Transfer of Small Molecules
Across Membrane-Mimetic Interfaces
A thesis submitted to the University of Manchester for the degree of Doctor of Philosophy in the Faculty of Engineering and Physical Sciences
2011
Matěj Velický
School of Chemistry List of Contents
Section Title Page List of Contents 2 List of Tables 5 List of Figures 6 Symbols 10 Abbreviations 14 Abstract 16 Declaration and Copyright Statement 17 Dedication and Acknowledgment 18 Chapter 1 Introduction 19 1.1 Drug Discovery 19 1.2 Parallel Artificial Membrane Permeation Assay 26 1.3 Permeation Assay under Hydrodynamic Control 29 1.4 Drug Absorption and pH-partition Hypothesis 31 1.5 Electrochemical Methods 33 1.5.1 Cyclic Voltammetry and Linear Sweep Voltammetry 33 1.5.2 Amperometry and Potentiometry 36 1.6 Liquid/Liquid Electrochemistry 37 1.6.1 Ion Transfer across Liquid/Liquid Interface 37 1.6.2 Ionic Partition Diagrams of Ionisable Drugs 42 1.6.3 Electron Transfer across ITIES 44 1.7 Bipolar Electrochemical Cell 46 1.8 Artificial Membrane Polarisation 48 1.9 Thesis Overview 50 Chapter 2 Materials, Equipment and Methods 52 2.1 Materials 52 2.2 Equipment 55 2.3 Methods 56 2.3.1 Permeation Assay under Hydrodynamic Control 56 2.3.2 Shake-Flask Method 60 2.3.3 Numerical Method 61 2.3.4 Permeation Assay with External Membrane Polarisation 62 2.3.5 Liquid/Liquid Electrochemistry 65 2.3.6 Rotating Bipolar Electrochemical Cell 73 2.3.7 Reference Electrodes 75
- 2 -
Section Title Page In Situ Artificial Membrane Permeation Assay under Chapter 3 79 Hydrodynamic Control 3.1 Introduction 79 3.2 Method Development 84 3.3 Analytical Transport Model 85 3.3.1 Derivation of the Analytical Transport Model 85 3.3.2 Permeability Terms 89 3.3.3 Permeability Hydrodynamic Model 90 3.3.4 Permeability-pH Dependence 92 3.3.5 Lag Time Determination 92 In Situ Time-Dependent Permeation and Numerical Transport 3.4 93 Model 3.5 Dependence of Effective Permeability on Stirring Rate 99 3.6 Permeability-pH Profiles 100 3.7 Permeability Hydrodynamics 110 3.8 Lag Time 115 3.8.1 Dependence on Stirring Rate 117 3.8.2 Dependence on Lipophilicity 120 3.8.3 Dependence on Concentration Gradient 121 3.9 Permeability Dependence on Concentration Gradient 123 3.10 Conclusions 125 Chapter 4 Permeation Assay with External Membrane Polarisation 127 4.1 Introduction 127 4.2 Experimental 130 4.3 Results and Discussion 131 4.3.1 Resistivity of the Permeation Cell 131 4.3.2 Open Circuit Potential Measurements 131 4.3.3 Cyclic Voltammetry on the Permeation Cell 134 4.3.4 Amperometric Measurements 143 4.4 Conclusions 148 Chapter 5 Prediction of Drug Absorption in Humans 150 5.1 Introduction 150 5.2 Experimental 155 5.2.1 Correction of Bioavailability for First Pass Hepatic Clearance 155 5.2.2 Correction for Paracellular Transport 156 5.2.3 Extrapolation of Effective permeability to Set Unstirred Water Layer 158 5.2.4 Absorption Data Dependence on Effective permeability 159 5.3 Correlation of Permeability Coefficients with Bioavailability 161 5.4 Conclusions 172
- 3 -
Section Title Page Chapter 6 Drug Transfer across Liquid/Liquid Interface 173 6.1 Introduction 173 6.2 Aqueous and Organic Electrolytes for Water/1,2-DCE System 177 6.3 Ion Transfer under Unstirred Conditions 180 6.3.1 Transfer of Fully Ionized Species across ITIES 180 6.3.2 Transfer of Partially Ionized Species across ITIES 188 6.3.3 Warfarin Water/1,2-DCE Partition Study 193 6.4 Drug Transfer Employing Rotating Membrane 198 6.5 Conclusions 203 Chapter 7 Reversible Electron Transfer in Rotating Bipolar Cell 204 7.1 Introduction 204 7.2 Experimental 207 7.3 Results and Discussion 208 7.3.1 Cyclic Voltammetry 208 7.3.2 Linear Sweep Voltammetry 209 7.4 Conclusions 214 Final Conclusions and Suggestions for Future Work 215 References 219 Appendix 233 A1 UV Spectra and Calibration Data of 31 Studied Drug Molecules 233 A2 Additional Optimization and Testing of the Permeation Cell 245 A3 Time-Dependent Permeation Profiles 252 A4 Additional Permeability and Lipophilicity Data 256 A5 ITIES Area Calibration 260 A6 Silver/Silver Sulphate Reference Electrode for L/L System 262
There are 59,468 words in this thesis, including endnotes and footnotes.
- 4 - List of Tables
No. Title Page Chapter 2 Purity of the BTPPATPBCl electrolyte verified by elemental 2.1 4 72 microanalysis Chapter 3 3.1 Lag time values for verapamil permeation at various donor pH 97 3.2 Lag time values of verapamil at different stirring rates and iso-pH 7.4/7.4 98 3.3 Permeability coefficients as function of the donor pH 101 Intrinsic and UWL permeability coefficients of warfarin, verapamil, 3.4 108 propranolol and cetirizine determined from permeability-pH dependence Comparison of the average intrinsic permeability values obtain from 3.5 109 hydrodynamic extrapolation and permeability-pH profile. Comparison of the unstirred water layer thickness determined from 3.6 114 hydrodynamic extrapolation, pH-profile and Levich equation Lag time and physicochemical properties of propranolol, quinine, 3.7 117 midazolam and verapamil. Permeability coefficients and the hydrodynamic exponent of propranolol 3.8 124 as a function of initial drug concentration in donor compartment Chapter 4 4.1 Molar ionic flux and ionic permeability coefficients 147 Chapter 5 Molar mass, charge state, pK , aqueous diffusion coefficient and absolute 5.1 a 154 human bioavailability of 31 selected drug molecules 5.2 Permeability coefficients of 31 studied drug molecules 165 Contribution of unstirred water layer, paracellular and transcellular 5.3 167 components to optimised effective permeability coefficient Chapter 6 Standard transfer potential, standard Gibbs energy of transfer, standard 6.1 partition coefficient and aqueous diffusion coefficient of perchlorate, 188 nitrate, iodide, TMA+ and TEA+ ions in water/1,2-DCE system 6.2 Partitioning of warfarin from the aqueous phase to 1,2-DCE 194 Appendix A1.1 Molar absorption coefficients of 31 studied drug molecules 233 A2.1 Effective permeability of verapamil for standard/reduced membrane area 251 Membrane retention and membrane diffusion coefficients of warfarin, A4.1 256 verapamil, propranolol, cetirizine as a function of donor compartment pH Membrane-donor distribution coefficients of warfarin, verapamil, A4.2 257 propranolol and cetirizine determined by shake-flask experiment A4.3 Membrane-donor distribution coefficients of 31 studied drug molecules 258 Membrane diffusion coefficients of 31 studied drug molecules determined A4.4 from membrane permeability and membrane/donor distribution 259 coefficients. Potential stability of reference electrodes prepared under various A6.1 263 conditions
- 5 - List of Figures
No. Title Page Chapter 1 1.1 LADMET concept of drug discovery 19 1.2 Structure of the small intestine in relation to drug absorption 23 1.3 Schematic of transport mechanisms across the epithelial cell monolayer 24 1.4 PAMPA method schematic 27 1.5 96-well microtitre plate used in PAMPA method 28 1.6 Schematic of a cyclic voltammogram in a redox couple system 34 1.7 Example of Randles-Ševčík plot 35
1.8 BTPPATPBCl4 38 1.9 Electric double layer formed at water/1,2-DCE interface 39 1.10 Potential profile across polarised water/1,2-DCE interface 39 1.11 Comparison of TMA+ transfer across ITIES and blank potential window 40 1.12 Ionic partition diagram of cetirizine in water/1,2-DCE system. 42 1.13 Detailed ionic partition diagram of cetirizine in water/1,2-DCE system. 43 1.14 Schematic of the ET between two redox couples across L/L interface 44 1.15 Schematic of the ET between two redox couples in the BEC 46 1.16 Schematic of the polarised artificial membrane permeation method 49 Chapter 2 Schematic diagram of the permeation cell used for in situ UV 2.1 57 measurement 2.2 Block scheme of the permeation and analysis procedure 60 2.3 Schematic diagram of the permeation cell with membrane polarisation 63 2.4 Block scheme of the membrane polarisation method 64 2.5 Schematic of the static L/L electrochemical cell 65 2.6 Schematic diagram of the rotating L/L electrochemical cell 67 2.7 Comparison of chloride and sulphate based electrolyte potential window 69
2.8 Metathesis reaction to produce the organic BTPPATPBCl4 electrolyte 70
2.9 Schematic of the organic BTPPATPBCl4 electrolyte preparation 71 2.10 Schematic diagram of the permeation cell modified to rotating BEC 73 Potential-time stability of the Ag/AgCl and Ag/Ag SO reference 2.11 2 4 76 electrodes 2.12 Potential-time dependence for Ag/AgTPBCl4 reference electrode 78
- 6 -
No. Title Page Chapter 3 Schematic diagram of the concentration profile across the donor- 3.1 85 membrane-acceptor tri-layer 3.2 Example of concentration-time plots for warfarin and verapamil 93 3.3 Numerical simulation of concentration profiles 95 3.4 Schematic diagram of membrane loading with hydrophilic/lipophilic drug 96 3.5 Dependence of the inverse of effective permeability on the stirring rate 99 3.6 Permeability – donor pH profile of warfarin 102 3.7 Permeability – donor pH profile of verapamil 103 3.8 Permeability – donor pH profile of propranolol 105 3.9 Permeability – donor pH profile of cetirizine 106 3.10 Hydrodynamic exponent α as a function of pH 110 3.11 Dependence of α on the membrane/buffer distribution coefficient 112 Permeation ln(k)-time plots of propranolol, quinine, verapamil and 3.12 116 midazolam 3.13 Permeation ln(k)-time plots of propranolol at donor/acceptor pH 7.4/7.4 118 3.14 Dependence of the lag time on the inverse angular velocity of stirring 120 Dependence of the lag time on the membrane/donor distribution 3.15 121 coefficient 3.16 Lag time dependence on the initial donor concentration 122 3.17 Permeability dependence on the initial donor concentration 123 Chapter 4 4.1 Schematic of the permeation of a molecule via different ways of transport 128 4.2 Composition of the aqueous and membrane phase 128 Open circuit potential difference between the acceptor and donor phase 4.3 132 measured for various membrane compositions (no drug) Open circuit potential difference between the acceptor and donor phase 4.4 133 measured for various membrane compositions (cetirizine) Cyclic voltammetry coupled with in situ UV measurement in the acceptor 4.5 135 (5 V to +5 V) 4.6 Plot of the time derivative of the absorbance against time 138 4.7 Cyclic voltammetry on the blank permeation cell 140 4.8 Cyclic voltammetry on the permeation cell containing 300 M cetirizine 142 4.9 Amperometry conducted simultaneously with in situ UV measurement 144 Overall charge passed through membrane in 10 min of amperometry 4.10 plotted against the applied potential difference between the acceptor and 145 donor phase
- 7 -
No. Title Page Chapter 5 5.1 Chemical structures of 31 selected drug molecules 153 5.2 Scheme of experimental/analytical method of drug absorption prediction 160 5.3 Correlation between fraction absorbed and effective permeability 161 Correlation between fraction absorbed and optimised effective 5.4 163 permeability Sum errors of optimized effective permeability – fraction absorbed 5.5 164 correlation
5.6 Correlation between membrane/aqueous phase distribution coefficient and 170 octanol/water distribution coefficient 5.7 Correlation between membrane/aqueous phase distribution coefficient and 171 octanol/water distribution coefficient (separate analysis) Chapter 6 6.1 Blank cyclic voltammograms on water/1,2-DCE interface 178 6.2 Perchlorate anion transfer across the ITIES 180 6.3 Randles-Ševčík plot of perchlorate anion transfer across the ITIES 181 Perchlorate anion transfer across the ITIES with internal reference 6.4 183 molecule 6.5 Nitrate anion transfer across the ITIES 184 6.6 Iodide anion transfer across the ITIES 185 6.7 Tetramethylammonium cation transfer across the ITIES 186 6.8 Tetraethylammonium cation transfer across the ITIES 187 6.9 Verapamil cation transfer across the ITIES 189 6.10 Warfarin anion transfer across the ITIES 190 6.11 Effect of mixing on peak current of warfarin transfer across ITIES 191 6.12 Scheme depicting warfarin partition at water/1,2-DCE interface 192 Effect of mixing on current reduced by employing organic phase pre- 6.13 193 saturation with warfarin 6.14 Partitioning of warfarin from the aqueous phase to 1,2-DCE 195 Partitioning of warfarin from aqueous phase to 1,2-DCE in presence of 6.15 197 tetraethylammonium cation in the aqueous phase 6.16 Tetraethylammonium partition spectra in 1,2-DCE 197 6.17 Cyclic voltammetry on the blank rotating liquid/liquid cell 199 6.18 Warfarin anion transfer across ITIES under unstirred conditions 200 6.19 Warfarin anion transfer across ITIES under controlled hydrodynamics 200 6.20 Propranolol cation transfer across ITIES under unstirred conditions 201 6.21 Propranolol cation transfer across ITIES under controlled hydrodynamics 202
- 8 -
No. Title Page Chapter 7 7.1 Geometry of rotating-disc electrode and permeation assay setup 205 7.2 Schematic of electrochemical reactions occurring on GC electrode surface 206 Cyclic voltammogram of 0.5 mM hexaammineruthenium(III) chloride 7.3 208 solution performed in BEC Linear sweep voltammogram of 0.5 mM hexaammineruthenium(III) 7.4 210 chloride solution performed in BEC 7.5 Levich plot of 0.5 mM hexaammineruthenium(III) reduction in the BEC 211 Linear sweep voltammograms of 0.5 mM hexaammineruthenium(III) 7.6 212 performed in BEC for 5 different paddle-rotating-disc electrode separation 7.7 Levich plot slope obtained for five different paddle-electrode distances 213 Appendix A1.1 UV absorbance spectra of 31 studied drugs 234 A2.1 Blank permeation experiment (no compound, buffer solution only) 246 Verapamil absorbance at pH 9.0/7.4 recorded in acceptor compartment as A2.2 248 a function of time for four different stirring rates A2.3 UV absorbance spectra of 10 mM aqueous buffers in de-ionized water 249 A2.4 UV absorbance spectra of the organic membrane components 250 Concentration-time plots for 31 studied drugs at donor/acceptor pH A3.1 252 6.5/7.4 A5.1 Determination of ITIES area via ion transfer of five different ionic species 260 Dependence of electrode potential stability on the charge and current A6.1 264 density A6.2 Potential of the silver/silver sulphate electrode in 0.1 M sodium sulphate 265 Potential response of the silver/silver sulphate electrode to the changing A6.3 266 logarithm of sodium sulphate concentration Potential response of the silver/silver sulphate electrode to the changing A6.4 267 logarithm of sodium chloride concentration
- 9 - Symbols
Roman symbols a, b permeability constants ai generic activity of the species i
o ai equilibrium activity of the species i in the organic phase o
w ai equilibrium activity of the species i in the aqueous phase w A generic membrane area
Ae working electrode area
Aint area of the liquid/liquid interface
Aλ solution absorbance at wavelength λ c generic concentration of a solute cA (cD) solute concentration in the acceptor (donor) phase, respectively cA(t) solute concentration in the acceptor phase at time t cD(0) initial solute concentration in the donor phase (at time = 0) cD(t) solute concentration in the donor phase at time t cD(τLAG) solute concentration in the donor phase at lag time
eq caq concentration of a drug in the aqueous after shaking
0 caq concentration of a drug in the aqueous phase prior to shaking ci concentration of the ion i cm(t) solute concentration in the membrane phase at time t credox concentration of the redox species
CLh first pass hepatic clearance D generic diffusion coefficient
Daq aqueous diffusion coefficient
Dm membrane diffusion coefficient
Dredox diffusion coefficient of the redox species E (electrode) potential E(t) electrode potential at time t E(Δφ) electric potential drop function E0 standard (electrode) potential
Ered (Eox) reduction (oxidation) peak potential, respectively
- 10 - 1/ 2 Eredox half-wave redox potential F Faraday constant F absolute bioavailability in humans
Fa fraction absorbed from intestinal lumen
Fg fraction escaping intestinal extraction
Fh fraction escaping hepatic extraction f(−) fraction of the anionic form of a solute f(+) fraction of the cationic form of a solute f(±/0) fraction of the neutral and/or zwitterionic form of a solute f0 neutral fraction of the solute
FR Renkin hydrodynamic sieving function G Graetz number
0, wo Gtr, i standard Gibbs energy of transfer of ion i between phases w and o H fitting constant h membrane thickness I current
Ilim (Ip) limiting (peak) current, respectively
Ired (Iox) reduction (oxidation) peak current, respectively J generic diffusive flux J(t) molar diffusive flux at time t
Ji molar flux of the ionic species i k function of concentration (permeability measurements) kB Boltzmann constant
Kd generic distribution coefficient
A Kd membrane/acceptor distribution coefficient
D Kd membrane/donor distribution coefficient
OCT Kd n-octanol/water distribution coefficient
KP permeability hydrodynamic constant
Ksp solubility product
Kδ unstirred water layer thickness hydrodynamic constant
Kτ lag time empirical constant l optical path
Mr molar mass
- 11 - n number of electrons involved in a reaction
NA Avogadro constant pH negative logarithm of the proton concentration pKa negative logarithm of the dissociation constant
Pe effective (measured) permeability coefficient
Pm membrane permeability coefficient
P0 intrinsic permeability coefficient
Pu unstirred water layer permeability coefficient
Pp paracellular permeability coefficient
AD Pe effective permeability coefficient (acceptor-to-donor transport)
DA Pe effective permeability coefficient (donor-to-acceptor transport)
AD Pm membrane permeability coefficient (acceptor-to-donor)
DA Pm membrane permeability coefficient (donor-to-acceptor)
AD Pi effective permeability coefficient of the ion i (acceptor-to-donor)
DA Pi effective permeability coefficient of the ion i (donor-to-acceptor)
o/w Pi partition coefficient of the species i between phases o and w
0, o/w Pi standard partition coefficient of the ion i between phases o and w Q charge
Qh hepatic blood flow R universal gas constant
Rf fractional membrane retention
Rf (∞) fractional membrane retention (at steady-state) rHYD solute‟s hydrodynamic radius
Rp pore radius S scaling factor T thermodynamic temperature t time
VA (VD) acceptor (donor) phase volume, respectively
Vaq (Vorg) volume of the aqueous (organic) phase, respectively
Vm membrane volume x generic distance zi charge of the ion i ΔE (electrode) potential difference
- 12 - Greek symbols
α hydrodynamic exponent β linear regression coefficient (hydrodynamic extrapolation)
δu unstirred water layer thickness ε molar absorption coefficient ε/δ porosity/path-length capacity factor η dynamic viscosity
κ function defined as F/NAkBT wavelength
w i chemical potential of the ion i in the aqueous phase w
0,w 0,o i ( i ) standard chemical potential of the ion i in phases w (o), respectively ~ i electrochemical potential of the ion i
~w ~o i ( i ) electrochemical potential of the ion i in phases w (o), respectively ν scan rate τ diffusion time constant
τint time constant of an interfacial transfer
τLAG lag time
τLAG, m lag time (arising from the partitioning/loading to a membrane)
τLAG, u lag time (related to transport in the unstirred water layer thickness)
τm time constant of diffusion through the membrane
τu time constant of diffusion through the unstirred water layer υ kinematic viscosity
Galvani potential
w o Galvani potential difference between phases w and o
w 1/2 o i half-wave transfer potential of the ion i between phases w and o
w 0 o i standard transfer potential of the ion i between phases w and o
w 1/ 2 oref half-wave potential of an internal reference molecule
w 0 oref standard transfer potential of an internal reference molecule
w ( o ) Galvani potential of the phase w (o), respectively Δφ electric potential drop at the channel surface (Caco-2 monolayer) ω angular velocity of stirring
- 13 - Abbreviations
1,2-DCE 1,2-dichloroethane ADME absorption, distribution, metabolism, excretion AgTPB silver tetraphenylborate
AgTPBCl4 silver tetrakis(4-chlorophenyl)borate BCS biopharmaceutics classification system BLM bilayer lipid membrane BTPPA+ bis(triphenylphosphoranylidene) cation BTPPACl bis(triphenylphosphoranylidene) chloride
BTPPATPBCl4 bis(triphenylphosphoranylidene) tetrakis(4-chlorophenyl)borate Caco-2 colorectal adenocarcinoma cell epithelial line CHES 2-(cyclohexylamino)ethanesulfonic acid CV cyclic voltammetry DC direct current DOPC dioleoyl phosphatidylcholine ET electron transfer GC glassy carbon GI gastrointestinal HTS high-throughput screening ISE ion-selective electrodes ITIES interface between two immiscible electrolyte solutions
KTPBCl4 potassium tetrakis(4-chlorophenyl)borate LADMET liberation, absorption, distribution, metabolism, excretion, toxicity LC/MS liquid chromatography/mass spectrometry L/L liquid/liquid MDCK Madin-Darby canine kidney epithelial cell line NPOE 2-nitrophenyloctyl ether OCP open circuit potential PAMPA parallel artificial membrane permeation assay BBB-PAMPA blood-brain barrier PAMPA BM-PAMPA bio-mimetic PAMPA DOPC-PAMPA dioleoyl phosphatidylcholine PAMPA
- 14 - DS-PAMPA double-sink PAMPA egg-PAMPA egg lecithin PAMPA HDM-PAMPA hexadecane PAMPA PET poly(ethylene terephthalate) PTFE polytetrafluoroethylene PVC polyvinyl chloride PVDF polyvinylidene fluoride RDE rotating-disc electrode SCE saturated calomel electrode SLM supported liquid membrane TATB tetraphenylarsonium tetraphenylborate TDDA+ tetradodecylammonium cation TDDABr tetradodecylammonium bromide
TDDATPBCl4 tetradodecylammonium tetrakis(4-chlorophenyl)borate TEA+ tetraethylammonium cation THATPB tetraheptylammonium tetraphenylborate TMA+ tetramethylammonium cation TMACl tetramethylammonium chloride TPB− tetraphenylborate anion − TPBCl4 tetrakis(4-chlorophenyl)borate anion UV ultraviolet UV-Vis ultraviolet-visible UWL unstirred water layer W− (HW) warfarin anion (neutral warfarin), respectively.
- 15 - University of Manchester
School of Chemistry
Matěj Velický
Doctor of Philosophy
Transfer of Small Molecules across Membrane-Mimetic Interfaces
October 6th 2011
Abstract
The presented thesis investigates the transfer of drug molecules across interfaces that mimic biological membrane barriers. The permeability of drug molecules across biological membrane mimics has been investigated in a novel artificial membrane permeation assay configuration using an in situ time-dependent approach and reproducible rotation of the membrane. A method to determine the membrane permeability from the knowledge of measured permeability and the applied stirring rate is presented. The initial transient of the permeation response, previously not observed in situ, is investigated and its importance in data evaluation is discussed. The permeability coefficients of 31 drugs are optimised for the conditions found in vivo and a correlation with the fraction absorbed in humans is presented.
The evidence for ionic and/or ion-pair flux across the artificial membrane obtained from measurement of permeability at different pH is supported by the investigation of the permeation assay with external membrane polarisation. The permeability coefficient of the solute‟s anionic form is determined.
Liquid/liquid electrochemistry has been used to study the transfer of ionized species across the interface between water and 1,2-dichloroethane. An alternative method to study the transfer of partially ionised drug molecules employing a rotating liquid/liquid interface is presented.
In addition, a bipolar electrochemical cell with a rotating-disc electrode is developed and its properties investigated in order to verify the hydrodynamics of the rotating artificial membrane configuration.
Finally, in support of the electrochemical techniques used is this thesis, a detailed preparation and evaluation of the silver/silver sulphate reference electrode is presented.
- 16 - Declaration
No portion of the work referred to in the thesis has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning.
Copyright Statement i. The author of this thesis (including any appendices and/or schedules to this thesis) owns any copyright or related rights in it (the “Copyright”) and he has given The University of
Manchester certain rights to use such Copyright, including for administrative purposes. ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as amended) and regulations issued under it or, where appropriate, in accordance with licensing agreements which the University has from time to time. This page must form part of any such copies made. iii. The ownership certain Copyright, patents, designs, trademarks and other intellectual property (the “Intellectual Property”) and any reproductions of copyright works in this thesis, for example graphs and tables (“Reproductions”), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such
Intellectual Property and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property
Rights and/or Reproductions.
iv. Further information on the conditions under which disclosure, publication and
commercialisation of this thesis, the Copyright and any Intellectual Property and/or
Reproductions described in it may take place is available in the University IP Policy, in
any relevant Thesis restriction declarations deposited in the University Library, The
University Library‟s regulations and in The University‟s policy on presentation of Theses.
- 17 - Dedication
I wish to dedicate this thesis to the memory of my grandfather, MUDr Milan Esler, a wise and noble man, whose life was one of the greatest inspirations to me.
Rád bych věnoval tuto disertační práci pamatce mého dědy, MUDr. Milana Eslera, moudrého a ušlechtilého člověka, jehož život byl pro mne jednou z největších inspirací.
Acknowledgement
First of all, I would like to acknowledge my supervisor Prof. Robert Dryfe for his tremendous help throughout the three years of my PhD research, expert guidance in the field of electrochemistry and also for his never-ending patience in revising of my various text submissions. Same acknowledgment goes to my industrial supervisor Dr. Kin Tam who provided me with an invaluable insight into drug discovery research. I also thank my industrial collaborator, AstraZeneca, and EPSRC for funding this project.
More thanks (but of no less value) go the following people who were involved in my research degree. Dr Matt Wood for training me in PAMPA method, Chris Slann for designing and manufacturing the equipment, Dr Dan Bradley for development of the numerical model, Dr Huong Ho for training in liquid/liquid electrochemistry, Dr Daniela
Plana and Dr Jeff Martin for their help and laugh in my early days, Adam „Vole‟ Cooper and Briony Setterfield-Price for the same in my late days, and finally all other people who were or are part of the electrochemistry group in School of Chemistry.
- 18 - Introduction
1.1 Drug Discovery
The current drug discovery process consists of drug candidate identification, synthesis, characterization, and screening of their physicochemical and biological properties. Drug discovery is a part of wider drug development process, which spans the invention of the molecule to the successful market entry. A major interest of the pharmaceutical industry is the orally administered drug. The candidate molecules are subjected to a drug discovery screening process that is designed to gather complex knowledge about the drug candidate in order to assess its ADME characteristics. ADME refers to Absorption, Distribution, Metabolism and Excretion of a drug molecule in the human body as shown in Fig. 1.1. Absorption comprises of administration, solubility and intestinal permeability of a drug molecule. Distribution to the target tissue is provided by the circulatory system. Metabolism of the drug is an adverse effect that most commonly occurs in the liver and in the intestine. Excretion describes the elimination of the excess drug, or its metabolites, after its biological action (urinary system). Recently, LADMET characteristics have been referred to, with an extension to Liberation of the active drug from an administration formula and Toxicity of a drug [1].
Figure 1.1 LADMET concept of drug discovery.
- 19 - Although pharmaceutical companies tend to have customised drug discovery pipelines, the physicochemical properties of interest and methods of their acquirement, however, are more or less standardised. Drug molecule solubility, dissociation constant, lipophilicity, permeability, hydrogen bonding, protein binding, etc., are amongst the most relevant physicochemical properties. Determination of these parameters is of interest to early drug discovery, which requires fast high-throughput screening (HTS) in order to narrow the fraction of potential drug candidates that are cleared to enter the late drug discovery stage of more complex assays including pre-clinical tests. Due to increasing need of HTS methods, the common trend is to replace complex and expensive in vivo assays with inexpensive in vitro and/or in silico equivalents, i.e. to put emphasis on the drug discovery stage rather than pre-clinical and clinical development. Unlike in vitro/silico methods, in vivo assays are usually not suitable for high-throughput screening.
On the other hand, in vitro and in silico methods often do not provide sufficient information about complex drug-biological system interaction [2]. Lipinski et al. introduced a guidance tool, rule of 5, to predict whether a substance is likely to become an orally active drug in humans based on its molar mass, octanol/water partition coefficient and hydrogen bonding properties [3]. The widely acknowledged Biopharmaceutics
Classification System (BCS) is based on the assumption that the same concentration profile of two drug substances in the gastrointestinal tract after oral administration will result in the same profile in the bloodstream. Dividing molecules into four groups depending on their solubility and permeability, BCS has proven to be a useful tool in crude drug classification for drug discovery applications [4, 5]. These simple classification rules, however, do not provide complete information on the molecular potency to become a marketed drug. In order to correctly rank the likeliness of the drug candidate to fail or succeed in the pre-clinical development, a series of in silico and in vitro assays is applied
- 20 - at the drug discovery stage [6]. The most common in silico and in vitro HTS methods implemented in the drug discovery pipeline are reviewed in [7].
The administration of a drug is crucial to its later fate in the human body. Oral administration is most common but there are other ways of administration including intravenous, inhalational, topical, etc. Intravenous administration is most advantageous as the bioavailability of a drug reaches 100% unless it is otherwise metabolised, and it is therefore the standard against which the other methods of administration are referred to.
Bioavailability is defined as the fraction of an administered dose of unchanged drug that reaches the systemic circulation. Drug solubility usually varies with the ambient pH and the concentration of other species. For the oral route, the transport of a drug through the gastrointestinal (GI) tract and then absorption to the bloodstream is considered. The pH of the GI tract ranges from about 1 in the stomach to 6.5 in the gut whereas bloodstream pH is about 7.4. In the case of a monoprotic ionisable drug, the knowledge of its charge state can be used to calculate the fraction of neutral species, f0, using the Henderson-
Hasselbalch equation:
1 f0 (1.1) (110(pHpKa ) )
The logarithm of the dissociation constant, pKa, is an important physicochemical parameter and various methods of its determination have been developed, ranging from potentiometry, UV-Vis spectrophotometry, liquid chromatography, NMR titration, capillary electrophoresis to computational methods [8-12]. A large fraction of ionized species will result in higher solubility in the aqueous phase (GI tract or bloodstream) but will decrease the rate of drug transfer across the lipophilic gut wall according to the pH- partition hypothesis [13], which is described later. Lipophilic drug molecules, on the other hand, will easily transfer across the gut wall but poor solubility will limit their absorption
- 21 - [14]. Assessment of drug lipophilicity has become a standard screening method in drug
o/w discovery with the model system being n-octanol/water. The partition coefficient, Pi , of a species i between the organic phase o and aqueous phase w is defined as follows:
o o/w ai log Pi log w (1.2) ai
o w where ai and ai are equilibrium activities of species i in the organic and aqueous phase, o and w, respectively. Methods to determine the octanol/water partition coefficient include the traditional shake-flask method or more advanced methods such as potentiometry, liquid chromatography or high-throughput membrane measurement [15-20] to overcome the limitations of the traditional approach [21]. Also, in silico methods to predict the octanol/water partition coefficient based on molecular solvatochromic properties such as dipolarity/polarisability, hydrogen bonding properties, and the intrinsic molar volume, have been developed [22-24].
Fig. 1.2 shows the structure of the small intestinal wall, where the major part of the drug absorption takes place. The interior of the small intestine has a tubular shape with circular protuberances. These formations consist of conical shaped filaments called villi, which increase the apparent absorption area of the intestinal wall. The monolayer of epithelial cells of the villus is the permeation barrier between the intestinal lumen fluid and blood capillaries.
The gastrointestinal tract provides mechanical stirring that enhances the absorption of the drug, which occurs mainly in the small intestine [25]. Similarly, on the opposite side of the intestinal wall the bloodstream convection enhances transport of the drug from the membrane to circulatory system. The mixing pattern in the GI tract gives rise to the unstirred water layer (UWL), i.e. the layer where the drug transport is merely governed by diffusion [26], and its thickness is dependent on the intensity of stirring and rate of drug
- 22 - permeation across the cell barrier. The UWL arising adjacent to the intestinal wall then effectively acts as a diffusion barrier for the drug. It was thought originally that the UWL thickness was about 600 μm and therefore the intestinal lumen was poorly stirred [27].
Figure 1.2 Structure of the small intestine in relation to drug absorption. (used with permission of Encyclopædia Britannica, Inc.)
An improvement in analytical techniques in later years allowed determination of the UWL thickness in human jejunum as ~ 30 – 200 μm [28, 29]. The methods of determination of the UWL thickness in vitro have been reviewed elsewhere [30]. A report on drug in vitro permeation across supported liquid membrane (SLM) that employed accurate stirring rates suggested that UWL thickness not only varied with applied stirring but was also strongly dependent on the drug lipophilicity [31].
The human gut wall consists of a tight monolayer of epithelial cells formed into conical shape to increase the available surface. There are three possible mechanisms of drug transfer across the epithelial cell wall as shown in Fig. 1.3. Paracellular transport refers to diffusion of a molecule through the tight junction between the epithelial cells. It depends on the pore size as well as the size and charge of the diffusing molecule. For
- 23 - large molecules with molar mass larger than 200 – 250 g mol−1 this process is regarded as less likely [32], although some reports state molar mass of 100 g mol−1 to be the threshold for paracellular transport [33]. Active transport, i.e. carrier-mediated cellular uptake, is governed by the presence of transport proteins specifically binding to a molecule and mediating its transfer between the apical and basolateral side of the membrane [34].
Finally, transcellular transport is the permeation of a drug directly across both apical and basolateral membranes of the epithelial cells. An ideal drug candidate will dissolve before it reaches the active absorption surface in the GI tract, where it will cross the gut wall either due to its high lipophilicity (transcellular transport), small size (paracellular) or via interaction with membrane proteins (active transport). Combination of all three transport means is a common phenomenon in drug absorption mechanisms.
Figure 1.3 Schematic of transport mechanisms across the epithelial cell monolayer. The blue diamond represents the drug molecule (taken from http://en.wikibooks.org).
It is evident that permeation of the drug candidate across the lipid membrane of the epithelium is one of the main interests in drug discovery. Lipid bilayers have been
- 24 - intensely studied using various experimental techniques since 1920‟s [35, 36] and also gained considerable attention in computational chemistry since early 1980‟s [37-39].
Attempts have been made to use bare lipid bilayer membrane (BLM) or solid-supported lipid bilayer for permeation studies [40, 41]. However, because the lipid bilayers are very fragile, various models using mixtures of organic solvents and lipids immobilized in membranes have often been explored instead. This approach gave rise to screening methods based on permeation of the drug across an organic filter separating two aqueous compartments. Caco-2 and MDCK assays employ heterogeneous human epithelial colorectal adenocarcinoma and Madin-Darby canine kidney cell monolayer, respectively, immobilized on a hydrophobic filter [42-45]. Caco-2 became a popular assay that is capable of prediction the rate of absorption in humans [46] and usually is placed in the intermediate discovery pipeline. The optimum conditions for in vitro trans-monolayer permeability assays were discussed by Youdim et al. [47]. The high cost and low throughput of these methods combined with time-consuming and condition-sensitive cell culture growth gave rise to the Parallel Artificial Membrane Permeation Assay (PAMPA), in which the cell culture is replaced by a lipid solution. Often PAMPA and Caco-2 methods complement each other in the same discovery setting, both having their benefits and disadvantages [44].
- 25 - 1.2 Parallel Artificial Membrane Permeation Assay
Since 1998, the PAMPA has become widely used by many pharmaceutical companies as a tool for the rapid assessment of drug permeability. As first described by
Kansy et al. [32], the method is based on passive diffusion of a molecule between two aqueous compartments separated by an artificial membrane soaked with a lipid solution in an organic solvent. The assay was originally designed to mimic the transcellular transport of orally administered drugs across the intestinal epithelium. The schematic of the assay concept is shown in Fig. 1.4. The two aqueous phases, donor and acceptor, model the physicochemical conditions in the small intestine (pH 6.5) and bloodstream (pH 7.4), respectively. In the following years, the organic phase immobilized within the membrane has been varied from the original use of egg lecithin in n-dodecane (egg-PAMPA) to modified composition such as dioleoyl phosphatidylcholine in dodecane (DOPC-PAMPA)
[48], complex Double-Sink method (DS-PAMPA) [8, 49, 50], n-hexadecane alone (HDM-
PAMPA) [51], mixtures of lipids dissolved in 1,7-octadiene in a „bio-mimetic‟ PAMPA
(BM-PAMPA) [52] and many others in order to mimic specific properties of biological membranes. The chemical selectivity and permeability levels of DOPC-, HDM- and DS-
PAMPA models were compared in [53]. A highly stable lipid/oil/lipid tri-layer membrane
PAMPA design with an option of long-term storage of pre-soaked membrane filters, showed a good correlation with human absorption data [54]. Flaten et al. showed how phospholipids vesicles immobilised on the hydrophobic filter could be an alternative barrier to drug permeation [55-57]. Seo et al. studied the effect of lipid structure on membrane fluidity and drug permeability [58]. Research on PAMPA also extends to non- oral absorption. Di et al. introduced porcine brain extract dissolved in n-dodecane to mimic the blood-brain barrier (BBB-PAMPA) [59] and Sinko et al. attempted to predict transdermal penetration of drugs [60]. Modified PAMPA has also found use in other application, such as evaluation of bioaccumulation of chemicals in fish [61].
- 26 - The methods of detection of the permeating analyte vary from the low-cost and fast in situ ultraviolet (UV) spectrophotometry to more selective liquid chromatography/mass spectrometry (LC/MS) methods. The reason for choice of LC/MS is mainly the large number of „difficult‟ molecules, which are unsuitable for UV analysis, although alternative methods have been developed to overcome these issues [62].
Figure 1.4 PAMPA method schematic
As reviewed above, many approaches and assay parameters have been described
[50], but the main principle of the method, however, remains the same. The assay, employing a commercial 96-well microtitre plates, enables the study of a large set of molecules in one experimental batch (Fig. 1.5). A drug molecule, originally present in the aqueous donor compartment diffuses across the hydrophobic membrane to the aqueous acceptor compartment and its concentration is then detected by an appropriate analytical technique. The drug lipophilicity, molecular size, pH and composition of the aqueous compartments, use of co-solvents, membrane structure and temperature are some of the most important parameters affecting the permeation [8, 63, 64]. The high-throughput screening PAMPA method only allows ex situ analysis of the donor and acceptor compartment. The real kinetic permeation profile therefore remains unknown, although
- 27 - construction of permeation curves from sample measurement at different time points is possible [8].
Figure 1.5 96-well microtitre plate used in PAMPA method.
The importance of the UWL thickness in vivo resulted in implementation of individual-well stirring to the PAMPA method [65]. Following this work, a permeation method prototype that controls hydrodynamic conditions (and therefore UWL thickness) in both donor and acceptor compartment was recently introduced by this research group
[31, 66]. The three different modes of transport across the intestinal epithelium were discussed above. Sugano et al. was first to implement a paracellular transport component in the PAMPA model to extend its predictability towards small molar mass molecules [67], an approach level followed by others [68]. The detailed analysis of the transcellular, paracellular and UWL transport across Caco-2 cell monolayers has been reported by
Adson et al. [69]. The use of controlled hydrodynamics and implementation of paracellular transport model has been investigated as a major part of this thesis.
Beside the PAMPA assay, other applications of supported liquid membranes or different relevant approaches and have been studied. These include electrokinetic migration across the SLM [70], the fluorescence method of charged compound transfer across liposome membrane bilayers [71], colorimetric screening of drug permeation through lipid barriers [72] or partitioning studies of liposome/micelle systems [73-75].
