0.45 Blood lipid S1 4 Ringer 10.9±4 .0 4 1 o- 1 12.5±9.3 4 1 o- 2 4.7±2.6 FIGURE 11.2 Low frequency conductance in Ringer, 100 and 1 O mM KCI to show the behaviour of blood lipid bilayers 15 • Ringer N BI 100mM KCI <' E 1111111 1OmM KCI CJ) §, Q) (.) C ~ t5 :::, "O C 0 (.) Egg Lee Egg Lee/Chol Blood Lipid BILAYER Chapter 11 : A study of bilayers formed from the lipids of mammalian erythrocyte membranes Table 11 .2 & Figure 11.2 Karolis; Thesis: THE DIELECTRIC CHARACTERfZATION OF UPID BILAYERS 174 those formed from blood lipid which contains about 25% sphingomyelin and 31 % lecithin (see Table 5.3). Sphingomyelin, contains a significant proportion of very long chain fatty acid derivatives such as behenate and lignocerate (22 and 24 carbon atoms respectively; see Table 5.4). The length of these chains, fully extended, can be shown to be 3.54 nmt. Therefore, the total thickness of the bilayer hydrocarbon region could be at least 7 .08 nm if no interdigitation or folding took place. The data in Table 11.1, however, suggests that the capacitance, corrected for the double layer (i.e. the geometrical capacitance Cg) clearly supports the contention, discussed in Chapter 6, that substantial interdigitation and folding take place in the centre of the bilayer. The thickness of the hydrocarbon region was determined to be 2.47 nm in 100 mM KCl and 3.14 nm in Ringer solution. Toe capacitance data is also consistent with the notion that the blood lipid bilayer has a net surface charge density of 5.8 x 10-3 C m-2. In Chapter 6 the surface charge density was associated with the inclusion of cholesterol in lecithin bilayers. The total phospholipids: cholesterol and triglycerides of the blood lipid samples were estimated to be in the % ratio 50: 21 : 5 with 20% as free cholesterol which is similar to the ratios employed in the lecithin cholesterol bilayers. The conductance of the blood lipid bilayers, presented in Table 11.2 and in histogram form Figure 11.2 was measured to be 3-6 times greater than was found with lecithin bilayers and lecithin-cholesterol bilayers respectively in 100 mM KCl. The conductance has been plotted against the solution concentration in Figure 11.3 where the total anion-cation concentration in a charged pore is also presented. The results appear to be consistent with the discussion in Chapter 7 regarding lecithin-cholesterol bilayers. The higher conductance measured with blood lipid bilayers may be associated with a reduced pore perimeter energy leading to larger pore radii due to the presence of sphingomyelin. Chapter 11: A Study of Lipid Bilayers Formed from the Lipids of Mammalian Erythrocyte Membranes page 11.6 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 175 11.5 SUMMARY 1. Bilayers formed formed from the lipids extracted from erythrocyte membranes exhibited similar properties to those formed egg lecithin. 2. The bilayer thickness was -2.5 nm. 3. The conductance was - 1.25 xt0-2 S m-2. 4. The variation in capacitance with electrolyte concentration suggests that the surface of the bilayer may have a residual charge. Chapter 11: A Study of Lipid Bilayers Formed from the Lipids of Mammalian Erythrocyte Membranes page 11.7 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 176 APPENDIX Al GLOSSARY OF MAJOR SYMBOLS Symbol Equation Meaning Am 6.1 ...... Area of the planar bilayer Ar 5.4 ...... Amplitude ratio a 2.3 ...... molecular area at the interface 2.4 ...... optimal surface area per molecule corresponding to the minimum free energy per molecule in a miscelle B 7.5 ...... radius of hydration bubble C 3.69 ...... capacitance Cct 6.3 ...... double layer capacitance Cg 3.70: 6.2 .. . geometrical capacitance : area specific capacitance Cm 