Download The

Mechanics of Inter-Monolayer Coupling in Fluid Surfactant Bilayers by Anthony K.C. Yeung B.A.Sc., University of British Columbia, 1983 M.A.Sc., University of British Columbia, 1987 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Physics) We accept this thesis as conformin to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June 1994 ©Anthony K.C. Yeung, 1994 _________________________ ___________________________ In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. (Signature) Department of The University of British Columbia Vancouver, Canada Date DE-6 (2/88) Abstract Fluid surfactant bilayers are composed of two mono-molecular sheets that are weakly held together by normal stresses. Except for viscous resistance, the monolayers are free to slide relative to one another — giving rise to “hidden” degrees of freedom within the composite structure. This thesis examines such an added level of complexity to the study of bi layer membranes. A continuum theory for monolayer-coupling is first developed, which forms the theoretical basis for the work reported here and for future analyses on strat ified fluid membranes. The phenomenological coefficient of dynamic (viscous) coupling between monolayers is then measured experimentally by a novel method called nanotether extrusion. This technique, which is developed by myself for this present investigation, en ables measurements of inter-monolayer viscous stresses in unsupported bilayers. Further, a useful spin-off from such a technique is the determination of bilayer bending rigidities. Finally, as an application of the present continuum model, the static and dynamic features of a bilayer vesicle’s Brownian shape undulations are predicted with the membrane con ceptualized as a stratified composite structure. Throughout this thesis, it is shown that the effects of bilayer stratification (monolayer-coupling) are very important. For example, the conformational dynamics of bilayer membranes on mesoscopic length scales (roughly between 1 to 100 nanometers) are governed by the inter-monolayer viscous forces; in such situations, dissipation due the surrounding hydrodynamics plays only a secondary role. 11 Contents Abstract ii Table of Contents iii List of Tables vii List of Figures viii Acknowledgements x 1 Introduction 1 1.1 Overview of the Thesis 3 1.2 Structure of Amphiphilic Molecules 5 1.2.1 Components of phospholipids 5 1.2.2 The four major phospholipids and cholesterol 6 1.2.3 Motional freedom of hydrocarbon chains 7 1.3 Structure of Bilayers 8 1.3.1 Hydrophobic effect and condensed interfacial structures 8 1.3.2 The gel and fluid phases of bilayers 10 1.3.3 Disorder inside the fluid bilayer 11 1.3.4 Interdigitation 13 1.3.5 Effects of cholesterol 14 1.3.6 Molecular motions and time scales 15 2 Mechanics of Monolayer Coupling 17 2.1 Equations of Mechanical Equilibrium 20 2.1.1 Stresses, strains and axisymmetry 20 111 2.1.2 Virtual work and the equilibrium equations 22 2.1.3 Equilibrium equations for a fluid membrane 25 2.1.4 Dividing one fluid membrane into two 27 2.2 Free Energy of Deformation 29 2.2.1 Elastic model for liquid crystalline membranes 29 2.2.2 Pure stretch 30 2.2.3 Pure bending and local curvature energy 31 2.2.4 Coupled layers and global curvature energy 33 2.2.5 Euler-Lagrange equations and mechanical equilibrium 35 2.3 Interlayer Viscosity 38 2.3.1 Phenomenological model and balance of tangential forces 38 2.3.2 Kinematics 39 2.3.3 Dynamic equation for a 41 3 Measurement of Interlayer Drag 42 3.1 General Description of Nanotether Extrusion 43 3.2 Summary of Equations and Experimental Strategy . 45 3.2.1 Two important equations 45 3.2.2 Experiment 1: Static measurement 46 3.2.3 Experiment 2: Dynamic measurement 47 3.3 Methods 48 3.3.1 Vesicles, solutions and beads 48 3.3.2 Micropipette setup 50 3.3.3 Experimental procedures 53 3.4 Data and Discussion 55 4 Thermal Undulations of Bilayer Vesicles 58 4.1 Mean Square Amplitudes: Statics 60 4.2 Correlation Function: Dynamics 62 4.2.1 Equilibrium equations for the bilayer 63 4.2.2 Interlayer drag and bilayer relaxation function . 64 4.2.3 Hydrodynamics 65 iv 4.2.4 Solution . 