- 28 - 1.3 Permeation Assay under Hydrodynamic Control
Although PAMPA is a high-throughput method widely used in the drug discovery pipeline, it has been discussed whether it has indeed significant advantages over other permeability assays such as Caco-2 [76]. Earlier, we have mentioned two fundamental issues related to PAMPA, specifically:
A. it relies upon ex situ analysis of a drug molecule.
B. contribution of the unstirred water layer to permeation is not taken into account.
Molloy et al. have developed a novel hydrodynamic approach to membrane permeability in order to overcome both these limitations of PAMPA [66]. This novel method was derived from the concept of the rotating-disc electrode (RDE), a system commonly used in electrochemistry [77, 78]. As a part of this thesis, the hydrodynamic method was validated and optimized on an experimental and theoretical basis [31].
The novel method, which implements features of both the original PAMPA and RDE, allows in situ study of the drug molecule permeation under hydrodynamic control and the assessment of the membrane permeability coefficient, Pm, by reducing the influence of the
UWLs. This is achieved by rotating the membrane at an adjustable frequency and thus introducing reproducible convective conditions to both sides of the membrane. The
−1 measured effective permeability coefficient, Pe (cm s ), is a net rate constant describing molecule transfer from the donor compartment across the artificial membrane to the acceptor compartment. If we assume that Pe consists of three terms, that is transport through two UWLs, transport through the membrane and interfacial transfer between the aqueous and organic phase, then for the diffusion time constant, τ, of the drug molecule diffusion from the bulk donor to bulk acceptor compartment we have:
2 u m 2int (1.3)
- 29 - where τu and τm are the time constants of diffusion in the UWL and membrane, respectively, and τint is the time of an interfacial transfer between the aqueous and organic phase. We can assume that the interfacial transfer term is always much lower compared to the previous two [79]. Another assumption in Eq. (1.3) is that the transfer is identical in both UWLs. For the effective permeability coefficient (which is an inverse of time constant normalized to the permeating distance) we can therefore write [80-83]:
1 2 1 2 1 u (1.4) Pe Pu Pm Daq Pm
where Pu and Pm are the permeability coefficients in the unstirred water layer and in the membrane, respectively, Daq is the diffusion coefficient of the drug molecule in the aqueous phase and δu is the UWL thickness. For the stirred system the UWL thickness δu is given by [77] :
1/ 2 u K (1.5)
where Kδ is a constant consisting of the donor/acceptor kinematic viscosity and the diffusion coefficient of the solute in the aqueous phase and ω the angular velocity of the stirring, defined in Eq. (3.16).
Consequently, a plot of the inverse effective permeability coefficient, 1/Pe,
−1/2 obtained under different stirring rates against ω , allows 1/Pe to be extrapolated to infinite angular velocity of stirring (i.e. zero UWL) and the first term of the right-hand side of Eq. (1.4) becomes zero. In this case Pe = Pm, yielding 1/ Pm as the intercept of Eq.
(1.4). One can thus determine the membrane permeability of a drug molecule, and moreover, from knowledge of the effective permeability dependence on stirring rate, the effective permeability for any given stirring rate or UWL thickness can be determined.
- 30 - 1.4 Drug Absorption and pH-partition Hypothesis
The oral bioavailability of a molecule is defined as the rate and extent to which an active drug substance is absorbed and becomes available to the general circulation [84].
The drug will reach 100% absolute oral bioavailability if the concentration profiles of oral and intravenous administration are the same. Usually, only data for the drug substances that successfully made it to pre-clinical and clinical drug development are available, as obtaining bioavailability data requires in vivo experiments on human subjects. Amidon et al. estimated human oral drug absorption based on its correlation with the rat intestinal permeability [85]. Parrott et al. overviewed the strategies of the intestinal absorption model development based on physiological data [86]. A mechanistic quantitative structure-activity relationship analysis of human intestinal absorption including transcellular and paracellular absorption component and transport through UWL has been performed by
Reynolds et al. [87].
An alternative to measurement of the oral bioavailability is determination of the intestinal permeability. Human intestinal permeability is determined by the intestinal perfusion technique in which the disappearance rate of the drug molecule from the perfused segment of small intestine is measured [88]. The disadvantage of this in vivo technique, i.e. requirement of awake and non-sedated human subjects (sadly, PhD students, usually), is balanced by the fact that the intestinal permeability provides information directly comparable with in vitro Caco-2, MDCK and PAMPA data. The review on intestinal permeability data and its relevance to bioavailability by Lennernäs et al. showed there is need for more in vivo studies in order to understand the complex interplay of drug transport mechanisms [89]. Intestinal permeability data analysis also showed that large hydrophilic molecules are hardly transferred across the intestinal epithelium unless they are substrates for mediated (active) transport. Also, a threshold of
300 g mol−1 for the molar mass of drugs transferred via paracellular transport was stated.
- 31 - The commonly acknowledged pH-partition hypothesis, described by Jacobs in
1940 [90], assumes that only the neutral fraction of a weak electrolyte can cross the cell membrane. This hypothesis was extended to transport across biological membranes by
Shore et al., who published work on gastric secretion of drugs [13]. This report studied the appearance of drug molecules in gastric juices of dogs after intravenous administration of the drug. As the drug concentration changed with its dissociation constant, it was deduced that only the non-ionised fraction of the drug molecule could be absorbed through the cell membranes. This assumption was applied to drug transport across the intestinal epithelium by the same research group [14] and also tested in alternative systems such as diffusion through polymeric membranes [91]. The pH-partition hypothesis is a good rule of thumb for permeation/partition of drugs. It was, however, criticised for being an oversimplification and neglecting the fact ionised species also permeate biological membranes, albeit at much slower rates than non-ionised species [92]. A number of reports in the 1990‟s showed an evidence of partitioning of the ionized form of drug molecules to phosphatidylcholine bilayers [93-95]. A non-ideal behaviour of sparingly soluble drugs, originated in the uneven changes in solubility and permeability, was also observed in permeation experiments with excipient molecules added [96]. In addition, paracellular transport through the tight junctions in the intestinal epithelia was shown to be more common for the cationic than other forms of drug molecules [97]. Similar observations were made for the epithelial monolayer in the Caco-2 assay, where significant transport of the ionised fraction was found when the neutral fraction concentration dropped to less than 10% [98].
- 32 - 1.5 Electrochemical Methods
Electrochemistry studies chemical reactions taking place in a solution at the interface of an electron and/or ionic conductor by applying an external potential difference across the interface and measuring the associated current response. Alternatively, the potential difference can be recorded as a function of an applied current. An example of an electrochemical process is oxidation and/or reduction of an electroactive species at a solid electrode. The electrochemical methods employed in this thesis include cyclic voltammetry, linear sweep voltammetry, amperometry and potentiometry. Comprehensive description of these methods can be found elsewhere [77, 78, 99]. The principles underlying them will only be briefly presented below.
1.5.1 Cyclic Voltammetry and Linear Sweep Voltammetry
Cyclic voltammetry (CV) is one of the many electrochemical methods that fall into the potential-sweep voltammetry family. CV is a potential-controlled method, usually using a three electrode system. The potential difference is applied between the working and reference electrode, whereas the current is measured between the counter and working electrode. Cyclic voltammetry satisfies the condition of Eq. (1.6), i.e. linear dependence of potential on time. The relationship between the current, I, and potential, E, is called the polarisation curve (1.7).
E(t) E(0) t (1.6)
I f (E) (1.7) where E(t) is the potential at time t, E(0) is the potential at time t = 0 and ν is the scan rate, i.e. dE/dt (sometimes called polarisation rate).
- 33 - Cyclic voltammetry, as its name indicates, uses a cyclic potential waveform. It consists of two parts – a forward and reverse sweep. The forward sweep can be either anodic (increasing potential) – then the reverse is cathodic (decreasing potential) – or the forward sweep is cathodic with a reverse anodic sweep. A cyclic voltammetry scan, also called a cyclic voltammogram, represents the polarisation curve of Eq. (1.7). Fig. 1.6 shows a cyclic voltammogram obtained from a solution phase redox couple.
Figure 1.6 Schematic of a cyclic voltammogram in a redox couple system.
Due to the process kinetics, an optimal starting potential, E(0), needs to be considered for every system. Usual practice is to start in the potential region where no charge transfer occurs – that is between +0.6 and +0.7 V in the case of the CV shown in
Fig. 1.6. Cyclic voltammetry is a very useful electrochemical method with high information content. In Fig. 1.6, one can see two characteristic peaks which correspond to the diffusion of the reduced and oxidised form of a redox couple, respectively. The half-
1/ 2 wave potential Eredox (an average of the oxidation and reduction peak potentials, Eox and
- 34 - Ered , respectively) is specific to the studied redox species and the oxidation (reduction),
whereas the peak current Iox ( I red ) provides information about its quantity. For a
reversible charge transfer reaction, the peak current, I p Iox Ired , is governed by the
Randles-Ševčík equation [77]:
1/ 2 nF 1/2 1/ 2 I p 0.4463 nFAeDredoxcredox (1.8) RT
where n is the number of electrons involved in the charge transfer, R = 8.314
J mol−1 K−1 is the universal gas constant, F = 96485 C mol−1 is the Faraday constant, T is the thermodynamic temperature, Ae is the interfacial area between the working electrode and electrolyte solution, Dredox is the diffusion coefficient of the redox species in the electrolyte, credox is the concentration of the redox species and is the scan rate. An example of a Randles-Ševčík plot that can be used for determination of the diffusion coefficient of the redox species is shown in Fig. 1.7.
Figure 1.7 Example of Randles-Ševčík plot.
- 35 - Linear sweep voltammetry consists of one linear potential sweep either in forward
(anodic) or reverse (cathodic) direction. It is essentially a half of the full cyclic voltammogram. This technique is suitable for analysing the rotating-disc electrochemical systems referred to earlier, where a limiting current value rather than a peak current value is measured. The limiting current, Ilim, can be related to the applied stirring rate via the
Levich equation (providing that low scan rates are used to ensure reversible charge kinetics and steady-state mass transport) [100]:
2/3 1/ 6 1/ 2 Ilim 0.62nFAe Dredoxcredox (1.9) where υ is the kinematic viscosity of the electrolyte solution and all the other symbols have the meaning defined previously.
1.5.2 Amperometry and Potentiometry
Amperometric methods are a subclass of voltammetric methods that employ measurement of current while the potential is held at a constant value. The data representation of an amperometric measurement is most commonly a current response as a function of time, i.e. chronoamperometry. Potentiometry, i.e. potential measurement can be either galvanostatic (constant applied current) or at zero current potential (potential measured without passing current through the working electrode).
Amperometric and potentiostatic methods were use in preparation and analysis of the reference electrodes, respectively.
- 36 - 1.6 Liquid/liquid Electrochemistry
In contrast to the common electrochemical methods employing (normally) a working electrode placed in the electrolyte solution where electrons are transferred across a solid/liquid interface, liquid/liquid (L/L) electrochemistry introduces a system where the working electrode is replaced by another liquid phase. The term for such a system is
ITIES (Interface between Two Immiscible Electrolyte Solutions). Both „ITIES‟ and „L/L interface‟ are used interchangeably to describe the interface between two liquids, which must be immiscible (or at least of well-restricted miscibility) and suitable electrolyte must exist for each liquid. Most common liquid/liquid electrochemical systems consist of an aqueous phase and an organic phase such as 1,2-dichloroethane (1,2-DCE) or nitrobenzene. Unique properties of the L/L interface compared to the surface of a solid electrode led to various applications such as particle deposition on the L/L interface, electron/ion transfer across the L/L interface and L/L extraction of ionized drugs [101-108].
1.6.1 Ion Transfer across Liquid/Liquid Interface
Drug transfer across L/L interfaces has been of interest in pharmacokinetics for about two decades [15, 17, 109, 110]. Determination of lipophilicity of drug molecules became the main pharmaceutical application of the ion transfer across the interface between two immiscible electrolyte solutions. Water/1,2-dichloroethane is the most commonly used system for L/L electrochemistry due to the unique balance between limited miscibility of the two phases and facile polarisability of the resultant interface. Water/nitrobenzene is a common alternative system in liquid/liquid electrochemistry [111]. The pharmaceutical standard, water/n-octanol system, has proven difficult to study using electrochemistry due to the high resistivity of this organic phase. Nevertheless, advanced techniques using a nanoscopic water/ n-octanol interface were successfully investigated [112, 113]. As a part of this thesis, transfer of selected drugs across the water/1,2-dichloroethane interface has
- 37 - been investigated under both unstirred and stirred conditions. The stirred system, with hydrodynamically controlled conditions given by an adaptation of the rotating-disc electrode, provides a new methodology for the determination of ionisable solute‟s diffusion coefficient, which has been, to the best of our knowledge, hardly covered in the literature.
Figure 1.8 bis(triphenylphosphoranylidene) ammonium tetrakis(4-chlorophenyl)borate
In order to carry out electrochemistry on the L/L system, an electrolyte is needed to facilitate charge transfer in both phases. Common electrolytes such as LiCl or Na2SO4 with high charge density are suitable as electrolytes in the water (polar) phase. In a non- polar organic phase, however, more lipophilic ions are needed. A common choice is bis(triphenylphosporanylidene) ammonium (BTPPA+) or tetraalkylammonium as the
cation and tetraphenylborate (TPB ) or tetrakis(4-chlorophenyl) borate (TPBCl4 ) as the anion of the organic electrolyte. An example of such an electrolyte is shown in Fig. 1.8.
For the cyclic voltammetry at the ITIES, one measures the potential differences
w (between two phases) denoted o , rather than the potential, E (as in standard electrochemistry). The existence of two different electrolyte ion pairs in the aqueous and organic phase, provided that the ions remain in their respective phases, allows application of a potential difference between two liquids without transferring any ion across the interface. This condition is maintained within the range of potentials called the
- 38 - w „potential window‟ (see below). Applying a Galvani potential difference, o , across the interface allows the electric double layer adjacent to the L/L interface to be established as shown in Fig. 1.9. We thus say that the interface is polarisable. The electric double layer is usually a few nanometres thick on the aqueous side (thicker on the organic side, depending on the solvent relative permittivity) and contains an excess of respective ions depending on the sign of the applied potential [114].
Figure 1.9 Electric double layer formed at water/1,2-DCE interface. The applied potential makes water more positive than 1,2-DCE in this case and the ITIES attracts − sodium and tetrakis(4-chlorophenyl)borate anions (TPBCl4 ) in their respective phases.
Providing the electrolyte ions remain in their respective phases, the electro-neutrality in bulk solution remains preserved and the potential profile across the ITIES resemble the one shown schematically in Fig. 1.10.
Figure 1.10 Potential profile across polarised water/1,2-DCE interface
- 39 - The existence of the potential region where no electrolyte ions are transferred allows application of a potential difference across the interface without the passage of
Faradaic currents. One can therefore analyse other processes occurring at the ITIES, such as transfer of ions that transfer within the potential region defined by the electrolytes, electron transfer or electrodeposition. The electrolyte ions, however, have limits to their non-transferability and a certain transfer potential exists for every ion. In practise, a
„potential window‟, i.e. potential region of current vs. potential independency limited by electrolyte cation (anion) transfer to the phase with more negative (positive) potential, respectively, is considered. Introduction of an ion, whose transfer potential lies within the potential window results in the detection of current corresponding to the transfer of the ionic species from one phase to another. The comparison of a blank potential window cyclic voltammogram (only aqueous and organic electrolytes are present in the system) and a cyclic voltammogram of the tetramethylammonium cation (TMA+) transfer across
ITIES is shown in Fig. 1.11.
Figure 1.11 Comparison of TMA+ cation transfer across ITIES (red curve) and blank potential window (black curve) in the same system using cyclic voltammetry. Measured in cell Ag|Ag2SO4| 30 mM Na2SO4, 0.3 mM TMACl, pH 7.4 (aq)| 15 mM TDDATPBCl4 −1 (1,2-DCE)| AgTPBCl4|Ag, scan rate 40 mV s . Start potential +0.2 V.
- 40 - There are two current onsets on the black curve in Fig. 1.11. The onset of current at the more positive potential differences (+0.7 V) is associated with sodium cation transfer from water to 1,2-DCE (estimated from comparison of standard Gibbs energies of
+ − − [115, 116] transfer of Na and TPB /TPBCl4 ). Similarly the onset at the lower (close to 0 V) potential difference represents sulphate anion transfer from water to 1,2-DCE (estimated from the standard Gibbs energy of transfer of tetradodecylammonium (TDDA+) cation, which was extrapolated from the tetra(methyl-hexyl)ammonium series data [117]). The red curve represents the TMA+ cation transfer back and forth between the water and 1,2-DCE phase. By applying a positive potential difference between the aqueous and organic phase, starting from +0.2 V, TMA+ transfers from the aqueous phase to 1,2-DCE showing a current peak with maximum about +0.52 V. A similar peak is observed on the reverse scan, i.e. when the organic phase becomes positive again and forces the TMA+ cation back to the aqueous phase. The initial sweep direction is important when considering the type of ion transferred across ITIES. The Randles-Ševčík equation, modified for the ion transfer across ITIES, was used for the determination of the aqueous diffusion coefficient:
1/ 2 zF 1/2 1/ 2 I p 0.4463 ziFAintDaq ci (1.10) RT
where zi is the charge of the transferred ion i, Aint is the ITIES area, Daq is the redox species diffusion coefficient in the electrolyte, ci is the bulk concentration of the ion i and other symbols have the meaning defined previously. The ion transfer of inorganic and organic ionic species under stationary and stirred conditions will be discussed in
Chapter 6.
- 41 - 1.6.2 Ionic Partition Diagrams of Ionisable Drugs
We have shown the importance of pH conditions to drug absorption in vivo. In a similar manner, when investigating the transfer of ionisable drugs across the ITIES, pH is an important condition to consider. In 1996, Reymond et al. introduced a theoretical method of construction of „ionic partition diagrams‟ [118]. Ionic partition diagrams become a useful tool to visualize the partitioning of various forms of an ionisable drug across the
ITIES [110, 119]. It allows representation of the species that predominantly exist depending on the Galvani potential difference across ITIES and pH of the aqueous phase, two main parameters of the ionic transfer. The ionic partition diagrams are a liquid/liquid electrochemistry adaptation of the well-known Pourbaix diagrams, commonly used in corrosion science [120]. The example of an ionic partition diagram of the zwitterionic antihistamine drug cetirizine taken from [121] is shown in Fig. 1.12.
Figure 1.12 Ionic partition diagram of cetirizine in water/1,2-DCE system at 25 °C. Taken from reference [121].
- 42 - [122] Cetirizine has three pKa values, 2.12, 2.90 and 7.98 and is present in five different
2+ + + − forms, XH3 (trihydrogen cation), XH2 (dihydrogen cation), XH (neutral form), X H
(zwitterionic form) and X− (cetirizine anion), in the aqueous solution. The fraction of the zwitterionic form is negligible in comparison to the neutral fraction [122]. The ionic partition diagram in Fig. 1.12 shows the structure of cetirizine and domains of predominance of the four charged states of the molecule. The solid lines denote the equiconcentration domains between transition from one charged state to another in the same phase or transfer of the same species across the ITIES. The vertical lines denote the dissociation equilibrium between charge states of cetirizine in the aqueous phase at pH = pKa. The horizontal lines denote the ion transfer between the aqueous and organic phase at standard transfer potential. Finally the lines with a finite gradient represent the potential and pH dependent transfer of species across the ITIES that involve an exchange of proton.
A detailed ionic partition diagram depicting the transfer mechanism of the charge states of cetirizine in the pH range 0 – 5 is shown in Fig. 1.13.
Figure 1.13 Detailed ionic partition diagram showing transfer mechanisms of charge states of cetirizine in water/1,2-DCE system at 25 °C. Taken from reference [121].
- 43 - The partitioning of the different charged forms of the partially ionized drug molecule is an important phenomenon that needs to be considered when studying transfer of its ions across the ITIES. As will be shown in sections 6.3.2 and 6.3.3, the partitioning of the drug neutral fraction (however negligible compared to the ionized fraction) from the aqueous to the organic phase disturbs the concentration equilibrium at the ITIES and hinders quantification of the ion transfer using conventional methods. To be more specific, the direct determination of the aqueous ionic diffusion coefficient using cyclic voltammetry (via Eq. 1.12) becomes impossible because of the simultaneous variation in the solute concentration. We present an alternative method employing stirring of the
ITIES that enables correct quantification of the ion transfer process.
1.6.3 Electron Transfer across ITIES
Another application of liquid/liquid electrochemistry is electron transfer (ET) across the ITIES [105]. Due to the molecular nature of the L/L interface, there is an absence of dislocation or reconstruction forces common at solid surfaces, and the ITIES represents a unique system for the investigation of heterogeneous electron transfer [123]. Unlike the transfer of an ionic species, the ET rate across the ITIES is often kinetically limited [102].
The schematic in Fig. 1.14 shows the electron transfer processes between two redox couples separated by the aqueous/organic interface.
Figure 1.14 Schematic of the ET between two redox couples across L/L interface.
- 44 - In order to study the ET kinetics the two redox couples have to remain in their respective phases. Separating the variation in the interfacial concentration of both redox species in the absence of specific adsorption of ions allows calculation of the observed electron transfer rate [124, 125]. Although ET at the ITIES was not directly investigated in this report, the fundamental concept was extrapolated to a system where two different redox couples are present in two aqueous phases separated by a solid rotating electrode
(see next section).
- 45 - 1.7 Bipolar Electrochemical Cell
Electron transfer across the ITIES shows remarkable similarities with a bipolar electrode system that has been of some interest in electrochemical applications [126]. The bipolar electrode system employs a pair of electrodes placed in a two-compartment electrochemical cell with two redox couples located in separate phases, similar to the liquid/liquid ET system. The configuration, where the redox couple pair in one phase is in excess compared to the redox couple pair in the other phase, results in conventional voltammetric behaviour, typical for electrochemistry on solid electrodes. The charge transfer becomes completely limited by the reactions of the low concentration redox couple, whereas the phase containing the excess of redox couple acts as solid phase electrode (becomes a source/sink of electrons) [127-129]. Hotta et al. introduced a liquid/liquid system where the two liquids were connected via electronic conductor. This setup enabled the investigators to separate electron transfer from ion transfer reactions at the interface [130, 131]. Recently, Plana et al. adapted this liquid/liquid configuration to a bipolar electrochemical cell (BEC) which consists of two aqueous phases that contain two different redox couples [132]. The schematic of the electron transfer reaction in the BEC is shown in Fig. 1.15.
Figure 1.15 Schematic of the ET between two redox couples in the bipolar electrochemical cell. Only one direction of redox reaction is shown, the opposite direction is also possible.
- 46 - The two aqueous phases were connected via a metallic electrode but mass transport between the two was prevented, which ensured that charge transfer only occured via electron transfer. Furthermore, physical separation of the electrolyte solution enables the use of identical (or at least miscible) solvents and broadens the application of the bipolar cell to electroless deposition, investigation of catalytic surface reaction or separation of the half-reactions of an electrochemical process. One of the aqueous phases contained an excess of both forms of the redox couple compared to the other aqueous phase, thus ensuring the simplified voltammetric response as described above. We have adapted the bipolar cell design to the permeation assay under hydrodynamic control in order to verify the flux sensitivity and stirring efficiency in the upper donor compartment
(see Chapter 7).
- 47 - 1.8 Artificial Membrane Polarisation
Supported liquid membranes (SLM) and their applications have been studied for several decades [133]. Polarisation of the SLM in drug systems has also been of some interest, particularly in such applications as liquid/liquid extraction [134-136]. However, in these studies, where 2-nitrophenyloctyl ether (NPOE), immobilized on a polypropylene membrane, was used to separate two aqueous compartments, relatively high voltages of
50 – 300 V DC were used for the extraction [70]. Such high over-potentials are most likely used to overcome the system resistivity (IR drop) and induce energy dissipation
(production of heat). A new micro-extraction chip format was recently introduced, applying a smaller voltage of 15 V [137]. Further reduction of applied potential to 1 – 10 V
DC was applied for SLMs containing 1-isopropyl-4-nitrobenzene [138]. The application of such high voltages is useful for bulk drug extraction but on the other hand it is not suitable for a qualitative/quantitative investigation of transport mechanism across SLMs. Recently,
Molina et al. reported a series of studies on ion transfer across liquid membranes separating two aqueous phases [139, 140]. The membrane consisted of NPOE immobilized on polyvinyl chloride (PVC). An extra added aqueous phase in combination with advanced electrochemical methods such as square wave voltammetry and differential pulse voltammetry results in powerful analytical techniques suitable for the investigation of complex samples. The authors also presented general analytical solutions for the current-potential response in this novel system [141]. Murtomäki et al. used polarisation of several different SLM types in a rotating diffusion cell to determine the effect of membrane composition on the rate of tetraalkylammonium ions transfer [142]. Ion transfer across a nitrobenzene-based SLM, compared with transfer across BLM [143], and ubiquinone mediated ET across BLM [144] were also reported. The same SLM system was used to study ion transfer coupled with electron transport [145]. Manzanares et al. used
NPOE-based SLM to determine the transfer rate constants of tetrabutylammonium [146].
- 48 - The morphology and electrochemical properties of cellulose ester, polytetrafluoroethylene and polycarbonate based SLMs were studied by Thompson et al. [147]. However, to our best knowledge, there are no reports on electrochemical polarisation of SLMs in permeability studies.
In order to investigate the ionic transfer across the organic membranes used in the
PAMPA method and to examine the pH-partition hypothesis discussed in section 1.4, we have modified the artificial membrane permeation assay under hydrodynamic control to a method with a polarisable organic membrane. The schematic of such a configuration is shown in Fig. 1.16. A pair of reference and counter electrodes was placed in each aqueous phase, i.e. donor and acceptor, and a small potential difference was applied across the membrane. The electrochemical methods were coupled with in situ spectrophotometric measurements of the drug permeation in the acceptor compartment.
Figure 1.16 A schematic of the polarised artificial membrane permeation method.
- 49 - 1.9 Thesis Overview
The presented thesis is divided into seven chapters. The present chapter provides an introduction to the thesis, Chapter two provides details of the methods of investigation and material used in this work. Chapters 3 to 7 present the experimental work and discussion of obtained results. Each results chapter contains a brief opening, which complements the introduction presented in the current chapter, and conclusions.
Chapter three presents a novel artificial membrane permeation method under hydrodynamic conditions, which has been developed and optimized to the final stage after several years of investigation in this research group. The method employs a rotating- diffusion cell where two aqueous compartments are separated by an organic supported liquid membrane. The permeation of the drug is investigated under well-defined hydrodynamic conditions with control over the unstirred water layer. In situ permeation- time profiles are obtained under hydrodynamic control and used to determine permeability coefficients. An advanced analytical transport model is derived to account for the membrane retention, two-way flux and pH gradient between the two compartments.
Moreover, a numerical permeation model was also compared to rationalise the time- dependent permeation profiles. Methods to determine the membrane permeability, intrinsic permeability, unstirred water permeability and permeation lag time are presented.
Chapter four introduces the same permeation method, which has been amended with external polarisation of the membrane. Several electrochemical methods including, potentiometry, amperometry, and cyclic voltammetry were coupled with spectrophotometric measurements and used to study drug permeation across the supported liquid membrane.
- 50 - Chapter five presents a permeability study of 31 different water-soluble drugs with known absolute oral bioavailability and human hepatic clearance data. The measured effective permeability coefficient is modified to include the paracellular transport derived from a previously reported Caco-2 permeability study and the effects of unstirred water layer anticipated in vivo. The permeability obtained under conditions of controlled hydrodynamics and the permeability measured under unstirred conditions are both correlated with the fraction absorbed in humans.
Chapter six describes the use of electrochemical methods to study ionised drug transfer across the liquid/liquid interface. After an initial validation study of fully ionized species in the water/1,2-dichloroethane system, three drug molecules are analysed. Due to the difficulties in analysis caused by the partitioning of the neutral drug fraction between the aqueous and organic phase, an alternative hydrodynamic approach was developed and successfully applied to transfer of partially ionised drug species across liquid/liquid interface.
Chapter seven presents a bipolar electrochemical cell, which operates as a bipolar analogue to the rotating-disc electrode system. This technique was developed to indirectly test the hydrodynamic properties of the rotating permeation setup via electrochemical methods. Final conclusions and suggestions for future work are then offered.
The Appendix attached at the end of this thesis provides additional data and results that were excluded from the main text to maintain readability and flow of the thesis. The
Appendix contains UV spectral data, permeation and lipophilicity data, permeation cell optimization results, details of liquid/liquid area determination and silver/silver sulphate reference electrode preparation/validation.
- 51 - Materials, Equipment and Methods
2.1 Materials
Chemicals Sodium dihydrogen phosphate (sodium phosphate) (98.5%), sodium sulphate
(99%), lithium chloride (99%), lithium perchlorate (95+%), potassium iodide (99%), hexaammineruthenium(III) chloride (98%), potassium hexacyanoferrate(III) (potassium ferricyanide) (99+%), potassium hexacyanoferrate(II) trihydrate (potassium ferrocyanide)
(99%), 2-(Cyclohexylamino)ethanesulfonic acid (CHES buffer) (99%), buffer solutions for pH meter calibration (pH 4.00, 7.00, 10.0), 1,9-decadiene (96%), 1,2-Dioleoyl-sn- glycero-3-phosphocholine (DOPC) (approx 99%), stearic acid (grade I approx 99%), tetramethylammonium chloride (TMACl) (97%), tetraethylammonium chloride (TEACl)
(99%), bis(tetramethylammonium) sulphate hydrate (TMA2SO4) (98%), bis(triphenylphosphoranylidene)ammonium chloride (BTPPACl) (98%), potassium tetrakis(4-chlorophenyl)borate (KTPBCl4) (98%), tetradodecylammonium bromide
(TDDABr) (≥99%), tetraheptylammonium tetraphenylborate (THATPB) (≥98%) tetradodecylammonium tetrakis(4-chlorophenyl)borate (TDDATPBCl4) (≥98%), toluene
(99.7%) and acetone (99%) were purchased from Sigma-Aldrich. Potassium chloride
(99%), sodium chloride (99.95%), sodium hydroxide (98.8%), hydrochloric acid
(analytical reagent grade, 38%) and sulphuric acid (98%) were purchased from Fisher
Scientific UK Ltd. Sodium acetate (98%) was purchased from BDH Merck Ltd (Poole,
UK). Potassium nitrate was obtained from Lancaster Synthesis Ltd (Morecambe, UK).
Bis(triphenylphosphoranylidene)ammonium tetrakis(4-chlorophenyl)borate
(BTPPATPBCl4) (≥98.5%) was synthesised from and using procedure described in section 2.3.5.
- 52 - Drugs
Acetaminophen (98%), antipyrine, atenolol (≥98%), betamethasone (≥98%), cefixime trihydrate (≥98%), cephalothin sodium salt (≥99%), cetirizine dihydrochloride
(≥98%), (±)-chlorpheniramine maleate salt (≥99%), colchicine (≥95%), diclofenac sodium salt, fexofenadine hydrochloride (>98%), midazolam hydrochloride, nafcillin sodium salt mohohydrate, naproxen (98%), norfloxacin, oxybutynin chloride (≥98%), pindolol
(≥98%), (±)-propranolol hydrochloride (≥98%), pyridoxine (≥98%), quinine, anhydrous
(≥98%), salicylic acid (≥99%), theophylline, anhydrous (≥99%), tolbutamide, (±)- verapamil (min 99%), warfarin (min 98%) and zopiclone were purchased from Sigma-
Aldrich, UK. Chlorthalidone, eprosartan, gatifloxacin, metolazone and risperidone were supplied by AstraZeneca, Alderley Park, UK.
Other materials
Precision ground glass donor tubes for the rotating permeation cell were obtained from Glass Precision Engineering Ltd (Leighton Buzzard, UK), “Durapore”®
Poly(vinylidene fluoride) (PVDF) hydrophobic membrane filters (0.45 μm pore size, 125
μm thickness, 75% porosity, 13 mm diameter) supplied by Millipore, were attached to the glass tubes using Araldite Rapid glue (Bostik Ltd, Stafford, UK) and cut to fit the tube outer diameter after two hours of drying (acceptor-side membrane area = 1.04 cm2, donor- side membrane area = 0.79 cm2). An apparent clear area of the membrane corrected for its porosity was 0.68 cm2. Poly(ethylene terephthalate) (PET) membranes (0.1 µm pore size,
13 mm diameter) were purchased from Osmonics Inc (Minnetonka, MN, USA). Water of
18.2 MΩ cm resistivity purified by a “PURELAB” Ultra-filtration unit (ELGA, UK) was used in solution preparation. Flexible plastic foil “Parafilm” (Pechiney Plastic Packaging
Inc, Chicago, IL, USA) was used to wrap the top of the donor compartment in unstirred permeation experiments. Glassy carbon disc electrode (0.3 cm diameter) was supplied by
- 53 - CH Instruments Inc (Austin, TX, USA), silver wire (0.75 mm diameter, 99.99%), gold wire (0.5 mm diameter, 99.99%), gold mesh (0.06 mm plain weave wire, 1024 per cm2, open area 65%, 99.99%), platinum wire (0.5 mm diameter, 99.99%) and platinum mesh
(0.1 mm plain weave wire, 420 per cm2, open area 62.7%) were obtained from Advent
Research Materials (Oxford, UK). Capacitors (100 nF) were purchased from Farnell
(Leeds, UK). Silver/silver chloride (Ag/AgCl), silver/silver sulphate (Ag/Ag2SO4), silver/silver tetraphenylborate (Ag/AgTPB) and silver/silver tetrakis(4- chlorophenyl)borate (Ag/AgTPBCl4) reference electrodes were prepared using method described in section 2.3.7.
- 54 - 2.2 Equipment
Solution pH was measured using a HI991300 pH meter (Hanna Instruments Ltd,
Leighton Buzzard, UK). UV spectra were acquired using a DH-2000-BAL spectrometer equipped with a DH-2000-BD deuterium bulb and fibre-optic cable (supplied by Ocean
Optics B.V., Duiven, The Netherlands) and controlled using a USB2000 interface
(Mikropack GmbH, Ostfildern, Germany). Rotation of the membrane was controlled using a Model 616 rotating-disc controller (EG&G Inc, Wellesley, MA, USA).
Electrochemical experiments were controlled using an Autolab PG100 potentiostat/galvanostat (Eco Chemie B.V., Utrecht, The Netherlands). Saturated calomel electrode CR4 was purchased from Thermo Russell (Auchtermuchty, Scotland, UK). A
Faraday cage, built in-house, was used to screen the electrochemical cell from external electrical noise.
The rotating permeation cell was made in-house in School of Chemistry. The cell consisted of an acceptor compartment made of polytetrafluoroethylene (PTFE), equipment stand and other accessories (Fig.2.1), and is described fully in section 2.3.1. Glass cells used in electrochemical measurements (Fig. 2.5 and 2.6) were also made in-house in
School of Chemistry.
Microsoft Excel 2003 and 2010 (Microsoft Corporation), Origin 8.5 (OriginLab
Corporation, Northampton, MA, USA) and GPES software 4.9 (Eco Chemie, Utrecht, The
Netherlands) were used to process measured data. The numerical permeation model was developed using Comsol “Multiphysics” software (Comsol UK, Hatfield, UK).
Simulations were executed on a desktop PC, however the geometric dimensions of the model also presented a challenge in terms of memory allocation, to maintain the mesh quality of the precursor models required nearly 45,000 elements per build. This led to a run time of 515 min per model run. The number of stored solutions also needed to be kept to < 150 per run, otherwise the model would crash due to lack of memory.
- 55 - 2.3 Methods
2.3.1 Permeation Assay under Hydrodynamic Control
UV calibration in the acceptor compartment
The optical path of the PTFE acceptor compartment was measured to be 32.5 ± 0.5 mm. The absorbance of the analyte solutions at several different concentrations was measured to obtain the analyte molar absorption coefficient, ε, at a given wavelength, , from the Beer-Lambert law:
A l c (2.1)
where A is the solution absorbance at wavelength λ, l is the optical path within the solution and c is the molar concentration of the analyte. To avoid uncertainty in the optical path length, the composite parameter ε· l was found when calculating the concentration from the absorbance. Absorption spectra of the studied drug molecules in 0.03 mol dm−3 sodium phosphate (pH 7.4) within the wavelength range of 200 – 400 nm can be found in Fig. A1.1,
Appendix.
Permeation cell assembly
The detailed cell design and its dimensions are shown in Fig. 2.1. The PTFE acceptor compartment was filled with 20 ml of 0.03 mol dm−3 sodium phosphate buffer solution at pH 7.4. When the pilot drug molecules, warfarin and verapamil, were tested,
0.01 mol dm−3 sodium phosphate was used. A poly(vinylidene fluoride) (PVDF) filter of apparent area 0.68 cm2 (average of donor and acceptor side area multiplied by filter porosity given by the supplier) attached to the donor glass tube was soaked with 14 μl of a
1,9-decadiene solution containing 1.5% weight dioleoyl phosphatidylcholine (DOPC) and
- 56 - 0.5% weight stearic acid. The tube was gently shaken for a few seconds and the excess solvent (ca. 2 μl) removed. Subsequently, a set volume (3 – 5 ml) of 30 mM buffer solution containing the drug molecule at a given pH was dispensed into the donor tube.
Sodium acetate (pH 3.5 – 5.5), sodium phosphate (pH 6.0 – 8.5) and CHES buffer (pH 8.5
– 10.0) were used as the donor phase buffers. The UV absorbance of the used buffers in de-ionized water was also recorded (See Fig. A2.3, Appendix).
Figure 2.1 Schematic diagram of the permeation cell used for in situ UV measurement: 1 – rotation controller, 2- paddle, 3 – glass tube (donor compartment), 4 – spacer disc, 5 – PTFE cogwheel tightly connected to the glass tube, 6 – PVDF membrane, 7 – acceptor solution, 8 – UV source optical path, 9 – quartz window, 10 – quartz lens, 11 – fibre-optic cable, 12 – PTFE acceptor cell, 13 – steel pad, 14 – steel pad screw.
The drug concentration in the donor solution was varied according to its solubility and the assay requirements (7 – 300 µM). The buffer concentration was sufficiently high to ensure that change in the drug concentration was always less than 1% of the buffer
- 57 - concentration (to maintain a constant pH). After dispensing the donor solution, the tube was placed in a cogwheel and a plastic paddle was fitted into the tube. The paddle, which was used to control stirring condition at the donor side, was stationary during the rotation.
Then the acceptor compartment was attached and fixed using a screwed pad and equipped with the fibre-optic cable. Finally the rotation controller was attached to a PTFE cogwheel, tightly embracing the donor tube.
In situ UV spectra time acquisition in the acceptor compartment
After assembly of the cell, the reference and dark spectra of the acceptor solution were taken. Stirring, and spectral time acquisition, were started simultaneously. Four different wavelength channels at the spectral peak maxima, plus one background channel, were recorded for permeation times of 20 – 30 min. A typical absorbance sampling period was 1 s. At the end of the permeation, the whole spectrum was taken as a comparison to the calibration spectrum. Permeation was conducted at ambient temperature 21.8 ± 0.3 °C
(mean standard deviation over 50 temperature measurements, measured during each experimental session). Beside temperature, many parameters such as choice of the membrane filter, solvent, lipid content or presence of co-solvents in the aqueous phase affect drug permeation. Choosing an ambient temperature has the advantage of being close to pKa measurement standards (25°C). The permeation assay under stationary conditions was conducted in the same permeation cell using a single-time data point (at t
~ 18 – 24 h). To reduce the evaporation of the sample, the permeation cell was sealed with
“Parafilm” foil for the duration of the experiment.
Permeation cell disassembly and donor compartment ex situ analysis
The permeation cell was disassembled and sample from the donor compartment was taken for later analysis. The acceptor compartment solution pH was checked in every
- 58 - third permeation experiment, and found not to change by more than 0.1 pH units. The whole spectrum and individual wavelength channels of the diluted donor solution were recorded along with the original donor solution sample and shake-flask samples.
Single pH point data generation
A permeation data set for a given donor pH and acceptor pH = 7.4 was obtained as follows. For the pilot drug molecules warfarin and verapamil the whole permeation data set (i.e. stirring rates 200, 250, 290, 400, 600, 1000 and 1500 rpm, corresponding to angular velocities of 21, 26, 30, 42, 63, 105 and 157 rad s−1) was obtained in a single experimental day using the same solutions and pH calibration/adjustment. This procedure was performed three times to reduce the experimental error. This procedure was optimized so that for all other drug molecules the stirring rates were ranging from 60 to
600 rpm, corresponding to angular velocities of 6 to 63 rad s−1). The reason for the change of stirring rate range was the investigation of the membrane stability at different stirring rates and effectiveness of stirring to induce sufficient mixing as discussed in section A2,
Appendix.