6.3 ...... measured capacitance Cp: Cn 7.11: 7.12. concentration of positive and negative ions respectively CT 5.6:6.1 .... . total capacitance : capacitance of the bilayer C 3.38 ...... ion concentration Dj 3.43 ...... diffusion constant Di 10.3 ...... data d 3.48 ...... membrane thickness E 3.6 ...... electrostatic field Ep 8.1 ...... energy to form a pore Eexp 10.4 ...... sum of experimental error Etheory 10.3 ...... sum of least squares error ei 10.4 ...... standard error of data eo 3.2 ...... electron charge F 3.38 ...... Faraday constant F(x) 3.14 ...... force between an ion and its image, as a function of the distance x to the interface f 10.1 ...... frequency G 3.50 ...... conductance GT 5.7 ...... total conductance g 1.3 ...... magnetic moment h 1.3 ...... Plank's constant H 1.3 ...... Magnetic field Appendix 1: Glossary of major symbols page Al.l Karalis; Thesis: THE DJEL.ECTRJC CHARACTERl7ATION OF UPID Bll.AYERS 177 Symbol Equation Meaning Ii, Ir 1.1 ...... Intensity of incident and refracted light, respectively Jj 3.42 ...... electrical current carried by the ionic species j Kindex 10.5 ...... correlation index k 2.1 ...... Boltzmann's constant L 7.13 ...... length of pore M 2.2 ...... reference state of miscelle Ma,M1 6.16 ...... molecular weight of alkane solvent, lipid acyl chains N 2.1 ...... aggregation number NA 3.19 ...... Avagadro's number Na, N1 6.18 ...... total number of alkane molecules, lipid acyl chains n 3.21 ...... ion concentration 1.1 ...... refractive indices of the bilayer 3.21 ...... origional ion concentration 3.37 ...... concentration of ions in the bilayer 1.2 ...... refractive indices of water n+, n_ 3.53 ...... concentration of cations and anions respectively p 3.38 ...... hydrostatic pressure r 3.1 ...... distance from a charged sphere R 3.38 ...... Universal Gas constant R 2.8 ...... radius of curvature of miscelle R paragraph 3.2.2 .. ion radius R 8.1 ...... radius of pore Re 2.10 ...... critical radius for formation of vesicle Re 1.1 ...... reflectance Ri 7.1 ...... ion radius t 1.1 ...... thickness of bilayer T 2.1 ...... absolute temperature T 10.3 ...... theoretical function LiUE 7.1 ...... the difference in electrostatic self energy LiUs 7.2 ...... energy involved in creation of additional interfacial area u 3.43 ...... absolute mobility V 3.48 ...... applied potential Vp 3.38 ...... partial molar volume w 3.6 ...... total energy stored by an ion in an electrostatic field w 8.1 ...... perimeter energy per unit perimeter length Wpore 7.7 ...... total self energy of an ion in a pore Appendix 1: Glossary of major symbols page Al.2 Karolis; Thesis: THE DIEUCTRIC CHARACTERIZATION OF UPID BILAYERS 178 Symbol Equation Meaning W(x) 3.15 ...... total energy stored in an electrostatic field, modified by the image forces, as a function of the distance x to the interface z 3.2...... valency 5.4...... Impedance of the electrical standard 5.4...... Total impedance X 3.13 ...... distance between a charge and the interface of two dielectric media 2.1 ...... mole fraction 3.2 ...... electric force operating on a unit charge 10.1...... admittance 3.11...... integer 1.3...... Bohr magneton 8.1...... interfacial free energy of bilayer 2.3 ...... interfacial free energy per unit area 3.38 ...... activity coefficient 10.5...... number of spectra 6.13 ...... difference in thickness between solvent free and solvent containing bilayer 2.7 ...... thickness of the hydrocarbon region of the bilayer 3.2 ...... dielectric constant 6.14 ...... dielectric of the hydrocarbon region of the bilayer 3.2 ...... dielectric constant of free space 6.4 ...... dielectric constant of aqueous medium 1.1 ...... angle of refraction 3.62, 6.4 ... . reciprical