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Investigation of interacting species in capillary electrophoresis by experimental and simulation methods Sun, Ying 2010

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    INVESTIGATION OF INTERACTING SPECIES IN CAPILLARY ELECTROPHORESIS BY EXPERIMENTAL AND SIMULATION METHODS  by   Ying Sun   B.Sc.Hons, University of Regina, 2005      A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY   in   THE FACULTY OF GRADUATE STUDIES  (CHEMISTRY)       THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)   April 2010  © Ying Sun, 2010  ii Abstract  Capillary electrophoresis (CE) with complexation additives in the background electrolyte utilizes both equilibrium and electric field in the separation process. Therefore, a comprehensive understanding of the analyte migration behavior in CE processes becomes essential to effectively control the chemical separation process and to achieve the full potential of this powerful analytical technique. Computer simulation is one of the best ways to visualize the instantaneous behaviors of physicochemical systems. After the success of our first simulation program SimDCCE, a JAVA based computer simulation model of dynamic complexation capillary electrophoresis (CoSiDCCE) was developed based on the differential mass balance equation, the governing principle of analyte migration in all separation techniques. CoSiDCCE is highly efficient, and is capable of demonstrating various types of the affinity interactions between multiple species in CE in real time or faster. With the simulation program, a thorough study of the mechanism of vacancy affinity CE was carried out. Thermodynamic binding constant was estimated with nonlinear regression methods. Thirteen scenarios in four different combinations of migration orders of free protein, free drug, and their complexes formed were studied. The specific protein-ligand interactions were determined using CE-frontal analysis, one of the most effective CE modes. A new algorithm was derived to calculate the binding parameters for higher order specific interaction in the presence of non-specific interactions. Computer simulation was used to study the migration behaviors of all species in the DCCE process.  iii CoSiDCCE was used to elucidate the determining factors that result in CE separations of amino acid enantiomers and predict the efficiency of the chiral selectors when used in other separation systems such as chromatography. With this program, the migration behavior of different species involved in the competitive dynamic complexation in chiral CE processes was investigated, and the change in migration orders in some chiral separations was explained. The binding constants and complex mobilities were also determined. In addition, a micellar electrokinetic chromatography method was developed to determine potentially anti-carcinogenic flavonoids in various wine samples. A systematic optimization of the separation buffer and concentration of surfactant was carried out to improve the reproducibility and sensitivity for the analysis of flavonoids.    iv Table of Contents  Abstract .................................................................................................................................... ii  Table of Contents.....................................................................................................................iv  List of Tables ......................................................................................................................... viii  List of Figures ..........................................................................................................................ix  Abbreviations .........................................................................................................................xiv  Acknowledgments ..................................................................................................................xvi  Co-authorship Statement .................................................................................................... xvii   Chapter 1 Introduction to Capillary Electrophoresis and Dynamic Complexation Capillary Electrophoresis ........................................................................................................1  1.1 Capillary Electrophoresis..................................................................................................2 1.1.1 Fundamental theory of capillary electrophoresis.......................................................3  1.1.2 Flow dynamics.........................................................................................................10  1.1.3 Joule heating ............................................................................................................12  1.2 Dynamic Complexation in Capillary Electrophoresis (DCCE)......................................14  1.2.1 Affinity Capillary Electrophoresis (ACE) ...............................................................15  1.2.2 Vacancy Affinity CE method ..................................................................................19  1.2.3 Hummel-Dreyer method..........................................................................................20  1.2.4 Vacancy Peak method..............................................................................................21  1.2.5 Frontal Analysis method..........................................................................................23  1.3 Simulation of Dynamic Complexation in Capillary Electrophoresis (SimDCCE) ........25   1.3.1 Unified separation science......................................................................................25   1.3.2 Mass balance equation............................................................................................26   1.3.3 Simulation of Dynamic Complexation in Capillary Electrophoresis (SimDCCE) 30  1.4 Description of Research..................................................................................................32   