Permeation data analysis
The raw absorbance data were corrected for the background contribution by subtracting the background channel absorbance. Then the absorbance was converted to concentration (based on the solute Beer-Lambert calibration, Figure A1.1, Appendix) and further to the ln(k) function (see below). From the slope of ln(k) dependence on time, the effective permeability (Pe) was calculated. Four wavelength channels were analysed in this way separately, and depending on the data quality, all of them or their subset averaged to produce the effective permeability value. A block scheme depicting the whole experimental and analysis procedure is shown in Fig. 2.2.
- 59 -
Figure 2.2 Block scheme of the permeation and analysis procedure.
2.3.2 Shake-Flask Method
The standard shake-flask method was employed to determine the membrane- aqueous phase distribution coefficient [21]. The lipid solution of 1.5% weight DOPC and
0.5% weight stearic acid in 1,9-decadiene was shaken with a buffer solution containing the drug molecule and left still for 24 h. The drug concentrations in the aqueous phase before and after shaking were measured using UV absorbance spectrophotometry and the distribution coefficient, Kd, was determined using following equation:
V (c0 ceq ) K aq aq aq (2.1) d V ceq org aq
0 where Vaq and Vorg are the volumes of the aqueous and organic phase respectively, caq and
eq caq are the aqueous drug concentrations prior and after shaking, respectively. The distribution coefficients determined for all 31 drug molecule studied in this thesis are listed in Table A4.3, Appendix.
- 60 - 2.3.3 Numerical model
A numerical transport model was constructed using the Comsol Multiphysics 2D diffusion and convection solver. The numerical code was written and executed by Daniel
Bradley, a former PhD student in the research group. The static permeability model was first modified to reflect the true geometry of the experimental system. This involved making several approximations.
First it was assumed that the internal structure of the membrane permitted diffusion in all directions equally, this assumption was based on microscopic observations of the membrane that showed it to be composed of interlocking fibres with no obvious order to the structure that would drive mass transport in a specific direction [148]. The membrane was treated as an entirely open volume in which the solute had apparent diffusion coefficient, Dm. It was further assumed that the binding process of membrane to glass tube (the boundaries of the compartments) was perfectly executed, the amount of membrane blocked by excess adhesive was, therefore, insignificant and there was no seepage of solution between the glass and the membrane. It was also assumed that the convection profile in the donor phase could be approximated as a rotating disc, although the convection profile in the real experiment would be constrained at the outer edge by the glass wall of the tube. Another implicit assumption was that the solute concentration within the membrane never reached the solubility limit, given the sub-millimolar aqueous concentrations involved. The membrane was assumed to operate as a sink with respect to the donor phase, in that it was assumed that no reverse mass transport occurred (from membrane to donor phase).
In reality, the mass transport of solute through the membrane would be influenced by a variety of factors including mean diffusion coefficient, mean path length, path length range, solute-lipid interaction and solute-surface interaction. In the model these influences are aggregated into an apparent membrane diffusion coefficient.
- 61 - The membrane-donor and membrane-acceptor boundaries were constructed as in the static membrane case, with the concentrations mapped onto the other side of the interface using an extrusion coupling variable. The direction and extent of flux across the interface was then determined from the respective interfacial concentrations and membrane-donor(acceptor) distribution coefficients. In this case the distribution coefficients were assumed to be different in each phase as by controlling the pH of the donor and acceptor phases, the ionisation of the solute will be altered. The distribution coefficient values for a given pH were obtained experimentally by the shake-flask method described above.
2.3.4 Permeation Assay with External Membrane Polarisation
For the purpose of membrane polarisation the permeation cell was connected to the potentiostat via a four-electrode configuration. The schematic of the modified cell is shown in Fig. 2.3. The whole permeation apparatus was placed in a Faraday cage to prevent noise from other electrical equipment. The permeation cell with mounted electrodes was assembled using the same procedure as described in section 2.3.1. The paddle had a dual function in this modification. It provided stirring and served as the conduit for the standard silver/silver chloride electrode at the same time. The platinum counter electrode was attached to the paddle body. The electrodes were connected to the potentiostat and both donor and acceptor counter – reference electrode pairs were shorted with a 100 nF capacitor to reduce the induced electrical noise. Also, the incremental steps of potential were set out of phase with the stirring rate to avoid multiplication of noise interference. The reference electrodes were made of silver/silver chloride by oxidizing the silver wire in 0.1 M KCl (See section 2.3.7). After the permeation cell was assembled, stirring was turned on with no UV absorbance detection for the first 10 minutes. During
- 62 - this period, the potential difference between the acceptor and donor phase, i.e. open circuit potential (OCP) was recorded. After the initial 10 minutes, the UV absorbance acquisition was started.
Figure 2.3 Schematic diagram of the permeation cell with membrane polarisation: 1 – rotation controller, 2- paddle, 3 – glass tube (donor compartment), 4 – spacer disc, 5 – PTFE cogwheel tightly connected to the glass tube, 6 – PVDF membrane, 7 – acceptor solution, 8 – Ag/AgCl reference electrodes, 9 – platinum counter electrodes, 10 – saturated KCl solution (inner reference electrode solution), 11 – glass frit, 12 – PTFE acceptor cell, 13 – steel pad, 14 – steel pad screw, 15 – UV source optical path, 16 – quartz window, 17 – quartz lenses, 18 – fibre-optic cable. The electrodes were connected to the potentiostat as follows: Counter 1 – counter, Ref 1 – reference, Counter 2 – working, Ref 2 – sense.
After another 10 min period, the potential difference was applied between the acceptor and donor phase (either via voltammetry or amperometry) while stirring and measuring the UV absorbance. A scheme depicting the whole experimental procedure is
- 63 - shown in Fig. 2.4. This standard procedure was varied in some cases as described in
Chapter 4.
Figure 2.4 Block scheme of the membrane polarisation method.
The aqueous phase was of the same basic composition as the standard permeation method, i.e. 30 mM sodium phosphate, with addition of 1 mM sodium chloride. Sodium phosphate was used to maintain the pH and also as a supporting electrolyte for the aqueous phase. Sodium chloride was added to provide a stable response for the silver/silver chloride electrode. The donor solution pH was kept at either 7.4 or 8.5. In the case where drug transport was studied, the donor phase contained 300 μM cetirizine. The acceptor solution pH was kept at 7.4 or 8.5. The membrane consisted of the same component as the standard permeation method, i.e. 1.5% weight DOPC and 0.5% weight stearic acid, and also contained 2.2% weight (10 mM) TDDATPBCl4. The organic electrolyte, TDDATPBCl4, was introduced to the membrane phase to enable its polarisation by providing an ionic support for the current passing through membrane.
- 64 - 2.3.5 Liquid/Liquid Electrochemistry
Static system
The unstirred (static) liquid/liquid electrochemistry experiments, specifically ion transfer across the interface between two immiscible electrolyte solutions (ITIES), were conducted in the liquid/liquid electrochemical cell depicted in Fig. 2.5.
The cell has a central cylinder-shaped body and two capillaries, which both end near the water/1,2-dichloroethane interface. Platinum mesh counter electrodes were placed in both water and 1,2-DCE, and silver/silver chloride(sulphate) reference electrodes were placed in each capillary. Hence, a four-electrode system was employed. The two reference electrodes control the potential difference between the two electrolyte solutions and the two platinum counter electrodes collect current passing through the interface. The preparation of reference electrodes is described below (section 2.3.7). By analogy with conventional electrochemistry at solid electrodes, the liquid/liquid interface with transferable ions passing across it, acts as a working electrode. The potentiostat/galvanostat was used to control the potential and to monitor the current. A Faraday cage was used to screen the electrochemical cell from the electrical noise.
Figure 2.5 Schematic of the static L/L electrochemical cell.
- 65 - The interface between the aqueous and organic phase is curved according to the contact angle of the liquids formed upon their contact with the glass cell. Measurement of the geometric area was avoided by employing accurate calibration experiments where several well-studied ionic species [102] were transferred across the interface: an interfacial area of 1.1 cm2 was thereby found (see section A5, Appendix). The flat geometric area was found to be 0.9 cm2. As discussed in section 1.6, electrochemistry at the ITIES requires two immiscible solutions. Because of the practical difficulties associated with the reference electrode stability in non-aqueous solutions, however, another aqueous phase (the „slug‟ in
Fig. 2.5), which acts as a reference electrode for the organic phase is usually employed (see section 2.3.7).
Rotating system
A novel liquid/liquid electrochemical system acting as an analogue to the rotating- disc electrode (RDE) system was designed. Unlike the RDE system, where the rotating- disc working electrode is a solid electrode, the novel rotating system employs a rotating membrane and another adjacent liquid phase. The experimental setup of the rotating liquid/liquid electrochemical modified permeation cell is shown in Fig. 2.6.
The aqueous phase was confined in the top glass tube with the membrane at the bottom. The paddle placed in the tube also served as the aqueous reference electrode. The organic phase was placed in the bottom electrochemical cell with a Luggin capillary coming to the membrane. Therefore the liquid/liquid interface was formed at the upper side of the membrane. The capillary also contained another aqueous phase containing a common ion with the organic phase, thus providing an external reference electrode for the organic phase.
The same membrane as in permeation study, that is PVDF, was used. The membrane area on the aqueous side, 0.79 cm2, was corrected for the apparent porosity of 0.75 (quoted by
- 66 - the supplier). Both counter and reference electrode pairs were shorted together with a 100 nF capacitor to reduce the external electrical noise.
Figure 2.6 Schematic diagram of the rotating L/L electrochemical cell: 1 – rotation controller, 2- paddle, 3 – glass tube (aqueous phase), 4 – spacer disc, 5 – PTFE cogwheel tightly connected to the glass tube, 6 – PVDF membrane, 7 – organic
phase, 8 – Ag/AgCl (Ag/Ag2SO4) reference electrodes, 9 – platinum counter electrodes, 10 – saturated KCl solution (inner reference electrode solution), 11 – glass frit, 12 – organic reference phase (slug), 13 – steel pad, 14 – steel pad screw. The electrodes were connected to the potentiostat as follows: Counter 1 – working, Ref 1 – sense, Counter 2 – counter, Ref 2 – reference.
Aqueous phase
A storage solution was used when preparing drug or other molecules for electrochemical experiments. First, the deionized water used for solution preparation was shaken with 1,2-DCE for 5 min and both phases were left in contact overnight. Then the aqueous electrolyte solution was prepared, containing x M sodium chloride or sodium
- 67 - sulphate as electrolyte (x = 0.01, 0.02, 0.03 or 0.05) and 0.01 or 0.03 M sodium dihydrogen phosphate as a buffer. The pH of the aqueous phase was then adjusted to 7.4 with 5 M sodium hydroxide.
A common choice for aqueous phase electrolyte in liquid/liquid electrochemistry is lithium chloride, due to its hydrophilic nature and consequentially large potential window.
The lithium cation was replaced with the sodium cation based on the following argument.
As opposed to lithium, sodium is an element naturally abundant in biological systems and
0, wo the standard Gibbs energies of transfer from water to 1,2-DCE, Gtr, i , for sodium and lithium are almost the same (55.9 and 55.6 kJ mol−1, respectively [115]) so that sodium will certainly not limit the potential window at positive potentials.
The most commonly used aqueous electrolyte anion, chloride, was in some cases replaced with sulphate anion. The reason is that chloride anions limit the potential window
0, wo 1 [149] G 51 kJ mol more than sulphate anions ( tr, Cl ). This was proven experimentally by comparing the blank potential windows for chloride and a sulphate-based solution (Fig. 2.7) as we are unaware of any literature value for the standard Gibbs energy of transfer for sulphate anion (Shioya et al. studied the sulphate transfer in water/1,2-DCE system, however, they did not provide the absolute value of the transfer potential / Gibbs energy of transfer [150]). As a result of using sulphate based electrolyte a novel alternative silver/silver sulphate electrode was prepared (2.3.7) and its properties tested (section A6, Appendix).
- 68 -
Figure 2.7 Comparison of chloride (black curve) and sulphate (green curve) based electrolyte potential window. The graph shows a current response to the applied Galvani potential difference between the aqueous and organic phase. Black curve measured in cell Ag|AgCl| 10 mM NaH2PO4, 10 mM NaCl, pH 7.4 (aq)| 10 mM BTPPATPBCl4 (1,2-DCE)| 1 mM BTPPACl, 10 mM NaCl|AgCl|Ag at scan rate 40 mV s−1. Green curve measured in cell Ag|Ag2SO4| 10 mM NaH2PO4, 10 mM Na2SO4, pH 7.4 (aq)| 10 mM BTPPATPBCl4 −1 (1,2-DCE)| 1 mM BTPPACl, 10 mM Na2SO4|Ag2SO4|Ag at scan rate 40 mV s .
Organic phase
The organic phase consisted of x mM of either bis(triphenylphosphoranylidene) ammonium tetrakis(4-chlorophenyl) borate (BTPPATPBCl4), tetraheptylammonium tetraphenylborate (THATPB) or tetradodecylammonium tetrakis(4-chlorophenyl) borate
(TDDATPBCl4) in 1,2-dichloroethane (x = 10, 15 or 20). BTPPATPBCl4 is not commercially available and was therefore synthesized in-house (see procedure below). An appropriate amount of the organic electrolyte was dissolved in 1,2-dichloroethane to obtain an organic electrolyte solution of the desired concentration. Shaking and overnight equilibrating of the 1,2-DCE phase with water was carried out as a final preparation step.
This was done for two reasons; to saturate 1,2-DCE with water, and to wash out any inorganic residues.
- 69 - Preparation of the BTPPATPBCl4 electrolyte
The BTPPATPBCl4 electrolyte for the organic phase was prepared by metathesis of two organic salts, bis(triphenylphosphoranylidene) ammonium chloride (BTPPACl) and potassium tetrakis(4-chlorophenyl) borate (KTPBCl4). Stoichiometric amounts of these two salts were dissolved in the organic solvent to produce the organic electrolyte bis(triphenylphosphoranylidene) ammonium tetrakis(4-chlorophenyl) borate
BTPPATPBCl4, according to the metathesis reaction in Fig.2.8.
Figure 2.8 Metathesis reaction to produce the organic BTPPATPBCl4 electrolyte.
An appropriate amount of the first salt BTPPACl was added to a stirred mixture of toluene and acetone (2:1) which was heated to 70°C. The overall volume of the mixture was about 300 ml. Acetone was used to increase the solubility of the salt. Once the BTPPACl had completely dissolved, a stoichiometric amount of KTPBCl4 was added. After 30 min of stirring at 70°C, the beaker with the mixture was cooled to the room temperature. The desired product of the reaction, BTPPATPBCl4, was thought to be dissolved in toluene whereas the insoluble inorganic salt (KCl) precipitated as white crystals. This procedure was adapted from [151] with some modifications. See scheme in Fig. 2.9 for the overview of the organic electrolyte preparation.
- 70 -
Figure 2.9 Schematic of the organic BTPPATPBCl4 electrolyte preparation.
To dispose of any KCl still present in the organic phase, several steps were made to increase product purity. First, toluene was evaporated on a rotary evaporator and white crystals of BTPPATPBCl4 were obtained (Alternatively crystallization at 50°C was carried out). The impure BTPPATPBCl4 crystals, which are highly hydrophobic were then washed with water and left in a sonic bath for one hour and filtrated subsequently – most of the potassium chloride was expected to be washed away with water. Dry organic electrolyte was then dissolved in ca. 150 ml of acetone and solution slowly evaporated at 40°C until the residual KCl precipitated. Acetone solution was then filtrated through a Büchner funnel, the organic electrolyte dissolved in the filtrate was recrystallized at 40 °C. At this stage, the product was considered to be chloride free, however some yellowish impurities were still present. The crystals were therefore dissolved in toluene at 70°C and a few decantation steps were carried out. The reaction product, preferably soluble in non-polar organic solvents, serves as charge carrier in the organic phase. The purity of the product, 98.5%, was determined by elemental microanalysis, performed in the School of Chemistry
(University of Manchester), shown in Table 2.1.
- 71 - Table 2.1 Purity of the BTPPATPBCl4 verified by elemental microanalysis.
mass fraction / % element % error expected found C 72.38 72.59 0.29 H 4.66 4.63 0.64 N 1.41 1.34 4.96 Cl 14.24 14.23 0.07 P 6.22 6.23 0.16 B 1.08 1.15 6.48
- 72 - 2.3.6 Rotating Bipolar Electrochemical Cell
A schematic of the permeation cell, modified to act as a rotating bipolar electrochemical cell (BEC), is shown in Fig. 2.10. The cell comprised of the same elements as the one shown in Fig. 2.3 except for the UV fibre optics. Two reference electrodes, two counter electrodes and a glassy carbon (GC) working electrode were added to complete the electrical circuit of the BEC.
Figure 2.10 Schematic diagram of the permeation cell modified to rotating BEC: 1 – rotation controller, 2- paddle, 3 – glass tube (donor compartment), 4 – spacer disc, 5 – PTFE cogwheel tightly connected to the glass tube, 6 – glassy carbon electrode, 7 – ferro/ferricyanide solution, 8 – Ag/AgCl reference electrodes, 9 – platinum counter electrode, 10 – saturated KCl solution (inner reference electrode solution), 11 – glass frit, 12 – PTFE acceptor cell, 13 – steel pad, 14 – steel pad screw, 15 – gold counter electrode. The electrodes were connected to the potentiostat as follows: Counter 1 – working, Ref 1 – sense, Counter 2 – counter, Ref 2 – reference.
The donor compartment only contained the oxidised form of the ruthenium complex, 0.5 mM hexaammineruthenium(III) chloride, at the beginning of the experiment.
- 73 - This complex is stable and an external source of electrons is required to reduce it to hexaammineruthenium(II). The acceptor compartment contains 25 mM of both oxidised and reduced forms of a second redox couple, here ferricyanide and ferrocyanide, respectively. The excess of ferrocyanide/ferricyanide was used to ensure that the reaction occurring at the bipolar electrode is purely limited by the diffusion of ruthenium complex, which enables to study the flux response to stirring in the donor compartment. In this configuration the ferro/ferricyanide solution effectively behaves as a metal electrode towards the rest of the cell and thus mimics a three electrode system [127, 152]. The acceptor compartment also contained 50 mM hydrochloric acid to improve the electrode kinetics and complete reversibility of the occurring reactions. Finally, 0.5 M potassium chloride
(supporting electrolyte) was present in both compartments. The electrochemical cell can be summarized by the following schematic:
Ag(s)│AgCl(s) │0.5 mM Ru(NH3)6Cl3(aq), 0.5 M KCl(aq) ║
25 mM K4Fe(CN)6(aq), 25 mM K3Fe(CN)6(aq), 50 mM HCl(aq)│AgCl(s) │ Ag(s)
A four electrode system with a pair of reference and counter electrode in each compartment was used. The reference electrodes were made of silver/silver chloride by oxidation of silver wire in 0.1 M KCl (see section 2.3.7). The reference electrode in the upper compartment was incorporated into the paddle and connected to the solution via a glass frit. A platinum mesh counter electrode was used in the upper compartment but it was avoided in the lower compartment to prevent the catalytic formation of insoluble mixed valence complexes on the platinum surface [132]. Therefore, a gold mesh counter electrode was used in the ferrocyanide/ferricyanide solution instead. The GC electrode
(not connected to the potentiostat) of area 0.18 cm2 served as working (bipolar) electrode, supporting electron transport between the redox species of upper and lower compartments.
The potential difference between the two aqueous phases was applied (positive potentials
- 74 - = donor phase more positive than the acceptor) and current measured between the two counter electrodes. The electrodes were connected to the potentiostat and both donor and acceptor counter – reference electrode pairs were shorted with a 100 nF capacitor to reduce induced electrical noise.
The electrochemical methods used to study electron transfer in the bipolar cell include cyclic voltammetry under unstirred conditions and linear sweep voltammetry for the rotating-disc electrode.
2.3.7 Reference Electrodes
Various reference electrodes were used to control the potential of the liquid phase in electrochemical experiments. The use of the common saturated calomel electrode
(SCE) was only limited to measurement in bulk containers. Most reference electrodes had to be prepared in-house to fit the electrochemical cell dimensions and the purpose of the experiment. Preparation of these electrodes is described herein.
Silver/silver chloride reference electrode
The most common reference electrode for the aqueous phase was a silver wire electrode coated with thin layer (20 – 50 μm) of silver chloride. The silver wire (99.99+%) was polished using fine sandpaper, flame-cleaned and immersed in 0.1 M KCl solution where it was oxidised by passing constant current (+5 mA) for 20 – 40 min. The stability of the
Ag/AgCl reference electrode prepared this way was unaffected by changes in current within the range +1 mA to + 5 mA. The Ag/AgCl reference electrode potential, E, is responsive to the chloride concentration (activity) as shown by the Nernst equation [153]:
0 RT E E ln a (2.2) F Cl
- 75 - where E0 = 0.222 V is the standard electrode potential (25 °C, against standard hydrogen electrode), R = 8.314 J mol−1 K−1 is the universal gas constant, F = 96485 C mol−1 is the
a Faraday constant and Cl is the activity of chloride ions in solution. The silver/silver chloride reference electrode potential stability with time is shown in Fig. 2.11.
Silver/silver sulphate reference electrode
An alternative reference electrode for the aqueous phase where the chloride based electrolyte was replaced with sulphate based one, was prepared. The silver/silver sulphate electrode was made by oxidizing of silver wire (99.99+% purity) in 0.1 M Na2SO4 solution.
Figure 2.11 Potential-time stability of the Ag/AgCl (A) and Ag/Ag2SO4 (B-E) reference electrodes. Aqueous solution contains 0.1 M Na2SO4 and 0.1 M NaCl. Current densities and times used for electrode preparation: A - high, 40 min; B - low, 17 h; C - low, 12 h; D – high, 6 h; E – high, 40 min. Low = 150 μA cm−2, high = 1.6 mA cm−2. The potentials were recorded after a month of storing the electrodes in saturated solution of KCl(A) and Na2SO4 (B-E). Measured in cell SCE| 0.1 M Na2SO4, 0.1 M NaCl (aq)| reference electrode.
After initial electrode preparation and subsequent testing of its stability it was found that more cautious control of the preparation conditions was required. The 0.1 M Na2SO4
- 76 - solution was degassed with argon for one hour prior to electrolysis. A thin layer of silver sulphate was formed on the wire surface. The solubility product of silver sulphate, Ksp, is
1.2 × 10−5 mol3 dm−9 [154], which may cause its dissolution during the experiment.
Therefore, the potential of several Ag/Ag2SO4 reference electrodes prepared at different current densities was checked against a commercial saturated calomel electrode (SCE). For the low current density used in electrolysis (150 μA cm−2 for about 17 h) the potential stability was excellent (See Fig. 2.11). The detailed exploration of the alternative silver/silver sulphate electrode system is discussed in section A6, Appendix.
Reference electrodes for the organic phase
The common approach to employ a stable and reproducible reference electrode for the organic phase is the introduction of another aqueous phase, which is in contact with the organic phase and contains a common partitioning ion with the organic phase, usually one of the ions of the organic electrolyte, to give a defined junction potential. The common partitioning ion maintains the equilibrium between the organic phase and the reference aqueous phase, in which a standard aqueous reference electrode can be used. The following liquid/liquid electrochemical cell scheme illustrates an example of this setup:
+ Ag|AgCl| 10 mM NaH2PO4, 10 mM NaCl, 0.3 mM tetraethylammonium (TEA ),
pH 7.4 (aq)| 10 mM BTPPATPBCl4 (1,2-DCE)| 1 mM BTPPACl, 10 mM NaCl|AgCl|Ag
The reference aqueous phase contains BTPPA+ cation as a common partitioning ion in this case. Other common partitioning ions used in liquid/liquid experiments were TPB−, and TDDA+.
Another approach is preparation of the reference electrode from silver wire coated with the anion of organic electrolyte and use of this electrode directly in the organic phase.
- 77 - [155] − − This has been reported in for TPB and TPBCl4 anions. Both silver/silver tetraphenylborate (Ag/AgTPB) and silver/silver tetrakis(4-chlorophenyl)borate
(Ag/AgTPBCl4) reference electrode were prepared, however, this approach was only used in cases with no other alternative due to slow stabilisation of the electrode potential as shown in Fig. 2.12.
Figure 2.12 Potential-time dependence for Ag/AgTPBCl4 reference electrode. Measured in cell: SCE| 1 mM BTPPACl, 10 mM Na2SO4, (aq)| 10 mM BTPPATPBCl4 (1,2-DCE)| AgTPBCl4|Ag.
- 78 - In Situ Artificial Membrane Permeation Assay under
Hydrodynamic Control
3.1 Introduction
In the last decade, the parallel artificial membrane permeation assay (PAMPA) has become a standard tool to predict human oral absorption of drug candidates in the early stages of the drug discovery pipeline. Although it is ideally suited only for transcellular absorption prediction, many advantages, such as high-throughput, low cost, possibility of pH profiling and stirring, over the conventional cell-based in vitro assays such as Caco-2
[42, 44] and MDCK [45], have made PAMPA a widely used screening method [8, 32, 50, 62, 76,
156, 157]. A number of groups have developed their own versions of PAMPA with the major difference being embedded in the membrane composition. The first supported liquid membrane (SLM) used in PAMPA consisted of egg-yolk lecithin in dodecane immobilised on a thin (100 μm) hydrophobic filter [32, 158]. The next generation of SLMs used 2% weight synthetic dioleoyl phosphatidylcholine in n-dodecane (DOPC-PAMPA)
[48]. This assay was a predecessor of a more advanced model called the Double-Sink method (DS-PAMPA) introduced by Avdeef et al. [8, 49, 50]. DS-PAMPA combines a pH gradient between the donor and acceptor solution (usually 5.0-7.4 and 7.4, respectively) and addition of chemical scavengers to the acceptor, to mimic the presence of serum proteins in blood. This results in double-sink conditions that suppress the back-flux permeation from the acceptor to donor compartment and shortens the experimental time.
A further advantage of this PAMPA version is the introduction of individual well stirring that enables the unstirred water layer (UWL) to be controlled on an empirical basis [65].
However, one drawback of this method is the high lipid content (20% by weight lecithin in dodecane) causing undesirably high membrane retention of lipophilic drugs. Sugano et
- 79 - al. used a mixture of various lipids dissolved in 1,7-octadiene to mimic the content of mammalian cell walls in a so-called „bio-mimetic‟ PAMPA (BM-PAMPA) [52], which gave an excellent prediction of the passive intestinal absorption in combination with a paracellular pathway model based on the Renkin function [67, 159]. Faller et al. introduced a version based on hexadecane, immobilized on a thin (10 μm) polycarbonate filter of low porosity, in order to resemble better the thickness of bi-layer membranes found in living cells (HDM-PAMPA) [51]. This group also used the PAMPA method for the high- throughput measurement of octanol/water partition coefficients [16]. More membrane models such as lipid-oil-lipid tri-layer membranes [54], liposome based membranes [55-57], n-octanol based lipid mixture precisely mimicking the Caco-2 monolayer [160, 161], blood- brain barrier mimics [59] and other approaches to permeability measurement [71, 134], or prediction of passive intestinal absorption [75] have been reported in the last decade. Also, the effect of lipid composition on permeability was investigated, based on a liposome permeation study [58].
Despite the rapid development of PAMPA since 1998, there are some issues that have been rarely, if at all, addressed in literature. First of all, many researchers still use inadequate analytical transport models to interpret their data. With increasing complexity of the assay, such as pH-gradient introduction, stirring, membrane retention, membrane saturation lag time, serum protein or precipitate presence, more advanced transport models need to be considered. An extensive list of the various transport models can be found in the literature [8]. Another issue is the ex situ analysis of the acceptor and donor wells and consequent single time-point data processing. Finally, the stirring of the aqueous phase has a profound effect on the permeability measurement and analysis.
Although the importance of stirring in permeability studies has been shown before
[49, 65, 69, 162, 163], most researchers still follow the unstirred version of PAMPA. The gastrointestinal tract provides mechanical stirring that enhances the absorption of the drug.
- 80 - The resultant unstirred water layer, i.e. the layer where the transport is merely governed by diffusion, arises adjacent to the intestinal wall. Similarly, on the opposite side of the intestinal wall the bloodstream convection enhances transport of the drug from the membrane to the circulatory system. Therefore an appropriate stirring analogy is needed for in vitro permeation models. Until recently, stirring of the aqueous compartment was employed using orbital shakers or magnetic stirrer bars. Such stirring methods result in turbulent stirring with unknown flux response to the applied stirring rate [65]. Some reports claim that the UWL layer could be as thick as 1.5–4.0 mm in the case of highly lipophilic/permeable molecules [65], which is supported by results presented below
(section 3.7). Since the UWL thickness in the human small intestine is assumed to be 30–
100 μm [88], the unstirred permeation assay does not match in vivo conditions correctly. As a consequence, the permeability of highly lipophilic drugs is underestimated due to the large UWL resistance hindering the permeation in the in vitro assay (e.g. verapamil, see below). Such underestimated permeability values do not give any information about the drug-membrane interactions and are not suitable for ranking of drug candidates within a specific membrane model. Moreover, the UWL affects the permeation to different extents, depending on the aqueous pH. In this chapter, a hydrodynamically controlled artificial membrane permeation study of thirty-one selected drug molecules is presented with detailed focus on four molecules of different charge types: warfarin (weak acid), verapamil (weak base), propranolol (weak base) and cetirizine (zwitterion).
Here, an in situ UV spectrophotometry measurement, resulting in an absorbance/concentration-time profile, is introduced. A similar approach has been reported by Kierstan et al. using polydimethylsiloxane membrane as a mimic for topical absorption of drugs [164]. An appropriate analytical model is derived to determine the effective permeability coefficient, Pe, using least-squares analysis of these time profiles.
The analytical model accounts for the following permeation attributes: pH-gradient
- 81 - between donor and acceptor compartments, membrane retention, membrane saturation lag time period and stirring.
The basic experimental method recently introduced from the Manchester electrochemistry group [66] was further developed into a single-permeation channel measurement designed to investigate physicochemical aspects of the drug permeation.
This novel method is an adaptation of the rotating-disc electrode system with its known transport equation with respect to the applied stirring rate [77, 100, 165, 166]. It employs in situ
UV measurement of the solute combined with stirring of both acceptor and donor compartments in a system with defined symmetric geometry. The acceptor pH is kept at
7.4, the donor pH is varied between 2.5 and 10.5. The standard permeation time is as short as 20-30 min and stirring rates in the range of 60-1500 rpm are used. The chosen membrane model comprised 1.5% weight of dioleoyl phosphatidylcholine and 0.5% weight stearic acid dissolved in 1,9-decadiene and immobilised on a hydrophobic PVDF filter. This membrane composition was based on collaboration with the industrial sponsor,
AstraZeneca. The solvent, 1,9-decadiene, is not too volatile, relatively safe to work with, and appears to be a good mimic of biological membranes [167].
The purpose of the study in sections 3.4 – 3.5 was therefore to examine drug permeation under controlled hydrodynamic conditions and to investigate the time- dependent flux of the compound observed in situ. In order to obtain an accurate permeability value, an analytical model allowing for the complexity of the assays as discussed above was developed (section 3.2 – 3.3). Furthermore, a numerical permeation model was developed to support experimental results. Permeability measurements of ionisable drug compounds as a function of pH along with permeability dependence on stirring rate, give two different approaches for the determination of the membrane permeability, intrinsic permeability and unstirred water layer permeability (see section
3.6). Permeability-pH profile data suggested an alternative transport mechanism across the
- 82 - membrane, which was subsequently studied using electrochemical techniques (Chapter 4).
In section 3.7 the hydrodynamic aspect of permeation were also studied and compared to the rather sparse literature data.
The scope of sections 3.8 – 3.9 was to investigate the temporal aspects of drug permeation that cannot be determined for the case of standard ex situ PAMPA analysis and empirical stirring. In particular the initial permeation transient phase also known as the lag time, τLAG, was investigated. The lag time is the time period required for the permeation to reach a steady-state and transport across the membrane to become governed by Fick‟s first law. Measuring concentration of the solute in real time allows accurate determination of the lag time. The effects of solute lipophilicity (membrane/donor distribution coefficient), stirring rate and concentration gradient between donor and acceptor, on this parameter were studied. Permeation properties of commercially available lipophilic drugs, midazolam, propranolol, quinine and verapamil were studied.
Propranolol permeation was studied in more depth to provide better understanding of lag time as a function of the aforementioned physicochemical properties. Related to this section is also Chapter 7, describing the modification of the permeation cell to an electrochemical bipolar cell in order to verify the hydrodynamics of the setup.
- 83 - 3.2 Method Development
The artificial membrane permeation assay under hydrodynamic control has previously been reported by this research group [31, 66]. The apparatus consists of buffered aqueous donor and acceptor compartments separated by a hydrophobic PVDF membrane
(Fig. 2.1). The solute (drug molecule) is dissolved in the donor compartment at an initial concentration cD(0) and is not originally present in the acceptor compartment. The flux of the solute, permeating across the membrane, is detected in situ in the acceptor compartment by UV spectrophotometry.
Sodium phosphate, sodium acetate and CHES buffer solutions were used depending on the target pH. The membrane consisted of 1,9-decadiene containing 1.5% weight DOPC and 0.5% weight stearic acid. Permeation was conducted at ambient temperature 21.8 ± 0.3 °C (mean standard deviation of > 50 measurements). The range of stirring rates was 60 – 1500 rpm, buffer concentration 30 mM (100 mM for warfarin and verapamil) and a fixed experimental run time 20 – 30 min. The organic phase(membrane)/aqueous phase distribution coefficients were determined using standard shake-flask methods. The detailed experimental procedure is described in section 2.3.2.
The analytical model used to determine permeability employs two-way flux equations (for donor-to-acceptor and acceptor-to-donor flux) and considers the following assay parameters: pH-gradient between the donor and acceptor compartment, drug retention in the membrane phase and lag time constant, τLAG (time necessary to reach the
[31] steady-state) . The concentration, cA(t), measured in situ in the acceptor compartment as a function of time, t, was transformed to a function, k, (See Fig. 3.2).
- 84 - 3.3 Analytical Transport Model
3.3.1 Derivation of the Analytical Transport Model
Various transport models with different limitations towards membrane retention, pH gradient, reverse-flux, lag time or surfactants have been summarised by Avdeef [8]. In order to interpret the data correctly, an advanced transport model that has been rarely used in PAMPA literature is presented herein. The model considers the pH-gradient between the donor and acceptor compartment (accounts for the reverse flux from the acceptor to the donor), takes the membrane retention into account (fraction of the drug molecule retained within the membrane) and corrects for the initial lag time, τLAG, (steady-state establishment across the donor-membrane-acceptor system). Correction for the lag time is important as the neglect of this factor leads to the permeability of lipophilic molecules being underestimated (conversely, the permeability of hydrophilic molecules is overestimated), as will be discussed below.
Figure 3.1 Schematic diagram of the concentration profile across donor- membrane-acceptor tri-layer for the case of: (a) zero UWL thickness, (b) non-zero UWL thickness. The distribution coefficient between the membrane and both donor and
acceptor, Kd = 2. Linear concentration distribution is assumed within the
membrane, time > τLAG.
The distribution of the drug in the donor-membrane-acceptor system is depicted in
Fig.3.1 for an (a) ideally stirred and (b) unstirred system. Both cases assume time > τLAG
- 85 - and therefore linear concentration distribution within the membrane. Fick‟s first law will apply for the permeation/diffusion in such a case.
The following relationships were used in the model derivation:
(i). Fick‟s first law applied to a homogeneous membrane:
DA AD Jt Pe cD t Pe cA t (3.1)
DA where J(t) is the time-dependent flux of the solute across the membrane, Pe and
AD Pe denote the effective permeability coefficients for the donor-to-acceptor and
AD acceptor-to-donor transport, respectively. Pe represents the reverse flux (acceptor-to- donor) transport that is usually neglected in PAMPA studies. Finally, cD(t) and cA(t) are the time dependent bulk concentrations of the solute in the donor and acceptor compartment, respectively. Note that by the effective permeability coefficient, Pe, we usually mean the donor-to-acceptor effective permeability coefficient, .
(ii). Diffusive flux at the membrane/donor interface:
V dc t Jt D D (3.2) A dt
(iii). Mass balance:
VDcD0 VDcDtVAcA tVmcm t (3.3)
where VD, VA and Vm are the volumes of the donor, acceptor and membrane, respectively,
A is the membrane area, cD(0) is the initial bulk solute concentration in the donor compartment and cm(t) is the time-averaged solute concentration within the membrane.
(iv). Finally, the expression for the fractional membrane retention Rf was used:
- 86 - VDcD tVAcA t Rf 1 (3.4) VDcD 0
We assume that for time > τLAG, Rf = Rf(∞) = const.
By combining Eq. (3.3) and (3.4) we obtain the mass balance equation containing the fractional membrane retention Rf:
VDcD0 VDcDtVAcA t Rf VDcD0 (3.5)
In the case of the ideally stirred system with zero UWL thickness, the effective permeability coefficients can be expressed as follows:
D K D PDA PDA m d (3.6) e m h
D K A PAD PAD m d (3.7) e m h
DA AD where Dm is the diffusion coefficient of the solute within the membrane, Pm and Pm are the membrane permeability coefficients of a solute for the donor-to-acceptor and
D A acceptor-to-donor flux, respectively. Kd and Kd are the solute distribution coefficients between the membrane-donor and membrane-acceptor, respectively, and h is the membrane thickness.
Combining equations (3.1), (3.2) and (3.5) we obtain a linear ordinary differential equation:
dc t D ac t b 0 (3.8) dt D where:
AP DA K A V a e 1 d D (3.9) D VD Kd VA
- 87 - and:
AD APe b cD 01 Rf (3.10) VA
The differential equation, Eq. (3.8), can be solved to obtain the analytical solution for times > τLAG:
lnk at LAG (3.11) where k is a function of the measured solute concentration in the acceptor compartment:
b V c 01 R A c t D f a V A k D (3.12) b c D LAG a
where cD(τLAG) is the solute bulk concentration in the donor compartment at time t = τLAG. Combining Eq. (3.6 – 3.7) and (3.9 – 3.10) we obtained the constant b/a, which is independent of the effective permeability:
b c 01 R D f (3.13) a K D V 1 d A A Kd VD
From the slope of the ln(k) vs. time plot, i.e. the constant a, Eq. (3.9), one directly obtains the effective permeability value. Note that τLAG is only a constant of integration so it could be treated as any time in the course of the experiment where Eq. (3.1 – 3.13) hold. In practice τLAG was chosen as the time at which the function of Eq. (3.11) starts to exhibit a linear behaviour.
- 88 - 3.3.2 Permeability Terms
Equations (3.1-3.13) describe the situation where the UWL thickness is zero and the solute concentration in the bulk donor (acceptor) solution and at the donor-membrane
(acceptor-membrane) interface is the same (Fig. 3.1a). In reality there is always a contribution of the UWL to the permeation and the bulk solute concentration in the donor compartment is always higher than at donor-membrane interface, as depicted in Fig. 3.1b
(likewise bulk solute concentration in the acceptor is always lower than acceptor- membrane interface concentration). Therefore what one measures is the effective permeability coefficient, Pe (or the apparent permeability coefficient in case of hidden assumptions such as no membrane retention of the solute and/or no solute reverse-flux from acceptor to donor compartment [8, 51]). The effective permeability consists of two independent terms: membrane permeability, Pm, corresponding purely to the transport through the membrane (no UWL contribution) and unstirred water layer permeability, Pu, corresponding to the transport through the two unstirred water layers adjacent to the membrane. Therefore the effective permeability can be described as the total resistance to passive transport across the tri-layer UWL(donor)-membrane-UWL(acceptor) system and is broken down into the two following terms [8, 65]:
1 1 1 (3.14) Pe Pu Pm
where Pu is the combined permeability of both donor and acceptor UWLs, Pm is the membrane permeability. In analogy to electrical circuits, the inverse permeability terms adds in a way similar to the electrical resistors connected in series.