Debye-Hiickel length 1.1 ...... wavelength of incident light 3.38 ...... electrochemical potential 3.39 ...... chemical potential of ionic species i 3.19 ...... chemical potential change of ionic species i 2.1 ...... free energy per molecule in a miscelle 3.38 ...... chemical potential V 1.3 ...... frequency V 2.7 ...... hydrocarbon chain volume Va 6.13 ...... alkane molar volume p 3.57 ...... charge density Appendix 1: Glossary of major symbols page Al3 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF LJPID BILAYERS 179 Symbol Equation Meaning p, p' 3.11 ...... distances from a charge and its image respectively Phc 6.15 ...... density of the hydrocarbon solvent Pr 3.20 ...... charge density a given distance r from the ion cr 3.68 ...... charge per unit area CJB 6.9 ...... bilayer surface charge crd 6.9 ...... diffuse charge in solution ~ 3.73 ...... diffuse surface charge crp 3.73 ...... polarisation charge 't 3.6 ...... volume enclosing influence of electrostatic field 't page 158 ... time constant 1.2 ...... angle of incidence dq> 1, dq>2 5.1, 5.2 ...... phase difference Appendix 1: Glossary of major symbols page Al.4 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID 811.AYERS 180 APPENDIX A2 INDEX of TABLES and DIAGRAMS TABLE/ PAGE LEGEND FIGURE CHAPTER 1 Table 1.1 4 Some important functions of biological membranes (Tien, 1974). Table 1.2 6 Composition of typical plasma membranes (Jain, 1972). Table 1.3 6 Phospholipid composition of various cellular membranes (Tao, 1982). Table 1.4 11 Comparison of some physical characteristics of bimolecular lipid membranes and natural membranes. Figure 1.1 2 The structure of cells a: Diagram of a typical animal cell (DeWitt, 1976). b: Diagram of a plant cell (Villee, 1977). Figure 1.2 5 Schematic drawing of molecular conditions of the cell proposed by Danielli and Davson (1935). Figure 1.3 7 Fluid Mosaic Model based on Singer and Nicholson (1972). Figure 1.4 10 Aggregated forms of amphipaths (Tien, 1972). Figure 1.5 13 Electron micrographs (Jain, 1972) a: Electron micrograph of the cell membranes of intestinal cells showing the three-layered structure (m=membrane; is=intercellular space). Magnification x 240,000. b: Electron micrograph of the plasma membrane from erythrocyte. The schematic diagram shows the interpretation as generally developed by Gorter-Grendel-Davson-Danielli-Robertson (see text). Figure 1.6 15 Schematic diagram showing the parameters used in optical studies of lipid bilayers. CHAPTER 2 Figure 2.1 21 A phosphatidyl choline. A structural presentation of the components chemically linked to form egg lecithin. CHAPTER 3 Figure 3.1 30 A schematic drawing of the membrane model proposed by Gorter and Grendel (1925). Appendix A2: Index of Tables and Diagrams page A2.J Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 181 INDEX of TABLES and DIAGRAMS (continued) TABLE/ PAGE LEGEND FIGURE CHAPTER 4 Figure 4.1 60 Experimental system consisting of the vibration free platform supporting the Faraday cage with the viewing system in front (centre); BULFIS computer (right). The membrane chamber assembly and amplifiers are situated in the Faraday cage. Figure 4.2 60 Experimental arrangement of the viewing system; the membrane chamber assembly and amplifiers. The syringe (centre bottom) was used to maintain equal hydrostatic pressure in both halves of the BLM cell (centre). Figure 4.3 61 Close up views of the bilayer chamber and amplifier assembly. The current electrodes are thicker than the voltage electrodes. The temperature transducer is located in the rear half of the beaker into which the polycarbonate cell is immersed. Figure 4.4 62 a: Schematic diagram of the lipid bilayer chamber assembly. b: The three