1.4.1 Computer simulation of five common capillary electrophoresis methods .............32   1.4.2 Behavior of interacting species in vacancy affinity capillary electrophoresis described by mass balance equation .................................................................................32   1.4.3 Using capillary electrophoresis-frontal analysis to characterize biomolecular interactions........................................................................................................................33   1.4.4 Characterization of Epidermal Growth Factor Receptor binding with Panitumumab by Capillary Electrophoresis Frontal Analysis .................................................................34   1.4.5 Chiral separation of amino acids using experimental and simulation methods......34   1.4.6 Separation of anti-carcinogenic flavonoids with micellar electrokinetic chromatography ................................................................................................................36  1.5 References ......................................................................................................................37  Chapter 2 Computer Simulation of Different Modes of ACE Based on the Dynamic Complexation Model ..............................................................................................................38  2.1 Introduction ....................................................................................................................39  2.2 Experimental Section......................................................................................................42  2.2.1 Instrumentation........................................................................................................42  2.2.2 Chemicals and solutions ..........................................................................................42   v 2.2.3 Determination of electrophoretic mobilities and viscosity correction factors.........43  2.2.4 Determination of relative UV intensity of BSA and warfarin.................................44  2.2.5 Procedures for DCCE modes...................................................................................44  2.3 Results and Discussion ...................................................................................................45  2.3.1 DCCE simulation model..........................................................................................45  2.3.2 Simulation output ....................................................................................................51  2.3.3 Simulation results ....................................................................................................53  2.4 Conclusion ......................................................................................................................61  2.5 References ......................................................................................................................62   Chapter 3 Behavior of Interacting Species in Vacancy Affinity Capillary Electrophoresis Described by Mass Balance Equation...................................................................................64  3.1 Introduction ....................................................................................................................65  3.2 Experimental Section......................................................................................................67  3.3 Results and Discussion ...................................................................................................69  3.3.1 Case I, μep,P ≈ μep,C > μep,L........................................................................................76  3.3.2 Case II, μep,P > μep,C > μep,L ......................................................................................80  3.3.3 Case III, μep,C > μep,P > μep,L .....................................................................................82  3.3.4 Case IV, μep,L > μep,P > μep,C .....................................................................................85  3.4 Conclusion ......................................................................................................................88  3.5 References ......................................................................................................................89   Chapter 4   Capillary Electrophoresis Frontal Analysis for Characterization of αvβ3 Integrin Binding Interactions ................................................................................................91  4.1 Introduction ....................................................................................................................92  4.2 Theory.............................................................................................................................95  4.2.1 Single binding stoichiometry...................................................................................95  4.2.2 Higher order binding stoichiometry.........................................................................98  4.3 Experimental Section....................................................................................................101  4.3.1 Peptide synthesis....................................................................................................101  4.3.2 Chemicals and solutions ........................................................................................102  4.3.3 CE conditions and procedures ...............................................................................103  4.4 Results and Discussion .................................................................................................105  4.4.1 CE Frontal analysis................................................................................................105  4.4.2 Binding parameters................................................................................................106  4.5 Conclusions ..................................................................................................................114  4.6 References ....................................................................................................................115   Chapter 5 Characterization of Epidermal Growth Factor Receptor Binding with Panitumumab by Capillary Electrophoresis Frontal Analysis ........................................117  5.1 Introduction ..................................................................................................................118  5.2 Experimental Section....................................................................................................120  5.2.1 Instrumentation......................................................................................................120  5.2.2 Chemicals and solutions ........................................................................................120  5.2.3 Capillary conditioning ...........................................................................................121  5.3 Results and Discussion .................................................................................................123   vi 5.4 Conclusion .................................................................................................................... 132  5.5 References .................................................................................................................... 133   Chapter 6 Computer Assisted Investigation into Principles of Chiral Separation in Capillary Electrophoresis .................................................................................................... 134  6.1 Introduction .................................................................................................................. 135  6.2 Experimental Section .................................................................................................... 137  6.2.1 Chemicals and solutions ........................................................................................ 137  6.2.2 CE Conditions and procedures .............................................................................. 137  6.2.3 Viscosity correction factor measurement .............................................................. 138  6.3 Simulation Procedure ................................................................................................... 140  6.4 Results and Discussion ................................................................................................. 143  6.4.1 Case I, tryptophan enantiomers ............................................................................. 143  6.4.2 Case II, dansyl-phenylalanine ................................................................................ 147  6.4.3 Selector concentrations .......................................................................................... 150  6.5 Conclusions .................................................................................................................. 156  6.6 References .................................................................................................................... 157   Chapter 7 Determination of Potentially Anti-carcinogenic Flavonoids in Wines by Micellar Electrokinetic Chromatography .......................................................................... 159  7.1 Introduction .................................................................................................................. 160  7.2 Experimental Section .................................................................................................... 163  7.2.1 Standards and reagents .......................................................................................... 163  7.2.2 Instrumentation and electrophoretic procedure ..................................................... 163  7.2.3 Sample preparation ................................................................................................ 164  7.3 Results and Discussion ................................................................................................. 165  7.3.1. Optimization of the MEKC separation conditions ............................................... 165  7.3.2 Regression equations, detection limits, recovery, and reproducibility for MEKC 167  7.3.3 Wine sample analysis ............................................................................................ 169  7.4 Conclusions .................................................................................................................. 172  7.5 References .................................................................................................................... 173   Chapter 8 Concluding Remarks .......................................................................................... 174 8.1 References .................................................................................................................... 177  Appendix A: Supporting Material ...................................................................................... 178  A.1 Calculation of Analyte Concentration Distribution and Analyte Mobilities ............... 179  A.2 Implementation ............................................................................................................ 186  A.3 Simulation Results ....................................................................................................... 192  A.4 References .................................................................................................................... 197  Appendix B: CoSiDCCE User Guide .................................................................................. 198  B.1 Introduction to User Interface ...................................................................................... 199  B.2 Tutorial for CoSiDCCE ............................................................................................... 