- 89 - 3.3.3 Permeability Hydrodynamic Model
Approximate relationships between the UWL permeability and stirring rate have been used in previous Caco-2 and PAMPA studies [65, 69]:
Pu KP (3.15)
where is the angular velocity of stirring, α is an empirical exponent and KP is a constant dependent on the aqueous diffusion coefficient of the solute Daq, the aqueous kinematic viscosity, υ, and geometrical factors of the permeation cell. The explicit form for the case of symmetric geometry of the rotating-disc electrode was found by Levich [100]. The unstirred water layer thickness, δu, can be expressed as follows:
1/ 3 1/ 6 1/ 2 u 1.61Daq (3.16)
The Levich solution applied to the single UWL permeability yields:
2/3 1/6 Pu 0.62 Daq (3.17)
In pharmaceutical applications α is often treated as an empirical value, ranging from 0.7 to 1.0, and usually determined by the best fit in UWL permeability analysis [65, 69,
163]. Combining Eq. (3.15) and (3.16), assuming α = 0.5 produces a relationship between the unstirred water layer thickness and unstirred water layer permeability:
Daq Pu (3.18) u
Equation (3.18) is an analogue to equations (3.6) and (3.7) where the membrane permeability, membrane diffusion coefficient and the membrane thickness are substituted for the UWL permeability, aqueous diffusion coefficient and the UWL thickness,
- 90 - respectively. Assuming the two UWLs adjacent to both sides of the membrane are the
[73, 81-83] same, the combination of Eq. (3.14) and (3.17) yields the Pe – dependency :
1 2 1 2/3 1/ 6 (3.19) Pe 0.62 Daq Pm
Measuring Pe at two or more different stirring rates allows extrapolation to infinite angular velocity, where Pu = 0 and Pe = Pm, which yields the membrane permeability value. For the rotating-diffusion configuration the α value is 0.5. With the exception of verapamil and propranolol the exponent was set to 0.5 when extrapolating membrane permeability. In the case of these two highly lipophilic basic drugs which were studied in great detail (see below) the exponent was set to be 1.0. This change in exponent is related to the rapid permeation of propranolol and verapamil at high pH due to their high lipophilicity. This results in the measured α higher than 0.5, i.e. deviating from the ideal hydrodynamics. The α higher than 0.5 invalidates the Pm extrapolation (Eq. (3.19) yields negative intercept).
An empirical linear expression relating the effective permeability to the angular velocity stirring can be used to determine an experimental value of the hydrodynamic coefficient α:
log Pe log (3.20)
where α and β are the linear regression coefficients determined by measuring Pe at two or more different stirring rates.
The permeation cell used in this work was designed to have the same hydrodynamic properties on both sides of the membrane as the rotating-disc electrode.
Supplementary electrochemical experiments were performed to test the effect of distance between the paddle and the membrane on the resultant membrane flux (See Chapter 7).
- 91 - These latter results suggest that the hydrodynamics follow well the Levich equation well for paddle-membrane separations between 5 and 13 mm; hence the experimental separation was kept within this range.
3.3.4 Permeability-pH Dependence
For ionisable compounds the membrane permeability (Pm) depends on pH. Eq.
(3.21) defines the pH independent intrinsic permeability P0, i.e. the permeability of the neutral fraction, assuming that the pH-partition hypothesis [13] is valid:
pHpKa P0 Pm 10 1 (3.21)
Combining Eq. (3.14) and (3.21) and using the Henderson-Hasselbalch equation [168], yields the well-known relationship between the effective permeability and solution pH:
1 1 (10(pH-pKa ) 1) (3.22) Pe Pu P0
(The sign in the exponent is + for acids and – for bases.) From the slope of this dependence and knowledge of the solute pKa, one is able to calculate P0. Similarly the
[51, 65] intercept yields Pu .
3.3.5 Lag Time Determination
The exact lag time value was determined using the following procedure. Two parts of the ln(k)-time dependence were fitted with polynomial and linear functions, respectively. The polynomial (second order) function was fitted to the initial non-linear part (usually 0 – 400 s) whereas the linear function was fitted to the linear part (generally
> 700 s). The intersection of the two fitting equations is the lag time, τLAG, which was determined by solving the two fitting equations.
- 92 - 3.4 In Situ Time-Dependent Permeation and Numerical Transport Model
The acceptor compartment absorbance (concentration) of the permeating drug was recorded as a function of time and transformed to a ln(k)-time plot according to Eq. (3.11).
Examples of such plots for both warfarin and verapamil are shown in Fig. 3.2. Both molecules are ionized to approximately the same extent at these conditions. The lag time
τLAG, was determined using the procedure described above. The slope, a, of the ln(k)-time function for time > τLAG was then used to calculate the effective permeability, Pe, using
Eq. (3.9).
- 93 -
Figure 3.2 Example of concentration-time plots for (a) warfarin (309 nm channel) at donor/acceptor pH 6.5/7.4, (b) verapamil (280 nm channel) at donor/acceptor pH 7.4/7.4. The extent of ionisation is roughly the same for the two compounds at these donor pHs. Data for 250 (green) and 600 (red) rpm are shown. Derived ln(k)-time plots based on Eq. (3.11) are shown for (c) warfarin and (d) verapamil. Fitted dashed lines show the linear permeation profile with no membrane loading effects.
From Fig. 3.2c-d it can be seen that warfarin exhibits a more linear ln(k)-time response than verapamil: the plot of the latter only becomes linear in the middle of the time course. The non-linear behaviour of the verapamil permeation is caused by its higher membrane-donor distribution coefficient (lipophilicity) in comparison to warfarin (see
- 94 - Fig. 3.2c-d). Due to the higher verapamil lipophilicity and its higher molar mass (slower diffusion) the membrane saturation period, i.e. lag time, is considerably enhanced.
Fig. 3.3 shows a numerical simulation of the solute concentration in the membrane and donor as a function of time, when the membrane-acceptor transport is blocked. For the warfarin case (Fig. 3.3a) at 300 s the membrane has almost reached saturation due to
D the low membrane-donor distribution coefficient (log Kd = 0.320 0.022) and moderate molar mass (308.33 g mol−1) of warfarin. For verapamil at the same time, (Fig. 3.3b) the concentration profile within the membrane has not reached saturation, simply because the amount of solute needed for membrane saturation requires a longer period of diffusion because of the higher membrane-donor distribution coefficient (log = 2.026 0.002) and larger size (molar mass 454.60 g mol−1) of verapamil.
Figure 3.3 Numerical simulation of concentration profiles showing membrane saturation with membrane-to-acceptor transport blocked. Left to right: acceptor, membrane, donor. Zero stirring rate. (a) warfarin, with following input parameters: initial donor −7 concentration, cD(0) = 3.05 × 10 mol cm−3, aqueous diffusion −6 2 coefficient, Daq = 4.30 × 10 cm s−1, membrane diffusion coefficient, −7 2 −1 Dmem = 5.50 × 10 cm s , distribution coefficient (membrane- donor), = 0.178. (b) verapamil, with following input parameters: −7 −3 cD(0) = 2.02 × 10 mol cm , Daq = −6 2 −1 3.57 × 10 cm s , Dmem = 5.50 × 10−7 cm2 s−1, = 101.4.
- 95 - The fact that the membrane needs to be saturated to reach steady-state in the donor-membrane-acceptor system has some important consequences. First of all, if all three compartments were attached together at the start of the data acquisition, the ln(k)- time profiles would show the same non-linear transient as shown in Fig. 3.2. During this transient the time derivative of ln(k) is steadily increasing to reach a constant value at time equal to LAG. The length of this transient depends on the lipophilicity and membrane diffusion coefficient of the drug molecule as discussed later. Higher lipophilicity and/or lower diffusion coefficients would lead to a longer initial transient phase, similarly the lower lipophilicity and/or higher membrane diffusion coefficient shorten the initial transient. Experimentally, however, the three components (donor, acceptor and membrane) were never attached at the same time. In the experimental setup employed, the donor solution was placed in contact with membrane first, with some 60 – 120 s elapsing before the acceptor was attached and the experiment was started.
Figure 3.4 Schematic diagram of membrane loading with (a) hydrophilic and (b) lipophilic drug molecule. After the donor solution and membrane are placed in contact, the membrane starts to fill up with the solute (indicated by the red dotted curve). After the acceptor is attached, the concentration within the membrane must (a) level down in the warfarin case or (b) level up in the verapamil case with steady-state (indicated by the green dotted line). Such membrane pre-loading results in specific transients on ln(k)-time plots shown in (c) warfarin and (d) verapamil.
- 96 - For the less lipophilic warfarin molecule, this time was sufficient to saturate the membrane and induce the opposite effect in the transient in order to level down the membrane concentration profile to the steady-state shown in Fig. 3.4a. For the highly lipophilic verapamil molecule, the short pre-acquisition delay of 60 – 120 s was not sufficient to reach the steady state within the membrane and a „normal‟ transient effect is observed (Fig. 3.4b). The concentration-time plots for all other studied drug molecules can be found in Fig. A3.1 (see Appendix).
As expected, the experimental lag time values obtained by fitting the linear and transient segment of ln(k)-time plot increase with membrane-donor distribution (Table
3.1). As a consequence of the transient behaviour, the conventional single time-point analysis, neglecting the lag time, will lead to underestimation (or conversely overestimation) of the effective permeability of lipophilic (hydrophilic) molecules, respectively.
Table 3.1 Lag time values for verapamil permeation at various donor pH (acceptor pH 7.4) in comparison with donor-membrane distribution coefficients.
D a b donor pH log Kd LAG / s 6.5 1.428 0.008 747 1.8 7.0 1.825 0.005 1064 0.5 7.4 2.026 0.002 1103 0.8 8.0 2.426 0.024 1773 4.7 8.5 2.558 0.013 1934 3.3 9.0 2.718 0.026 3803 14.3 a The values obtained using the shake-flask method. b The lag time values were obtained by solving a set of two equations: 1. quadratic, fitted to non-linear transient segment of ln(k)-time plot; 2. linear, fitted to linear segment of ln(k)-time plot.
The errors were determined from a combined error of the linear and polynomial fit for an individual measurement and three independent measurement of the lag time.
- 97 - The lag time also depends of the stirring rate, suggesting that enhanced diffusion across both aqueous sides of the membrane leads to rapid establishment of the steady-state across the donor-membrane-acceptor interfaces. The lag time values for seven different stirring rates in verapamil iso-pH 7.4/7.4 permeation are listed in Table 3.2.
Table 3.2 Lag time values of verapamil at different stirring rates and iso-pH 7.4/7.4. Lag time was determined using the same method as in Table 3.1.
stirring rate / rpm LAG / s 200 1765 8.9 250 1552 4.4 290 1276 2.8 400 1372 2.3 600 1103 0.8 1000 1003 4.7 1500 471 3.1
The errors were determined from a combined error of the linear and polynomial fit for an individual measurement and three independent measurement of the lag time.
- 98 - 3.5 Dependence of Effective Permeability on Stirring Rate
The effective permeability coefficient was found as a function of the angular velocity of stirring as shown in Fig. 3.5 for warfarin and verapamil. The data were analysed assuming that the exponent α from Eq. (3.17) had the symmetric geometry value of 0.5 for warfarin, and the upper limiting value of 1.0 used in Caco-2 studies for verapamil [163]. The intercept of this dependence is the reciprocal of the membrane permeability (1/Pm). Using α = 0.5 for the verapamil at high donor pH case gave an intercept that fell into the negative region, implying very rapid permeation and breakdown of the ideal hydrodynamics. In order to obtain the membrane permeability coefficient by extrapolation, α = 1.0 was used for verapamil (which yields positive intercept values up to pH 8.0).
Figure 3.5 Dependence of the inverse of effective permeability on the stirring rate for (a) warfarin at pH = 6.5/7.4, (b) verapamil at pH 7.4/7.4. The warfarin and verapamil effective permeability values are plotted against −0.5 and −1.0, respectively. The membrane permeability is equal to the inverse of the vertical axis intercept. The data points are arithmetic means of three measurements (each being average of four wavelength channels), the error bars are standard deviation of the mean.
- 99 - 3.6 Permeability-pH Profiles
The effective permeability as a function of stirring rate was measured at different pH values of the donor solution, while keeping the acceptor pH constant (7.4). The permeability-pH profiles obtained for warfarin (acid), verapamil (base), propranolol
(base) and cetirizine (zwitterion) over a wide range of pH are shown in Fig. 3.6 – 3.9. The permeation data obtained under hydrodynamic control were supplemented with the unstirred data obtained in the same permeation cell. The membrane-donor distribution coefficient determined for all studied pHs can be found in the Table A4.2, Appendix.
Permeability hydrodynamic analysis
The hydrodynamic membrane permeability coefficient (filled diamonds in Fig. 3.6
– 3.9) was extrapolated from the dependence of the effective permeability on stirring rate via Eq. (3.19). The intrinsic permeability coefficient (unfilled diamonds in Fig. 3.6 – 3.9) was calculated from the hydrodynamic membrane permeability coefficient. The average
P0 value is plotted as a horizontal dashed line. The corresponding average Pm value, calculated using Eq. (3.21) is plotted as a solid curve. Finally the hydrodynamic UWL permeability coefficient, Pu, was calculated separately for each stirring rate and pH using
Eq. (3.14) (dashed curves in Fig. 3.6 – 3.9). The membrane and intrinsic permeability coefficients obtained from hydrodynamic extrapolation are listed in Table 3.3 along with the effective permeability coefficient obtained under unstirred conditions and the unstirred water layer permeability coefficient. The errors in Table 3.3 were obtained as a combined sum of the standard deviations of the three independent measurements (measuring Pe) and linear fit errors (as in Fig. 3.5). Experimental errors of simple laboratory measurements, such as volume determination, concentration calibration etc., were not included. The
„0.00‟ values indicate that the calculated errors are lower than the format of decimal places used, magnified by the fact that the values are in log format.
- 100 - Table 3.3 Permeability coefficients as function of the donor pH (description in the text)
Warfarin (average log P0 = −2.206 ± 0.032) a b c d donor pH log Pe (unst) log Pm log P0 log Pu (250rpm) 3.5 −4.43 0.03 −2.37 0.00 −2.35 0.00 −3.08 0.02 4.0 −4.37 0.02 −2.33 0.00 −2.37 0.00 −3.10 0.00 4.5 −4.34 0.02 −2.37 0.00 −2.20 0.00 −3.08 0.00 5.0 −4.36 0.06 −2.59 0.01 −2.19 0.01 −3.16 0.02 5.5 −4.38 0.02 −2.99 0.00 −2.23 0.00 −3.14 0.01 6.0 −4.38 0.01 −3.53 0.01 −2.33 0.01 −3.36 0.00 6.5 −4.50 0.01 −3.95 0.02 −2.26 0.02 −3.34 0.01 7.0 −4.71 0.02 −4.29 0.04 −2.11 0.04 −3.37 0.05 7.4 −4.97 0.01 −4.64 0.03 −2.06 0.03 −3.81 0.02 8.0 −5.41 0.02 −5.25 0.03 −2.07 0.03 −3.97 0.03
Verapamil (average log P0 = −0.893 ± 0.102) a b c d donor pH log Pe (unst) log Pm log P0 log Pu (250rpm) 5.5 −5.81 0.04 −4.37 0.02 −0.80 0.02 −4.29 0.03 6.0 −5.38 0.02 −3.68 0.01 −0.61 0.01 −3.73 0.02 6.5 −5.04 0.03 −3.34 0.04 −0.77 0.04 −3.51 0.00 7.0 −4.71 0.04 −2.91 0.01 −0.84 0.01 −3.28 0.02 7.4 −4.59 0.03 −2.69 0.01 −1.01 0.01 −3.22 0.04 8.0 −4.36 0.02 −2.43 0.01 −1.33 0.01 −3.12 0.01 8.5 −4.42 0.03 − − − 9.0 −4.53 0.05 − − − 9.5 −4.49 0.05 − − − 10.0 −4.56 0.05 − − −
Propranolol (average log P0 = −1.533 ± 0.352) a b c d donor pH log Pe (unst) log Pm log P0 log Pu (280rpm) 5.5 −5.48 0.01 −4.52 0.00 −0.49 0.00 −3.65 0.03 6.5 −5.07 0.01 −3.84 0.01 −0.81 0.01 −3.17 0.01 7.4 −4.77 0.02 −3.26 0.01 −1.13 0.01 −2.72 0.02 8.5 −4.29 0.00 −2.85 0.00 −1.78 0.00 −2.50 0.00 9.5 −4.32 0.00 −2.65 0.00 −2.33 0.00 −2.45 0.01 10.5 −4.40 0.00 −2.70 0.00 −2.65 0.00 −2.63 0.02
Cetirizine (average log P0 = −4.148 ± 0.067) a b c d donor pH log Pe (unst) log Pm log P0 log Pu (280rpm) 2.5 −5.02 0.02 −4.54 0.01 −3.99 0.01 −4.25 0.01 3.5 −4.80 0.04 −4.35 0.01 −4.25 0.01 −3.64 0.02 4.5 −4.98 0.02 −4.33 0.01 −4.32 0.01 −3.61 0.01 5.5 −4.88 0.01 −4.27 0.01 −4.26 0.01 −3.57 0.00 6.5 −4.82 0.02 −4.25 0.01 −4.23 0.01 −3.72 0.02 7.4 −4.77 0.03 −4.25 0.03 −4.15 0.03 −3.69 0.04 8.5 −5.06 0.00 −4.46 0.02 −3.83 0.02 −3.25 0.01
a Effective membrane permeability coefficient obtained under unstirred conditions. b Membrane permeability coefficient extrapolated using Eq. (3.19). c The intrinsic permeability coefficient calculated using Eq. (3.21). d The UWL permeability coefficient calculated using Eq. (3.14).
- 101 - The permeability-pH profile of warfarin in the range of pH 3.5 – 8.0 is shown in
[8] Fig. 3.6. Warfarin is a weak acid, with pKa = 4.82 . It is therefore predominantly ionized in the pH range of 6.5 – 8.0 and there is little change in the effective permeability with stirring rate at this pH. The permeation is membrane-limited in this pH region (Pu >> Pm).
In the pH range of 3.5 − 6.5 the permeability separation with stirring rate increases and permeation becomes diffusion-limited, as the aqueous phase permeability becomes
[62] comparable with that of the membrane (Pu ≈ Pm) .
Figure 3.6 Permeability – donor pH profile of warfarin at constant acceptor pH 7.4. The marks represent the apparent permeability values at different stirring rates: black square – unstirred, red circle – 250 rpm, brown circle – 400 rpm, yellow circle – 600 rpm, green circle – 1000 rpm and blue circle – 1500 rpm. The filled diamond symbols represent the membrane permeability extrapolated from hydrodynamics using Eq. (3.19) (the exponent α used in this extrapolation was 0.5), the unfilled diamond symbols are corresponding intrinsic permeability coefficients calculated using Eq. (3.21). All data points are arithmetic means of three independent measurements. The error bars are not shown as their size is comparable or smaller than symbol marks used here. The dashed curves represent the UWL permeability values calculated using Eq. (3.14). The uppermost horizontal dashed line is the average intrinsic permeability. The solid curve represents the membrane permeability calculated from the dashed line using Eq. (3.21).
- 102 - [8] Verapamil is a weak base with pKa = 9.07 . The verapamil permeability-pH profile in the range of pH 5.5 – 10.0 is shown is Fig. 3.7. One can see the overall effective permeability separation with stirring rate is much wider across the whole pH range compared to that of warfarin. The difference between the unstirred permeability coefficient (filled black squares) value and membrane permeability coefficient is more than 1.7 log units for the standard PAMPA conditions (donor/acceptor pH 6.5/7.4). The
UWL thickness in the unstirred assay at these pH conditions is 3830 m (calculated using equation (3.17), where Daq is given in Table 5.1 and Pu is found from Eq. (3.14)). Such a large UWL thickness makes the assessment of the membrane resistance to permeation impossible. This clearly shows how important the stirring and knowledge of the UWL contribution is to permeation.
Figure 3.7 Permeability – donor pH profile of verapamil at constant acceptor pH 7.4. The marks represent the apparent permeability values at different stirring rates: black square – unstirred, red circle – 250 rpm, brown circle – 400 rpm, yellow circle – 600 rpm, green circle – 1000 rpm and blue circle – 1500 rpm. The filled diamond symbols represent the membrane permeability extrapolated from hydrodynamics using Eq. (3.19) (the exponent α used in this extrapolation was 1.0), the unfilled diamond symbols are corresponding intrinsic permeability coefficients calculated using Eq. (3.21). The data lines/curves have the same meaning as in Fig. 3.6. All data points are arithmetic means of three independent measurements. The error bars are not shown as their size is comparable or smaller than symbol marks used here.
- 103 - Although Pu is generally assumed to be constant, the hydrodynamically extrapolated values show a dependence on pH (see the dashed curves in Fig. 3.6 and 3.7), with Pu falling for both solutes as their degree of ionization increases. The intrinsic permeability values extrapolated from the permeability-stirring rate relationship Eq. (3.19) also show a dependence on pH (unfilled diamond symbols), which is inconsistent with the pH-partition hypothesis [13]. In both the warfarin and verapamil cases, the intrinsic permeability increases slightly in the membrane-limited transport region (high pH for warfarin, low pH for verapamil). A possible explanation of this phenomenon is the transport of the ionized solute as ion-pairs, which would increase the intrinsic permeability in the membrane-limited pH region. Ion-pairing is likely to be facilitated by the charged organic components within the membrane rather than the aqueous phase counter-ions of low lipophilicity. Ion-pairing mechanisms facilitating permeation/partition were reported in previous literature [169-172] and it is predominantly observed for hydrophilic ionised molecules combined with lipophilic counter-ions [170]. This mechanism explains the variation in both Pu and P0.
The widely employed pH partition hypothesis assumes that only the neutral fraction of the ionised solute can partition into the membrane and contribute to the solute flux from the donor to the acceptor compartment [13, 173]. This hypothesis has, however, been questioned with experimental data suggesting that an ionic component to the flux exists [174]. Results for the drugs warfarin and verapamil show that the overall flux across the artificial membrane is higher than expected and implies that another form than the neutral is being transported, most likely as ion-pairs or true ions. This observation was therefore investigated in more detail, by extending the study to two other drug molecules,
[8] propranolol and cetirizine. The permeability – pH profile of the weak base (pKa = 9.53 ), propranolol in the range of pH 5.5 – 10.5 is shown in Fig. 3.8. According to the pH
- 104 - partition hypothesis, the intrinsic permeability, P0, should be independent of pH.
Measured P0 values, however, increase with decreasing overall flux across the membrane.
Intrinsic permeability increases with decreasing pH (Fig. 3.8). In other words, the overall flux across the membrane is higher than expected. At low pH, where only small fraction of propranolol is present as neutral molecules, the chance of detecting another form of transport, i.e. ionic/ion-paired, significantly increases.
Figure 3.8 Permeability – pH profile of propranolol. The marks represent the apparent permeability values at different stirring rates: black square – unstirred, red circle – 60 rpm, yellow circle – 110 rpm, and blue circle – 280 rpm. The filled diamond symbols represent the membrane permeability extrapolated from hydrodynamics using Eq. (3.19) (the exponent α used in this extrapolation was 1.0), the unfilled diamond symbols are corresponding intrinsic permeability coefficients calculated using Eq. (3.21). The data lines/curves have the same meaning as in Fig. 3.6. All data points are arithmetic means of three independent measurements. The error bars are not shown as their size is comparable or smaller than symbol marks used here.
Similar results were observed for the zwitterion, cetirizine, studied in the range of pH 2.5 – 8.5. Cetirizine is present in five known forms in aqueous solutions, double- ionized cation, single-ionized cation, neutral form, zwitterionic form and cetirizine anion.
The molecule has three dissociation constants, pKa = 2.12, 2.90 and 7.98, and the
- 105 - zwitterionic fraction is negligible compared to the neutral fraction [122]. The intrinsic permeability was found to increase both at the low and high pH end – Fig. 3.9, corresponding to its amphoteric nature (being in cationic and anionic form at low and high pH, respectively). An interesting fact to note is that the coloured dashed curves in Fig. 3.9 denoting the UWL permeability lie above the intrinsic permeability value. This observation supports the finding that cetirizine permeation is generally a membrane- limited process.
Figure 3.9 Permeability – pH profile of cetirizine. The marks represent the apparent permeability values at different stirring rates: black square – unstirred, red circle – 60 rpm, yellow circle – 110 rpm, and blue circle – 280 rpm. The filled diamond symbols represent the membrane permeability extrapolated from hydrodynamics using Eq. (3.19) (the exponent α used in this extrapolation was 0.5), the unfilled diamond symbols are corresponding intrinsic permeability coefficients calculated using Eq. (3.21). The data lines/curves have the same meaning as in Fig. 3.6. All data points are arithmetic means of three independent measurements. The error bars are not shown as their size is comparable or smaller than symbol marks used here.
Further to the permeability measurement, membrane retention defined by Eq. (3.4) and membrane diffusion coefficient calculated from Eq. (3.6) were recorded for all four
- 106 - drug molecules as a function of pH. The membrane retention values (in %), %Rf, and membrane diffusion coefficients are listed in Table A4.1, Appendix. As expected, membrane retention increases with increasing effective permeability of the drug. The membrane retention was set to zero in cases where the calculated value was negative due to experimental error (negative %Rf values were not generally lower than −5%).
Permeability-pH analysis
From the dependence of the effective permeability on pH, Eq. (3.22), the intrinsic permeability coefficient, P0, was calculated by least-squares analysis for all the stirring rates shown (0, 250, 400, 600, 1000 and 1500 rpm for warfarin and verapamil; 0, 60, 110 and 280 rpm for propranolol and cetirizine). The UWL permeability coefficient, Pu, was calculated separately for each stirring rate using Eq. (3.22). The UWL and intrinsic permeability coefficients of warfarin, verapamil, propranolol and cetirizine derived from the permeability-pH dependence are listed in Table 3.4. Note that both listed permeability coefficients increase with higher stirring rate applied. The increasing UWL permeability coefficient corresponds to the decreasing UWL thickness. The increasing intrinsic permeability coefficient, however, indicates that permeability-pH analysis is not a universal method and depends on the given hydrodynamic conditions.
- 107 - Table 3.4 Intrinsic and UWL permeability coefficients of warfarin, verapamil, propranolol and cetirizine determined from permeability-pH dependence.
Warfarin (average logP0 = −2.106 ± 0.019) a a stirring rate / rpm log P0 log Pu 0 −2.19 0.04 −4.39 0.08 250 −2.09 0.03 −3.39 0.04 400 −2.12 0.02 −3.17 0.03 600 −2.11 0.02 −3.13 0.03 1000 −2.06 0.03 −3.29 0.05 1500 −2.07 0.01 −3.13 0.02
Verapamil (average logP0 = −1.069 ± 0.237) a a stirring rate / rpm log P0 log Pu 0 −2.22 0.07 −4.52 0.05 250 −1.04 0.04 −3.13 0.06 400 −0.93 0.02 −3.02 0.03 600 −0.86 0.01 −2.79 0.02 1000 −0.74 0.02 −2.50 0.04 1500 −0.63 0.03 −2.62 0.02
Propranolol (average logP0 = −0.828 ± 0.191) a a stirring rate / rpm log P0 log Pu 0 −1.39 0.05 −4.62 0.04 60 −0.73 0.02 −3.54 0.03 110 −0.67 0.01 −3.39 0.03 280 −0.53 0.02 −3.26 0.01
Cetirizine (average logP0 = −3.872 ± 0.267) a a stirring rate / rpm log P0 log Pu 0 −4.10 0.07 −4.74 0.05 60 −3.79 0.04 −4.24 0.06 110 −3.88 0.02 −4.24 0.04 280 −3.72 0.03 −4.22 0.02
a Values obtained by the least-squares analysis of Eq. (3.22).
The values in the table represent means of three independent measurements and corresponding standard deviations combined with linear fit errors used in the calculation. Experimental errors of simple laboratory measurements, such as volume determination, concentration calibration etc., were not included.
- 108 - Comparison of the intrinsic permeability determined using the two approaches – hydrodynamic analysis and pH profile analysis is shown in Table 3.5. Results obtained from the two methods show reasonable agreement with the exception of propranolol, which shows a 0.7 log unit difference in measured permeability. To conclude, the hydrodynamic analysis outweighs the pH profile analysis as it only requires analysis at single pH point in order to determine P0 and Pu. The pH profile analysis, on the other, hand requires multiple pH point measurements in order to provide reasonable accuracy in determination of P0 and Pu.
Table 3.5 Comparison of the average intrinsic permeability values obtain from hydrodynamic extrapolation and permeability-pH profile.
a b drug log P0 (hydrodynamic) log P0 (pH profile) warfarin −2.21 0.03 −2.11 0.02 verapamil −0.89 0.10 −1.07 0.24 propranolol −1.53 0.35 −0.83 0.19 cetirizine −4.15 0.07 −3.87 0.27
a The intrinsic permeability average over the measured pH range obtained by the least-square analysis of Eq. (3.22). b Values obtained by the least-squares analysis of Eq. (3.22).
The values in the table represent means of three independent measurements and corresponding standard deviations. Experimental errors of simple laboratory measurements, such as volume determination, concentration calibration etc., were not included.
- 109 - 3.7 Permeability hydrodynamics
The experimental value of the hydrodynamic exponent α from Eq. (3.20) will be different from the theoretical value of 0.5, which is applicable only in the case of diffusion limited transport in the symmetrical rotating-disc case. The α values reported in the literature for empirical stirring approaches with permeation assays were obtained as a best-fit of the stirring-based analysis of UWL permeability. The exponent varied from
0.709 [65] in PAMPA studies to 0.8 [69] and 1.0 [163] in Caco-2 studies. In fact, the exponent
α is dependent on the membrane permeability and its value varies with solute identity and assay pH. Plotting the effective permeability against angular velocity in log-log units yields α as a gradient.
Figure 3.10 Hydrodynamic exponent α as a function of pH calculated by least-squares analysis of log Pe – log dependence, Eq. (3.20), for (a) warfarin, (b) verapamil, (c) propranolol and (d) cetirizine. The error bars are standard deviations calculated from the least-square analysis error. The dashed line represents the theoretical rotating-disc electrode system value of α, which would be observed in a system with symmetric geometry and solely diffusion limited transport.
- 110 - Fig. 3.10 shows the dependence of α on donor pH for warfarin, verapamil, propranolol and cetirizine. It increases with increasing neutral fraction for warfarin, verapamil, propranolol and cetirizine. Comparing the data in Fig. 3.10 with Fig. 3.9 it is evident that α is a measure of the effective permeability separation with stirring rate. As expected, for warfarin (Fig. 3.10a), α increases to its limiting value of 0.5 in the UWL diffusion-limited low pH region. The verapamil data (Fig. 3.10b), however, suggest non- standard hydrodynamic behaviour with α value exceeding 1.0 at high pH. Similar behaviour was observed in the case of propranolol permeation (Fig. 3.10c). The cetirizine data suggest only small dependence of alpha on pH with slight decrease at the two membrane limited regions, which is in agreement with zwitterionic nature of cetirizine. In the case of warfarin and cetirizine, α of 0.5 can be used in the membrane permeability extrapolation as the experimental α value is always under the 0.5 diffusion limit (Fig.
3.10a and 3.10d) and the extrapolation to the infinite stirring rate will yield a positive intercept (Fig. 3.5a). In case of propranolol and verapamil at high pH, however, the extrapolation to the infinite stirring rate will yield a negative intercept (Fig. 3.5b) corresponding to an experimental α value higher than the diffusion limit of 0.5 (Fig. 3.10b and 3.10c). For these reasons, an α value of 1.0 (literature value of Caco-2 assays [163]) was used for the membrane extrapolation of verapamil and propranolol. Due to atypical hydrodynamic behaviour of verapamil (which we attribute to fast permeation/high lipophilicity as discussed below), the membrane extrapolation still yielded a negative intercept at high pH (Fig. 3.10b – α is higher than 1 for pH ≥ 9).
As shown earlier, the hydrodynamic exponent, α, from Eq. 3.20 describes the permeation sensitivity to stirring. The lower the value of α, the more membrane limited permeation becomes, conversely a higher α value means transport limited permeation which is sensitive to stirring. The α value depends on the drug lipophilicity, fraction of neutral species and diffusion coefficients in the aqueous and membrane phase. Theoretical
- 111 - limits are α = 0 (permeation controlled by transport through the membrane) and α = 0.5
(theoretical value according to Eq. (3.17) – permeation controlled by transport through the aqueous solution).
We hypothesize that α correlates with the lipophilicity of the molecule
(membrane/buffer distribution coefficient at pH 6.5). Fig. 3.11 shows α as a function of lipophilicity for all 31 drug molecules studied in this work.
Figure 3.11 Dependence of α on the membrane/buffer distribution coefficient for the pH 6.5/7.4 permeation experiment of 31 studied drug molecules. Distribution coefficients were determined by shake-flask method (pH 6.5, Table A4.3, Appendix) and α calculated using Eq. (3.20). Horizontal axis error bars – standard deviation of three independent measurements, vertical axis error bars – goodness of fit used in α extrapolation (Eq. 3.20).
The correlation in Fig. 3.11 can be described empirically by the following equation:
3 2 0.0125 log Kd 0.0424 log Kd 0.0732 log Kd 0.0905 (3.23)
- 112 - One possible explanation for the deviation of α from 0.5 was the difference in the hydrodynamics from the conventional rotating-disc configuration. In the case studied here, the active membrane area occupies the whole face of the donor compartment (see
Fig. 2.1). Consequently, if this factor were significant, reducing the membrane area should bring α to 0.5 (or lower, depending on the system pH, see above). The hydrodynamic behaviour of verapamil (and propranolol) permeation at donor/acceptor pH 7.4/7.4 was investigated using a reduced apparent membrane area (0.1 cm2) on the donor side. Both the effective permeability coefficients and α values obtained from the standard and reduced membrane area experiment were, however, almost identical (See Table A2.1,
Appendix) indicating that the discrepancy seen with verapamil is not due to the hydrodynamic properties of the cell. Hence, a preliminary explanation of the atypical hydrodynamic behaviour of verapamil can be found in its high lipophilicity and correspondingly high permeability value.
An important parameter to consider, when simulating conditions found in vivo, is the unstirred water layer thickness, δu. UWL thickness as a function of stirring rate was determined using three different analytical approaches as shown in Table 3.6. The
„hydrodynamic‟ value was determined as an average of UWL thicknesses measured at different pH. The individual UWL thicknesses were calculating from Eq. (3.18) using hydrodynamic UWL permeability values (Eq. (3.14)). The „pH-profile‟ value was also determined from Eq. (3.18) using a UWL permeability value obtained from the least- square analysis of Eq. (3.22). Finally, the „Levich‟ value was obtained using the Eq.
(3.16).
Results in Table 3.6 show that UWL thicknesses obtained using the three different methods are in good agreement, with the pH profile analysis value being mostly the highest and Levich equation value mostly the lowest. The only exception is cetirizine, whose Pu values show high variation depending on the method of determination.
- 113 - Table 3.6 Comparison of the unstirred water layer thickness determined from: (a) hydrodynamic extrapolation, (b) pH-profile and (c) Levich equation.
Warfarin a b c stirring rate / rpm δu (HD) / m δu (pH) / m δu (Levich) / m 0 611 43 659 51 − 250 41 17 67 23 25 400 33 11 40 16 20 600 28 7 36 14 16 1000 20 8 52 12 12 1500 15 5 37 11 10
Verapamil a b c stirring rate / rpm δu (HD) / m δu (pH) / m δu (Levich) / m 0 832 38 739 43 − 250 34 11 30 17 22 400 25 7 23 10 18 600 16 4 14 5 14 1000 7 2 7 2 11 1500 4 9 3 9
Propranolol a b c stirring rate / rpm δu (HD) / m δu (pH) / m δu (Levich) / m 0 1180 102 1221 114 − 60 82 17 101 21 50 110 47 5 71 12 37 280 17 3 53 14 23
Cetirizine a b c stirring rate / rpm δu (HD) / m δu (pH) / m δu (Levich) / m 0 1107 84 1352 232 − 60 207 26 447 45 47 110 179 35 423 53 35 280 91 24 405 33 22
a UWL thickness determined from Eq. (3.18) using hydrodynamic UWL permeability value, averaged over all studied pH data points. b UWL thickness determined from Eq. (3.18) using UWL permeability value obtained from the least-square analysis of the pH-profile (Eq. 3.22). c UWL thickness calculated using Eq. (3.16).
The values in the table represent means of three independent measurements and corresponding standard deviations. Experimental errors of simple laboratory measurements, such as volume determination, concentration calibration etc., were not included.
- 114 - 3.8 Lag Time
The lag time, τLAG, is a time at which the permeation system, consisting of the donor, membrane and acceptor, reaches a steady-state and the permeation is driven only by the solute concentration gradient between the bulk donor and acceptor.
Mathematically, in the initial transient period the permeation follows a complex pattern of solute partitioning to the membrane and diffusion according to Fick‟s second law:
c 2c D (3.23) t x2 where c is the solute concentration, t is time, x is the position and D is the diffusion coefficient (aqueous and/or in the membrane). After time t = τLAG, when the steady-state across the donor-membrane-acceptor system has been established, the permeation can be approximated by Fick‟s first law:
c J D (3.24) x where J is the diffusive flux and other symbols have the same meaning as above. As the system reaches the steady-state, ln(k) becomes linear with time. Before the steady-state is reached, ln(k) shows a non-linear dependence on time which can be approximated with a parabolic function. The ln(k) – time plots of four drug molecules, propranolol, midazolam, quinine and verapamil, are shown in Fig. 3.12. Note that the lag time of verapamil is longer than the actual time of measurement. Careful examination of the permeation profile shows that the steady-state was not completely reached within the 20-minute experiment.
The permeation was carried out at donor/acceptor pH 6.5/7.4 and stirring rate 280 rpm.
- 115 -
Figure 3.12 Permeation ln(k) – time plots of propranolol, quinine, verapamil and midazolam (donor/acceptor pH 6.5/7.4 and stirring rate 280 rpm) showing the varying lag time. The initial donor concentration was 320, 255, 210 and 80 M for propranolol, quinine, verapamil and midazolam, respectively. The intercepts represent lag time values determined using procedure described in section 3.3.5.
The non-linear behaviour occurs due to the loading of the membrane with the solute. This has previously been supported by a numerical simulation referred to in section
3.4 [31]. After the donor-membrane-acceptor system has been assembled, the solute has to reach a steady-state concentration within the membrane. Membrane loading with drug and therefore the lag time depends on:
(1) The total amount of solute partitioning to the membrane, i.e. the initial donor
concentration, membrane/donor distribution coefficient and membrane thickness.
(2) The rate at which the solute is transported, i.e. aqueous and membrane diffusion
coefficient (proportional to the solute size) and stirring of the aqueous
compartments.
Reports on in vitro permeation across lipid bilayers and supported liquid membranes quote lag time values in the range of 1 – 60 min [164, 175, 176]. Lag times values of the propranolol, midazolam, quinine and verapamil along with their molar mass, distribution and aqueous diffusion coefficients are listed in Table 3.7.
- 116 - Table 3.7 Lag time and physicochemical properties of propranolol, quinine, midazolam and verapamil.
−1 D a −6 2 −1 b e drug Mr / g mol log Kd Daq /10 cm s τLAG / s propranolol 259.34 1.96 ± 0.01 4.70 781 ± 47 quinine 324.42 0.86 ± 0.00 4.21 782 ± 19 midazolam 325.78 1.96 ± 0.01 4.20 1036 ± 35 verapamil 454.60 1.43 ± 0.01 3.57 1416 ± 78
a Membrane/aqueous buffer drug distribution coefficient determined using shake-flask method at aqueous pH 6.5 and temperature 22 °C. b Aqueous diffusion coefficient calculated using Eq. (4) in ref. [62]. c Lag time values determined by extrapolation of the polynomial and linear segment of ln(k) – time dependence measured at donor/acceptor pH 6.5/7.4 and stirring rate 280 rpm. The errors were determined from a combined error of the linear and polynomial fit for an individual measurement and three independent measurement of the lag time.
The intestinal residence time has been reported to be between 1 – 3 h [25]. It is shown that for the drug molecules investigated in this report, the lag time is well within the intestinal residence time, suggesting that the initial transient phase of permeation is unlikely to be an issue to hinder drug absorption in vivo. However, for lipophilic molecules where the doses are low, the expected longer lag times could be an issue and might potentially lead to unexpectedly poor absorption in pre-clinical and/or clinical studies. It would be of great interest to study the lag time on a larger number of lead molecules from a wider chemical space.
3.8.1 Dependence on Stirring Rate
Stirring decreases the unstirred water layer thickness and thus increases measured effective permeability. Fig. 3.13 shows ln(k) time profiles of propranolol obtained at stirring rate 60, 80, 110, 160 and 280 rpm.