components of the polycarbonate cell. Figure 4.5 64 Experimental arrangement used to photograph each bilayer. Long surviving bilayers were photographed many times; usually coinciding with the commencement of a new sequence of measurements. Figure 4.6 66 Schematic diagram of the amplifier circuitry. Figure 4.7 67 Block diagram of the signal generator and data aquisition system, the Biophysics Ultra Low Signal Impedance Spectrometer (BULFIS). CHAPTER 5 Table 5.1 74 Analytical data of isolated egg lecithin. Table 5.2 74 % fatty acid composition of isolated egg lecithin. Table 5.3 76 Lipids of the normal human red cell membrane. Table 5.4 76 Predominant fatty acids of phospholipids in normal human red cell membrane. Table 5.5 91 Component values used in the test of the fitting routine and confirmation of the Maxwell-Wagner description of the data. The figures appearing in italics are the model component values after allowing for a supposed bilayer area of 3.87 x 10-6 m2. Table 5.6 93 A comparison of Maxwell-Wagner model component values, estimated from admittance measurements of an hard-wired circuit over the frequency range 0.01 to 1<>4 Hz, with those values used in the circuit. Appendix A2: Index of Tables and Diagrams page A2.2 Karolis; Thesis: THE DIEUCTRJC CHARACTERIZATION OF UPID BILAYERS 182 INDEX of TABLES and DIAGRAMS (continued) TABLE/ PAGE LEGEND FIGURE CHAPTER 5 ( continued) Figure 5.1 73 a: Space-filling model of a phosphatidylcholine molecule (Stryer, 1975). b: Atom numbering and notation for torsion angles for phosphatidylcholine (Hauser et al, 1981). Figure 5.2 73 Space filling model of cholesterol (Stryer, 1975). Figure 5.3 73 Space-filling model of cyclosporin A (Knott, 1987). Figure 5.4 81 The various stages of lipid bilayer formation are shown in a sequence of six of photographs. A full description of the processes is provided in the text. The experimental arrangement was that described in The Viewing System (paragraph 4.2.2). The torus is clearly visible surrounding a region of lipid that is thinning from the bottom upwards. A bimolecular region, (bilayer filled with solvent), appeared spontaneously at the bottom of the hole in the septum. This black region grew in size until it filled between 80-90% of the hole. The bilayer, formed in less than 10 minutes but continued to sequester solvent for a period of 1 hour. The lipid mixture was lecithin and cholesterol disolved in n-hexadecane. The aqueous medium was 1 mM KCl and the temperature 25°C. Figure 5.5 84 The experimental arrangements used in the amplifier calibration proceedure. At low frequencies the upper configuration was used. At frequencies > 3 kHz the lower arrangement was adopted. The input capacitance of each amplifier is represented by the capacitors connected across the amplifier input terminals. R 1 and R2 were set at 1 kil to ensure that the reactance of the input capacitance of each amplifier could be neglected. Figure 5.6 91 Electrical (Maxwell-Wagner) model of the lipid bilayer. Circuit 1 depicts the bilayer as a single sheet of dielectric bounded by an electrolyte (Gsoln). The capacitance (Che) is due exclusively to the hydrocarbon region. The conductance (Gshunt) due to pathways through this low dielectric region. The other circuits assume that the bilayer consists of two or more dielectrically distinct regions. Figure 5.7 92 a: The mean capacitance of hard-wired Maxwell-Wagner circuits plotted against frequency. b: Expanded view of data shown above to show structure as the number of elements increases. Appendix A2: Index of Tables and Diagrams page A23 Karolis; Thesis: THE DIELECTRIC CHARACTERfZAT/ON OF UPJD BILAYERS 183 INDEX of TABLES and DIAGRAMS (continued) TABLE/ PAGE LEGEND FIGURE CHAPTER 5 ( continued) Figure 5.8 92 a: Capacitance spectrum of a 2-element hard-wired Maxwell- Wagner circuit. I-element fit. 1 element for the bilayer and 1 for the electrolyte. b: Capacitance spectrum of a 2-element hard-wired Maxwell- Wagner circuit. 