65 4.3 Discussion 66 5 Summary 69 Bibliography 72 APPENDICES A From Virtual Work to Equilibrium Equations 77 B Analysis of Tether Extrusion 80 B.1 Dynamics of n in Vesicle-Tether Junction 80 B.1 .1 Péclet number and order-of-magnitude arguments 80 B.1.2 Integrating the low Péclet number equation 82 B.1.3 Kinematics 83 B.2 Balance of Forces 83 B.2.1 Vesicle region 84 B.2.2 Vesicle-tether junction 84 B.2.3 Entering tether region 84 B.3 Dynamics of on Sphere 85 B.3.1 Simplifying dynamic equation for c 86 B.3.2 Boundary value problem and general solution 86 B.3.3 Constant rate of extrusion 88 B.3.4 Constant tether force 88 B.4 Other Dissipative Effects 89 C Force Transducer: Analysis and Calibration 91 C.1 Force Balance 91 C.2 Numerical Solution 93 C.3 Results and Calibration 95 D Vesicle Undulations: Equilibrium Calculations 96 v E Vesicle Undulations: Deterministic Dynamics 100 E.1 Bilayer Shell •• . 100 E.1.1 Geometry 100 E.1.2 Kinematics • . 102 E.1.3 Forces 103 E.1.4 Modal expansion 104 E.2 Hydrodynamics 105 E.3 Matching Boundary Conditions • • .. 106 E.3.1 Laplace transform • . 106 E.3.2 Matching kinematic boundary conditions: No-slip • .. 107 E.3.3 Matching stress boundary conditions: Force balance • . 108 F Relaxation Function for the Bending Moment 110 vi List of Tables I Summary of Results from Nanotether Experiment 57 vii List of Figures 1.1 Molecular structure of a phospholipid molecule 113 1.2 Molecular structure of a cholesterol molecule 114 1.3 Torsional potential between two CR2 groups 115 1.4 Molecular shapes and condensed structures 116 1.5 Molecular order profiles 117 2.1 Axisymmetric geometry 118 2.2 Stresses on a curved shell segment 119 2.3 Defining the origins in the thickness direction 120 2.4 Simple model for interlayer drag 121 3.1 The nanotether experiment 122 3.2 Experimental setup 123 3.3 Photograph of nanotether experiment 124 3.4 Tether pulling sequence 125 3.5 Determination of tether radius 126 3.6 Dynamic tether force vs. extrusion rate 127 B.1 Magnified view of the vesicle-tether junction 128 B.2 Axial force balance on nanotether 129 C.1 Mechanical analysis on force transducer 130 viii C.2 Calibration of force transducer 131 C.3 Experimental and theoretical transducer characteristics 132 ix Acknowledgements I would like to thank Evan Evans, my research supervisor, for introducing me to this stimulating research problem and for his guidance and support. I also extend my sincere gratitude to all the people in the lab for their technical and, more importantly, emotional support throughout this ordeal: To Wieslawa Rawicz, who has given me the help when I most needed it; to Andrew Leung, for being the nicest person and for the liquid nitrogen; to David Knowles, for providing encouragement, comic relief and lamb chops; to Susan Tha, without whose assurance I would have seriously doubted the completion of this thesis; to Hans-Günter Döbereiner, for keeping me company in the lab during off-hours; to Ken Ritchie, who provides candies, cookies and comic relief of a more innocent nature and the list goes on I would also like to thank the members of my supervisory committee: Professors Boye Ahlborn, Ed Auld and Myer Bloom. They have been genuine scholars and gentlemen. x Chapter 1 Introduction The lipid bilayer is the fundamental component of all biological cell membranes. It is a condensed material that forms spontaneously as surfactant molecules of the right shapes (discussed later in this chapter) are introduced into an aqueous environment. Its struc ture consists of two mono-molecular surfactant layers that are weakly held together by van — der Waals attraction resulting in a molecularly thin composite (‘—i 4 nm) whose surface can extend to macroscopic dimensions (exceeding 10 im). Iii addition to its biological relevance, the unique properties of the bilayer have stimulated much interest in the com munity of condensed matter physics [Leibler, 1989; Bloom et al., 1991; Lipowsky, 1991]. Being a two dimensional condensed material, the bilayer exhibits a rich set of phases and phase transitions [Silver, 1985; Gennis, 1989]. In three dimensions, the 2-D fluid has properties of a liquid crystal — which has led to the “liquid crystal approach” to bilayer energetics [Helfrich, 1973]. The fluid membrane is also unique for its extraordinary flexi bility: Due to its “thinness”, the bilayer is a macroscopic body whose conformations are susceptible to molecular (thermal) agitations. For a flaccid membrane, thermally-driven surface undulations occur over a wide spectrum of wavelengths, with the macroscopic ones clearly visible under the light microscope. Such surface undulations tend to increase the configurational entropy of the system, giving rise to the notions of “entropy-driven forces” and “fluctuation-induced repulsions” when the undulations are either suppressed by a lateral tension or confined in a narrow gap [Helfrich, 1978; Lipowsky and Leibler, 1986; Evans and Rawicz, 1990].

Load more