200     B.2.1 Simulate the interaction mechanism for species ................................................... 200     B.2.2 Determine binding constant, K, using enumeration algorithm ............................. 208   vii B.3 Ten Type of DCCE Binding Interactions ....................................................................216      B.3.1 Evaluation of mass transfer equation...................................................................216      B.3.2 Association and dissociation processes................................................................216  B.4 References....................................................................................................................224   Appendix C: Publications ...................................................................................................225    viii List of Tables   Table 2.1  The conditions for DCCE experiments ...................................................................44  Table 3.1  Experimental obtained results for Case (a), (b) and (c) where the concentration of the BSA is fixed, and the concentration of the warfarin is varied............................................74  Table 3.2  Simulation conditions for 13 scenarios. ..................................................................82  Table 7.1  Regression analysis on calibration curves, recovery, and detection limits ...........167  Table 7.2  Results of the recovery for this MEKC method (n = 3) ........................................168  Table 7.3  Reproducibility of the studied flavonoids using MEKC (n = 3) ...........................169  Table 7.4  Assay results for the flavonoids in 10 wine samples in μg mL-1(n = 3)................170   Table A.1.  Cell arrangement in the memory of a PC. ...........................................................184  Table B.1  The type of reactions that can be studied in the CoSiDCCE program..................200  Table B.2  The list of the experimental conditions used to simulate the interaction of tryptophan with α-CD. ...........................................................................................................201   ix List of Figures   Figure 1.1  A schematic representation of a 75 μm (i.d.) × 375 μm (o.d.) fused silica capillary coated with polyimide.................................................................................................................4  Figure 1.2  Diagram of capillary electrophoresis system. ..........................................................5  Figure 1.3  Representation of the silanol groups inside of the capillary. ...................................7  Figure 1.4  Schematic representation of the electrical double layer formed at a negatively charged inner capillary wall in contact with an electrolyte solution. .........................................9  Figure 1.5  The velocity of ions (A) with and (B) without the presence of electroosmotic flow ..................................................................................................................................................10  Figure 1.6  Cross section flow profile of liquid due to (A) hydrodynamic flow and (B) electroosmotic flow. .................................................................................................................11  Figure 1.7  Illustration of initial conditions of different modes of dynamic complexation in capillary electrophoresis: (A) affinity CE, (B) vacancy affinity CE, (C) Hummel-Dreyer, (D) vacancy peak, and (D) frontal analysis method........................................................................15  Figure 1.8  Schematic representation the ACE method. TΔ  reflects the change on the migration time of the free analyte and analyte-additive complex (•).......................................17  Figure 1.9  Schematic representation of the VACE method. Peak identification: the mixture of the free analyte and analyte-additive complex (•) and free additive (*). TΔ represents the shift of the free additive trough.........................................................................................................20   Figure 2.1  The user interface (UI) of SimDCCE.....................................................................50  Figure 2.2  Simulation of ACE/HD. .........................................................................................54  Figure 2.3  Simulation of CE-FA experiments.........................................................................56  Figure 2.4  Simulation of VACE/VP. BGE: 50 mM phosphate buffer containing 40 μM BSA and various concentrations of warfarin: (A) 100 μM; (B) 200 μM; (C) 400 μM. Injected sample: 50 mM phosphate buffer (no BSA or warfarin). Injection time: 20 s. ........................57  Figure 2.5  Simulated concentration profiles for ACE. ............................................................60  Figure 3.1  Illustration of migration of the injection zone along the capillary and the formation of the negative peaks ................................................................................................................72   x Figure 3.2  Comparison study of experimental and simulated electropherogram for CE-VACE method ......................................................................................................................................73  Figure 3.3  Simulated concentration profiles for Case I...........................................................77  Figure 3.4  (A) Simulated electropherograms for scenario I-1, I-2 and I-3. (B) Simulated electropherograms for scenario I-1, I-4 and I-5........................................................................78  Figure 3.5  Simulated concentration profiles for Case II..........................................................79  Figure 3.6  Simulated electropherograms for scenario II-1 to II-3...........................................80  Figure 3.7  Simulated concentration profiles for Case III ........................................................83  