2-element fit. 1 element for the bilayer and 1 for the electrolyte. c: Capacitance spectrum of a 3-element hard-wired Maxwell- Wagner circuit. 3-element fit. 2 element for the bilayer and 1 for the electrolyte. d: Capacitance spectrum of a 4-element hard-wired Maxwell- Wagner circuit. 4-element fit. 3 element for the bilayer and 1 for the electrolyte. e: Capacitance spectrum of a 5-element hard-wired Maxwell- Wagner circuit. 5-element fit. 4 element for the bilayer and 1 for the electrolyte. CHAPTER 6 Table 6.1 99 a: The capacitance of egg lecithin bilayers. 101 b: The ca[acitance of egg lecithin-cholesterol bilayers. Table 6.2 104 The double layer capacitance and its contribution to the measured capacitance. Table 6.3 111 The low frequency measured capacitance (Cm) of bilayers formed from n-hexadecane in different concentrations of HCl . Table 6.4 112 The low frequency area specific capacitance (C~ of bilayers formed with n-hexadecane in different concentrations o KCl corrected for the series double layer. Figure 6.1 115 Natural logarithm of the double layer capacitance vs the molarity of the electrolyte for different bilayer systems. Figure 6.2 116 Natural logarithm of the double layer capacitance vs the molarity of the electrolyte for lecithin-cholesterol bilayers (Cd(L-C)); charged membrane (Cd( +)/5.8xlQ-3 C m-2); and electrolyte only (Cd). CHAPTER 7 Table 7.1 128 The low frequency area specific conductance (Gg) of bilayers formed with n-hexadecane in KCl solutions of different concentrations. Table 7.2 129 The additional energy DU required by an ion to place in a pore spanning a lipid bilayer. Appendix A2: Index of Tables and Diagrams page A2.4 Karolis; Thesis: THE DIEU:CTRJC CHARACTERIZATION OF UPID BILAYERS 184 INDEX of TABLES and DIAGRAMS (continued) TABLE/ PAGE LEGEND FIGURE CHAPTER 7 ( continued) Table 7.3 129 The anion and cation concentration of a univalent electrolyte in the region of the charged bilayer surface. Table 7.4 129 Calculated ion concentration in pores of different radii spanning a bilayer with a net surface charge of 5.8 x 10-3 C m-2. Figure 7.1 122 Transmembrane pore. The dielectric constant of the pore is the same as the water. The symbols have the same meaning used in the text. Figure 7.2 129 Conductance of lecithin-cholesterol bilayers and the sum of the anion and cation concentrations in transmembrane pores. The charged pores were assumed arbitrarily to have a surface charge concentration of 5.8 x 10-3 C m-2 and the pore radius was assumed to be 1.33 x lQ-9 m. CHAPTER 8 Table 8.1 139 The low frequency area specific capacitance (Cg) of bilayers formed with 11-hexadecane in 100 mM KCl corrected for the series double layer. Figure 8.1 138 Capacitance and conductance spectra for an egg lecithin bilayer formed in 100 mM KCl at 25°C. Figure 8.2 138 Capacitance and conductance spectra for an egg lecithin-cholesterol bilayer formed in 100 mM KCl at 25°C. Figure 8.3 138 Expanded view of the capacitance and conductance spectra for an egg lecithin bilayer and an egg lecithin-cholesterol bilayer formed in 100 mM KCl at 25°C. Figure 8.4 138 Manual sequential fitting of different parts of the capacitance spectra of lecithin data. Figure 8.5 139 a: The capacitance of the different regions of bilayers consisting of lecithin; lecithin-cholesterol and lecithin-oxidised cholesterol in 100 mM KCl at 25°C. b: The conductance of different regions of bilayers consisting of