- 117 -
Figure 3.13 Permeation ln(k) – time plots of propranolol (225 nm channel) at donor/acceptor pH 7.4/7.4. Data for stirring rates 60 rpm (black), 80 rpm (red), 110 rpm (orange), 160 rpm (green) and 280 rpm (blue) are shown. The lag time calculated for three stirring rates, 60, 110 and 280 rpm, is indicated.
Similar to the permeability terms, there are two separate components contributing to the overall lag time value. One component, τLAG,m, arises from the partitioning and loading of solute to the membrane whereas the other one, τLAG,u, occurs due to solute transport through the unstirred water layer adjacent to the both sides of the membrane.
The observed lag time, τLAG, is a sum of the two.
LAG LAG, u LAG, m (3.25)
For the membrane loading process itself, the lag time can be approximated from the
Fick‟s second law as [133, 177]:
h2 LAG, m (3.26) 6Dm
- 118 - Using a similar relationship, where thickness and membrane diffusion coefficient are replaced with UWL thickness, δu, and aqueous diffusion coefficient, Daq, for the UWL dependent term the following relationship is obtained:
2 2 u h LAG K (3.27) Daq 6Dm
where Kτ is an empirical constant. The aqueous term in Eq. (3.27) can be further expressed as function of stirring rate (Eq. (3.17)):
2 1/3 1/3 1 h LAG 2.6 K Daq (3.28) 6Dm
Lag time values measured for propranolol permeation at several different stirring rates are plotted in Fig. 3.14. The graph shows a linear dependence of τLAG, on inverse angular velocity of stirring, 1/ω, for propranolol at donor/acceptor pH 6.5/7.4. According to Eq. (3.28), the intercept of this dependence should be equal to τLAG,m. Substituting the membrane thickness (assumed to be 125 – 200 m due to excess of organic solvent immobilised on the membrane filter) and the membrane diffusion coefficient (calculated from Eq. (3.6) and averaged over the values measured at different donor pH 5.5 – 10.5) to
Eq. (3.26) yields membrane lag time value τLAG,m of 113 – 290 s. This is in a good agreement with the experimental value of 236 ± 2 s (Fig. 3.14). From the slope of the τLAG, dependence on 1/ω the constant Kτ of Eq. (3.27 – 3.28), was also calculated. Although it is expected that the experimental Kτ value would be a small number related to the membrane geometry (similar to the 1/6 factor of the second term in the Eq. (3.27 – 3.28)), a Kτ value of 130 is found.
- 119 -
Figure 3.14 Dependence of the lag time on the inverse angular velocity of stirring for propranolol permeation at donor/acceptor pH 6.5/7.4. Lag time values are the means of three measurements, the vertical-axis error bars standard deviations of the three. The intercept corresponds to the membrane loading time, τLAG,m, at infinite stirring.
3.8.2 Dependence on Lipophilicity
For an ionisable solute, the lag time is dependent on the membrane-donor distribution coefficient, and therefore on pH. This is consistent with the basic idea of solute partitioning from the donor to the membrane phase at the beginning of permeation.
The higher the distribution coefficient, the more time it will take for the bulk solute to saturate the membrane (process becomes diffusion limited). A graph showing the lag time changing with the membrane-donor distribution coefficient of propranolol for stirring rates 60, 110 and 280 rpm is in Fig. 3.15. Note that the lag time dependence on stirring rate is much stronger than the dependence on the distribution coefficient. This once again shows the importance of controlled hydrodynamic conditions in permeation assays.
- 120 -
Figure 3.15 Dependence of the lag time on the membrane/donor distribution coefficient of propranolol (permeation at donor/acceptor pH 6.5/7.4 and stirring rates 60, 110 and 280 rpm). Lag time values are means of three measurements, the vertical-axis error bars standard deviations of the three.
3.8.3 Dependence on Concentration Gradient
Lag time not only depends on the solute fraction partitioning to the membrane but also on the total amount of solute present in the donor phase prior to permeation. To determine the lag time at different concentration gradients between donor and acceptor solution, permeation of propranolol was carried out at donor/acceptor pH 7.4/7.4 and stirring rates 60, 110 and 280 rpm. Initial drug concentration in the donor solution, cD(0), was varied between ca. 30 and 300 M. The lag time was found to decrease with an increase in concentration gradient between the donor and acceptor phase as shown in Fig.
3.16. This observation suggests an obvious explanation that the larger concentration gradient generates a larger driving force for diffusion and therefore leads to a shorter lag time to establish the steady-state. This underlines the importance of unified inter- laboratory permeation assay standard in the cases where the analytical permeability model
- 121 - does not allow for the lag time. In such cases the data coming from different research groups are not directly comparable.
Figure 3.16: Lag time dependence on the initial donor concentration of propranolol at donor/acceptor pH 7.4/7.4 and stirring rates of 60, 110 and 280 rpm. Lag time values are means of three measurements, the vertical-axis error bars standard deviations of the three.
- 122 - 3.9 Permeability Dependence on Concentration Gradient
PAMPA, Caco-2 or MDCK permeability models and also the model used here implicitly assume that the measured permeability is independent of the concentration gradient between the donor and acceptor solution [8, 31, 32, 42, 45, 48, 49, 51, 52]. In order to examine this assumption, we have performed permeation measurements of propranolol at four different initial donor concentrations. Permeation was performed at donor/acceptor pH 7.4/7.4 to ensure the same distribution coefficient between the membrane/donor
(acceptor), respectively. Surprisingly, permeability was found to be slightly dependent on donor/acceptor concentration gradient. Fig. 3.17 shows the unstirred, effective (stirring rates 60, 110 and 280 rpm) and membrane permeability measured for different initial drug concentration in the donor compartment, cD(0).
Figure 3.17 Permeability dependence on the initial donor concentration of propranolol at donor/acceptor pH 7.4/7.4 and stirring rates of 60, 110 and 280 rpm. Permeability values are means of three measurements, the vertical-axis error bars standard deviations of the three.
- 123 - Although the increase in permeability with decreasing concentration gradient is not substantial, these findings show that the permeability is a parameter non-comparable in interlaboratory studies, as the initial donor concentration changes with specific assay requirements and/or drug solubility.
The hydrodynamic exponent, α, and the intrinsic permeability, P0, calculated from
Eq. (3.20) and (3.21), respectively, were also measured and found to be concentration gradient dependent. The values of Pe(unstirred), Pe (280 rpm), Pm, P0, and α for different initial drug donor concentrations are listed in Table 3.8. As shown, all permeability coefficients and also the hydrodynamic exponent α increase with a decrease in concentration gradient. At present no satisfactory explanation is available for this interesting observation, although a solute-lipid interaction, enhancing transport across the membrane, would clarify the observed behaviour.
Table 3.8 Permeability coefficients and the hydrodynamic exponent of propranolol as a function of initial drug concentration in donor compartment (donor/acceptor concentration gradient).
cD(0) / M log Pe (unstirred) log Pe (280rpm) log Pm log P0 α 317.1 ± 4.2 −4.77 ± 0.02 −3.37 ± 0.01 −3.26 ± 0.01 −1.13 ± 0.01 0.33 ± 0.01 152.3 ± 0.1 −4.56 ± 0.01 −3.37 ± 0.01 −3.25 ± 0.00 −1.12 ± 0.00 0.37 ± 0.01 64.6 ± 0.2 −4.53 ± 0.03 −3.33 ± 0.01 −3.20 ± 0.01 −1.11 ± 0.01 0.40 ± 0.01 37.5 ± 0.2 −4.49 ± 0.02 −3.32 ± 0.02 −3.06 ± 0.00 −0.93 ± 0.00 0.54 ± 0.00
The values in the table represent means of three independent measurements and corresponding standard deviations combined with any linear fit errors used in the calculation. Experimental errors of simple laboratory measurements, such as volume determination, concentration calibration etc., were not included.
- 124 - 3.10 Conclusions
The permeability of drug molecules has been investigated in a PAMPA configuration using a time-dependent approach: to the best of our knowledge, this is the first attempt using such an in situ analysis. We have been able to measure directly effective permeability coefficients as high as 4305 10−6 cm s−1 and as low as 2.5 10−6 cm s−1 under stirred conditions, in comparison to the range of 47 10−6 cm s−1 to 0.8
10−6 cm s−1 under unstirred conditions. The effect of unstirred water layer permeability on the effective permeability has been clearly revealed by the use of the hydrodynamic
(rotating) system. Measurement of permeability as a function of pH and stirring rate gives an apparent pH dependence of the membrane permeability, from which we infer that some transport of ionized solutes occurs, most likely via an ion-pairing mechanism. The hydrodynamics of the rotating-disc describe the permeability of the moderately lipophilic molecules (warfarin and cetirizine) well, but deviations are seen for the highly lipophilic solutes (verapamil, propranolol). Further work studying the transport dependence of permeability on the external polarisation of the membrane will be revealed in Chapter 4.
The use of an in situ permeability measurement, coupled with controlled hydrodynamics, allows the accurate measurement of intrinsic permeability, and has revealed that a significant “lag time” exists before a steady membrane transport rate is established. The lag time values varied from 420 to 1900 s for the four studied drugs and applied conditions (solute distribution coefficient 7 – 160, stirring rate 60 – 280 rpm, concentration gradient 40 – 320 M). The lag time is strongly correlated with the lipophilicity of the solute, leading to differing initial forms of the concentration transient.
Failure to account for this lag time leads to an underestimation of permeability for lipophilic molecules (and conversely permeability overestimation for hydrophilic molecules), which is potentially a significant problem for PAMPA, given the current focus in the pharmaceutical industry on target molecules of increasing lipophilicity.
- 125 - Variability of the membrane loading lag times with solute‟s physicochemical properties was demonstrated from permeation of four lipophilic drug molecules, with detailed analysis performed for propranolol. Results show that lag time decreases with an increase in stirring rate due to decreasing thickness of unstirred water layer, which accelerates the transport of the drug to the organic membrane. Similarly, the lag time decreases with an increase in the concentration gradient due to increasing driving force for permeation.
Increasing membrane/donor distribution coefficient (lipophilicity) has been proven to slightly prolong lag time as more of the solute is required to partition from donor to the membrane. Rather unexpected results were obtained when concentration gradient between the donor and acceptor was varied. The effective (unstirred and stirred), membrane and intrinsic permeability coefficients and hydrodynamic exponent increase with decreasing concentration gradient.
- 126 - Permeation assay with external membrane polarisation
4.1 Introduction
Polarisation of the organic membrane separating two aqueous phases has been reported in the field of liquid/liquid electrochemistry [139-143, 145, 146] and for drug extraction
[70]. High voltages of 300 V DC were used for drug extraction [134-136] although attempts were made to reduce applied potential to smaller voltages of 1 – 15 V DC [137, 138]. Here, external membrane polarisation is applied to the artificial membrane permeation assay under hydrodynamic control. The basic concept of this approach was to apply a relatively small potential difference (−5 to +5V) between the two aqueous phases and study the resultant effect on permeation.
Due to the hydrophobic nature of the organic membrane the most favoured way of transporting the drug molecule is via its neutral form. The pH-partition hypothesis assumes that the transport occurs exclusively via the neutral fraction of the drug molecule
[13]. Results from detailed analysis of permeability coefficients as a function of pH suggest that some other form of transport is observed at conditions where the neutral fraction of the drug becomes negligible (see section 3.6). Indeed, the pH-partition hypothesis is often criticised for its limited applicability as contradictory results have been observed [92-95, 97,
98]. Also, some researchers report partitioning of other forms such as zwitterions, ion-pairs and/or true ions into the lipophilic phase [74, 172, 178, 179].
A model system chosen for analysis was a donor solution containing 300 μM cetirizine at pH 8.5. This drug molecule has a reasonable molar absorption coefficient and a high amount of unknown non-neutral flux was observed at this pH (compare Fig. 3.9).
Cetirizine is a zwitterionic drug compound with three dissociation constants, pKa = 2.12,
2.90 and 7.98 [122]. About 23% of the drug is present as its zwitterionic form at pH 8.5, the
- 127 - rest of it is present as the monovalent anion (less than 0.001% in neutral form). Therefore applying a positive potential difference between the acceptor and donor compartment (i.e. making acceptor phase more positive) should theoretically enhance the flux of cetirizine across the membrane. This could, in an ideal case, be detected by the UV absorbance measurements. Fig. 4.1 depicts the experimental setup with three possible ways of transport.
Figure 4.1 Schematic of the permeation of a molecule via different ways of transport.
The organic membrane used in the permeation method with external polarisation consists of three organic components dissolved in a lipophilic solvent, namely 1,9- decadiene (see Fig. 4.2). Combined with the drug molecule, cetirizine, present in the donor phase, the permeation cell is a complex system.
Figure 4.2 Composition of the aqueous and membrane phase
- 128 - The organic membrane components are a possible source of interference in cetirizine detection, both for the UV absorbance and electrochemical methods. For this reason, the permeation cell containing various combinations of membrane organic components and drug molecules present/absent in the donor phase was studied using potentiometric, voltammetric and amperometric methods coupled with UV spectrophotometry.
- 129 - 4.2 Experimental
The detailed experimental procedure including the schematic of the permeation cell with external membrane polarisation (Fig. 2.3) can be found in section 2.3.4. Briefly, the permeation cell was equipped with a four electrode system (two counter and two reference electrodes) and a potential difference was applied between the donor and acceptor phases. Sodium chloride was added to the buffered aqueous phase to maintain stability of the silver/silver chloride reference electrodes. The organic membrane phase also included an organic electrolyte, tetradodecylammonium tetrakis(4- chlorophenyl)borate (TDDATPBCl4), to support the current passing through the membrane, as the attempts to use the standard membrane failed. The current-potential dependence of the system with the standard membrane composition (with no added electrolyte) showed an ohmic response indicating that the current was simply limited by the high resistance of the organic layer. The solubility of the organic electrolyte in 1,9- decadiene was found to be higher than 0.1 mol dm−3, which was sufficient to perform electrochemical measurements on the membrane. The only difference between the permeation method presented in Chapter 3 and the modified polarised method presented here is, therefore, the presence of the organic electrolyte in the membrane.
Apart from the UV spectrophotometry, the methods used for permeation with membrane polarisation included zero current potentiometry, amperometry and cyclic voltammetry. Also, cyclic voltammetry and amperometry measurements synchronized with the UV absorbance acquisition, i.e. spectro-electrochemical methods, were used.
- 130 - 4.3 Results and Discussion
4.3.1 Resistivity of the Permeation Cell
Before the model drug molecule, cetirizine, could be studied, blank permeation experiments in a system only containing buffer solution were conducted. When the standard permeation assay membrane composition was used, the resistivity between the acceptor and donor phase was found to be 400 – 500 kΩ m (for several independent permeation cell assemblies). Such a high resistivity can be attributed mostly to the 125 m thick organic membrane as the resistivity of the aqueous phase at these conditions does not usually exceed 2 Ω m (measured on a cell without the membrane). High resistivity rendered the voltammetric measurements irreproducible and application of a potential difference in the range of 0 – 1 V resulted in no change in measured UV absorbance. In order to reduce the solution resistivity, 10 mM organic electrolyte, TDDATPBCl4, was added to the organic membrane. The average permeation cell resistivity dropped to 30 –
50 kΩ m, i.e. about 10-fold, after the electrolyte was added. The solution resistivity was found from the measured resistance and geometric properties of the permeation cell.
4.3.2 Open Circuit Potential Measurements
As described in section 2.3.4, permeation was started simultaneously with stirring without measuring UV absorbance for 10 min. During this period the open circuit potential (OCP) difference between the acceptor and donor phase was measured. The
OCP difference is the potential difference measured with virtually no external intervention to the electrochemical system induced by the potentiostat. The OCP was corrected for the potential difference between the two reference electrodes in the aqueous compartments.
OCP differences measured at various membrane compositions for the blank permeation cell system (no drug molecule) at donor/acceptor pH 8.5/7.4 are shown in Fig. 4.3.
- 131 -
Figure 4.3 Open circuit potential difference between the acceptor and donor phase measured for various membrane compositions (no drug). Black curve: standard membrane composition + TDDATPBCl4, i.e. 1.5% weight DOPC, 0.5% weight stearic acid and 2.2% weight TDDATPBCl4 in 1,9-decadiene; red curve: electrolyte only, i.e. 2.2% weight TDDATPBCl4 in 1,9-decadiene, green curve: 1.5% weight DOPC and 2.2% weight TDDATPBCl4 in 1,9-decadiene, blue curve: 0.5% weight stearic acid and 2.2% weight TDDATPBCl4 in 1,9-decadiene. Measured in blank (no drug molecule) permeation cell. Aqueous phase contained 30 mM sodium phosphate and 1 mM sodium chloride solution at pH 7.4 (acceptor) and 8.5 (donor). The potential value was corrected for the absolute potential difference between the two reference electrodes (+150 mV).
With the exception of the case where only the organic electrolyte is present in the membrane solvent, all studied cases show a stable potential-time response after the initial
60 s of measurement. The average difference in OCP between the case with the organic electrolyte only and the normal PAMPA membrane composition with organic electrolyte
(black and red curves in Fig. 4.3) is +100 mV. Introduction of DOPC and stearic acid into the membrane therefore decreased the potential difference between the acceptor and donor phases. In the case where only stearic acid and the organic electrolyte were present, the response was very similar to that of standard membrane composition. When only DOPC and organic electrolyte were present in the membrane the potential further dropped by another 60 mV below the standard membrane composition response. Note that the
- 132 - potential measurement in the permeation cell indicates that the supported liquid membrane separating the two aqueous phases is a continuous medium with a function similar to liquid and polymer based ion-selective electrodes (ISE). These ISE contain chelating agents designed to mediate ion-exchange of various charged species [77].
The open circuit potential measurement was also carried out for the permeation system containing the drug molecule, cetirizine, in the donor compartment at 300 μM. The variation of the OCP measured for different membrane compositions has significantly decreased and also the overall OCP value has decreased compared to the case where no drug molecule is present in the donor compartment. Fig. 4.4 shows the OCP for different membrane composition in a system containing cetirizine. Comparison with Fig. 4.3 indicates that the presence of cetirizine anion in the permeation cell reduces the observed potential difference between different membrane composition cases.
Figure 4.4 Open circuit potential difference between the acceptor and donor phase measured for various membrane compositions (cetirizine). The colour scheme showing the different membrane composition is the same as in Fig. 4.3. Both aqueous phases contained 30 mM sodium phosphate and 1 mM sodium chloride solution at pH 7.4 (acceptor) and 8.5 (donor). The donor phase contained 300 μM cetirizine. The potential value was corrected for the absolute potential difference between the two reference electrodes (+150 mV).
- 133 - 4.3.3 Cyclic Voltammetry on the Permeation Cell
Cyclic voltammetry in the range −5 to +5 V
In order to examine the current response to the potential applied between acceptor and donor phase, a series of cyclic voltammetric measurements was carried out. The potential window, i.e. the potential difference range, of the blank permeation system is an important indicator of the membrane polarisability and stability of the membrane components with respect to the applied potential. A large potential window, in the range of −5 to +5 V was explored first. Fig. 4.5 shows a cyclic voltammogram for three different systems recorded simultaneously with the UV absorbance in the acceptor compartment at a constant stirring rate of 120 rpm. A similar experimental method was presented by
Kakiuchi et al. for an ion transfer across a liquid/liquid interface [180, 181]. Three different cases were studied by cyclic voltammetry in this wide potential range: blank permeation cell (no drug molecule) with membrane only containing solvent and the organic electrolyte, blank permeation cell with standard permeation assay membrane and organic electrolyte, and finally a permeation cell containing 300 μM cetirizine in the donor compartment and standard permeation assay membrane with organic electrolyte. The cyclic voltammogram in Fig. 4.5a was obtained by sweeping the potential from 0 to + 5V, then down to −5 V and back to the 0 V at scan rate of 40 mV s−1. The red curve corresponds to the system with no drug molecule and only containing the organic electrolyte and solvent in the membrane. The red curve shows the lowest current response up to ca. +1.5 V, which indicates that the organic electrolyte tends to stay in the membrane. Above +2 V the current response of the red curve rises above the other two showing that this membrane composition is no longer stable and the organic electrolyte
− has been driven out of the membrane (anion TPBCl4 to the acceptor compartment and cation TDDA+ to donor compartment). The likely explanation for this observation might be an increased membrane viscosity that inhibits ion transfer (black and blue curves).
- 134 -
Figure 4.5 Cyclic voltammetry coupled with in situ UV measurement in the acceptor (5 V to +5 V). Graph (a) shows cyclic voltammograms measured at three different conditions: membrane only containing solvent and organic electrolyte and no drug in the donor (red), standard membrane + organic electrolyte and no drug in the donor (black), and standard permeation assay membrane + organic electrolyte and 300 μM cetirizine drug in the donor (blue). Graph (b) shows the response in the acceptor measured via UV absorbance. The absorbance was measured at 230 nm. The voltammogram was obtain by scanning from 0 to + 5V, then down to −5 V and back to the 0 V at 40 mV s−1. Both aqueous phases contained 30 mM sodium phosphate and 1 mM sodium chloride solution at pH 7.4 (acceptor) and 8.5 (donor). The membrane was rotating at 120 rpm and cyclic voltammetry was started at 300 s. The potential value was corrected for the absolute potential difference between the two reference electrodes (+150 mV). The inset graph (a) shows the detail of the four observed peaks (with drug molecule) corrected for the response of the standard membrane (no drug molecule). The inset graph (b) shows the whole UV spectra in the range of 200 – 400 nm at t = 1000 s for the three studied cases.
- 135 - − This would lead to the anionic component of the electrolyte, TPBCl4 , being detected in the acceptor compartment via UV absorbance as shown in Fig. 4.5b. It has been shown that DOPC and stearic acid driven to the aqueous phase mainly contribute to the non- wavelength specific background increase in absorbance (Figure A2.1, Appendix). As the inset graph in Fig. 4.5b shows, in the case of cyclic voltammetry, the background absorbance did not increase. Therefore the observed change in the absorbance in the wavelength range of 200 – 280 nm can be predominantly attributed to the organic electrolyte (TDDATPBCl4). This is also supported by measured absorbance spectra of
+ TPBCl4 , TDDA , stearic acid, DOPC and 1,9-decadiene emulsion in the aqueous buffer
solution (Fig. A2.4, Appendix). The results show that TPBCl4 has much higher molar absorbance than the other organic membrane components and the shape of its UV spectrum closely resembles the one obtained in the small inset graph of Fig. 4.5b. The absorbance measurement with time in Fig. 4.5b shows that as the potential is swept to the positive value, the organic membrane components are driven out and detected in the acceptor with a point of inflexion at +5 V but when the potential is swept back to negative values, the absorbance reaches a plateau and only slightly decreases. This suggests that the process of polarising of the membrane in this potential range is irreversible and the organic electrolyte transfer to the aqueous phase is being effectively dispersed/dissolved by stirring, which prevents its reverse accumulation in the membrane phase. The proposed irreversible transport is supported by the initial concentration of the TDDATPBCl4,
DOPC and stearic acid in the membrane (10 – 20 mM) and their theoretical maximum concentration in the aqueous phase after they were fully transferred out of the membrane
(6 – 12 M) (calculated from the volume of the aqueous phases). Stearic acid and
+ TPBCl4 / TDDA ions shown to be soluble at this concentration and DOPC is known to form micelles in aqueous solutions [182]. The concentration difference and extensive
- 136 - stirring of the aqueous phase will hinder the reverse transport of these organic components to the membrane.
The membrane only containing the organic electrolyte shows the highest absorbance plateau in Fig. 4.5b, which is consistent with the current response on the cyclic voltammetry (red curves). The other two cases show a more than 2-fold decrease in absorbance plateau, indicating increased membrane stability with respect to the applied potential. As suggested earlier, the likely increase in viscosity of the organic membrane phases, when DOPC and stearic acid are added, possibly leads to a hindered ion transport resulting in more stable membrane. Another explanation for the observed increase in the membrane stability is a screening effect of the ionic components of the membrane.
The other two curves in Fig. 4.5a, i.e. standard membrane + electrolyte + no drug molecule in donor (black) and standard membrane + electrolyte + 300 μM cetirizine in donor (blue), have a similar current response for the potential sweeps from 0 to +1.5 V and 0 to −1.5 V, which are higher than for the pure electrolyte case. For the higher potentials, above +2 V however, the components seem to be stabilized and the current is lower for the complex membrane case. Furthermore, the case with the drug molecule present in the donor compartment shows the lowest current response of all three cases as complemented by the UV absorbance measurement. This would complicate the control of ionic drug flux across the membrane as other membrane components would be driven out.
It is interesting to discuss the permeation cell voltammetric behaviour in the negative region, i.e. 0 to −5 V. In the range from 0 to −2 V the negative current response of the pure electrolyte membrane is lower than the one of standard membrane with or without drug in donor compartment, which are almost identical. In the range of −2 to −5
V, a distinct difference between the three cases is observed. The pure organic electrolyte case shows the smallest absolute current response in this negative potential region. The case of standard membrane with no drug molecule in the donor shows a larger absolute
- 137 - current and lastly the case of the standard membrane with cetirizine in the donor shows the largest current. Also, four distinct peaks are observed on the cyclic voltammogram of the permeation cell containing the drug molecule at potentials −0.9, −3.4, −4.2 and −5.0
V. These peaks are likely to be related transfer of the various ionised complexes formed between the cetirizine anion and the cationic forms of membrane components.
A plot of the time derivative of the absorbance, dAλ/dt, against time results in a shape similar to the typical diffusion peak observed in cyclic voltammogram as shown in
Fig. 4.6. The charge passed and the observed absorbance are related in a similar manner
[183] as their time derivatives, current and dAλ/dt, as the both report on the solute flux . The shape of the derivative curve suggests an irreversible transport of organic membrane components to the acceptor phase, consistent with observation in Fig. 4.5b. The absorbance derivative would have yielded the shape shown in the inset graph (Fig. 4.6) in the case of reversible transfer.
Figure 4.6 Plot of the time derivative of the absorbance against time. The differential values were obtained from the absorbance – time plot in Fig. 4.6. The symmetrical peak with maximum height found at 420 s, is consistent with the typical current response on cyclic voltammogram. The inset graph shows theoretical reversible transport shape.
- 138 - Cyclic voltammetry in the range of −1 to +1 V
Further investigation of the response of the permeation cell to external polarisation via cyclic voltammetry in the smaller potential range, −1 to +1 V, was carried out. All the possible combinations of the components in the membrane, with and without drug molecules in the donor phase, were examined to investigate the effect of polarisation on the membrane stability and the source of the measured UV absorbance response in the acceptor phase. The results for the various combinations of the membrane components
(organic electrolyte TDDATPBCl4, DOPC and stearic acid) are shown in Fig. 4.7. Four different cases were studied by cyclic voltammetry in the −1 V to +1 V potential range with no drug present in system: membrane only containing solvent and the organic electrolyte, membrane containing stearic acid and organic electrolyte, membrane containing DOPC and organic electrolyte and standard permeation assay membrane (both
DOPC and stearic acid) + organic electrolyte. From Fig. 4.7a one can conclude that for the standard membrane case the largest current response in both positive and negative parts of the cyclic voltammogram is observed (black curve). The same results were observed in
Fig. 4.5 in the potential range of 2 to +1.5V. This is expected since the standard membrane contains largest amount of organic components likely to be driven out from membrane by applied potential. The next largest current response was observed for membrane containing DOPC and organic electrolyte followed by the membrane only containing the organic electrolyte. Surprisingly, the membrane containing stearic acid and organic electrolyte case shows the smallest current response in the positive potential region. This suggests that stearic acid stabilizes the membrane when added to the pure electrolyte. The inset graph in Fig. 4.7a shows the voltammogram with the absolute current value. This shows that cyclic voltammetry is not fully symmetrical (reversible) and higher current responses are observed for the positive potential shoulder of the voltammetric curve.
- 139 -
Figure 4.7 Cyclic voltammetry on the blank permeation cell (no drug in donor phase) coupled with in situ UV measurement in the acceptor compartment (1 V to +1 V). Graph (a) shows cyclic voltammograms measured for several different membrane compositions: membrane only containing the organic electrolyte in 1,9-decadiene (red), membrane containing stearic acid and organic electrolyte (blue), membrane containing DOPC and organic electrolyte (green) and standard permeation assay membrane + organic electrolyte (black). The inset graph (a) shows the voltammograms with absolute current value. Graph (b) shows the response in acceptor compartment measured via UV absorbance. The voltammogram was obtained by scanning from 0 to + 1V, then down to −1 V and back to 0 V at 40 mV s−1. Both aqueous phases contained 30 mM sodium phosphate and 1 mM sodium chloride solution at pH 7.4 (acceptor) and 8.5 (donor). The membrane was rotating at 120 rpm and cyclic voltammetry started at 300 s. The potential value was corrected for the absolute potential difference between the two reference electrodes (acceptor/donor +150 mV).
- 140 - The corresponding UV absorbance profiles in Fig. 4.7b show little change for all three cases where either DOPC (green) or stearic acid (blue) or both (black) are present in the membrane. This is consistent with results shown in Fig. 4.5 where no change in absorbance was detected below an applied potential difference of +1.5 V. In the case of pure electrolyte a slight increase in absorbance is observed when the positive potential is applied (red curve, Fig. 4.7b). In the ideal case, the UV absorbance of the membrane organic components as well as their voltammetric response would be minimal over a large potential window. This would ensure that, when analysing the system containing the drug molecule, the organic components do not significantly interfere with the measured signal.
Identical experiments, with variable membrane composition, were carried using
300 M cetirizine in the donor compartment. Fig. 4.8 shows CVs recorded simultaneously with the UV absorbance in the acceptor compartment at a constant stirring rate of 120 rpm. The CVs in Fig. 4.8a show similar behaviour to those of Fig. 4.7a. The system with the standard membrane composition has the largest current response in both the positive and negative potential regions (black curve). The current response decreases for the case of DOPC + electrolyte membrane (green curve) and is lowest for the case of pure organic electrolyte (red curve). Unlike the experiments with no drug in the donor phase, the case of stearic acid + electrolyte membrane (blue curve) shows a higher current response than the pure electrolyte case. This behaviour suggests that negatively charged stearic acid inhibits cetirizine anion retention in the membrane and accelerates its permeation to the acceptor compartment. The corresponding UV absorbance profile in Fig. 4.8b (blue curve) also shows increasing signal in the acceptor, whereas absorbance of the other cases follows the same trend as in the case with no drug in the donor phase. Unfortunately, no pronounced excess current, which would allow reliable quantitative analysis, was observed for the case with cetirizine molecule present in the donor phase (Fig. 4.8a) when compared with the current response of the blank permeation cell (Fig. 4.7a).
- 141 -
Figure 4.8 Cyclic voltammetry on the permeation cell containing 300 M cetirizine in the donor coupled with in situ UV measurement in the acceptor (1 V to +1 V). Graph (a) shows cyclic voltammograms measured for several different membrane compositions: membrane only containing the organic electrolyte in 1,9-decadiene (red), membrane containing stearic acid and organic electrolyte (blue), membrane containing DOPC and organic electrolyte (green) and standard permeation assay membrane + organic electrolyte (black). Graph (b) shows the response in the acceptor measured via UV absorbance at 230 nm. The voltammogram was obtained by scanning from 0 to + 1V, then down to −1 V and back to the 0 V at 40 mV s−1. Both aqueous phases contained 30 mM sodium phosphate and 1 mM sodium chloride solution at pH 7.4 (acceptor) and 8.5 (donor). The membrane was rotating at 120 rpm and cyclic voltammetry was started at 300 s. The potential value was corrected for the absolute potential difference between the two reference electrodes (+150 mV).
- 142 - 4.3.4 Amperometric Measurements
Amperometric measurement of the current flowing across the polarised membrane at constant applied potential difference between the acceptor and donor phase was employed to investigate the effect of membrane polarisation on drug permeation. The range of applied potential difference between acceptor and donor phase was −3 V to +3 V.
A new membrane batch was used each time to ensure reproducibility. In situ UV absorbance in the acceptor phase was measured simultaneously with the electrochemical method. The detailed experimental procedure is described in section 2.3.4. Briefly, the permeation cell was assembled and permeation was initiated at a stirring rate of 120 rpm.
UV absorbance acquisition was started 10 min after the cell assembly. After another 10 min period the amperometric measurement was started.
Fig. 4.9 shows the amperometric response of the permeation cell at various potential differences and the corresponding UV absorbance response in the acceptor phase. As one can deduce from the amperometric response in Fig. 4.9a, the current has similar behaviour for all the positive applied potential differences. The current rapidly drops in the first 10 s and then reaches a steady value after 100 s for potential difference <
+1V. For the potential difference ≥ +0.65 V current seems to slightly decrease over the whole experimental time. The steady current value changes with applied potential difference as expected. The small inset graph in Fig. 4.9a shows the first 30 s of the amperometric measurement. Concluding from results in section 4.3.2 where the blank permeation system (no drug in donor phase) was analysed and absorbance measurements in Fig. 4.9b we conclude that the initial high current response for potential difference ≥
+650 mV is caused by the organic components of the membrane being driven out to the acceptor compartment. The applied potential difference below +650 mV has not affected the UV absorbance signal due to the fact that the flux of the neutral form is still several- fold higher than the flux of the ionic form (see below).
- 143 -
Figure 4.9 Amperometry conducted simultaneously with in situ UV measurement in the acceptor. Permeation cell contained 300 M cetirizine. Graph (a) shows current measured as a function of time at various applied potential difference between the acceptor and donor phase. The inset graph (a) shows the current response for initial 30 s. Graph (b) shows the UV absorbance measured in situ in the acceptor. The inset graph (b) shows the UV absorbance response at 230 nm for the applied potential difference of −3 V. Both aqueous phases contained 30 mM sodium phosphate and 1 mM sodium chloride solution at pH 7.4 (acceptor) and 8.5 (donor). The membrane was rotated at 120 rpm and amperometry was started at 600 s. The potential value was corrected for the absolute potential difference between the two reference electrodes (+150 mV).
- 144 - Nevertheless, the positive current response suggests, that the anionic form of cetirizine is being transported from the donor to the acceptor phase across the organic membrane.
More evidence in support of the idea that the transport of the drug between the donor and acceptor phase can be controlled comes from applying high negative potential differences between the acceptor and donor phase, thus driving anionic forms of drug against the diffusive flux. The applied potential difference of −3 V retarded the permeation of the drug to the extent detectable by UV absorbance as shown in inset graph in Fig. 4.9.
The overall charge passed through the permeation cell was calculated for each applied potential in order to quantify the ionic flux across the organic membrane. The graph in Fig. 4.10 shows the charge passed through the membrane over a period of 10 min for several applied potential in the range of −3 V to + 3V. The dependence of charge on potential can be approximated by hyperbolic tangent function (commonly used to describe a charge transfer in ion-exchange membranes [133]) as indicated by the dashed red curve.
Figure 4.10 Overall charge passed through membrane in 10 min of amperometry plotted against the applied potential difference between the acceptor and donor phase. The membrane was rotating at 120 rpm. The equation in the top right corner is the best fit of the data using the tanh function.
- 145 - The charge, Q, passed through membrane is related to the molar diffusive flux of
[77] the ionic species, Ji, by following equation :
Q J i (4.1) zi FAt
Where zi is the charge of the transferred ionic species i, F is the Faraday constant, A is the area of the membrane and t is the time over which the current is passed through the membrane. Eq. (4.1) assumes that the current flowing through the membrane (and therefore molar diffusive flux) is constant with time. This is a reasonable assumption for times longer than 30 s allowing an approximate quantification of the potential-induced permeation.
As discussed earlier in this section, for the potential difference smaller than +650 mV, the majority of the measured current response is due to cetirizine anion transfer.
Modifying Eq. (3.1) for the ionic fraction of the drug molecule we arrived at:
DA AD J i Pi cD Pi cA (4.2)
DA AD Where Pi and Pi denote the effective permeability coefficients for the donor-to- acceptor and acceptor-to-donor transport of the ionic fraction of the molecule, respectively, cD and cA are the bulk concentration of the drug molecule in the donor and acceptor phase, respectively. Assuming that the cetirizine concentration in the acceptor phase is negligible compared to donor phase and its bulk concentration in the donor phase
has practically not changed from the initial value, cD(0) , we can calculate the donor-to- acceptor permeability coefficient of the ionic fraction of cetirizine as:
DA J i Pi (4.3) cD (0)
- 146 - The molar ionic flux and corresponding permeability coefficient values calculated for the applied potential difference in the range −3V to + 3V, assuming that the charge of the transferred cetirizine anion is −1, are listed in Table 4.1.
Table 4.1 Molar ionic flux and ionic permeability coefficients calculated from the charge passed through the membrane at several potential differences between the acceptor and donor phase.
−1 −2 DA −1 DA ΔE / mV Q / mC Ji / mol s cm Pi / cm s log Pi −3050 −17.9 4.5 × 10−10 (4.5 × 10−6)* (−5.832) −1050 −8.7 2.2 × 10−10 (7.2 × 10−7)* (−6.146) −50 0.2 6.2 × 10−12 2.0 × 10−8 −7.700 50 0.4 1.1 × 10−11 3.5 × 10−8 −7.461 250 1.5 3.8 × 10−11 1.2 × 10−7 −6.906 450 2.6 6.7 × 10−11 2.2 × 10−7 −6.666 650 5.7 1.5 × 10−10 4.7 × 10−7 −6.327 950 8.5 2.2 × 10−10 (7.0 × 10−7)* (−6.155) 2950 15.9 4.0 × 10−10 (1.3 × 10−6)* (−5.884)
* theoretical values that include the appearance of organic membrane components in the acceptor phase as detected via amperometry/UV spectrophotometry.
Comparison of the permeability coefficient of the cetirizine ion measured using the amperometric method with the effective permeability coefficient measured using
DA permeation assay at the same stirring rate (section 3.6), log Pe = −4.597, suggests that the ionic fraction permeates at a rate which is about 50 to 1200 fold slower than the neutral fraction in the range of applied potential difference. In contradiction to the pH- partition hypothesis, our findings show that the lipophilic barrier is not permeable exclusively to the neutral fraction of the ionisable drug molecule. The open circuit potential difference between the acceptor and donor phase for the system containing the cetirizine is ca. −50 mV. For the amperometric method at this applied potential, i.e. mimicking the system with no externally applied polarisation, a non-zero current is detected, corresponding to the ionic fraction permeability of 2.0 × 10−8 cm s−1.
- 147 - 4.4 Conclusions
The artificial membrane permeation method was successfully extended to a spectrophotoelectrochemical method with an external polarisation of the membrane at constant stirring rate of 120 rpm. This extended method employed the same aqueous solutions and organic membrane, the only difference was the addition of 1 mM sodium chloride to the aqueous phase (for reference electrode stability) and 10 mM organic electrolyte to the membrane to reduce the resistivity of the system. The open circuit potential difference was measured for various membrane conditions and, for the model system containing cetirizine in the donor phase, a value of −50 mV was found. A series of cyclic voltammograms for various membrane compositions was carried out in order to examine the electrochemical stability of individual organic components of the membrane and to establish a potential window suitable for drug permeation study under polarised conditions.
Based on results obtained from cyclic voltammetry, an amperometric measurement, i.e. application of the constant potential difference between the acceptor and donor phase, was employed. The permeation of the zwitterionic drug cetirizine at donor/acceptor pH 8.5/7.4 was performed under constant applied potential in the range of
−3V to + 3V. About 23% of cetirizine is present in its anionic form at pH 8.5. The combined analysis of amperometry and corresponding UV absorbance measured in situ in the acceptor phase suggest that organic components remain contained within the membrane at positive potential differences smaller than +650 mV. The charge passed through the membrane in this potential range was attributed to transfer of cetirizine anion and the corresponding molar flux and permeability coefficient of the anion was found.
The permeability coefficient of the ionic fraction was found to be 50 – 1200 fold lower than the permeability coefficient of the neutral fraction determined by the permeation assay with no external polarisation in the range of potential differences −50 to + 650 mV.
- 148 - In the range of potentials higher than +650 mV the membrane was found to be unstable toward the applied potential. The current and corresponding absorbance response observed suggested that the organic membrane components (specifically TDDATPBCl4) are driven into the aqueous acceptor phase. Despite the pH-partition hypothesis statement that only the neutral fraction of ionized species can permeate through lipophilic membranes, the flux of cetirizine anion was detected at an applied potential difference equal to the equilibrium value. The permeability coefficient of cetirizine anion was determined to be 2.0 × 10−8 cm s−1.