Figure 3.8  Simulated electropherograms for scenario III-1 to III-3 ........................................84  Figure 3.9  Simulated concentration profiles for Case IV........................................................86  Figure 3.10  Simulated electropherograms for scenario IV-1 and IV-2 ...................................86  Figure 4.1  Ideal and experimental CE-FA profiles .................................................................97  Figure 4.2  Binding isotherms of cRGDfK-488 and cRADfK-488 to αvβ3 integrin..............107  Figure 4.3  Specific binding isotherms of cRGDfK-488 to αvβ3 integrin..............................109  Figure 4.4  Simulated concentration profiles for CE-FA .......................................................112  Figure 4.5  Comparison of the experimental result (solid line, a) with the simulation result (short dash line, b) for one of the CE-FA runs .......................................................................113   Figure 5.1  Calibration curve of the antibody.........................................................................122  Figure 5.2  A set of representative electropherograms of antibody and antibody binding to EGFR.. ....................................................................................................................................125  Figure 5.3  Binding isotherms of EGFR to antibody..............................................................128  Figure 5.4  Simulated concentration profiles for CE-FA. ......................................................130  Figure 5.5  Comparison of the experimental result (solid line) with simulation result (short dash line) for one of the CE-FA runs......................................................................................131  Figure 6.1  Experimental and simulated results for the separation of 1 mM L/D- Trp racemic mixture with α-CD: (A) 20 mM α-CD; (B) 50 mM α-CD; (C) 100 mM α-CD in 0.1 M phosphate buffer. ....................................................................................................................144   xi Figure 6.2  Chiral separation of L- and D-Trp with HP-β-CD. BGE: (A) 20 mM; (B) 50 mM; (C) 100 mM HP-β-CD in 0.1 M phosphate buffer. Injected sample: 1 mM L/D-Trp racemic mixture....................................................................................................................................145  Figure 6.3  Simulated electropherograms for the separation of 1 mM L/D-Trp mixture with HP-β-CD ranging from 110 mM to 200 mM in 0.1 M phosphate buffer. Detailed conditions are provided in the Supporting Material.................................................................................146  Figure 6.4  Electropherograms for the separation of dansyl-L/D-Phe racemic mixture with no chiral selector (A), α-CD concentration of 50 mM (B), 100 mM (C) and HP-β-CD concentration of 50 mM (D) and 100 mM (E). ......................................................................149  Figure 6.5  CoSiDCCE simulated concentration profiles for tryptophan enantiomers and their complexes with α-CD (Case I) and for dansyl-phenylalanine enantiomers and complexes with HP-β-CD (Case II).  Concentration of chiral selectors: (A) 20 mM; (B) 50 mM; (C) 100 mM; (D) 500 mM; (E) 1 M; (F) 50 M.............................................................................................152  Figure 6.6  Experimental and CoSiDCCE simulated electropherograms for the separation of tryptophan enantiomers with 50 mM α-CD when (A) different (B) identical and (C) zero complex mobilities are used. ..................................................................................................153  Figure 6.7. Experimental and CoSiDCCE simulated electropherograms for the separation of dansyl-Phe enantiomers with 50 mM HP-β-CD when (A) ,ep LCμ = 1.814×10-5 cm2V-1s-1and ,ep DCμ  = 2.219×10-5 cm2V-1s-1; (B) ,ep LCμ = ,ep DCμ = 1.814×10-5 cm2V-1s-1; (C) ,ep LCμ = ,ep DCμ = 0, which is the case when chiral stationary phase is used in chromatography. ......................155   Figure 7.1  The chemical structures of the investigated flavonoids .......................................162  Figure 7.2  Electropherogram obtained from a standard mixture of six flavonoid compounds ................................................................................................................................................166  Figure 7.3  (a) and (b) are electropherograms obtained from diluted extracts of a red wine and a white wine respectively under optimum conditions ............................................................171  Figure A.1  User interface of CoSiDCCE. Region 1: control panel for the simulation process. Region 2: selector for the simulation modes and input for experimental conditions for simulation parameters. Region 3: simulation animation display window..............................187  Figure A.2  Simulated concentration profiles for the separation of 1mM L/D-Trp in 0.1 M phosphate solution with 20 mM α-CD in 0.1 M phosphate solution. Sample injection time: 3s, 0.5 psi. Separation voltage: +22.5 kV, KLC = 8.15 M-1 and KDC = 11.82 M-1. The concentration profiles of the five species are displayed in time sequence: (A) 0 s (before the injected sample start migrating toward the outlet); (B) 4.0 s; (C) 10.0 s; (D) 96.0 s. ......................................194   xii Figure A.3  Simulated electropherograms for the separation of 1mM L/D-Trp recamic mixture, with HP-β-CD ranging from 110 mM to 200 mM in 0.1 M phosphate buffer.......................195  Figure B.1  The user interface of CoSiDCCE is divided into three regions: 1. the simulation control panel; 2. the simulation setting panel defines experimental conditions and simulation parameters; 3. the display panel displays the animation of the simulated concentration profiles of the analytes. ........................................................................................................................199  Figure B.2  Screenshot