lecithin; lecithin-cholesterol and lecithin-oxidised cholesterol in 100 mM KCl at 25°C. Appendix A2: Index of Tables and Diagrams page A2.5 Karolis; Thesis: THE DIELECTRIC CHARACTERfZATION OF UPID BILAYERS 185 INDEX of TABLES and DIAGRAMS (continued) TABLE/ PAGE LEGEND FIGURE CHAPTER 8 ( continued) Figure 8.6 141 A sketch of the total energy required to form a pore as a function of the pore radius (Equation 8.1). For small pores the energy cost associated with the cuived perimeter of the pore increases with the pore radius faster than the energy saving associated with the decreased area of the planar portions of the bilayer-water interface. For large pores the reverse is true; the total energy required to form a pore reaches a maximum at a critical radius Re. A pore of this radius would grow spontaneously and lead to lysis. (Coster, 1990). CHAPTER 9 Table 9.1 148 Physio-chemical properties of Cyclosporin-A. Table 9.2 150 The low frequency area specific capacitance (Cg) of egg lecithin -cholesterol bilayers containing CsA and formecl with n-hexadecane in 100 mM KCl solutions of different concentration. Table 9.3 151 The low frequency area specific conductance (G_g) of egg lecithin -cholesterol bilayers containing CsA and formed with n-hexadecane in 100 mM KCl solutions of different concentration. Figure 9.1 147 Structural formula of cyclosporin A (CsA) Figure 9.2 149 a: Mean capacitance spectra for an egg lecithin/cholesterol bilayer containing cyclosporin A, formed in 100 mM KCl at 250c. The error bars lie within the plot symbol. b: Expanded view of the capacitance spectra for an egg lecithin/cholesterol bilayer containing cyclosporin A; lecithin bilayer and a lecithin bilayer containing cholesterol, formed in 100 mM KCl at 25°C. Figure 9.3 152 a: The capacitance of the different regions of bilayers consisting of lecithin; lecithin-cholesterol and lecithin-cholesterol-CsA in 100 mM KCl at 25°C. b: The conductance of different regions of bilayers consisting of lecithin; lecithin-cholesterol and lecithin-cholesterol-CsA in 100 mM KCl at 25°C. Appendix A2: Index of Tables and Diagrams page A2.6 Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BILAYERS 186 INDEX of TABLES and DIAGRAMS (continued) TABLE/ PAGE LEGEND FIGURE CHAPTER 10 Table 10.1 161 J- parameters. Table 10.2 162 Bilayer statistics. Table 10.3 163 Multilayer dielectric model of the bilayer. Table 10.4 165 Time constant of the different regions of the bilayer in 100 mM KCI. Figure 10.1 164 Capacitance and conductance of the bilayer regions. Figure 10.2 164 Time constant of the different regions of the bilayer in histogram form. CHAPTER 11 Table 11.1 173 Low frequency measured capacitance (Cm) of bilayers formed in n-hexadecane in different concentrations of KCI and Ringer solution. Table 11.2 174 Low frequency area specific conductance (Gif of bilayers formed in n-hexadecane in different concentrations of Cl and Ringer solution. Figure 11.1 173 Formation of blood lipid bilayer in 100 mM KCI. Figure 11.2 174 Low frequency conductance in Ringer, 100 and 10 mM KCl to show the behaviour of blood lipid bilayers. Figure 11.3 175 Conductance of blood lipid bilayers and the sum of the anion and cation concentrations in transmembrane pores. Appendix A2: Index of Tables and Diagrams page A2.7 KAROLIS; Thesis: THE DIELECTRIC CHARACTERl?AT/ON OF LIPID BILAYERS TABLE B1 BULRS FREQUENCY ALE # F s V G1 G2 A L1 L2 D D M M Channel 1 Channel2 PHASE RATIO 0 10 10 0 0 0 225 0 25 .61 E-2 .1 0E-1 .00 .982147 1 11 10 0 0 0 225 0 25 .00E+0 .00E+0 .00 .977500 2 12 10 2 0 0 225 0 25 .00E+0 .00E+0 .00 .977500 3 13 10 2 0 0 225 0 25 .14E-1 .24E-2 .00 .977500 4 14 10 2 0 0 225 0 25 .10E-1 -.12E-1 .00 .977500 5 15 1 0 2 0 0 225 0 25 .40E-1 -.27E-1 .00 .977500 6 16 10 2 0 0 225 0 25 .13E-1 .25E-1 .00 .997500 7 1 7 1 0 2 0 0 225 0 25 .15E-1 .24E-1 .00 .997500 8 18 1 0 2 0 0 225 0 25 -.18E-1 .95E-1 .00 .997500 9 19 1 0 4 0 0 225 0 25 -.12E-1 .93E-1 .00 .997500 1 0 20 10 4 0 0 225 0 25 -.18E-1 .82E-1 .00 .997500 11 21 1 0 4 0 0 225 0 50 -.25E-1 .74E-1 .00 .997500 12 22 1 0 4 0 0 225 0 100 -.23E-1 .71 E-1 .00 .997500 13 23 10 4 0 0 225 0 150 -.28E-1 .56E-1 .00 .997500 14 24 1 0 6 0 0 225 0 200 -.15E-1 .39E-1 .00 .997500 15 25 1 0 9 0 0 225 0 255 .55E-1 .85E-2 .00 .997500 16 26 10 1 0 0 0 225 1 0 -.41 E-2 .13E-1 .00 .997500 17 27 10 12 0 0 225 1 0 .52E-1 .84E-1 .00 .997500 18 28 1 0 13 0 0 225 1 0 .60E-1 .78E-1 .00 .997500 19 29 1 0 14 0 0 225 1 0 .52E-1 .90E-1 .00 .997500 20 30 1 0 15 0 0 225 1 0 .61E-1 .75E-1 .00 .997500 21 31 10 15 0 0 225 1 0 .54E-1 .84E-1 .00 .997500 22 32 1 0 15 0 0 225 1 0 .63E-1 .84E-1 .00 .997500 23 33 1 0 15 0 0 225 1 0 .56E-1 .85E-1 .00 .997500 24 34 1 0 15 0 0 225 1 0 .43E-1 .83E-1 .00 .997500 25 35 1 0 15 0 0 225 1 0 .43E-1 .81E-1 .00 .997500 26 36 1 0 15 0 0 225 1 0 .47E-1 .90E-1 .00 .997500 27 37 10 15 0 0 225 1 0 .48E-1 .80E-1 .00 .997500 28 38 1 0 15 0 0 225 1 0 .47E-1 .84E-1 .00 .997500 29 39 1 0 1 5 0 0 225 1 0 .48E-1 .88E-1 .00 .997500 30 40 1 0 15 0 0 225 1 0 .60E-1 .77E-1 .00 .997500 31 41 1 0 15 0 0 225 1 0 .52E-1 .85E-1 .00 .997500 32 42 1 0 15 0 0 225 1 0 .62E-1 .83E-1 .00 .997500 33 43 10 15 0 0 225 1 0 .49E-1 .90E-1 .00 .997500 34 44 10 15 0 0 225 1 0 .54E-1 .82E-1 -.20E-1 .997500 35 45 1 0 15 0 0 225 1 0 .52E-1 .93E-1 -.25E-1 .997599 36 46 1 0 15 0 0 225 1 1 0 .51E-1 .90E-1 -.30E-1 .997849 37 47 9 15 0 0 225 1 50 .31 E-1 .66E-1 -.50E-1 .997900 38 48 9 15 0 0 225 1 100 .39E-1 .56E-1 -.90E-1 .997900 39 49 8 15 0 0 225 1 150 .22E-1 .61 E-1 -.12 .998000 40 47 9 15 3 0 225 1 200 .21E-1 .59E-1 -.20 .998499 41 48 9 15 3 0 225 1 250 .12E-1 .40E-1 -.32 .998999 42 49 8 15 3 0 225 1 250 .15E-1 .43E-1 -.43 1.000000 43 47 9 15 9 0 225 1 255 .33E-1 .45E-1 -.50 1.001000 44 48 9 15 9 0 225 1 255 .28E-1 .46E-1 -.95 1.001000 45 49 8 15 9 0 225 1 255 .12E-1 .40E-1 -1.2 1.003000 46 47 9 15 27 0 225 1 255 .18E-1 .39E-1 -2.2 1.008000 47 48 9 15 27 0 225 1 255 .15E-1 .46E-1 -3.7 1.019990 48 49 8 15 27 0 225 1 255 .24E-1 .51 E-1 -6.2 1.024990 Appendix B: Data Storage and Preselltation TableB.I Karolis; Thesis: THE DIELECTRIC CHARACTERIZATION OF UPID BI I.AYERS 187 APPENDIX B DATA STORAGE AND PRESENTATION 8.1 BULFIS FREQUENCY FILE The signal generator and transient recorder boards received instruction via the frequency file, shown in Table B. I. This table included the corrections required to match the two amplifier circuits for relative phase and gain (columns 11 and 12 respectively), discussed in Chapter 5. The meaning of the column headings follows: # Entry number corresponding to particular frequency data point (implied but not printed). F sets the rate at which the the function in the signal generator is clocked. The clocking rate was calculated according to the formula: 106 F clocking rate (Hz) = 1024 x 2 2 S number of analogue steps for the sinusoidal output of the signal generator according to 2s V number of periods over which the transient recorder boards sample and average. G G 1 defines the number of periods of the sine function loaded into the signal generator 02 defines the location of the function (0 = EPROM; 1 = Disk) A sets the amplitude of the output signal (0 = 0 V: 255 = 5 V) L LI, L2 select the RC filters on the output of the signal generator. D sets the DC offset on the output signal (volts). M correction factors for the relative phase and gain of the differential amplifiers at each frequency. Appendix B: Data Storage and Presentation page BJ.I Karolis; Thesis: THE DIELECTRIC CHARACTERfZATJON OF LIPID BILAYERS TABLE B2 PRESENTATION OF THE DATA DURING DATA AQUISITION The data was taken during an investigation of an unmodified lecithin-cholesterol bilayer in a solution of 1 mM KCI. The bilayer was 7 hours old and filled 93% of the hole in the septum. (see text for description of symbols) R (OHMS) C (FARADS) S-R (OHMS) 9.9E+08 .15113E-7 .56E+5 AREA (cm 112) STRAY CAP. (CH 0, 1) (FARADS) 5.85E-02 .00E+0 .00E+0 # COEFFICIENTS HERTZ DEGREES OHMS US cm 112 UF cm 112 voltage current 6 .2E-2 .5E-3 .106E-1 -53 322E+6 .31493E-1 .63648 7 .3E-3 .3E-3 .149E-1 -61 272E+6 .29755E-1 .58911 8 .3E-3 .3E-3 .212E-1 -69 203E+6 .30073E-1 .58720 9 .2E-3 .7E-4 .298E-1 -74 149E+6 .30339E-1 .58681 1 0 .2E-3 .7E-4 .425E-1 -79 107E+6 .30314E-1 .58359 11 .2E-3 .5E-4 .596E-1 -82 774E+5 .30507E-1 .58369 12 .1 E-2 .7E-4 .851 E-1 -81 546E+5 .43831 E-1 .57894 13 .2E-3 .5E-4 .119 -85 390E+5 .31667E-1 .58224 14 .1 E-3 .4E-4 .170 -87 274E+5 .32451 E-1 .58068 15 .1 E-3 .2E-4 .238 -87 196E+5 .34723E-1 .58064 16 .1 E-3 .2E-4 .340 -88 137E+5 .38106E-1 .58030 17 .1 E-3 .2E-4 .476 -88 985E+4 .44955E-1 .57892 18 .8E-4 .2E-4 .681 -88 689E+4 .53694E-1 .57882 19 .8E-4 .2E-4 .953 -88 494E+4 .64408E-1 .57728 20 .8E-4 .2E-4 1.36 -88 345E+4 .9491 0E-1 .57748 21 .8E-4 .2E-4 1.90 -88 247E+4 .14856 .57684 22 .8E-4 .2E-4 2.72 -88 173E+4 .24015 .57582 23 .8E-4 .2E-4 3.81 -88 124E+4 .42811 .57464 24 .8E-4 .2E-4 5.44 -87 869E+3 . 79211 .57378 25 .8E-4 .2E-4 7.62 -86 621E+3 1.4672 .57328 26 .8E-4 .2E-4 10.8 -85 436E+3 2.8503 .57030 27 .8E-4 .2E-4 15.2 -84 312E+3 5.4222 .56740 28 .8E-4 .2E-4 21.7 -82 220E+3 10. 753 .56106 29 .8E-4 .2E-4 30.5 -79 158E+3 20.470 .55043 30 .8E-4 .2E-4 43.5 -74 113E+3 39. 786 .53034 31 .8E-4 .2E-4 61.0 -69 838E+2 72.297 .49715 32 .8E-4 .2E-4 87.1 -61 625E+2 129.32 .43958 33 .8E-4 .3E-4 122 -53 493E+2 207.42 .36172 34 .1 E-3 .3E-4 174 -43 405E+2 305.64 .26454 35 · .1 E-3 .5E-4 244 -34 355E+2 395.74 .17749 36 .2E-3 .6E-4 348 -26 325E+2 471.04 .10613 37 .7E-4 .2E-4 488 -20 308E+2 519.82 .61833E-1 38 .6E-4 .2E-4 697 -14 298E+2 553.72 .33738E-1 39 .4E-4 .1 E-4 976 -11 291E+2 573.92 .18997E-1 40 .1 E-3 .2E-4 146E+1 -8.4 287E+2 588.63 .95352E-2 41 .1 E-3 .4E-4 209E+1 -6.7 284E+2 596.23 .53354E-2 42 .1 E-3 .4E-4 292E+1 -5.6 283E+2 599. 75 .32465E-2 43 I .4E-3 .1 E-3 439E+1 -5.2 283E+2 601.21 .19837E-2 441 .7E-3 .2E-3 627E+1 -5.5 282E+2 597.96 .14636E-2 Appendix B: Data Storage and Prese11tatio11 Table B.2 Karolis; Thesis: THE D/EUCTRIC CHARACTERIZATION OF UPID 8/UYERS 188 B.2 BULFIS IMPEDANCE MEASURING MODE The impedance data was stored on floppy disk and simultaneously displayed on the visual display unit in the format appearing in Table B.2. R (OHMS) Resistance of calibrated reference resistor. C (FARADS) Capacitance of calibrated reference capacitor. S-R (OHMS) Series resistor (impedance chosen to match that of electrolyte). AREA (cm2) Area of hole in the septum. This value was used to convert the units of capacitance and conductance of the bilayer to unit area. This value was adjusted after the actual area was determined photographically. STRAY CAP. Corrections for the stray capacitance. The data in the columns (from left to right): # The entry number of the corresponding frequency data point stored on floppy disk. COEFF'S(V,C)Normalised parameters required to generate sine wave functions to the measured voltage and current signals recorded by BULFIS. HERTZ The frequency of the AC signal output from the signal generator. DEGREES The phase of the measured impedance. OHMS The magnitude of the measured impedance. µS cm·2 The impedance expressed as an equivalent conductance and µF cm·2 capacitance. 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