Following this analysis, it would be interesting to study transfer of a fully ionized drug across the polarised membrane. In such a case, the overall flux across the membrane would be much smaller than for the partially ionised drug and therefore the current/absorbance change induced by applied potential would be more easily detected.
- 149 - Prediction of Drug Absorption in Humans
5.1 Introduction
It has been shown recently that the original design of the parallel artificial membrane permeation assay (PAMPA) as it was introduced in 1998 [32] has some limitations with regard to the understanding of permeability and the correspondence with conditions found in vivo [8, 30, 31, 47, 62, 65, 156]. The main issue from the drug discovery viewpoint is a poor correlation of PAMPA permeability with human oral absorption in comparison to the cell-based assays. Because of the advantages, however, such as high- throughput, low cost, possibility of pH profiling and stirring, over the conventional cell- based in vitro assays [42, 44, 45] PAMPA still remains of interest in the early drug discovery pipeline. Chapter 3 describes development of a rotating-diffusion cell with two aqueous compartments, separated by a lipid-impregnated artificial membrane, for the determination of drug permeability under conditions of controlled hydrodynamics [31].
With this novel experimental setup, the three most neglected theoretical and experimental problems, namely: reproducible stirring (controlling the convection/diffusion), in situ permeability measurement (accurate determination of the permeability coefficient) and use of the appropriate analytical model (considering lag time, two-way flux, pH-gradient and membrane retention) have been addressed and resolved. In this chapter, this refined assay is applied to a diverse set of water-soluble drugs with the explicit aim of establishing a correlation with literature bioavailability data and developing a tool to predict drug absorption in humans that could be used as a tool in early drug discovery.
Primarily, PAMPA is designed to mimic transcellular transport across human intestine epithelial cells. As a result, the low permeability response of small hydrophilic
1 molecules (Mr < 250 g mol ) often does not correlate with their high bioavailability due to the simultaneous paracellular route for their in vivo transport. Inspired by recent work
- 150 - from the laboratories of Sugano [67, 184] and Avdeef [43, 68, 185] a paracellular component based on the Renkin function [186] is incorporated into the model described in Chapter 3.
The paracellular permeability model derived from a recent detailed analysis of the Caco-2 permeability data of Adson et al. was employed for this purpose [185]. The measured effective permeability coefficient is corrected for the paracellular transport occurring in vivo thus expanding the range of drugs that can be properly ranked by this permeation assay.
As a part of this analysis, a novel approach to determine the optimal effective permeability as a function of unstirred water layer thickness is obtained, which can be converted to the corresponding stirring rate. The unstirred water layer, i.e. the aqueous layer adjacent to the membrane, where the flux of the solute is diffusion limited, is accurately controlled using the rotating-diffusion device [31, 66]. First, the effective permeability is measured for at least two stirring rates. Then, using the known analytical solution relating solute flux to applied stirring rate [100], the effective permeability at any given stirring rate is calculated. This approach, only applied to date on an empirical basis
[65], allows us to match the permeation experiment to conditions anticipated in vivo (where
UWL thickness is believed to be on the order of 10 – 1000 microns depending on various conditions and experimental methods used [28, 29, 43, 65, 69, 89]).
In this work, 31 commercially available drug molecules (9 weak acids, 9 bases, 8 neutral molecules and 5 zwitterions, Fig. 5.1) were used as a training set for the hydrodynamic permeation assay. Selected physicochemical properties of 31 drug molecules studied in this chapter are listed in Table 5.1. Drugs, where the first pass hepatic clearances are low to moderate, and with published human absolute bioavailability spanning from low to high values, were deliberately selected. The human bioavailability data were corrected for the first pass hepatic clearance to avoid erroneous correlation with permeability. Drugs with no known active transport were selected for the training set.
- 151 - Moreover, care was taken to include drugs with moderate to good aqueous solubility, to ensure the absorption process was not solubility-limited. In other words, the selected compounds generally fall within the Biopharmaceutics Classification Scheme (BCS) class
I (high solubility and permeability) and III (high solubility and low permeability). These conditions (BCS class I and III, no known active transport issue, and moderate clearance) are deemed necessary to ensure that passive permeability is the major factor driving absorption. The goal was to find a correlation between the in vitro drug permeability coefficient and fraction absorbed determined in vivo, using the approach described above.
The development of a predictive model for the absolute bioavailability with the capability to deal with solubility limited absorption, active transport and clearance issues is beyond the scope of this work.
- 152 -
Figure 5.1 Chemical structures of 31 selected drug molecules.
- 153 -
Table 5.1 Molar mass, charge state, pKa, aqueous diffusion coefficient and fraction absorbed of 31 selected drug molecules.
−1 a −6 2 −1 b c drug Mr / g mol charge pKa Daq / 10 cm s %Fa acetaminophen 151.17 N 9.63 (acid) [8] 6.12 89 ± 11 antipyrine 188.23 N 1.44 (base) [8] 5.49 100 ± 0 atenolol 266.34 B 9.54 [8] 4.64 65 ± 18 betamethasone 392.46 N − 3.84 82 ± 0 cefixime 453.45 A 2.10, 3.73 [187] 3.58 49 ± 16 cephalothin 396.44 A 2.35 [188] 3.82 0 ± 0 cetirizine 388.89 Z 2.90, 7.98 [122] 3.86 86 ± 14 chlorpheniramine 274.79 B 4.00, 9.20 [189] 4.57 58 ± 30 chlorthalidone 338.77 N 9.40 (acid) [190] 4.12 67 ± 10 colchicine 399.44 N 1.70 (base) [191] 3.81 55 ± 0 diclofenac 296.15 A 3.99 [8] 4.40 82 ± 18 eprosartan 424.53 A 5.30 [192] 3.69 14 ± 0 fexofenadine 501.66 Z 4.25, 9.53 [193] 3.41 58 ± 0 gatifloxacin 375.39 Z 5.94, 9.21 [194] 3.92 100 ± 0 metolazone 385.84 N 9.70 (acid) [8] 3.87 68 ± 0 midazolam 325.78 N − 4.20 68 ± 32 nafcillin 414.48 A 2.65 [195] 3.74 35 ± 0 naproxen 230.26 A 4.18 [8] 4.98 87 ± 13 norfloxacin 319.33 Z 6.25, 8.50 [196] 4.25 58 ± 23 oxybutynin 357.49 B 6.90 [189] 4.02 100 ± 0 pindolol 248.32 B 9.54 [8] 4.80 98 ± 2 propranolol 259.34 B 9.53 [8] 4.70 100 ± 0 pyridoxine 169.18 Z 4.90, 8.91 [196] 5.79 95 ± 5 quinine 324.42 B 8.55, 4.24 [8] 4.21 85 ± 15 risperidone 410.49 B 3.10, 8.10 [197] 3.76 75 ± 25 salicylic acid 138.12 A 2.88, 13.55 [8] 6.39 99 ± 0 theophylline 180.18 N 8.55 (acid) [8] 5.61 84 ± 16 tolbutamide 270.35 A 5.40 [198] 4.60 88 ± 8 verapamil 454.60 B 9.07 [8] 3.57 84 ± 4 warfarin 308.33 A 4.82 [8] 4.32 93 ± 7 zopiclone 388.81 B 6.76 [8] 3.86 100 ± 0 a Charge state of the drug: A – acid, B – base, N – neutral, Z – zwitterion. b Aqueous diffusion coefficients calculated using Eq. (4) in ref. [62]. c Average fraction absorbed (in percent) calculated the absolute bioavailability taken from several sources [84, 199-205], which was corrected for hepatic clearance using Eq. (5.2). Errors are determined as a range of values spread over different literature sources. For those molecules where errors in the published bioavailability values are not available, the average error value of 9% (in italic) was used in the analysis.
- 154 - 5.2 Experimental
The permeability coefficients were determined using the method previously described in section 2.3.1 and data analysis carried out using the mathematical approach presented in section 3.3. The model used to incorporate the paracellular component in the permeability model is presented below.
5.2.1 Correction of Bioavailability for First Pass Hepatic Clearance
The absolute drug bioavailability is defined as a fraction of an administered dose of drug that reaches the systemic circulation. Taking first pass hepatic metabolism and gut wall metabolism into consideration, absolute drug bioavailability, F, may be expressed as
[206]:
F Fa Fh Fg (5.1)
where Fa, Fh and Fg represent the fraction absorbed from the intestinal lumen, fraction escaping hepatic extraction, and fraction escaping intestinal extraction, respectively. In this thesis, we make an assumption that the gut metabolism of the drug in the training set is negligible and therefore Fg ~ 1. For practical reasons, drug physicochemical properties measured by high-throughput screening methods are compared with the fraction absorbed,
Fa, which is the rate and extent of absorption and systemic availability determined relative to an intravenous dose. In order to correlate the permeability directly with fraction absorbed from the intestinal lumen, the absolute bioavailability was corrected for the first pass hepatic clearance to obtain the fraction absorbed, using following equation [207]:
F F F F a CL CL (5.2) Fh Fg h h (1 ) Fg (1 ) Qh Qh
- 155 - Where CLh is the first pass hepatic clearance and Qh is the hepatic blood flow. CLh values
[208] 1 1 [206] were obtained from and Qh = 23 ml min kg from . The averaged absolute bioavailability values, F, were obtained from several sources [84, 199-205].
5.2.2 Correction for Paracellular Transport
The paracellular term proposed by Avdeef et al. [185], based on work of Adson et al. [69, 97], was used here to correct for the flux of small molecules through intercellular junctions in vivo. This term accounts for the paracellular transport dependent on molar mass and the charge state of the drug. Paracellular permeability, Pp, is based on three
Caco-2 assay parameters relating to the structure of the porous cell junctions: a pore capacity factor, ε/δ (porosity to path-length ratio), pore radius, Rp, and electrical potential
[185] drop at the channel surface, Δφ. The equation used to calculate Pp is :
r P D F HYD E (5.3) p aq R R p
where ε/δ is a porosity/path-length capacity factor, Daq is the aqueous diffusion
[62] coefficient, calculated using an empirical formula based on solute molar mass, Mr :
log D 4.15 0.488 log M (5.4) aq r
The term FR(rHYD/Rp) in Eq. (5.3) is the Renkin hydrodynamic sieving function for cylindrical water channels expressed as follows [186]:
2 3 5 r r r r r F HYD 1 HYD 1 2.104 HYD 2.09 HYD 0.95 HYD (5.5) R R R R R R p p p p p
- 156 - where rHYD is the solute‟s hydrodynamic radius and Rp is the pore radius. Molecular hydrodynamic radii were calculated using the Sutherland–Stokes–Einstein spherical- particle equation [185]:
21.8 kB T rHYD (0.92 ) (5.6) M r 6Daq
−23 −1 where kB = 1.381 × 10 J K is the Boltzmann constant, T is the thermodynamic temperature, η is dynamic viscosity of the solvent (0.00890 g cm-1 s-1, water, 25°C, [154]).
The function E(Δφ) in Eq. (5.3) describes the electric field across the intercellular junctions (pores) due to negatively charged ions [185]:
E f( / 0) f() f (5.7) 1 e e 1
Where f(±/0), f(+) and f(–) are the concentration fractions of neutral/zwitterionic, cationic and anionic forms, respectively, κ is a function defined as κ = (F/NAkBT), where F is the
23 −1 Faraday constant and NA = 6.022 × 10 mol is the Avogadro constant. Δφ is the potential drop across the pore.
−1 In the present study, the parameters Rp = 12.9 Å, ε/δ = 0.78 cm , Δφ = –30 mV, were taken from Avdeef [185] who based these parameters on a re-analysis of the Caco-2 permeability data of several paracellular markers published by Adson et al. [97]. There were several reasons why Adson‟s paracellular model was used. The model was derived based on data obtained at 25 °C, therefore is applicable to the system presented here.
Other paracellular models were also tested. Adson‟s model, however, has proven to be the best choice as the fitting calculations provided a stable solution and the model implements the second largest pore size from paracellular models presented in [185]. The two-
- 157 - component permeation model described earlier [31] was corrected for the paracellular transport observed in the Caco-2 assay as follows:
1 1 1 (5.8) Pe Pu S Pm Pp
where Pe, Pu, Pm and Pp are the effective, unstirred water layer, membrane and paracellular permeability coefficients, respectively. The variable, S, is a scaling factor.
The choice of the scaling factor depends on a particular permeability assay/paracellular model used. In this report, the S value was varied and its optimum value was found from the best fit of the effective permeability and human bioavailability in the plug-flow model, as discussed later.
The physical meaning of Eq. (5.8) is that the inverse of the effective permeability is directly proportional to the inverse of UWL permeability (independent of membrane or in vivo mimic properties) and the inverse of the membrane permeability corrected for the paracellular transport across Caco-2 epithelial cells. The scaling factor, S, normalises membrane permeabilities to a level comparable to those generated from the paracellular model (see above).
5.2.3 Extrapolation of Effective permeability to Set Unstirred Water Layer
The hydrodynamic model reported previously allows extrapolation of the effective permeability to a given stirring rate mimicking hydrodynamic conditions found in the human small intestine [31]. The permeability can thus be optimised to mimic UWL properties in vivo. A given UWL thickness, δu, can be transformed to a corresponding stirring rate using the following relationship based on the Levich equation [100] as shown in
Eq. (3.16). The measured effective permeability can be extrapolated to any given stirring
- 158 - rate providing the relationship between the two is known. In practise, we measured Pe as a function of stirring rate and used Eq. (3.20) to extrapolate Pe for a set angular velocity of stirring.
The effective permeability of all 31 drug molecules was measured three times to find an average value, Pe. Cetirizine, diclofenac, naproxen, propranolol, theophylline, verapamil and warfarin were analysed at six different stirring rates (60, 80, 110, 160, 280 and 600 rpm). Chlorpheniramine, fexofenadine, norfloxacin, pindolol, pyridoxine, salicylic acid and tolbutamide were analysed at three different stirring rates (60, 160 and
600 rpm). The rest of the drug molecules were analysed at two different stirring rates (60 and 280 rpm).
5.2.4 Absorption Data Dependence on Effective permeability
The fraction absorbed was fitted against the plug-flow absorption model [85, 209]:
%Fa G 1 exp H Pe (5.9) where G represents the Graetz number (a dimensionless number describes laminar flow in the intestine, treated as a tube, in the plug flow model). In the present study, G and H are regarded as fitting constants. %Fa represents the fraction absorbed in humans under assumption that drug is not substrate for metabolic processes in the gut.
The overview of the whole experimental/analytical method is shown in a block scheme in Fig. 5.2.
- 159 -
Figure 5.2 Scheme of experimental/analytical method of drug absorption prediction from the effective permeability corrected for paracellular transport.
- 160 - 5.3 Correlation of Permeability Coefficients with Fraction Absorbed
Initially, the permeability as determined under unstirred conditions was investigated. The correlation between the fraction absorbed and the effective permeability under unstirred conditions for all thirty-one drug molecules is shown in Fig. 5.3. The colours of the symbols represent the charge state of the drugs at the physiological pH (red
– acids, green – bases, blue – zwitterions, grey – neutral). It is clear that effective permeability determined under unstirred conditions, and without correction for the paracellular transport component, does not provide a good model for the prediction of the fraction absorbed.
Figure 5.3 Correlation between the fraction absorbed and effective permeability under unstirred conditions (donor/acceptor pH 6.5/7.4). The permeability data are averages of three measurements, horizontal axis error bars standard deviation of the three, vertical axis error bars taken from Table 5.1. The horizontal axis error bars are smaller than the data points where not shown. Colour scheme: red – acids, green – bases, blue – zwitterions, grey – neutral.
With the exception of cephalothin, nafcillin and eprosartan, all data points are clustered together with no apparent ranking (high permeability – high %Fa, low permeability – low
- 161 - %Fa). It is also important to notice that the permeability of the small molar mass drugs, (<
200 g mol−1, acetaminophen, antipyrine, pyridoxine, salicylic acid, theophylline) which generally show high fraction absorbed (%Fa > 95), is systematically low.
In order to improve the ranking for these drugs, a paracellular transport component, whose contribution increases with decreasing molar mass was introduced.
Additionally, the permeability data with controlled hydrodynamics was used to mimic stirred conditions in vivo. The stirred conditions were set to be 0.5 rad s1 of angular velocity, which corresponds to a UWL thickness of ~ 200 μm and ~ 160 μm for the
−1 smallest and largest molecules, respectively (salicylic acid, Mr = 138.12 g mol and
−1 fexofenadine, Mr = 501.66 g mol ) The UWL thickness adjacent to the human intestinal epithelium has been reported to be in the range of 35 – 274 m [28, 29, 89, 210]. The chosen
UWL thickness of 200 m in the present study is within the range found in the literature and corresponds well with a median value of 188 m for antipyrine as reported by
Lennernäs [28].
Fig. 5.4 shows the fraction absorbed of the 31 drug molecules as a function of the effective permeability (logPe) with the solid curve representing the best fit to Eq. (5.9).
The optimized parameters are: H = 100 cm−1 s, G = 2.14 × 106, S = 0.014. The dotted curves are derived from estimated errors in the log Pe values with an average value of
0.35, which is based on the lab-to-lab variability of the Caco-2 paracellular parameters as estimated by Avdeef [185]. For the upper dashed curve, parameter H is 100 cm−1 s, while a value of 85 cm−1 s is used for the lower dashed curve (in part, to reflect the estimated errors in the %Fa data). The estimated errors in the %Fa data were determined as a range of values spread over different published absolute bioavailability values. For those molecules where errors in the published bioavailability values are not available, the average error value of 9% was used. It can be seen that fraction absorbed of the molecules
- 162 - is generally well predicted, within experimental uncertainty, by the approach developed in this study.
Figure 5.4 Correlation between the fraction absorbed and optimised effective permeability (including paracellular components calculated using Eq. (5.8) for the set hydrodynamic conditions – angular velocity 0.5 rad s1 (ca 200 μm of UWL thickness)). The horizontal axis error bars (not shown in the graph) are considered to be 0.35 log units. The solid curve is the best fit of the function represented by Eq. (5.9). The dashed curves are based on estimated errors in the log Pe values (0.35). Colour scheme: red – acids, green – bases, blue – zwitterions, grey – neutral.
The above treatment, including a paracellular component into the permeability term, has been extended to different hydrodynamic conditions, namely membrane limited
(infinite stirring) and static (no stirring) case. The comparison of the plug-flow model sum errors for the membrane (ω → ∞ rad s1), unstirred case (ω = 0 rad s1) and stirring at in vivo transport rate (ω = 0.5 rad s1) is shown in Fig. 5.5. The optimised effective permeability at ω = 0.5 rad s1 (corresponds to UWL thickness of 200 m) exhibits the lowest error value, thus providing the best correlation with the fraction absorbed. Note the large difference between the stirred and static case, as opposed to only a small difference
- 163 - between the stirred and membrane cases. This suggests that PAMPA permeability with proper control of hydrodynamics, and the incorporation of paracellular component are useful for the prediction of human bioavailability [31, 65, 156].
Figure 5.5 Sum errors of optimized effective permeability – fraction absorbed correlation. Results are shown for the membrane (ω → ∞ rad s1), unstirred (ω = 0 rad s1) and stirred (ω = 0.5 rad s1) conditions. Sum error = (%F(literature) - %F(model)) 2 + 1000 x p, where p represents a count of the point (including the error bar) falling outside the dotted lines in Figure 5.4. The graph leads to an optimised UWL thickness value of 200 μm having the best effective permeability – fraction absorbed correlation.
Table 5.2 summarizes the permeability data collected for the selected set of drug molecules. The effective permeability, Pe, membrane permeability, Pm and intrinsic permeability, P0 were determined using the method described earlier. The paracellular permeability, Pp, was calculated using Eq. (5.8). The membrane diffusion coefficient was also calculated using Eq. (3.6) for all 31 drug molecules (Table A4.4, Appendix).
- 164 - Table 5.2 Permeability coefficients of 31 studied drug molecules
a b c d e drug log Pe (unst) log Pm log P0 log Pp log Pe (200 μm) acetaminophen −5.40 ± 0.03 −5.50 ± 0.03 −5.50 ± 0.03 -6.09 -6.07 antipyrine −5.31 ± 0.02 −5.09 ± 0.03 −5.09 ± 0.03 -6.22 -6.15 atenolol −5.23 ± 0.16 −4.64 ± 0.03 −2.43 ± 0.03 -6.24 -6.04 betamethasone −4.66 ± 0.02 −3.98 ± 0.01 −3.98 ± 0.01 -6.80 -5.78 cefixime −5.69 ± 0.02 −5.11 ± 0.08 −0.71 ± 0.08 -7.23 -6.77 cephalothin −4.37 ± 0.02 −5.67 ± 0.04 −1.52 ± 0.04 -7.09 -6.95 cetirizine −4.82 ± 0.02 −4.25 ± 0.01 −4.12 ± 0.01 -6.80 -6.02 chlorpheniramine −5.01 ± 0.01 −3.64 ± 0.01 −0.94 ± 0.01 -6.26 -5.46 chlorthalidone −5.06 ± 0.03 −4.70 ± 0.08 −4.70 ± 0.08 -6.67 -6.3 colchicine −4.78 ± 0.02 −5.48 ± 0.02 −5.48 ± 0.02 -6.82 -6.71 diclofenac −4.32 ± 0.02 −3.37 ± 0.01 −0.90 ± 0.01 -6.83 -5.21 eprosartan −5.78 ± 0.02 −4.95 ± 0.02 −3.73 ± 0.02 -7.14 -6.63 fexofenadine −4.91 ± 0.17 −4.50 ± 0.04 −4.60 ± 0.04 -7.06 -6.27 gatifloxacin −5.63 ± 0.01 −5.34 ± 0.05 −5.23 ± 0.05 -6.70 -6.58 metolazone −5.30 ± 0.01 −4.85 ± 0.03 −4.85 ± 0.03 -6.79 -6.43 midazolam −4.35 ± 0.02 −3.03 ± 0.03 −3.03 ± 0.03 -6.63 -5.03 nafcillin −5.73 ± 0.03 −4.85 ± 0.02 −1.00 ± 0.02 -7.13 -6.58 naproxen −4.55 ± 0.04 −4.14 ± 0.01 −1.69 ± 0.01 -6.63 -5.9 norfloxacin −5.72 ± 0.15 −5.39 ± 0.02 −5.24 ± 0.02 -6.52 -6.46 oxybutynin −4.53 ± 0.01 −2.97 ± 0.00 −2.43 ± 0.00 -6.54 -5.07 pindolol −5.59 ± 0.07 −4.85 ± 0.16 −1.98 ± 0.16 -6.18 -6.07 propranolol −5.07 ± 0.01 −3.65 ± 0.01 −0.21 ± 0.01 -6.22 -5.45 pyridoxine −6.10 ± 0.09 −5.23 ± 0.03 −5.10 ± 0.03 -6.16 -6.12 quinine −5.09 ± 0.01 −3.60 ± 0.00 −1.55 ± 0.00 -6.40 -5.44 risperidone −4.93 ± 0.03 −3.81 ± 0.07 −2.19 ± 0.07 -6.62 -5.67 salicylic acid −5.03 ± 0.03 −4.82 ± 0.10 −0.66 ± 0.10 -6.32 -6.17 theophylline −5.63 ± 0.11 −5.74 ± 0.10 −5.76 ± 0.10 -6.19 -6.18 tolbutamide −4.59 ± 0.02 −4.09 ± 0.02 −2.71 ± 0.02 -6.73 -5.87 verapamil −5.04 ± 0.03 −3.34 ± 0.04 −0.89 ± 0.04 -6.73 -5.27 warfarin −4.49 ± 0.01 −3.95 ± 0.02 −2.21 ± 0.02 -6.79 -5.75 zopiclone −4.65 ± 0.01 −3.89 ± 0.02 −3.44 ± 0.02 -6.63 -5.69
a Effective permeability coefficient obtained under unstirred conditions, not corrected for paracellular transport. b Membrane (Pm) coefficient obtained from hydrodynamic extrapolation. c Intrinsic (P0) permeability coefficients calculated from Eq. (3.21). d Paracellular permeability coefficient calculated from Eq. (5.3). e Optimised effective permeability coefficient, calculated from Eq. (5.8) using scaling factor S = 0.014, stirred conditions ω = 0.5 rad s1 (UWL ~ 200 μm).
The values in the table represent means of three independent measurements and corresponding standard deviations combined with any linear fit errors used in the calculation. Experimental errors of simple laboratory measurements, such as volume determination, concentration calibration etc., were not included.
- 165 - The contributions of the three different transport mechanisms; namely UWL limited, transcellular, and paracellular for the 31 molecules are listed in Table 5.3. The percentages are calculated using Eq. (5.8), with the optimized S value and an UWL thickness of 200 m. This advanced permeation model offers some insights into the transport mechanisms. As shown in Table 5.3, for molecules with molar mass < 250 g mol−1, the transport is predominantly governed by the paracellular route. This is not totally unexpected, as the size of the molecule is generally proportional to the molar mass.
As the mass decreases it is more likely that the molecule would be transported via a paracellular route. For molecules with molar mass > 250 g mol−1, the transcellular pathway becomes the major route of transport, but the paracellular route appears to be available for molecules even with molar mass > 300 g mol−1. The absorption of zwitterions (e.g. norfloxacin, gatifloxacin) or anion (cefixime) may be enhanced by active processes via organic anion transporter proteins [34]. Colchicine is another surprising molecule which shows a significant percentage of paracellular transport despite its molar mass approaching 400 g mol−1. It has been reported that multiple efflux processes are involved in the absorption of colchicine in small intestine, which contributes to its low and variable bioavailability [211]. Colchicine absorption in humans may be complicated by the fact that this drug is known to cause diarrhoea by the decrease of intestinal water
[212] transport . Nevertheless, the measured Pm value of colchicine are very low (see Table
5.2), which clearly signals the potential issues in intestinal absorption. It should be noted that the active processes could be difficult to delineate from the passive paracellular transport, and are beyond the scope of the present study. This issue would, however, merit further investigation to unravel the transport mechanisms.
- 166 - Table 5.3 Contribution of unstirred water layer, paracellular and transcellular components to optimised effective permeability coefficient.
−1 drug Mr / g mol %UWL %para %trans acetaminophen 151.17 0 95 5 antipyrine 188.23 0 84 16 atenolol 266.34 0 64 36 betamethasone 392.46 1 9 89 cefixime 453.45 0 35 65 cephalothin 396.44 0 73 27 cetirizine 388.89 2 16 82 chlorpheniramine 274.79 9 13 78 chlorthalidone 338.77 0 43 57 colchicine 399.44 3 74 23 diclofenac 296.15 3 2 95 eprosartan 424.53 1 31 68 fexofenadine 501.66 1 16 83 gatifloxacin 375.39 0 76 24 metolazone 385.84 0 45 55 midazolam 325.78 27 1 71 nafcillin 414.48 6 25 69 naproxen 230.26 1 18 81 norfloxacin 319.33 4 80 15 oxybutynin 357.49 43 1 56 pindolol 248.32 1 76 23 propranolol 259.34 7 15 78 pyridoxine 169.18 3 86 10 quinine 324.42 9 9 82 risperidone 410.49 12 9 79 salicylic acid 138.12 2 67 30 theophylline 180.18 0 96 4 tolbutamide 270.35 1 14 85 verapamil 454.60 17 2 80 warfarin 308.33 1 9 90 zopiclone 388.81 2 11 87
In the present study, Fg is assumed to be close to unity in the data analysis. While this assumption may be valid for most of the drugs of low hepatic clearance, the molecules, which are likely to be cytochrome P450 substrates, could be vulnerable to gut
[213] wall metabolism . In such a case, it would be desirable to take Fg into consideration.
Midazolam and verapamil are typical examples, with reported Fg of 0.51 and 0.65,
- 167 - [213] respectively . Taking these Fg values into consideration, the %Fa values of these two molecules would be 100%, which are in good agreement with our model predictions (Fig.
5.4). It has been suggested that Fg could also depend on the dose strength, and saturable first pass metabolism is more likely to occur in the small intestine, because of the
[214] substantial drug concentration gradient during absorption . It is plausible that Fg value could vary in normal healthy human subjects, as in the case of midazolam [215]. The variability in gut metabolism is partly reflected in the large Y-error bar of midazolam
(Fig. 5.4). As far as we are aware, little Fg data, if any, has been published on other drugs studied in this work. Despite the selection of molecules being restricted to drugs with low to moderate first pass hepatic clearances, there are only 3 molecules, namely pindolol, propranolol and verapamil, which show hepatic clearance values greater than 25% of the liver blood flow (< 10% of the total number of drugs in the set). We envisage that for majority of the drugs (>90%), oral absorption was not hampered by extensive gut wall and/or hepatic metabolisms.
Applicability of the predictive model
We note that Avdeef has developed a similar in-combo model (based on cell-based permeability combined with a paracellular transport component) for predicting human jejunal permeability (HJP) [185]. Obviously HJP is the most direct parameter for developing models based on any in vitro permeability measures. In reality, jejunal permeability is often unavailable and is not routinely evaluated in pharmaceutical industry. As far as we are aware, a recent review reported the most extensive collection of
HJP data (53 compounds) to date [43]. On selection of the training compounds employed here, it was found that bioavailability data were readily available on a wider range of marketed drugs, which allowed a degree of chemical diversity to be introduced into the training data set.
- 168 - Generally, the oral route is the preferred way of administration for pharmaceuticals because of patient convenience. However, other routes of administration could be developed if the treatment is likely to offer clinical benefits to patients. Therefore, it is of great interest for the discovery project to identify research compounds that are unlikely to show good oral exposure at an early stage. Poor oral bioavailability could arise for a number of reasons, including metabolic liability (high clearance), efflux transport or other active processes, gut wall metabolism, suboptimal physical properties such as poor solubility, or poor permeability. As the lead chemical series progress along the discovery pipeline, a cascade of in vitro tests would be performed to identify the aforementioned issues that could potentially lead to poor oral exposure. Instead of testing the research compounds on live animals, this simplistic approach would allow the discovery project to spot the issues more quickly, and trigger the design and synthesis of the next round analogues with the goal to moderate any risk. The model developed in this study would help to predict the fraction absorbed in the absence of other detrimental factors such as clearance, efflux, solubility. Together with other in vitro assessments in the testing cascade, this model would be particularly useful to help the prioritisation of the most promising research compounds for pharmacokinetics studies, with the goal of reducing the usage of live animals on those compounds that are unlikely to show a reasonable level of exposure.
While the rotating-diffusion cell described in this work studies only one compound at a time, it is crucial to establish the rigorous computation approach to derive the permeability parameter, and develop the predictive model. We are currently in the process of developing a parallelized/high throughput version of this permeability assay.
- 169 - Correlation between partitioning into the membrane and n-octanol
It is also interesting to correlate the membrane/aqueous phase distribution coefficient measured in this report with the octanol/water distribution coefficient used in high-throughput screening setting in the early drug discovery. Fig. 5.6 shows the correlation between the two distribution coefficients at pH 7.4 of the aqueous phase. The solid line represents the correlation with unity slope. The linear fit for all drug molecules yields a slope of 0.7153, indicating that, on average, selected drugs interact stronger with n-octanol than with the membrane (DOPC and stearic acid in 1,9-decadiene).
Figure 5.6 Correlation between membrane/aqueous phase distribution coefficient and octanol/water distribution coefficient. The solid curve is the 1:1 linear dependence between horizontal and vertical axis. The dashed line is the best linear fit for all 31 data points. Drug molecules colour scheme: red – acids, green – bases, blue – zwitterions, grey – neutral.
A separate analysis for four charge types, neutral, zwitterion, base and acid, is shown in
Fig. 5.7. Neutral molecules show the highest correlation slope of 0.887, followed by zwitterions and bases, 0.794 and 0.704, respectively. The correlation for acid molecules,
- 170 - however, shows a very low slope of 0.3584. This is not unexpected given that the membrane phase contains negatively charged stearic acid, which reduces the affinity of anions to the membrane.
Figure 5.7 Correlation between membrane/aqueous phase distribution coefficient and octanol/water distribution coefficient. The dashed lines are the best linear fits for the respective drug charge types. Drug molecules and linear fit colour scheme: red – acids, green – bases, blue – zwitterions, grey – neutral.
- 171 - 5.4 Conclusions
A hydrodynamic permeation method is presented herein and shown to yield an improved correlation with fraction absorbed of drugs in humans. The optimised effective permeability coefficient is calculated at stirred conditions corresponding to the unstirred water layer thickness of 200 μm and includes the paracellular transport component to mimic transport through the intercellular junctions found in vivo. The optimised effective permeability coefficient and the effective permeability coefficient obtained under unstirred conditions are correlated with the fraction absorbed. Comparison of the two shows that the optimisation method presented here outperforms the unstirred PAMPA method for the prediction of the fraction absorbed in humans. Ideally, the collected permeability should be compared with human jejunal permeability which is a direct measure of drug absorption across the intestinal wall. The amount of available literature data on human jejunal permeability is limited to about 40 drug molecules. Here, a more generic group of drug molecules with diverse physicochemical properties is chosen. When correlating permeability coefficients with the fraction absorbed a few assumptions and corrections were taken into account. First, the drug molecules with no active transport across the epithelial cell were chosen for the training set. The absolute bioavailability literature values were corrected for the first pass hepatic clearance while assuming that gut metabolism is negligible, and finally drugs with little or no solubility issues were included in this study. The introduced method is feasible for high-throughput screening setting in early drug discovery.
- 172 - Drug Transfer across the Liquid/Liquid Interface
6.1 Introduction
The principle of applying electrochemical methods at the interface between two immiscible electrolyte solutions has been introduced in section 1.6.1. The fundamental theory of ion transfer across the L/L interface and its application has been described
[102-105] elsewhere . For the purely ionic transfer of p ions i (with a charge number zi) between the phase w and o (and no electron transfer) the partition can be described:
p p zi ,w zi ,o ik ik (6.1) k k
~ At equilibrium, the electrochemical potential of each ion, i , is the same in both phases:
~w ~o i i (6.2)
The electrochemical potential of the ion i in the phase w is given by the sum of the chemical and the electrical term:
~w w w i i ziF (6.3)
w w where i is the chemical potential of ion i in phase w, F is the Faraday constant and is the bulk electrical potential of phase w (Galvani potential of phase w). Substitution for the chemical potential gives the following expression for the electrochemical potential:
~w 0,w w w i i RT ln ai ziF (6.4)
- 173 - 0,w w where i is the standard chemical potential and ai the activity of the ion i in the phase w. R is the universal gas constant and T the thermodynamic temperature.
From Eq. (6.2) and Eq. (6.4) we obtain the Galvani potential difference between
w the phases w and o, o :
0,w 0,o RT ao w w o i i ln i (6.5) o w zi F zi F ai
w 0 Definition of the standard transfer potential of the ion i between phases w and o o i , gives the Nernst equation for ion transfer across the interface between phases w and o:
RT ao w w 0 ln i (6.6) o o i w zi F ai
Assuming that transfer is purely ionic (no redox reaction or ion-pairing) we arrive at:
0,w 0,o 0,wo w 0 i i Gtr,i oi (6.7) ziF ziF
0,wo Where Gtr, i is the standard Gibbs energy of transfer of ion i from the phase w to the phase o. This relationship can be directly used when investigating the ion lipophilicity.
From Eq.1.2 (section 1.1) and Eq. (6.6) we obtain an expression for the partition
o/w coefficient, Pi , between phases o and w:
o o/w ai zi F w 0 zi F w log Pi log w o i o (6.8) ai RT ln10 RT ln10
- 174 - 0,o/w We can then define the standard partition coefficient of the ion Pi which is independent of the Galvani potential difference between phases w and o and represent the intrinsic value for the ion i.
z F log P0,o/w i w 0 (6.9) i RT ln10 o i
The standard partition coefficient can be easily calculated from the standard transfer potential which is accessible via cyclic voltammetry at ITIES. In contrast to the shake-flask experiment and „apparent value‟ of partition coefficient from Eq. (6.8), we can obtain an intrinsic value – standard partition coefficient, independent of particular potential conditions using cyclic voltammetry as a potential controlled method [15, 178].
w 0 The standard transfer potential o i of an ion i can be calculated from the following equation:
w 0 w 1/2 w 1/2 w 0 o i o i oref oref (6.10)
w 1/2 where o i is the half-wave potential of the ion i obtained from cyclic voltammetry
w 1/ 2 (section 1.5.1) and o ref is the observed half-wave potential of an internal reference
w 0 molecule whose standard transfer potential o ref is known.
Because of practical reasons (the absolute potential cannot be measured), the tetraphenylarsonium tetraphenylborate standard potential (TATB) scale has been used at the liquid/liquid interface, this is analogous to the standard redox potential scale based on
+ [17, 216] the H /H2 redox couple . The centre of symmetry of the current–potential curve
w [217-219] should correspond to o 0 under several assumptions .
The method of cyclic voltammetry has been widely employed for drug transfer across the L/L interface. It has been used to determine the drug intrinsic lipophilicity
- 175 - (standard partition coefficient) as well as its diffusion coefficient [17]. Work was presented both on anionic and cationic transfer [15, 178]. Also, a linear correlation was found between the neutral form partitioning from water to 1,2-DCE and from water to n-octanol [15]. This is important as water/n-octanol is a standard system in pharmaceutical research but it is unsuitable for voltammetry, due to its very low polarity. Interesting work has been presented on possible ion-pairing of cationic drugs with lipophilic anions [178].
This chapter demonstrates the use of liquid/liquid electrochemistry in ion transfer across the ITIES for fully ionized species. Then it focuses on transfer of partially ionized drug molecules and studies the interplay of the drug partitioning and diffusion via a stirred
(rotating) configuration of the ITIES.
- 176 - 6.2 Aqueous and Organic Electrolytes for Water/1,2-DCE System
An ideal liquid/liquid system would be easy to assemble, stable in time and provide a large potential window in which the species of interest could be analysed. A common choice of L/L configuration for ion transfer setting is an aqueous phase containing lithium chloride as electrolyte and an organic solvent, such as 1,2- dichloroethane, containing an organic electrolyte such as BTPPATPBCl4. An additional
„reference‟ aqueous phase containing common partitioning ion with the organic phase is usually connected to the system.
Herein, we have examined several alternative configurations including use of commercial available organic electrolytes and use of alternative reference electrodes. Two different water-soluble electrolytes, lithium chloride and sodium sulphate, were studied.
Three different organic electrolytes soluble in 1,2-DCE were examined. BTPPATPBCl4 was prepared by metathesis and purified as described in 2.3.5, THATPB and
TDDATPBCl4 were used as received. Blank cyclic voltammograms of the liquid/liquid electrochemical cell, only containing solvent and supporting electrolytes, are shown in
Fig. 6.1. The voltammograms are corrected to lie on a respective potential scale where tetramethylammonium cation transfer occurs at 0.5 V.
The first organic electrolyte, BTPPATPBCl4, was used both with lithium and sodium sulphate as the aqueous electrolyte. The results, and also literature data, suggest that the choice of lithium or sodium as the cation of the aqueous electrolyte does not affect the potential window width as the standard transfer potentials of these two ions in water/1,2-DCE are almost identical [115]. Selection of the sulphate anion over chloride
(green curve in Fig. 6.1), however, increases the potential window in the negative region where anions are transferred from the aqueous phase.
- 177 -
Figure 6.1 Blank cyclic voltammograms on water/1,2-DCE interface showing potential windows for several electrolytes and reference electrode configurations. Voltammograms are corrected to fit the relative potential scale at which TMA+ cation transfer potential is 0.5 V. Black curve measured in cell Ag|Ag2SO4| 10 mM NaH2PO4, 30 mM Na2SO4, pH 7.4 (aq)| 15 mM TDDATPBCl4 (1,2-DCE)| AgTPBCl4|Ag. Red curve measured in cell Ag|Ag2SO4| 10 mM NaH2PO4, 30 mM Na2SO4, pH 7.4 (aq)| 15 mM THATPB (1,2- DCE)|AgTPB|Ag. Blue curve measured in cell Ag|AgCl| 10 mM NaH2PO4, 10 mM NaCl, pH 7.4 (aq)| 10 mM BTPPATPBCl4 (1,2-DCE)| 1 mM BTPPACl, 10 mM NaCl (aq)|AgCl|Ag. Green curve measured in cell Ag|Ag2SO4| 10 mM NaH2PO4, 10 mM Na2SO4, pH 7.4 (aq)| 10 mM BTPPATPBCl4 (1,2-DCE)| 1 mM BTPPACl, 10 mM −1 Na2SO4 (aq)|Ag2SO4|Ag. Cyclic voltammogram were obtained at scan rate 40 mV s .