of the extended Reaction Type Selector panel..................................201  Figure B.3  Screenshot of the parameter panel after all the experimental conditions were set in ................................................................................................................................................203  Figure B.4  Screenshot of the control panel in “Interaction” tab. ..........................................205  Figure B.5  Screenshot of the Control Panel. .........................................................................206  Figure B.6  Screenshot of the CoSiDCCE program at the initial stage of the simulation......206  Figure B.7  Screenshot of the CoSiDCCE program during a simulation run.........................207  Figure B.8  Screenshot of the CoSiDCCE program when (A) the “Save Current Data” button is clicked, and (B) the file is successfully saved. ...................................................................208  Figure B.9  The user interface of the  “Binding Constant” determination function is divided into two regions: 1. Control Panel; 2. Simulation Parameter Panel. ......................................209  Figure B.10  Screenshot of the settings panel on the User Interface of “Binding Constant” determination function after experimental migration time Texp, estimated binding constant Kmin and Kmax, complex mobility μep,C, min and μep,C, max, and interval ΔK and Δμep,C were set in ................................................................................................................................................210  Figure B.11  Screenshot of the message window. ..................................................................210  Figure B.12  Screenshot of the Control Panel of the Binding Constant tab. ..........................211  Figure B.13  The sample of a 3-D and 2-D data file generated..............................................211  Figure B.14  A 3-D surface which is cut through by a plane to produce a 2-D curve, which is then projected onto the bottom plane: (1) The 3-D surface, (2) the cutting planes, (3) the intersection between 1 and 2, and (4) the projected intersection curve. Reprinted with permission...............................................................................................................................212  Figure B.15  2-D graph generated from the simulation program with μep,A/μep,C as the x axis. [p-Nitrophenol]) 2mM. Each curve is composed of data points. Each color of the curves corresponds to one additive (α-cyclodextrin) concentration. Three shapes (circle, square, and  xiii triangle) in one color correspond to three ACE runs under identical experimental conditions. The red rectangle indicates the intersection of eight sets of curves. Reprinted with permission ................................................................................................................................................213  Figure B.16  Two sets of generated regression data for the 2-D curve, (x1, y1) and (x2, y2), are listed side by side in a new SigmaPlot worksheet. ...........................................................214   xiv Abbreviations  ACE: Affinity Capillary Electrophoresis ACN: Acetonitrile BSA: Bovine Serum Albumin BGE: Background Electrolyte CD: Cyclodextrin α-CD: α-cyclodextrin CE: Capillary Electrophoresis CEC: Capillary Electrophoresis Chromatography CE-FA: Capillary Electrophoresis - Frontal Analysis CoSiDCCE: Computer Simulation of Dynamic Complexation Capillary Electrophoresis CSP: Chiral Stationary Phase CV: Coefficient of Variation CZE: Capillary Zone Electrophoresis DCCE: Dynamic Complexation Capillary Electrophoresis E: Electric field strength EOF: ElectroOsmotic Flow ESI-MS: Electrospray Ionization-Mass Spectroscopy GC: Gas Chromatography HD: Hummel-Dreyer 1H NMR: Proton Nuclear Magnetic Resonance HP-β-CD: hydroxypropyl-β-cyclodextrin HPLC: High Performance Liquid Chromatography K: Binding constant LIF: Laser Induced Fluorescence LOD: Limit of Detection MEKC: Micellar ElectroKinetic Chromatography MEKCC: Micellar Electro-Kinetic Capillary Chromatography MeOH: Methanol NECEEM: Non-Equilibrium Capillary Electrophoresis of Equilibrium Mixtures  xv Phe: Phenylalanine RAM: Random Access Memory RAD: Arginine-alanine-aspartic-acid RGD: Arginine-glycine-aspartic-acid RP HPLC: Reversed Phase High Performance Liquid Chromatography RSD: Relative Standard Deviation SDS: Sodium Dodecyl Sulfate SFC: Supercritical Fluid Chromatography SimDCCE: Simulation model of Dynamic Complexation Capillary Electrophoresis SPR: Surface Plasmon Resonance TLC: Thin Layer Chromatography Try: Tryptophan UV: Ultraviolet VACE: Vacancy Affinity Capillary Electrophoresis VP: Vacancy Peak      xvi Acknowledgments  I would like to thank my supervisor, Dr. David D.Y. Chen, for providing an environment which encourage successful research and for his advice and encouragement throughout my research. I want to acknowledge my former and current lab colleagues, coworkers and collaborators, Kingsley Donkor, Ning Fang, Sonya Cressman, Alison Holiday, Xuefei Zhong, Jane Maxwell, Chang Liu, Koen Raedschelders and Hong Zhang for sharing their knowledge and experience about CE. Finally, I would like to thank my husband Pengzhou for all of his support, and to thank my parents for their encouragement and love throughout the years.              xvii Co-authorship Statement   For the co-authored Chapter 2, I contributed 90% of the experimental design, 90% of the research and data analysis and 90% of the manuscript preparation. The program used in Chapter 2 was developed by the co-author Ning Fang. For the co-authored Chapter 3, I contributed all of the experimental design, 95% of the research and data analysis, and I wrote the draft of the manuscript. The computer program was developed by the co-author Ning Fang. For the co-authored Chapter 4, I contributed to 90% of the experimental design, 85% of the research and data analysis, and I wrote draft of the manuscript. The co-author Sonyna Cressman helped to prepare the biological samples, and co-auther Ning Fang developed the computer program used in Chapter 4. For the co-authored Chapter 7, I contributed to 85% of the experimental design, 80% of the research and data analysis and 90% of the draft of the manuscript. The co-author Ning Fang helped to prepare the solutions used in the experiments in Chapter 7.           