An aqueous reference phase containing common partitioning ions with the organic phase,
BTPPA+, was used in this configuration. The disadvantage of this configuration is the tedious preparation of the organic electrolyte and related impurities which distort the current signal (green curve in Fig. 6.1 at potentials 0.0 – 0.2 V). Another electrolyte used here was tetraheptylammonium tetraphenylborate (THATPB) along with a sulphate based aqueous electrolyte (red curve in Fig. 6.1). This electrolyte system shows the smallest potential window.
- 178 - Finally, tetradodecylammonium tetrakis(4-chlorophenyl)borate, TDDATPBCl4 organic electrolyte was used as the organic electrolyte. This electrolyte (when used with chloride base aqueous electrolyte) provides a very wide (> 0.7 V) potential window. Both
− systems with internal reference solution, with the common partitioning ion TPBCl4 and system using organic reference electrode, Ag/AgTPBCl4 directly immersed in solution were successfully tested. The latter case is shown as the black curve in Fig. 6.1. High purity TDDATPBCl4 is available from chemical suppliers, hence there is no need for its synthesis and purification.
- 179 - 6.3 Ion Transfer under Unstirred Conditions
6.3.1 Transfer of Fully Ionized Species across the ITIES
The transfer of various ionic species was studied using cyclic voltammetry at the water/1,2-dichloroethane interface. Fig. 6.2 shows cyclic voltammograms of perchlorate anion transfer across this type of ITIES. Voltammograms were recorded in 0.2 mM lithium perchlorate solution for various scan rates in the range of 5 – 150 mV s−1.
Figure 6.2 Perchlorate anion transfer across the ITIES. Measured in cell Ag|AgCl| 10 mM NaH2PO4, 10 mM NaCl, 0.3 mM LiClO4, pH 7.4 (aq)| 10 mM BTPPATPBCl4 (1,2-DCE)| 1 mM BTPPACl, 10 mM NaCl (aq)|AgCl|Ag at scan rates 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 120 and 150 mV s1. Starting potential difference was 0.7 V.
The scan was started at 0.7 V towards the positive potential window edge first.
Perchlorate anion stays in the water phase under these conditions. As the potential difference between water and 1,2-DCE phase is swept to negative values, i.e. the water phase is made negatively charged, the perchlorate anion starts to transfer to the 1,2-DCE
- 180 - with a peak transfer potential of 0.31 V. During the reverse scan from the negative potential vertex (0.15 V), the perchlorate anion transfers back to the water phase at peak potential ca. 0.37 V. From the negative (cathodic) peak current one is able to determine the diffusion coefficient of the transferred anion in water (or equivalently for this sign of current, for a cation in the 1,2-DCE phase). Similarly the positive (anodic) peak current would yield the diffusion coefficient of the transferred cation in water, or anion in 1,2-
DCE, respectively. Measuring the peak current at different scan rates allows determination of the diffusion coefficient in the respective phase.
Figure 6.3 Randles-Ševčík plot of perchlorate anion transfer across the ITIES. Shown on the plot is the cathodic peak current dependence on the square root of scan rate in the range of 20, 30, 40, 50, 60, 70, 80, 90, 100 and 120 mV s1.
The Randles-Ševčík plot, i.e. peak current plotted against square root of scan rate, of perchlorate diffusion in the aqueous phase (negative peak current) is shown in Fig. 6.3.
Eq. (1.10) was used to calculate the aqueous diffusion coefficient from the slope of the
- 181 - Randles-Ševčík plot. The aqueous diffusion coefficient of perchlorate anion was determined to be 1.80 × 105 cm2 s1, which is in excellent agreement with literature value of 1.79 × 105 cm2 s1 [154].
The peak current is a quantitative measure of the ion transfer as it is proportional to the bulk concentration of the ion. The qualitative identification of the ionic species, i, can be made from the peak position on the potential axis. In order to determine the transfer potential of the ion an internal reference compound with known transfer potential on the aforementioned TATB scale needs to be added to the aqueous phase (section
w 0 6.1.2). Tetramethylammonium cation ( 160 mV, TATB scale ) was chosen as o TMA the internal reference compound and its transfer analyzed using cyclic voltammetry together with perchlorate anion. The cyclic voltammogram is shown in Fig. 6.4. Eq. (6.10)
w 0 allows the calculation of the ions standard transfer potential, o i , from its half-wave
w 1/2 w 1/ 2 potential, o i , the half-wave potential of the internal reference compound, o ref , and
w 0 standard transfer potential of the internal reference compound, o ref . Standard Gibbs energy of transfer, standard partition coefficient between and standard transfer potential of perchlorate anion in water/1,2-DCE system were determined from Eq. (6.7), (6.9) and
0, wo 1 w 0 (6.10) as G 10.6 kJ mol , o 109 mV (TATB scale) and tr, ClO4 ClO4
0, o/w log P 1.86 , respectively . The reported standard Gibbs energy of transfer of ClO4
0, wo 1 [117] perchlorate anion is G 17 kJ mol . The difference between the measured and tr, ClO4 the literature values can be attributed to both the ohmic resistance compensation and the concentration of the supporting electrolyte employed in the respective experimental procedures.
- 182 -
Figure 6.4 Perchlorate anion transfer across the ITIES with internal reference molecule + TMA . Measured in cell Ag|AgCl| 10 mM NaH2PO4, 30 mM NaCl, 0.3 mM LiClO4, 0.1 mM TMACl, pH 7.4 (aq)| 10 mM BTPPATPBCl4 (1,2-DCE)| 1 mM BTPPACl, 30 mM NaCl (aq)|AgCl|Ag at scan rate 40 mV s1. Start potential difference 0.5 V.
Cyclic voltammetry and subsequent analysis, i.e. determination of the aqueous diffusion coefficient and standard transfer potential (standard partition coefficient), were performed for four other ionic species, including tetramethylammonium itself. See Fig.
6.5 – 6.8 for cyclic voltammograms of nitrate, iodide, tetramethylammonium and tetraethylammonium ion transfer across the ITIES. All these molecules are derived from strong electrolytes in aqueous solution and were therefore suitable for validation of the
L/L electrochemistry technique under the conditions used. Also, the data collected for these ions were used for accurate determination of the curved interfacial area between water and 1,2-DCE phase (section A5, Appendix).
- 183 -
Figure 6.5 Nitrate anion transfer across the ITIES. Measured in cell Ag|Ag2SO4| 10 mM NaH2PO4, 30 mM Na2SO4, KNO3, pH 7.4 (aq)| 20 mM BTPPATPBCl4 (1,2-DCE)| 1 mM BTPPACl, 30 mM Na2SO4 (aq)|Ag2SO4|Ag at scan rates 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 120 and 150 mV s1. Starting potential difference was 0.6 V. The small inset graph shows the cyclic voltammogram with the internal reference compound TMA+ at scan rate of 40 mV s1.
The nitrate anion, whose cyclic voltammograms of transfer are shown in Fig. 6.5, transfers on the very edge of the negative part of the potential window. The standard
w 0 transfer potential of nitrate anion was found to be o 288 mV (TATB scale) , NO3
0, wo 1 corresponding standard Gibbs energy of transfer G 27.8 kJ mol and standard tr, NO3
0, o / w partition coefficient between 1,2-DCE and water log P 4.9 . Reported standard NO3
0, wo 1 [117] Gibbs energy of transfer of nitrate anion is G 34 kJ mol . The aqueous tr, NO3 diffusion coefficient was found to be 1.97 × 105 cm2 s1 (literature value of 1.90 × 105 cm2 s1 [154]).
- 184 -
Figure 6.6 Iodide anion transfer across the ITIES. Measured in cell Ag|Ag2SO4| 10 mM NaH2PO4, 30 mM Na2SO4, 0.3 mM KI, pH 7.4 (aq)| 20 mM BTPPATPBCl4 (1,2-DCE)| 1 mM BTPPACl, 30 mM Na2SO4 (aq)|Ag2SO4|Ag at scan rates 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 and 150 mV s1. Start potential difference was 0.6 V. The small inset graph shows the cyclic voltammogram with the internal reference compound TMA+ at scan rate of 40 mV s1.
Cyclic voltammogram of iodide anion transfer across water/1,2-DCE is shown in
Fig. 6.6. Iodide transfers between perchlorate and nitrate anion on the potential scale with
w 0 standard transfer potential 210 mV (TATB scale) . Standard Gibbs energy of o I transfer and partition coefficient of iodide ion in water/1,2-DCE system are
0, wo 1 0, o / w G 20.3 kJ mol and log P 3.9 , respectively. Reported standard Gibbs tr, I I
0, wo 1 [117] energy of transfer of iodide anion is G 26 kJ mol . The aqueous diffusion tr, I coefficient was determined as 2.00 × 105 cm2 s1 (literature value of 2.05 × 105 cm2 s1
[154]).
- 185 -
Figure 6.7 Tetramethylammonium cation transfer across the ITIES. Measured in cell Ag|Ag2SO4| 10 mM NaH2PO4, 30 mM Na2SO4, 0.3 mM TMA2SO4, pH 7.4 (aq)| 15 mM TDDATPBCl4 (1,2-DCE)| AgTPBCl4|Ag at scan rates 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 120 and 150 mV s1. Start potential difference was 0.3 V.
Cyclic voltammogram of tetramethylammonium cation (TEA+) transfer across water/1,2-DCE is shown in Fig. 6.7. Tetramethylammonium was used as internal reference compound. Standard Gibbs energy of TMA+ transfer across water/1,2-DCE interface is 15.4 kJ mol−1 [216]. This value was used to calculate standard transfer potential and partition coefficient of TMA+ ion in water/1,2-DCE system,
w 0 0, o / w 160 mV (TATB scale) and log P 2.7 , respectively. The aqueous o TMA TMA diffusion coefficient found to be 1.18 × 105 cm2 s1 (literature value of 1.20 × 105 cm2 s1 [154]).
- 186 -
Figure 6.8 Tetraethylammonium cation transfer across the ITIES. Measured in cell Ag|AgCl| 10 mM NaH2PO4, 10mM LiCl, pH 7.4 (aq)| 10 mM BTPPATPBCl4 (1,2-DCE)| 1 mM BTPPACl, 10 mM LiCl (aq)|AgCl|Ag at scan rates 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 and 150 mV s1. Start potential difference was 0.15 V.
The last fully ionized compound to study was tetraethylammonium cation. The cyclic voltammogram of its transfer across water/1,2-DCE is shown in Fig. 6.8. As tetraethylammonium transfers close to tetraethylammonium, determination of standard transfer potential is not feasible using the method used for perchlorate, nitrate and iodide ions. The literature value of standard Gibbs energy of TEA+ transfer across water/1,2-
DCE interface is 1.8 kJ mol−1 [216]. From this value, the standard transfer potential
w 0 19 mV (TATB scale) and partition coefficient in water/1,2-DCE system, o TEA
0, o / w log P 0.3 TEA , were calculated. The aqueous diffusion coefficient found to be 8.71 ×
106 cm2 s1 (literature value of 8.68 × 106 cm2 s1 [154]).
Table 6.1 summarized the physicochemical properties of perchlorate, nitrate, iodide, TMA+ and TEA+ determined from their transfer across water/1,2-DCE interface.
- 187 - Table 6.1 Standard transfer potential, standard Gibbs energy of transfer, standard partition coefficient and aqueous diffusion coefficient of perchlorate, nitrate, iodide, TMA+ and TEA+ ions in water/1,2-DCE system
w 0 6 2 1 0,wo 1 o i / mV 0,o/w Daq /10 cm s ion Gtr, i / kJ mol log Pi (TATB scale) (measured/literature) perchlorate −109 10.6 −1.9 18.0/17.9 nitrate −288 27.8 −4.9 19.7/19.0 iodide −210 20.3 −3.9 20.0/20.5 TMA+ +160 15.4 −2.7 11.8/12.0 TEA+ +19 1.8 −0.3 8.7/8.7
6.3.2 Transfer of Partially Ionized Species across the ITIES
The main reason to employ liquid/liquid electrochemistry in the present work was to study the transfer of drug molecules across the ITIES. Although this application has been intensively studied and many links to pharmaceutical application have been established there is only a limited number of reports on some aspects of drug transfer across ITIES. The majority of reports in this field focus on determination of ionized drug lipophilicity, i.e. transfer potential, and its relevance to membrane transport of the drug [15,
178]. Surprisingly, there are virtually no reports on the drug diffusion coefficients determined by the procedure described in the previous section. Kontturi et al. reported aqueous diffusion coefficients of 9 drug molecules but did not provide details on the method of their determination [17]. The difference between the fully ionized species, whose diffusion coefficients are well covered in literature, and drug molecules, is that most drugs are weak acids, weak bases or zwitterions. These partially ionized species have pH dependent ionic/neutral fraction distribution. Accordingly, drug transfer across the ITIES has been examined with an emphasis on determination of the aqueous diffusion coefficient.
- 188 - Transfer of two model compounds, warfarin and verapamil, across the ITIES between water and 1,2-DCE was studied under unstirred conditions. Fig. 6.9 shows the cyclic voltammogram of verapamil transfer across the water/1,2-DCE interface.
[8] Verapamil is a weak base with pKa = 9.07 . The cyclic voltammetry was carried out at aqueous pH 7.4. At this pH verapamil is strongly ionized and only about 2% is present in the neutral form.
Figure 6.9 Verapamil cation transfer across the ITIES. Measured in cell Ag|Ag2SO4| 10 mM NaH2PO4, 30 mM Na2SO4, 0.3 mM verapamil, pH 7.4 (aq)| 20 mM BTPPATPBCl4 (1,2-DCE)| 1 mM BTPPACl, 30 mM Na2SO4 (aq)|Ag2SO4|Ag at scan rates 5, 10, 20, 30, 40, 50, 70, 80, 90, 100, 120 and 150 mV s1. Start potential difference was 0.3 V.
The same peak current analysis presented in the previous section was used to determine the aqueous diffusion coefficient of verapamil. Unlike the five fully ionised species
(perchlorate, nitrate, iodide, TMA+ and TEA+), the measured aqueous diffusion coefficient of the verapamil cation, 9.70 × 107 cm2 s1, was almost 4-fold lower than the
- 189 - literature value, 3.57 × 106 cm2 s1 (calculated from Eq.(8) in [62]). Repeated attempts were made to quantify verapamil transfer across the ITIES using various configurations of both the aqueous and organic phase, verapamil concentration and potentiostat settings, to ensure that the methodology used was valid. However, in all cases the measured aqueous diffusion coefficient was consistently low.
[8] Another drug molecule, warfarin, which is a weak acid with pKa = 4.82 , was analysed to confirm or disprove the unusual behaviour of verapamil. Warfarin transfer was carried out at pH 7.4, at which only about 0.3% of the drug is present in its neutral form, the other 99.7% is present in the anionic form. Cyclic voltammograms of warfarin anion transfer across water/1,2-DCE interface are shown in Fig. 6.10.
Figure 6.10 Warfarin anion transfer across the ITIES. Measured in cell Ag|Ag2SO4| 10 mM NaH2PO4, 30 mM Na2SO4, 0.5 mM warfarin, pH 7.4 (aq)| 20 mM BTPPATPBCl4 (1,2-DCE)| 1 mM BTPPACl, 30 mM Na2SO4 (aq)|Ag2SO4|Ag at scan rates 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 120 and 150 mV s1. Start potential difference was 0.7 V. The small inset graph shows the cyclic voltammogram with the internal reference compound TMA+ at scan rate of 40 mV s1.
- 190 - The warfarin transfer potential was determined to be
w 0 59 mV (TATB scale) . Standard Gibbs energy of transfer and partition o W coefficient of iodide ion in water/1,2-DCE system, calculated from Eq. (6.7) and (6.9), are
0, wo 1 0, o / w G 5.7 kJ mol and log P 1.0, respectively. The aqueous diffusion tr, W W coefficient was determined as 6.97 × 107 cm2 s1. As with the verapamil case, this value is about 6-fold lower that value predicted by Eq. (8) in reference [62], 4.32 × 106 cm2 s1.
Figure 6.11 Effect of mixing on the peak current of warfarin transfer across ITIES. Four pairs of CVs were measured to observe the current decrease with increasing idle time. Black curves were obtained immediately after mixing the aqueous phase. Coloured curves were obtained x min after the black curve was obtained (x = 0, 5, 10 and 30). No further decrease in current was observed after 30 min, which suggests steady-state establishment between the drug neutral form partitioning to the organic phase and the diffusion of the drug from the bulk solution to the interface. Measured in cell Ag|Ag2SO4| 10 mM NaH2PO4, 30 mM Na2SO4, 0.3 mM warfarin, pH 7.4 (aq)| 10 mM BTPPATPBCl4 (1,2- 1 DCE)| 1 mM BTPPACl, 30 mM Na2SO4 (aq)|Ag2SO4|Ag at scan rate 40 mV s .
- 191 - Suspecting that the consistently low value of the measured diffusion coefficient indicated an unknown process occurring at the L/L interface, warfarin transfer was investigated after the aqueous phase was mixed. The mixing of the aqueous phase and subsequent warfarin transfer after various time intervals from 0 to 30 min shows that peak current changes and is highest immediately after mixing. That implies that the concentration of warfarin near the liquid/liquid interface decreases with time, therefore affecting the calculated diffusion coefficient values. Cyclic voltammograms showing the effect of mixing on measured transfer current are shown in Fig. 6.11. It is postulated that the reason for this is partitioning of neutral fraction of the drug molecule from the aqueous phase to the organic. Although at pH 7.4 only 0.3% of neutral warfarin is present, this amount could be sufficient to act as „channel‟ for partitioning of warfarin from water to
1,2-DCE according to the scheme given in Fig. 6.12.
Figure 6.12 Scheme depicting warfarin partition at water/1,2-DCE interface
The same experiment was repeated at pH 11 (7 × 105 % neutral form of warfarin): it was found that the effect of mixing was still evident, although lowered by about 50%.
The above explanation is supported by the high value of partition coefficient of the neutral
o / w [112] form log P HW 3.62 (1,2-DCE/water) , and also the shake-flask experiments carried out in this report (see next section). In order to avoid this hindrance we employed an experiment at pH 11 with the organic phase pre-saturated with warfarin (shaken with an
- 192 - excess of the aqueous phase containing warfarin at the same concentration and pH as in the electrochemical experiment). In the latter case, the current increased and was no longer dependent on pre-mixing as shown in Fig. 6.13. This straightforward solution, however, did not lead to the correct diffusion behaviour value but resulted in the other extreme, i.e. the aqueous diffusion coefficient value being about 22-fold higher than expected (9.5 × 105 cm2 s1). This is due to the pre-concentration of the drug on the aqueous side of the interfacial layer at potentials > +0.6 V.
Figure 6.13 Effect of mixing on current reduced by employing organic phase pre- saturation with warfarin. 1,2-DCE was shaken with the aqueous phase containing 0.3 mM warfarin at pH 11. Series of consecutive cyclic voltammograms obtained 0, 8 and 15 min after mixing is shown. Measured in cell Ag|Ag2SO4| 10 mM NaH2PO4, 30 mM Na2SO4, 0.3 mM warfarin, pH 11.0 (aq)| 10 mM BTPPATPBCl4 (1,2-DCE, saturated with 1 warfarin)| 1 mM BTPPACl, 30 mM Na2SO4 (aq)|Ag2SO4|Ag at scan rate 40 mV s .
6.3.3 Warfarin Water/1,2-DCE Partition Study
Shake-flask experiments were carried out in order to verify the hypothesis that the neutral fraction of warfarin partitions to the 1,2-DCE. The Beer-Lambert calibration of
- 193 - warfarin in 1,2-DCE in the near UV region was carried out to measure the concentration of warfarin directly in 1,2-DCE. Equal volumes of pure 1,2-dichloroethane and the aqueous solution (50 mM sodium sulphate (or 1 M tetraethylammonium chloride), 10 mM sodium phosphate, pH 7.4, 9.2 or 11.0) containing 0.3 mM warfarin were placed in contact and left still for a set period of time thus mimicking the situation during the liquid/liquid electrochemical experiments. After a set time period, a sample of 1,2-DCE phase was collected and transferred to a quartz cuvette for UV spectrophotometry. Both organic and aqueous phase samples were collected and analysed after the water/1,2-DCE system had been shaken and left to equilibrate overnight. Table 6.2 summarizes the results obtained from the shake-flask study at three different aqueous pHs, 7.4, 9.2 and 11.0.
Table 6.2 Partitioning of warfarin from the aqueous phase to 1,2-DCE. The table shows the concentration of warfarin in 1,2-DCE. 1,2-DCE saturated with water was left in contact with the aqueous phase containing 50 mM sodium sulphate or 100 mM tetraethylammonium chloride, 10 mM sodium phosphate and 0.3 mM warfarin at pH 7.4, 9.2 or 11.0, respectively. Contact times were 15 min, 35 min, 70 min and ca. 18 h (marked as overnight in the table). Partition study was carried out for two counter-ions, sodium and TEA+.
sodium counter-ion tetraethylammonium counter-ion
pH time / min warfarin conc / M pH time / min warfarin conc / M 15 48 15 13 35 67 35 34 7.4 7.4 70 123 70 64 overnight ~300 overnight ~250 15 11 15 35 23 35 9.2 9.2 70 38 70 overnight 125 overnight not comparable spectra, possible ion- 15 - 15 pairing 35 - 35 11.0 11.0 70 4 70 overnight 4 overnight
- 194 - Results on the left-hand side in Table 6.2, where sodium was used as aqueous phase counter-ion, show rapid partitioning of warfarin to 1,2-DCE which decreases with increasing pH according to decrease of the fraction of neutral form. This is consistent with the results presented in the previous section where the concentration decrease was reduced by changing the pH from 7.4 to 11.0. The partition coefficient of the warfarin neutral form, calculated from the equilibrated concentration of pH 9.2 and 11.0 measurements,
o / w (Eq. (1.2), using concentration instead of activities) was found to be log P HW 4.01
(literature value 3.62, [112]). The spectrum of the organic phase in Fig. 6.14 shows that only the neutral form of warfarin is present when the sodium counter-ion is used
(comparison with calibration spectra of warfarin in 1,2-DCE and literature data [220]). This suggests that there is no ion-pairing process of warfarin transfer to 1,2-DCE involved and that only the neutral form present in the aqueous phase passively partitions into 1,2-DCE, when the sodium counter-ion is used.
Figure 6.14 Warfarin partitioning from the aqueous phase to 1,2-DCE. Black curve is a UV absorbance calibration spectrum of warfarin in the organic phase, Blue, green and gold curves show UV absorbance partition spectrum of warfarin in the organic phase for the pH of aqueous phase 7.4, 9.2 and 11.0, respectively. Aqueous phase consisted of 10 mM NaH2PO4, 50 mM Na2SO4, 0.3 mM warfarin.
- 195 - The same experiment where the sodium counter-ion was replaced with tetraethylammonium was carried out to investigate possible ion-pairing with a lipophilic cation. The aqueous phase consisted of 10 mM sodium sulphate and 100 mM
+ tetraethylammonium chloride (replacement for 100 mM Na from 50 mM Na2SO4).
The results on the right hand side of Table 6.2 show that from pH 7.4 of the aqueous phase partitioning of warfarin to the organic phase is slightly hindered compared to the previous case. Interestingly, the organic phase spectrum changes when warfarin partitions from the aqueous phase at pH 9.2 and 11.0 as shown in Fig. 6.15. The shape of partition absorbance spectrum in 1,2-DCE for pH 7.4 case (blue curve) is identical to calibration spectra in 1,2-DCE (red curve in Fig. 6.15). As the pH of the aqueous phase changes to
9.2 and 11.0 (green and gold curve, respectively), the shape of the spectrum resembles the warfarin calibration spectra in the aqueous phase (red curve). This suggests that ion- pairing occurs between the warfarin anion and tetraethylammonium cation and the product of this process is detected in 1,2-DCE phase.
The possible warfarin signal interference with tetraethylammonium partitioning to
1,2-DCE was excluded by performing shake-flask experiments with blank tetraethylammonium aqueous solution. The UV absorbance measurement only revealed a peak of negligible magnitude in the low-wavelength part of the spectrum as shown in Fig.
6.16.
The above results show that the neutral form of warfarin passively transfers from the aqueous phase to 1,2-DCE to an extent that hinders the quantification of the current measured via voltammetry. Furthermore, ion-pairing transfer of the drug is observed, when a lipophilic counter-ion is added to the aqueous phase.
- 196 -
Figure 6.15 Partitioning of warfarin from aqueous phase to 1,2-DCE in presence of tetraethylammonium cation in the aqueous phase. Black and red curves are calibration spectra in 1,2-DCE and water, respectively. Blue curve is warfarin partition spectrum in 1,2-DCE for the aqueous pH 7.4. Green and gold curves are warfarin partition spectra in 1,2-DCE for the aqueous phase pH 9.2 and 11.0, respectively. Aqueous phase contained 10 mM NaH2PO4, 100 mM TEACl, 0.3 mM warfarin, at pH 7.4, 9.2 or 11.0.
Figure 6.16 Tetraethylammonium partition spectra in 1,2-DCE. Blue, green and gold curves show UV absorbance spectrum of the organic phase for the pH of the aqueous phase 7.4, 9.2 and 11.0, respectively. Aqueous phase consisted of 10 mM NaH2PO4, 100 mM TEACl.
- 197 - 6.4 Drug Transfer Employing Rotating Membrane
In order to overcome the difficulties with determination of the aqueous diffusion coefficient of partially ionised drug molecules, the rotating cell applied in Chapter 3 for permeability measurement was adapted for liquid/liquid electrochemistry with a lipophilic membrane (PVDF) separating the aqueous and organic phases. This setup is also a modification of the permeation assay with external polarisation discussed in Chapter 4.
Similar approaches investigating tetraethylammonium transfer in a rotating L/L system, separated by a poly(ethylene terephthalate) (PET) membranes have been reported previously from this laboratory [221, 222]. The aqueous phase leakage observed in PET membranes, however, led us to use PVDF membranes used in the PAMPA setup. The aim was to use the membrane to stabilise the interface and hence enable interfacial rotation, thereby, stirring the aqueous and organic phases. Correctly applied stirring will maintain a steady flux of solute to the interface and therefore counter the spontaneous decrease of the drug concentration at the aqueous side of the interface, caused by partitioning of the drug neutral fraction to the organic phase. The detailed experimental setup can be found in section 2.3.5.
Linear sweep voltammetry was used to analyse drug molecule transfer across the water/1,2-DCE interface under stirred conditions. Unlike voltammetry under unstirred conditions, where the current response to the ion transfer is a peak function, voltammograms under stirred conditions have a characteristic sigmoidal shape with a constant limiting current. Applying the relationship between the limiting current, Ilim, and stirring rate (Levich equation, Eq. (1.9)), for the aqueous side of the L/L system gives:
2 / 3 1/ 6 1/ 2 Ilim 0.62ziFAintciDaq (6.11) where all the symbol have the same meaning as defined previously. Two drug molecules, warfarin and propranolol, were studied using the rotating membrane liquid/liquid
- 198 - electrochemistry at aqueous pH 7.4. Both drugs are predominantly ionized at this pH, only a small fraction of neutral drug is present (warfarin = 0.3%, propranolol = 0.7%). The blank (no drug molecule) cyclic voltammetry, carried out to validate the novel liquid/liquid electrochemistry setup for stirring rates in the range from 60 to 600 rpm, is shown in Fig. 6.17.
Figure 6.17 Cyclic voltammetry on the blank rotating liquid/liquid cell. Measured in cell: Ag|AgCl| 30 mM NaH2PO4, 30 mM NaCl, pH 7.4 (aq)| 15 mM TDDATPBCl4 (1,2- −1 DCE)| 0.5 mM KTPBCl4 (aq)|AgCl|Ag at scan rate 20 mV s . Voltammograms have similar shape for all applied stirring rates (60, 110, 280 and 600 rpm).
Before the linear sweep voltammetry was measured, the cyclic voltammogram under unstirred conditions were obtained for potential scan rates 5, 10, 20, 40 and 80 mV s−1 and the aqueous diffusion coefficient determined as described in previous section. This was done to compare the data obtained under unstirred conditions (analysis using Randles-
Ševčík Eq. (1.10)) with data obtained under controlled hydrodynamics (analysis using
Levich Eq. (6.11)) both measured in the same liquid/liquid cell. Cyclic voltammograms measured under unstirred conditions are shown in Fig. 6.18, linear sweep voltammograms measured under controlled hydrodynamics are shown in Fig. 6.19.
- 199 -
Figure 6.18 Warfarin anion transfer across ITIES under unstirred conditions. Measured in cell: Ag|AgCl| 30 mM NaH2PO4, 30 mM NaCl, 0.3 mM warfarin, pH 7.4 (aq)| 15 mM TDDATPBCl4 (1,2-DCE)| 0.5 mM KTPBCl4 (aq)|AgCl|Ag at scan rates 5, 10, 20, 40, 60 and 80 mV s−1. Start potential difference was −0.5 V. The small inset graph shows the Randles-Ševčík plot for the cathodic peak current and scan rate.
Figure 6.19 Warfarin anion transfer across ITIES under controlled hydrodynamics. Measured in cell: Ag|AgCl| 30 mM NaH2PO4, 30 mM NaCl, 0.3 mM warfarin, pH 7.4 (aq)| 15 mM TDDATPBCl4 (1,2-DCE)| 0.5 mM KTPBCl4 (aq)|AgCl|Ag at scan rates 2 mV s−1 and stirring rates 60, 80, 110, 160, 280 and 600 rpm. Start potential difference was −0.5 V. The small inset graph shows the Levich plot.
- 200 - Data analysis show that the aqueous diffusion coefficient of warfarin calculated from the Randles-Ševčík equation for the case of cyclic voltammetry under unstirred
7 2 1 conditions is still low, Daq 3.54 10 cm s . An analysis of the linear sweep voltammetry with controlled hydrodynamics yields an aqueous diffusion coefficient of
3.72 × 106 cm2 s1 (predicted value 4.32 × 106 cm2 s1, calculated from Eq. (8) in reference [62]), which is a great improvement over the unstirred method. Sodium chloride was used as an aqueous electrolyte over sodium sulphate for the rotating liquid/liquid cell to ensure maximum reference electrode stability in this novel system. The disadvantage of this particular system is that the chloride ions limiting the potential window interfere with warfarin transfer and could distort the measured limiting current. For this reason, another drug molecule, propranolol, was studied using the rotating L/L cell to confirm the methodology used here is valid. Fig. 6.20 and Fig. 6.21 show propranolol transfer under unstirred and stirred conditions, respectively.
Figure 6.20 Propranolol cation transfer across ITIES under unstirred conditions. Measured in cell: Ag|AgCl| 30 mM NaH2PO4, 30 mM NaCl, 0.3 mM propranolol,pH 7.4(aq)| 15mM TDDATPBCl4(1,2-DCE)| 0.5 mM KTPBCl4 (aq)|AgCl|Ag at scan rates 5, 10, 20, 40, 60 and 80 mV s−1. Start potential difference was −0.6 V. The inset graph shows the Randles-Ševčík plot for the cathodic peak current and scan rate.
- 201 -
Figure 6.21 Propranolol cation transfer across ITIES under controlled hydrodynamics. Measured in cell: Ag|AgCl| 30 mM NaH2PO4, 30 mM NaCl, 0.3 mM propranolol, pH 7.4 (aq)| 15 mM TDDATPBCl4 (1,2-DCE)| 0.5 mM KTPBCl4 (aq)|AgCl|Ag at scan rates 2 mV s−1 and stirring rates 60, 80, 110, 160, 280 and 600 rpm. Start potential difference was −0.6 V. The small inset graph shows the Levich plot.
The aqueous diffusion coefficient of propranolol calculated from the Randles-Ševčík equation for the case of cyclic voltammetry under unstirred conditions is
7 2 1 Daq 1.94 10 cm s . Similar to the warfarin case, an analysis of the linear sweep voltammetry with controlled hydrodynamics yields an improved aqueous diffusion coefficient value of 3.21 × 106 cm2 s1 (predicted value 4.70 × 106 cm2 s1, calculated from Eq. (8) in reference [62]).
The above results show that rotating L/L electrochemistry is a suitable method to study the transfer or weak acid or base drug molecules across the L/L interface. Moreover, this method allows an accurate determination of the aqueous diffusion coefficient, whilst avoiding the requirement to oxidise or reduce the drug species.
- 202 - 6.5 Conclusions
Liquid/liquid electrochemistry has been used to study the transfer of ionized species across the interface between water and 1,2-DCE. Several aqueous and organic electrolytes configurations as well as the use of alternative reference solutions and electrodes were studied to find optimal conditions for ion transfer across water/1,2-DCE interface. The organic electrolyte TDDATPBCl4 was found to be the best compromise between the solubility in the organic phases, width of the potential window, commercial availability and purity. The aqueous electrolyte containing sulphate as the anion proved to give the largest potential window. Sulphate electrolytes, however, require the use of the silver/silver sulphate electrode, whose non-reproducible potential response limits its application. Ion transfer of five fully ionized species, perchlorate, nitrate, iodide, tetramethylammonium and tetraethylammonium was carried out as method validation and liquid/liquid interface area calibration. The method to determine the aqueous diffusion coefficient and standard partition coefficient of the ionic species was demonstrated. The same method was applied to the transfer of partially ionized drug molecules, warfarin and verapamil. The fundamental phenomena of the drug neutral fraction partitioning to the organic phase, which invalidated analysis to determine the diffusion coefficient, was postulated and consequently proven by partition shake-flask studies using UV spectrophotometry. An alternative method, which employed an organic membrane fitted on the liquid/liquid interface and allowed rotation of the interface, was designed. Analysis of two drug molecules, warfarin and propranolol, showed that the aqueous diffusion coefficient is correctly determined using this novel method.
- 203 - Reversible Electron Transfer using the Rotating Bipolar Cell
7.1 Introduction
The rotating-disc electrode (RDE) is a model system from which the permeation assay has been derived. In this system the RDE is a stirred working electrode in an aqueous solution. Unlike electrochemical methods operating under unstirred conditions where the transport is solely limited by diffusion, the rotating-disc electrode system allows control over solute flux towards the electrode with applied stirring. The limiting current from Eq. (6.11) measured in a rotating system relates to the solute flux, J, as follows:
2 / 3 1/ 6 1/ 2 J 0.62cDaq (7.1) where all the symbols have the same meaning as defined previously.
The permeation method presented as a part of this thesis consists of three liquid phases with two interfaces as opposed to one liquid and one solid phase in RDE system.
The solid RDE is replaced with a membrane and an adjacent liquid phase. Due to the ability to control flux with stirring, the contribution of the aqueous transport can be separated from the transport through the membrane simply by extrapolating to infinite stirring conditions.
In the permeation assay the membrane becomes analogous to the rotating-disc electrode. Therefore uniform stirring has to be induced on both sides of the membrane.
This was achieved by stirring the membrane, rather than having a stirrer in each aqueous phase. However, the geometry of the rotating permeation assay slightly varied from the rotating-disc electrode, as shown in Fig. 7.1.
- 204 -
Figure 7.1 Geometry of (a) rotating-disc electrode and (b) permeation assay setup.
Whereas the lower acceptor compartment has the same geometry as the RDE, the upper donor compartment was constructed where the rotating area has the same diameter as the donor solution. For this reason, a stationary paddle was introduced in the donor phase to suppress the angular flow induced by solution movement due to adhesive forces with the glass tube. Once the angular flow is suppressed, the flow normal to the electrode remains and hydrodynamics identical to one of the acceptor side of the membrane is achieved. The other main difference is that the active membrane area occupies the whole rotating platform on the acceptor side and about 80% of rotating platform on the donor side. In the conventional RDE setup the active electrode area occupies about 10 – 20% in the centre of the rotating platform. The reason for this is to avoid turbulence that might occur at the edges of the rotating platform as indicated by hydrodynamic simulations and laser Doppler velocity measurement [223]. The large area chosen in the case of the permeation assay was to increase solute flux and, therefore, increase detection sensitivity.
Because of these differences, verification was needed to show that the implemented permeation system has the same response as the rotating-disc electrode system. Therefore, an electrochemical experiment to verify whether the hydrodynamic
- 205 - properties in the upper (donor) compartment of the permeation cell are those of the rotating-disc electrode system was designed. The permeation cell was modified to the bipolar electrochemical cell (BEC) configuration where the membrane was replaced by a rotating-disc electrode and instead of the solute permeating through the membrane, two reversible, water-soluble redox couples were introduced to both upper and lower (donor and acceptor) compartments. This setup enables reversible electron transfer between the two redox couples to be studied, where the phases are physically separated by the electrode. The rotating-disc electrode capable of exchanging electrons between the two solution compartments was made of glassy carbon (GC). The GC electrode occupied ca.
17% of the rotating area. The donor compartment contains hexaammineruthenium chloride complex, which mimics the permeating solute from PAMPA. Rather than permeating through a membrane, the complex is transported to the GC electrode surface where it gains (or loses) an electron and is thus reduced (or oxidised). The acceptor compartment contains a redox couple, potassium ferrocyanide and potassium ferricyanide.
The schematic of the electrochemical reaction occurring at the two glassy carbon surfaces is shown in Fig. 7.2. An unstirred BEC configuration, which was used to study the same electrochemical reaction was reported recently [132].
Figure 7.2 Schematic of electrochemical reactions occurring on GC electrode surface. (a) reduction of the ruthenium complex, (b) oxidation of the ruthenium complex.
- 206 - 7.2 Experimental
The detailed experimental procedure, including the schematic of the modified
BEC (Fig. 2.10), can be found in section 2.3.6. Briefly, a four electrode system (two counter and two reference electrodes) was used to apply a potential difference between the donor and acceptor phases. The glassy carbon rotating-disc electrode separating donor and acceptor compartments provided electron exchange between the phases containing ferrocyanide/ferrocyanide (acceptor) and hexaammineruthenium(III)/(II) redox couples.
The electrochemical methods used to study electron transfer in the bipolar cell include cyclic voltammetry under unstirred conditions and linear sweep voltammetry on the rotating-disc electrode. Cyclic voltammetry was used to determine the potential window and location of the reduction peak of the ruthenium complex. Linear sweep voltammetry was used to obtain the limiting current value at each given stirring rate.
- 207 - 7.3 Results and Discussion
7.3.1 Cyclic Voltammetry
The cyclic voltammetry performed on the bipolar cell under unstirred conditions was used to determine the potential window and location of the reduction peak of the ruthenium complex.
Figure 7.3 Cyclic voltammogram of 0.5 mM hexaammineruthenium(III) chloride solution performed in BEC. Potential was swept at 30 mV s−1. The other cell part contains 25 mM K4Fe(CN)6 and 25 mM K3Fe(CN)6 in acidic solution (50 mM HCl). Both compartments contained 0.5 M KCl as supporting electrolyte. The resistivity of the electrochemical cell was 250 Ω m.
A cyclic voltammogram carried out on the bipolar cell under unstirred conditions is shown in Fig. 7.3. The potential difference was applied between donor and acceptor phase and current was measured between the counter electrodes. As the potential is swept from +0.2 V to −1.2 V, the reduction peak of the ruthenium complex, i.e. change of the oxidation state from 3+ to 2+, occurs at a potential of −0.628 V. This peak corresponds to
- 208 - the hexaammineruthenium(III) diffusion to the glassy carbon electrode, gain of an electron and reduction to hexaammineruthenium(II). The observed current decay corresponds to the diffusion layer adjacent to the GC electrode being depleted. When the potential is swept back, the oxidation peak (II to III) occurs at a potential of −0.506 V.
The oxidation peak corresponds to the hexaammineruthenium(II) oxidation back to hexaammineruthenium(III). The peak separation of this redox process is 122 mV, which is about double the expected value for this process, i.e. 59 mV. This is most likely caused by the surface quality of the GC electrode and/or interfacial conditions between the electrode and the holder, inducing a non-linear flux.
7.3.2 Linear sweep voltammetry
The reduction shoulder of the cyclic voltammetry was used to study the effect of paddle-RDE separation on solute transport using the linear sweep voltammetry technique.
Linear sweep voltammetry performed on the bipolar cell with the paddle-electrode separation of 10 mm is shown in Fig. 7.4. The potential difference between donor and acceptor was initially kept at −0.27 V for 30 s and swept from −0.27 V to −0.65 V. The sweep rate of 2 mV s−1 was employed to maintain steady-state mass transport [77]. The donor compartment with the GC electrode was rotating at rates 60, 80, 110, 160, 280 and
600 rpm.
- 209 -
Figure 7.4 Linear sweep voltammogram of 0.5 mM hexaammineruthenium(III) chloride solution performed in the BEC. Voltammetry was performed at different stirring rates of the rotating-disc electrode: black – 60 rpm, brown – 80 rpm, red – 110 rpm, yellow – 160 rpm, green – 280 rpm, blue – 600 rpm. The limiting current, Ilim, was measured. Potential −1 was swept at constant scan rate 2 mV s . The other cell part contains 25 mM K4Fe(CN)6 and 25 mM K3Fe(CN)6 in acidic solution (50 mM HCl). Both compartments contained 0.5 M KCl as supporting electrolyte. The electrochemical cell resistivity between the two reference electrodes was 250 Ω m. The paddle – rotating-disc electrode separation was 10 mm.
As opposed to voltammetry under unstirred conditions (Fig. 7.3), where the reduction
/oxidation of the species is represented by a distinct peak, the voltammetry under stirred conditions shows a constant current plateau, i.e. the limiting current, Ilim. This is due to the constant flux provided to the electrode by stirring (rotation-induced) whereas under unstirred conditions the diffusion layer is depleted and current drops.
The limiting current was determined as depicted in Fig. 7.4. The background current response was extended over the current plateau (potential difference below −0.6
V). The extended background current should be parallel to the plateau current as observed in Fig. 7.4 and the limiting current, Ilim, is determined as the difference of the two. The limiting current was subjected to analysis according to Eq. (6.11). In Fig. (7.5) the limiting current as a function of stirring rate (angular velocity of stirring) is shown.
- 210 -
Figure 7.5 Levich plot of 0.5 mM hexaammineruthenium(III) reduction in the BEC. The limiting current, Ilim, is plotted here as a function of angular velocity of stirring (of the rotating-disc electrode). Linear sweep voltammetry from which this plot was derived was performed at different stirring rates of the rotating-disc electrode: 60, 80, 110, 160, 280 and 600 rpm (Fig. 7.4). The paddle-RDE separation was 10 mm.
Substitution of the number of electrons involved in the reaction, n = 1, Faraday constant, F = 96485 C mol1, rotating-disc electrode area, A = 0.18 cm2, ruthenium complex bulk concentration and aqueous diffusion coefficient, c = 5 × 107 mol cm3 and
6 2 1 [132] 2 −1 [154] Daq = 5.99 × 10 cm s , respectively, and kinematic viscosity, υ = 0.01 cm s , to the Levich equation, Eq. (6.11), yields:
6 1/ 2 Ilim 3.810 (7.2)
3.8 × 10 A rad s is the theoretical slope value of the dependence between the limiting current and angular velocity of stirring. The experimentally determined slope for paddle – rotating-disc electrode separation of 10 mm is 5.0 × 10 A rad s (Fig. 7.5).
The theoretical and experimental values are close and the main reason for the difference could be inaccuracies due to significant background current.
- 211 -
Figure 7.6 Linear sweep voltammograms of 0.5 mM hexaammineruthenium(III) performed in BEC for 5 different paddle – rotating-disc electrode separation: (a) 3 mm, (b) 5 mm, (c) 7 mm, (d) 10 mm, (e) 13 mm (only measured at four stirring rates). Voltammetry was performed at different stirring rates of the rotating-disc electrode: black – 60 rpm, brown – 80 rpm, red – 110 rpm, yellow – 160 rpm, green – 280 rpm, blue – 600 rpm. Potential was swept at constant scan rate 2 mV s−1.
This BEC modification of the rotating-disc system was applied to the rotating permeation cell in order to study hydrodynamic properties in the donor compartment, namely the effect of the stirring paddle distance from the RDE. Preliminary electrochemical results obtained earlier within this research group suggest that the rotating cell hydrodynamics follows the Levich equation when the paddle-RDE separation is within the range of 5 – 10 mm [166]. Consequently linear sweep voltammetry was recorded
- 212 - for several different paddle-RDE separations within the range of 3 – 13 mm as shown in
Fig. 7.6.
Levich plots were constructed for all the voltammograms and the slopes determined. Experimental slope values obtained this way for 3 mm, 5 mm, 7 mm, 10 mm and 13 mm paddle – electrode separations are compared in Fig. 7.7.
Figure 7.7 Levich plot slope obtained for five different paddle-electrode separations. The horizontal red line represents the theoretical Levich plot slope value.
Comparison of the different paddle-electrode separations used shows that 10 mm is the optimum value as the Levich slope obtained experimentally is closest to the theoretical value although all the experimental slope was generally about 1 – 2 units higher than the predicted value. However, considering the variation in the slope values, it is safe to assume that, perhaps with the exception of 3 mm case, the paddle-electrode separation does not majorly affect the hydrodynamics of the BEC within the studied range. This is expected, as its bare paddle/baffle function is to prevent tubular solution movement (induced by adhesive forces), rather than to actively stir the solution.
- 213 - 7.4 Conclusions
The rotating bipolar electrochemical cell was developed to confirm that the hydrodynamic transport between the membrane and the paddle in the top (donor) compartment of the permeation cell is that of rotating-disc electrode. The permeable membrane was replaced with a solid rotating-disc electrode method that supported electron transfer between redox species in the donor and acceptor compartment. Replacing the permeation method with an electrochemical analogue of the same geometry thus provides additional independent confirmation of the cell hydrodynamic properties.
The limiting current was plotted against square root of stirring rate, which showed linear dependence as expected for a rotating-disc electrode system. Furthermore the slope of the dependence showed little deviation from the theoretical value (paddle-RDE separation 10 mm). Linear sweep voltammetry and Levich plot analysis was also used to study the effect of distance (separation) between paddle and rotating-disc electrode. The measured Levich slopes suggest that there is only small variation in the results for separation within the range 5 – 13 mm with 10 mm being the optimum. The separation of
3 mm showed slight deviation from the expected behaviour.
- 214 - Final Conclusions and Suggestions for Future Work
The work presented in this thesis has sought to develop and apply novel methods in the field of in vitro drug permeation screening and liquid/liquid electrochemistry.
The novel hydrodynamically controlled artificial permeation assay was used to assess permeability of drug molecules in situ. This is one of the few attempts to study permeation of drug molecules in real time without the adverse effects of ex situ analysis.
The controlled hydrodynamics allows accurate determination of the drug permeation rate in the lipophilic membrane without being obscured by the effect of the unstirred water layer in unstirred systems. Measurement of permeability as a function of pH indicates that some transport of ionized solutes occurs across the lipophilic membrane. These findings are supported by results obtained using the electrochemically polarised permeation configuration. Despite the pH-partition hypothesis statement that only the neutral fraction of ionized species can permeate through lipophilic membranes, an ionic flux, however small, was detected across the lipophilic membrane.
The evidence of the ionic flux across the membrane was supported by electrochemical study of the ionisable drug transfer where a potential difference was applied between the two aqueous compartments. Results from this modified permeation assay with external membrane polarisation showed that the small applied potential differences, on the order of a few hundred millivolts, can enhance the permeability of an ionisable drug. The flux of the ions was quantified using amperometric data and determined to be several-fold lower than the flux of the neutral fraction. Although the data obtained using the polarised membrane permeation method was often hard to interpret and analyse due to the high complexity of the system, it is believed that this research deserves further investigation on a simpler model system. The proposed setup should employed a
- 215 - membrane with only 1,9-decadiene as a solvent and organic electrolyte to support the current. Also the studied drug molecule should be fully ionised so that its UV absorbance response is not lost in the large response from the transfer of the neutral fraction across the membrane. This system would allow more accurate quantification and better understanding of the transport phenomena.
As a result of the use of time-dependent permeability, a significant lag time, i.e. initial transient period before permeation follows the Fick‟s first law, is directly observed from concentration-time dependence. The lag time is found to be correlated with the lipophilicity of the solute and membrane stirring rate. This presents an issue for most pharmaceutical permeation methods, where the analytical permeability model assumes
Fick‟s first law behaviour throughout the whole experimental time. As a result, the permeability value is underestimated (lipophilic molecules) or overestimated (hydrophilic molecules) and incorrect ranking pattern of drug molecules is obtained. It is important to note that reduction of the unstirred water layer thickness via stirring of the membrane significantly reduces the lag time and therefore shortens the minimum experimental time.
Shorter experimental times increase the throughput of the method and reduce its cost.
From this point of view, the most important parameters affecting the length of the lag time are the stirring rate and concentration gradient between the donor and acceptor compartments. Unexpectedly, the permeability coefficients were found to be slightly dependent on the concentration gradient between the two aqueous compartments.
The presented permeation method was applied to a set of 31 chemically diverse drug molecules with aim to predict their absolute oral bioavailability. The effective permeability obtained under unstirred conditions did not show good correlation with the absolute oral bioavailability. It was therefore corrected for the unstirred water layer
- 216 - thickness anticipated in vivo. Also, a paracellular component, mimicking the transport through the intercellular junctions occurring in vivo was included in the permeability equations. The resultant optimised effective permeability showed an improved correlation with the absolute oral permeability over the non-optimised effective permeability. The presented method has proven to be an advance over the current passive permeation assay, however, further research on possible scale-up of the method is needed to establish whether it could be used in the current drug discovery setting.
As shown in a recent analysis of in vivo and in vitro findings for marketed drugs, transcellular and paracellular transport are most likely to coexist with active, i.e. carrier- mediated transport across biological membranes [224]. These results show that in vitro permeation assays only provide part of the information needed to fully understand and predict drug absorption.
Another promising application of the hydrodynamically controlled method is prediction of absorption of drug through the blood-brain barrier (BBB). The UWL thickness of BBB is believed to be less than 1 m, which suggests conditions equivalent to almost infinite stirring [225]. The presented method directly allows measurement of membrane permeability, i.e. permeability at conditions with virtually non-existent UWL.
Correlation of the membrane permeability with the absorption through BBB could, therefore, offer a good in vitro prediction model.
Liquid/liquid electrochemistry at the water/1,2-DCE interface was employed with aim of studying the lipophilicity and diffusion properties of drug molecules. The transfer of drug molecules across the ITIES was studied using cyclic voltammetry and the partition coefficients between 1,2-DCE and aqueous phase were determined. A fundamental hindrance in determination of the diffusion coefficient was found and attributed to the partially ionised character of the drug molecules which interferes with the
- 217 - mass transport at the ITIES. Therefore a rotating membrane L/L electrochemistry method was introduced and linear sweep voltammetry rather than cyclic voltammetry used. The results obtained using this approach this showed good agreement with those predicted from a conventional analysis of mass-transport in the rotating system. The method offers a new way of determination of the diffusion coefficient of partially ionised drug molecules, which has (to best of the author‟s knowledge) not previously been described in literature.
Finally, a method employing two redox couples separated by a solid electrode was developed using the permeation assay equipment. This rotating bipolar electrochemical cell was used to mimic the permeation assay while using a different analytical method, i.e. cyclic voltammetry. The aim was to confirm the transport regime between the donor and acceptor solution compartments, and also to find the optimum distance between stirring paddle and the electrode/membrane separating the two compartments.
- 218 - References
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- 232 - Appendix
A1 UV Spectra and Calibration Data of 31 Studied Drug Molecules
Table A1.1 Molar absorption coefficients of 31 studied drug molecules at maximum absorbance wavelength (30 mM sodium phosphate at pH 7.4).
−1 −1 drug wavelength / nm absorption coefficient / M cm acetaminophen 245 10072 ± 6 antipyrine 245 9359 ± 3 atenolol 225 8714 ± 1 betamethasone 240 14179 ± 7 cefixime 290 22716 ± 5 cephalothin 240 13730 ± 3 cetirizine 233 14582 ± 3 chlorpheniramine 225 11055 ± 2 chlorthalidone 220 22869 ± 10 colchicine 245 34796 ± 12 diclofenac 220 19021 ± 3 eprosartan 230 24352 ± 4 fexofenadine 222 15479 ± 6 gatifloxacin 285 25562 ± 5 metolazone 245 34213 ± 7 midazolam 230 24276 ± 2 nafcillin 230 54125 ± 12 naproxen 232 78790 ± 14 norfloxacin 275 32755 ± 6 oxybutynin 220 3819 ± 0 pindolol 220 30154 ± 12 propranolol 225 30882 ± 9 pyridoxine 220 14833 ± 4 quinine 235 27138 ± 7 risperidone 235 11942 ± 4 salicylic acid 232 6805 ± 3 theophylline 275 9965 ± 2 tolbutamide 227 11714 ± 5 verapamil 230 14726 ± 4 warfarin 220 20963 ± 8 zopiclone 310 11804 ± 3
The absorption coefficient values in the table represent the best fit obtained from 3 – 6 different concentration samples, errors were determined from the Beer-Lambert linear fit error.
- 233 - - 234 - - 235 - - 236 - - 237 - - 238 - - 239 - - 240 - - 241 - - 242 - - 243 -
Figure A1.1 UV absorbance spectra of 31 studied drugs in 30 mM sodium phosphate at pH 7.4. The vertical lines indicate four wavelength channels that were used for analysis of permeability experiments.
- 244 - A2 Additional Optimization and Testing of the Permeation Cell
Blank permeation experiments were carried out to examine the membrane stability under stirred conditions. Running an experiment with no compound present in either the donor or acceptor solution revealed the contribution of the membrane composition to the
UV response in the acceptor compartment. Such experiments were done at three different stirring rates 250, 600, and 1500 rpm. The membrane composition was varied from „dry‟ membrane (containing no organic solvent), pure 1,9-decadiene, and 1.5% weight DOPC,
0.5% weight stearic acid in 1,9-decadiene as normally used in the assay. Both donor and acceptor compartments contained 10 mM sodium phosphate buffer at pH 7.4. Absorbance spectra were taken in the acceptor compartment after 30 min of blank permeation experiment. From comparison of the spectra in Fig. A2.1a-c it is possible to estimate the contribution of each membrane component to the background spectrum. This also defines the limit of quantification for the absorbance of the compound depending on the wavelength. In Fig. A2.1a („dry‟ membrane), a peak is observed around 220 nm that does not change significantly with stirring rate. This peak could be attributed to either optical properties of the cell, impurities or the lower signal sensitivity of the UV spectrometer in the low-wavelength region. The peak increases by a factor 2-3 in Fig. A2.1b (pure 1,9- decadiene) and also changes its shape when compared to Fig. A2.1a, showing the contribution of the 1,9-decadiene to the background absorbance. There is no significant change in absorbance spectra with stirring rate. Finally, Fig. A2.1c (standard assay lipid solution in 1,9-decadiene) shows a considerable difference between the stirring rates, although the shape of the spectrum does not substantially deviate from previous cases.
Background absorbance changes almost uniformly across the whole wavelength range by more than 10-fold between 600 and 1500 rpm. This suggests the formation of lipid structures extracted from the membrane causing light scattering in the acceptor compartment. Inverse micelles are suggested to be the most likely structure.
- 245 - The time acquisition of this background absorbance (300 nm) is shown in Fig.
A2.1d. This shows that the background absorbance rises steadily throughout the experiment. This experimental uncertainty is to some extent treated by correcting the compound‟s absorbance for the background wavelength while assuming that this scattering is uniform across the whole wavelength range. However, to ensure the membrane stability, the operational stirring rate range was changed to 60 – 600 rpm to after the pilot compounds warfarin and verapamil were tested.
- 246 -
Figure A2.1 Blank permeation experiment (no compound, buffer solution only) at iso- pH conditions (7.4) carried out at different stirring rates. Three different membrane compositions were studied: (a) no solvent, (b) pure 1,9-decadiene, (c) 1.5% weight DOPC, 0.5% weight stearic acid in 1,9-decadiene. Blue curve – 1500 rpm, red curve – 600 rpm and green curve – 250 rpm, absorbance spectra obtained after 30 min of permeation. The absorbance-time acquisition for background channel (300 nm) is plotted in (d) with the same colour theme.
The absorbance signal could also be distorted by insufficient mixing in the case of high solute flux into the acceptor compartment. In such a case the measured concentration
- 247 - just below the rotating membrane would be higher than the corresponding bulk concentration in the acceptor cell. Experiments with the highly permeable solute verapamil at donor/acceptor pH 9.0/7.4 were carried out to rule this out. After 30 min of verapamil permeation, the stirring was switched off and the two compartments detached.
Verapamil absorbance at 230 nm was recorded with time as shown in Fig. A2.2. Over the measured time range, the absorbance signal does not drop at stirring rates 250 and 600 rpm. This would be expected if the measured and bulk absorbance were equal. However there is a clear drop in the absorbance signal for high stirring rates of 1000 and 1500 rpm.
This is unambiguously due to the dispersed lipid being settled down /coagulating after switching off the stirring and it is consistent with the stirring effects described above.
Figure A2.2 Verapamil absorbance at pH 9.0/7.4 (230 nm channel) recorded in acceptor compartment as a function of time for four different stirring rates. The rotation was stopped and the donor and acceptor compartments were detached after 30 s as shown by the vertical dotted line.
- 248 - UV absorbance of the aqueous buffers
Although the UV spectra were referenced to the blank buffer solution used before each permeation/UV acquisition experiment, the UV absorbance spectra of all the buffers used were recorded to investigate possible source of error. Three different buffers were selected for permeation experiments in the pH range 2.5 – 3.5, 6.0 – 8.5, 11.0 – 12.0
(sodium phosphate), 4.0 – 5.5 (sodium acetate) and 9.0 – 10.5 (CHES buffer). The UV absorbance spectra are shown in Fig. A2.3. Sodium phosphate, most commonly used in the assay, shows moderate absorbance with two peaks around 230 and 280 nm. CHES buffer shows low absorbance throughout the examined wavelength range with a small absorption peak around 215 nm. Sodium acetate, however, shows a high absorbance peak around 220 nm which will result in increased experimental error when analysing spectra of drugs absorbing in the low wavelength region.
Figure A2.3 UV absorbance spectra of 10 mM aqueous buffers in de-ionized water. Sodium phosphate (black curve) and CHES buffer (blue curve) show low to moderate UV absorbance whereas sodium acetate (red curve) shows significant absorbance peak around 220 nm.
- 249 - UV absorbance of the organic membrane components in the aqueous phase
UV absorbance spectra of the organic membrane components were recorded in the aqueous buffer solution to estimate the interference of their UV absorbance with the measured signal of the drug molecule. Potassium tetrakis(4-chlorophenyl)borate, tetradodecylammonium bromide, stearic acid and DOPC were individually dissolved in
30 mM sodium phosphate at pH at concentration of 10 M. This roughly corresponds to the their concentration in the acceptor phase in the case where the whole membrane content (13 – 14 l) are dissolved/dispersed in the acceptor solution (20 ml). All these molecules are soluble in water at this concentration with exception of DOPC, which is known to form micelles [182]. These are observed indirectly via wavelength-unspecific scattering in the UV absorbance spectra. Also, 10 l of 1,9-decadiene was dispersed in the phosphate buffer solution and UV absorbance spectrum of the emulsion was recorded.
The resultant UV spectra are shown in Fig. A2.4.
Figure A2.4 UV absorbance spectra of the organic membrane components in 30 mM sodium phosphate buffer solution at pH 7.4. Red curve: 10 M KTPBCl4, green curve: 10 M DOPC, yellow curve: 10 M stearic acid, blue curve: 10 M TDDABr, black curve: 10 l of 1,9-decadiene dispersed in 20 ml of the sodium phosphate buffer.
- 250 - Reduced apparent membrane area test
Table A2.1 shows the comparison between the standard permeation experiment and reduced membrane area experiment, which was discussed in section 3.7, confirming that the permeation cell follows the hydrodynamics of the rotating-disc electrode.
Table A2.1 Effective permeability of verapamil for standard/reduced membrane area at donor/acceptor pH 7.4/7.4. Hydrodynamic exponent α calculated by least-square analysis of log Pe – log dependence.
log Pe stirring rate / rpm standard area (α = 0.665) reduced area (α = 0.657) 250 −3.334 0.005 −3.331 0.067 400 −3.244 0.010 −3.197 0.067 600 −3.095 0.016 −3.093 0.133 1000 −2.896 0.013 −2.935 0.067 1500 −2.840 0.021 −2.820 0.032
The values in the table represent means of three independent measurements and corresponding standard deviations combined with any linear fit errors used in the calculation. Experimental errors of simple laboratory measurements, such as volume determination, concentration calibration etc., were not included.
- 251 - A3 Time-Dependent Permeation Profiles
Concentration-time plots of the drug molecules are shown in Fig. A3.1. Type of lag time, i.e. membrane oversaturation (most molecules – indicating fast diffusion and/or low lipophilicity) or undersaturation (midazolam, naproxen, propranolol, quinine – indicating slow diffusion and/or high lipophilicity) can be deduced from the shape of the curve.
- 252 -
- 253 -
- 254 -
Figure A3.1 Concentration-time plots for 31 studied drugs at donor/acceptor pH 6.5/7.4. Data obtained at stirring rates of 60 rpm (red), 160 (golden) and 280 rpm (blue) are shown. The vertical concentration axis scale was intentionally kept in the ranges of 0 – 1 M, 0 – 2 M and 0 – 5 M to allow a reasonable comparison of the graphs.
- 255 - A4 Additional Permeability and Lipophilicity Data
Table A4.1 Membrane retention and membrane diffusion coefficients of warfarin, verapamil, propranolol and cetirizine as a function of donor compartment pH. (The values are means of three independent measurements, the errors are based on standard deviations of the means).
Warfarin Verapamil a −6 2 −1 b a −6 2 −1 b donor pH %Rf Dm / 10 cm s donor pH % Rf Dm / 10 cm s 3.5 4.6 0.7 0.83 0.04 5.5 0.0 0.0 0.14 0.00 4.0 0.4 0.7 0.94 0.05 6.0 0.2 0.2 0.27 0.00 4.5 4.1 1.6 1.03 0.02 6.5 2.1 0.7 0.21 0.00 5.0 6.2 2.8 1.70 0.11 7.0 6.9 1.3 0.21 0.00 5.5 4.0 1.3 1.07 0.01 7.4 6.1 1.7 0.24 0.01 6.0 1.5 0.6 0.88 0.08 8.0 10.8 1.8 0.17 0.01 6.5 0.0 0.1 0.67 0.09 8.5 16.3 3.7 − 7.0 0.0 0.0 1.29 0.45 9.0 16.6 3.3 − 7.4 0.9 0.7 1.61 0.16 9.5 20.1 3.1 − 8.0 0.0 0.1 2.26 0.06 10.0 10.7 2.5 − Average 2.2 0.7 1.23 0.16 Average 9.0 2.3 0.16 0.03
Propranolol Cetirizine a −6 2 −1 b a −6 2 −1 b donor pH %Rf Dm / 10 cm s donor pH %Rf Dm / 10 cm s 5.5 0.0 0.0 0.18 0.02 2.5 1.0 0.4 0.88 0.00 6.5 0.7 0.6 0.18 0.04 3.5 2.0 0.4 0.68 0.01 7.4 4.1 2.0 0.28 0.07 4.5 0.0 0.0 0.25 0.00 8.5 1.9 0.3 0.25 0.01 5.5 3.2 0.4 0.32 0.01 9.5 11.2 1.0 0.18 0.03 6.5 0.5 0.3 0.39 0.03 10.5 3.1 0.8 0.18 0.01 7.4 4.4 0.4 0.36 0.03 Average 3.5 1.7 0.18 0.02 8.5 3.2 0.5 0.29 0.00 Average 2.2 0.7 0.45 0.09
a Membrane retention (in % of the initial donor concentration) calculated using Eq. (3.4) b Membrane diffusion coefficient calculated using Eq. (3.6).
The values in the table represent means of three independent measurements and corresponding standard deviations. Experimental errors of simple laboratory measurements, such as volume determination, concentration calibration etc., were not included.
- 256 - Table A4.2 Membrane-donor distribution coefficients of warfarin, verapamil, propranolol and cetirizine determined by shake-flask experiment (Eq. (2.1)).
Warfarin Verapamil D donor pH log Kd donor pH log 3.5 1.81 0.02 5.5 0.58 0.04 4.0 1.79 0.01 6.0 0.99 0.01 4.5 1.72 0.00 6.5 1.43 0.01 5.0 1.28 0.03 7.0 1.83 0.01 5.5 1.08 0.01 7.4 2.03 0.00 6.0 0.62 0.01 8.0 2.43 0.02 6.5 0.32 0.02 8.5 2.56 0.01 7.0 −0.30 0.02 9.0 2.72 0.03 7.4 −0.75 0.03 9.5 3.02 0.04 8.0 −1.51 0.08 10.0 3.11 0.05
Propranolol Cetirizine
donor pH log donor pH log 5.5 0.33 0.04 2.5 −0.38 0.11 6.5 1.00 0.02 3.5 −0.09 0.18 7.4 4.5 1.38 0.02 0.37 0.01 8.5 1.85 0.01 5.5 0.33 0.03 9.5 2.19 0.00 6.5 0.27 0.02 10.5 2.14 0.01 7.4 0.29 0.02 8.5 0.17 0.02
The values in the table represent means of three independent measurements and corresponding standard deviations. Experimental errors of simple laboratory measurements, such as volume determination, concentration calibration etc., were not included.
- 257 - Table A4.3 Membrane-donor distribution coefficients of 31 studied drug molecules
D a A a OCT b drug log Kd (pH 6.5) log Kd (pH 7.4) log Kd (pH 7.4) acetaminophen −0.70 ± 0.03 −0.98 ± 0.22 0.26 antipyrine −1.51 ± 0.00 − c 0.11 atenolol −2.00 ± 0.43 −1.10 ± 0.05 −1.70 betamethasone 1.02 ± 0.02 − c 1.9 cefixime −1.21 ± 0.03 −1.82 ± 0.31 −1.71 cephalothin 0.38 ± 0.01 −0.85 ± 0.21 −2.21 cetirizine 0.27 ± 0.02 0.29 ± 0.02 1.24 chlorpheniramine 0.27 ± 0.01 0.98 ± 0.02 1.13 chlorthalidone 0.54 ± 0.06 0.75 ± 0.01 0.98 colchicine −0.59 ± 0.02 − c 1.12 diclofenac 0.95 ± 0.01 0.48 ± 0.01 1.11 eprosartan −1.35 ± 0.26 −1.72± 0.37 −0.90 fexofenadine 0.62 ± 0.01 0.89 ± 0.05 0.6 gatifloxacin −0.34 ± 0.01 −0.39 ± 0.03 −0.82 metolazone 0.27 ± 0.00 −0.66 ± 0.22 1.64 midazolam 1.96 ± 0.01 1.90 ± 0.02 3.4 nafcillin −0.76 ± 0.02 −2.10 ± 0.00 −0.72 naproxen 0.11 ± 0.02 −0.59 ± 0.06 0.23 norfloxacin −0.29 ± 0.03 −0.38 ± 0.04 −1.04 oxybutynin 2.09 ± 0.00 3.22 ± 0.01 3.65 pindolol −0.07 ± 0.01 0.52 ± 0.01 −0.20 propranolol 1.00 ± 0.02 1.38 ± 0.02 1.25 pyridoxine −1.96 ± 0.32 −1.92 ± 0.04 −1.10 quinine 0.86 ± 0.00 1.42 ± 0.01 2.16 risperidone 0.01 ± 0.03 0.83 ± 0.02 2.05 salicylic acid −0.87 ± 0.23 −0.74 ± 0.02 −1.62 theophylline −0.97 ± 0.03 − c −0.12 tolbutamide 0.19 ± 0.04 −0.79 ± 0.11 0.45 verapamil 1.43 ± 0.01 2.03 ± 0.00 2.42 warfarin 0.32 ± 0.02 −0.75 ± 0.03 0.86 zopiclone 0.22 ± 0.03 0.65 ± 0.00 1.1 a Membrane/aqueous buffer drug distribution coefficients determined using shake-flask method at aqueous pH 6.5 or 7.4, respectively, temperature 22°C (this work). Values are means of three measurements, errors standard deviation of the mean. Experimental errors of simple laboratory measurements, such as volume determination, concentration calibration etc., were not included. b Octanol/water(pH 7.4) drug distribution coefficients determined using shake-flask method at 25 °C (AstraZeneca, Alderley Edge, UK). c A log Kd (7.4) was not measured for these neutral molecules and it was assumed to be equal to log (6.5).
- 258 -
Table A4.4 Membrane diffusion coefficients of 31 studied drug molecules determined from membrane permeability and membrane/donor distribution coefficients.
−1 −6 2 −1 a drug Mr / g mol Dm / 10 cm s acetaminophen 151.17 0.20 ± 0.05 antipyrine 188.23 3.29 ± 0.16 atenolol 266.34 16.27 ± 0.33 betamethasone 392.46 0.12 ± 0.03 cefixime 453.45 1.57 ± 0.06 cephalothin 396.44 0.01 ± 0.00 cetirizine 388.89 0.45 ± 0.02 chlorpheniramine 274.79 0.48 ± 0.12 chlorthalidone 338.77 0.07 ± 0.02 colchicine 399.44 0.16 ± 0.04 diclofenac 296.15 0.48 ± 0.08 eprosartan 424.53 3.10 ± 0.14 fexofenadine 501.66 0.05 ± 0.01 gatifloxacin 375.39 0.12 ± 0.06 metolazone 385.84 0.10 ± 0.03 midazolam 325.78 0.13 ± 0.04 nafcillin 414.48 1.02 ± 0.12 naproxen 230.26 0.76 ± 0.09 norfloxacin 319.33 0.12 ± 0.01 oxybutynin 357.49 0.11 ± 0.03 pindolol 248.32 0.20 ± 0.05 propranolol 259.34 0.18 ± 0.04 pyridoxine 169.18 8.50 ± 0.65 quinine 324.42 0.43 ± 0.11 risperidone 410.49 1.91 ± 0.16 salicylic acid 138.12 1.50 ± 0.02 theophylline 180.18 0.20 ± 0.07 tolbutamide 270.35 1.64 ± 0.09 verapamil 454.60 0.16 ± 0.02 warfarin 308.33 1.23 ± 0.09 zopiclone 388.81 0.97 ± 0.24
a Membrane diffusion coefficient calculated from Eq. (3.6). The values are means of three measurements, the errors are standard deviations of the means. Experimental errors of simple laboratory measurements, such as volume determination, concentration calibration etc., were not included.
- 259 - A5 ITIES Area Calibration
In order to accurately determine the curved liquid/liquid interface area, ion transfer was studied with five different ionic species (see section 6.3.1) and the aqueous diffusion coefficient of the ions was determined from Randles-Ševčík equation (1.10). The ionic strength of the aqueous solution and consequently the activity coefficient of the ionic species were calculated to include activity rather than concentration in the calculation.
The area in the Randles-Ševčík equation was considered as the variable parameter. The difference between the diffusion coefficients calculated for a given interfacial area and the literature diffusion coefficient taken from [154] was determined and the standard deviation of the average difference was plotted against the input interface area. A graph showing this calibration curve is shown in Fig. A5.1.
Figure A5.1 Determination of ITIES area via ion transfer of five different ionic species. Ion transfer on ITIES was carried out in the electrochemical cell of the following configuration: Ag|Ag2SO4| 10 mM NaH2PO4, 30 mM Na2SO4, 0.3 mM X, pH 7.4 (aq)| 20 mM BTPPATPBCl4 (1,2-DCE)| 1 mM BTPPACl, 30 mM Na2SO4 (aq)|Ag2SO4|Ag, where X is lithium perchlorate, potassium nitrate, potassium iodide, tetramethylammonium sulphate or tetraethylammonium chloride.
- 260 - The ionic species chosen for calibration were perchlorate, nitrate, iodide, tetramethylammonium and tetraethylammonium ions. A series of cyclic voltammogram was performed for each ionic species for the scan rate in the range of 5 to 150 mV s−1.
From the slope of the peak current plotted against the scan rate (Randles-Ševčík equation) the diffusion coefficient was determined. A minimum standard deviation was found at interface area 1.1 cm2, which is reasonable given the flat geometrical area of 0.9 cm2 from the electrochemical cell cross-section (the curved interface over the cross-section will occupy slightly larger area).
- 261 - A6 Silver/Silver Sulphate Reference Electrode for L/L System
A silver/silver sulphate reference electrode was introduced in the liquid/liquid configuration where sulphate based, rather than chloride based, aqueous electrolyte was used. In most applications silver/silver chloride reference electrodes are used in aqueous media and are therefore well documented in literature [153, 226-229]. There are, however, limited reports examining the silver/silver sulphate reference electrode [230-232]. As indicated in section 2.3.7, preliminary results showed that preparation of the silver/silver sulphate electrode requires accurate control of the conditions such as solution degassing, silver wire cleaning, current density and charge passed in silver wire oxidation. For these reasons as well as for the fact that solubility product of silver sulphate is 1.2 × 10−5 [154], an extensive study of the silver/silver sulphate reference electrode stability and its response depending on the mode of preparation, was performed.
The silver/silver sulphate electrodes were prepared by oxidising the polished and flamed high purity silver wire in 0.1 M sodium sulphate solution at current densities varying between 1 × 10−5 – 1 × 10−3 A cm−2 and overall charge passed 0.6 – 14 C. The solution was degassed with argon for 20 min prior to oxidation. The potential stability of the electrode was then measured for 60 min against saturated calomel electrode in 0.1 M sodium sulphate solution immediately after electrode preparation and 1 month after electrode storage in saturated sodium sulphate solution. The potential response was classified into four categories: excellent – change in potential is no more than 1 mV after 5 min, good – change in potential is no more than 5 mV after 5 min, average – change in potential is no more than 10 mV after 5 min, poor – change in potential is larger than 20 mV after 5 min. Potential stability of the electrodes prepared under various current densities and overall charge passed through the electrode is summarised in table A6.1.
- 262 - Table A6.1 Potential stability of reference electrodes prepared under various conditions. Explanation to potential stability classification can be found in text.
High current density electrode preparation current density / A cm−2 1 × 10−3 charge passed / C 5 3 1 colour (immediate) white/crystalline white/crystalline white/crystalline colour (after 1 month) white/crystalline white/crystalline white/crystalline potential stability in 0.1 M sodium sulphate Good Excellent N/A (immediate) potential stability in 0.1 M sodium sulphate Average Average Poor (after 1 month) electrode number H1 H2 H3
Medium current density electrode preparation current density / A cm−2 1 × 10−4 charge passed / C 14 7 1
colour (immediate) white/crystalline white/crystalline white/crystalline colour (after 1 month) white/crystalline white/crystalline white/crystalline potential stability in 0.1 M sodium sulphate Poor Good N/A (immediate) potential stability in 0.1 M sodium sulphate N/A N/A Poor (after 1 month)
electrode number M1 M2 M3
Low current density electrode preparation current density / A cm−2 2 × 10−5 1 × 10−5 charge passed / C 1.5 1 0.6 0.9 colour (immediate) grey grey/black white/grey white/grey colour (after 1 month) grey/brown grey/brown grey/black grey/black potential stability in 0.1 M sodium sulphate Good N/A N/A Good (immediate) potential stability in 0.1 M sodium sulphate Average Excellent Good Good (after 1 month) electrode number L4 L2 L3 L5
- 263 -
The potential stability expressed as the change in potential (mV) in the time interval 5 –
60 min after immersing the electrodes in 0.1 M sodium sulphate was plotted as a function of charge and current density used in electrode preparation – Fig. A6.1. It can be concluded that the best potential stability (less than 1 mV change in potential over 60 min period) is obtained for the overall charge 1 C passed at low current density (1 × 10−5
A cm−2).
Figure A6.1 Dependence of electrode potential stability on the charge and current density used. The potential stability expressed in mV represents the change in potential in the time interval <5, 60> min after immersion of the electrodes in 0.1 M sodium sulphate.
The graph showing the potential response of selected silver/silver sulphate electrode with time is shown in Fig. A6.2.
- 264 -
Figure A6.2 Potential of the silver/silver sulphate electrode in 0.1 M sodium sulphate against saturated calomel electrode. Potential was recorded after 1 month of electrode storage in saturated sodium sulphate solution. The electrode numbers and preparation conditions correspond to those in Table A6.1.
As can be seen in Fig. A6.2, the electrodes marked as LX (where X is 2, 3, 4 or 5) show the most stable potential response. These electrodes were prepared by oxidation at current densities ≤ 2 × 10−5 A cm−2. The difference between the absolute potential value of these electrodes and its measurement-to-measurement variability, however, led to an examination of the electrode response with changing sulphate concentration. The ideal silver/silver sulphate reference electrode potential, E, should be dependent on the logarithm of the sulphate concentration in solution, according to the following form of the
Nernst equation:
0 RT RT ln10 E E 0 ln Ksp(Ag2SO 4 ) log a 2- (A6.1) Ag /Ag 2F 2F SO4
- 265 - 0 + 0 Where E is the standard reduction potential of the Ag /Ag couple, K (Ag SO ) is Ag /Ag sp 2 4
the solubility product of silver sulphate, a 2- is the activity of sulphate anion and other SO4 symbols have their usual meaning. The potential of the prepared silver/sulphate electrodes in solution was measured with several different concentrations of sodium sulphate.
Surprisingly, the electrode potential remained constant over about three orders of magnitude as shown in Fig. A6.3. The constant potential response seems to deviate for the two most concentrated solutions.
Figure A6.3 Potential response of the silver/silver sulphate electrode as a function of the logarithm of sodium sulphate concentration. The electrode numbers and preparation conditions correspond to those in Table A6.1.
The silver/silver sulphate electrode does not therefore show the expected linear dependence on the common logarithm of sulphate concentration with the expected theoretical slope equal to RTln10/2F from Eq. (A6.1). Interestingly, the electrode potential showed a linear dependence where both sulphate and chloride ions are present
- 266 - [233], and the observed slope was approximately RTln10/F, i.e. double the predicted value. Suspecting that chloride ions might have stronger effect on interfacial electrode reactions than sulphate ions, the behaviour in solution was investigated where the sulphate concentration was kept constant and chloride concentration was changed. Fig. A6.4 shows the silver/silver sulphate electrode potential as a function of the logarithm of the chloride concentration.
Figure A6.4 Potential response of the silver/silver sulphate electrode as a function of the logarithm of sodium chloride concentration. The concentration on sodium sulphate was kept constant at 0.02 M. The electrode numbers and preparation conditions correspond to those in Table A6.1.
The potential response is linear with slope equal to 55 mV which is close to theoretical value of 59 mV, i.e. RTln10/F at 298 K. Based on these observations it is concluded that the silver/silver sulphate electrode is covered with layer of silver chloride when immersed in solution containing chloride ions. Silver sulphate is much more soluble
- 267 - −5 3 −9 than silver chloride (solubility products Ksp(Ag2SO4) = 1.2 × 10 mol dm , Ksp(AgCl) =
1.8 × 10−10 mol2 dm−6, [154]) and therefore an exchange of sulphate for chloride ion is likely in the thin interfacial layer. The potential of such electrode will change with the common logarithm of chloride concentration linearly with slope of RTln10/F, according to the following expression:
0 RT RT ln10 E E 0 ln K (AgCl) log a - (A6.2) Ag /Ag 2F sp F Cl
where K (AgCl) is the solubility product of silver chloride and a - is the activity of sp Cl chloride anion. This also explains why in solution containing pure sulphate the potential of silver/silver sulphate electrode changes with each experiment as a lack of chloride ions will lead to a non-reproducible response. At higher sulphate concentrations (> 0.1 M) the potential starts to respond to increasing concentration. The most likely reason for this is the chloride impurity present in the sodium sulphate solid used in solution preparation (for
2 −5 1 M SO4 gives about 2 × 10 M Cl , Sigma Aldrich). The lowest concentration point in the chloride graph (2 × 10−5 M, Fig. A6.4) and the highest concentration point in the sulphate graph (1 M, Fig. A6.3), for the electrode L2, have indeed both the same potential value ca. 225 mV vs. SCE.
In conclusion, the silver/silver sulphate electrode is a good alternative to the silver/silver chloride electrode in systems where use of chloride ions should be avoided
(such as L/L electrochemistry system with sulphate based aqueous electrolyte to expand the potential window). Although the electrode response is not reproducible in pure sulphate solutions and its potential cannot be related to sulphate concentration according to Eq. (A6.1) presented earlier, the potential value itself is stable with time with the deviation less than 1 mV over 60 min period. The current density and charge passed
- 268 - through during electrode preparation are crucial to its performance with the best conditions found 1 C passed at 1 × 10−5 A cm−2. The electrode was also found to mimic the behaviour of the silver/silver chloride electrode in chloride solutions of concentration
6 × 10−5 M and higher.
- 269 -