1                     Chapter 1   Introduction to Capillary Electrophoresis and Dynamic Complexation of Solutes in Capillary Electrophoresis               2  1.1 Capillary Electrophoresis  The term “electrophoresis” refers to the migration of charged particles in an electrical field, and was first used by Leonor Michaelis to separate proteins based on their isoelectric points (PI) in 1909 [1]. In 1937, Arne W.K. Tiselius, a student of Theodor H.E. Svedberg who won the Nobel Prize for Chemistry in 1926 for his studies in the chemistry of colloids and for his invention of the ultracentrifuge, separated serum proteins, including albumin, and α-, β- and γ-globulins by moving boundary electrophoresis on the basis of their electrical charge and mobility in an electric field, which provided the first intimation of the potential use of electrophoretic analysis for biologically-active molecules [2, 3]. Carrier-free electrophoresis in a 3 mm inner diameter tubes was demonstrated by Stellan Hjerten in 1967 [4]. Fourteen years later, James Jorgenson and Krynn Lukas demonstrated the first high performance capillary electrophoresis (CE) separation with 75 μm inner diameter capillary and a fluorescence detector [5]. Since then, capillary electrophoresis, a separation technique based on differential migration of charged substances in a solution under the influence of an electric field in a narrow bore silica capillary, has become a widely used separation technique for the analysis of many types of analytes, ranging from small molecules (inorganic ions, nucleotides) to proteins, DNAs and even viruses.  The high speed, high column efficiency, high resolution, and the ease of automation are among the advantages usually observed for CE over other types of separation techniques, such as slab gel and paper electrophoresis, high performance liquid chromatography (HPLC), and gas chromatography (GC) [6].  3  1.1.1 Fundamental theory of capillary electrophoresis   The use of capillary as an electromigration channel for separation of a diverse array of analytes, including biological macromolecules, not only presents a unique approach to separation, but also comes with several advantages over the standard solid support approach. Performing electrophoresis separations in capillaries allows much higher electric fields to be applied than in normal gel electrophoresis, which allows separations to be performed much more rapidly. In CE, fused-silica capillaries used typically have an inner diameter (i.d.) of 20 to 100 μm, and an outer diameter (o.d.) of 375 μm, with a length of 20 to 100 cm, and are externally coated with polyimide, which gives flexibility and durability to a capillary that would otherwise be very fragile (Figure 1.1). The volumes required to fill the capillary are in the microliter (μL) range. Typical injection volumes are 1 to 50 nL, but in some cases, volumes of up to about 1 μL can be injected. The low sample consumption of CE is ideal for biomolecules such as DNA/RNA and proteins, when only small amounts of analyte are available [7]. In addition, the high surface-to-volume ratio of capillaries with these dimensions allows for very efficient heat dissipation, diffusing Joule heat generated during electrophoresis.  4   Figure 1.1. A schematic representation of a 75 μm (i.d.) × 375 μm (o.d.) fused silica capillary coated with polyimide.    A schematic representation of a CE instrument is shown as Figure 1.2. It consists of two buffer reservoirs, a sample reservoir, a silica capillary, a high voltage power supply and a detector. The negative electrode is the cathode, which attracts cations, and the positive electrode is the anode, which attracts anions. Electrophoresis is performed by filling the reservoirs and capillary with a buffer solution (also called background electrolyte, BGE). Based on the experimental needs, either bare fused silica inner wall or polymer coated inner wall capillaries can be used. To inject a sample, the capillary inlet is placed into a sample vial and a relatively low pressure (0.5 psi) or low electric field (0.5 kV) is applied. During electrophoretic separation, the voltage used can be from 5 kV to 30 kV. High heat dissipation efficiencies of the narrow columns allow separations to be performed at high field strengths that vary from 100 to 600 -1V cm⋅ . The electric field causes the solutes to migrate through the capillary. When solutes migrate through the detector window, signals are collected and sent to a computer for display. The plot of a detector response versus time is called an 5  electropherogram. Because the analytes migrate through the detector at different times, an electropherogram is produced with the separated compounds appear as peaks with different migration times. The commonly used online detectors are ultraviolet absorbance (UV), photo diode array (PDA), and laser induced florescence (LIF) detectors. In some cases, CE is also coupled with mass spectrometry through an interface to obtain structural information of the separated compounds. + - CathodeAnode samplebuffer buffer Detector Capillary High voltage  power supply Computer V   Figure 1.2. Diagram of a capillary electrophoresis system.   In CE, the electrophoretic mobility, epμ , is characteristic of individual ions and is determined by the ion velocity v ( 1scm −⋅ ) per unit electric field E ( -1V cm⋅ ) as given:    ep E μ = v                       (1.1) In a homogenous electric field, electrostatic force, Fe, and frictional force, Ff, are the two factors acting on a hard spherical particle moving through a liquid. Electrostatic force is 6  proportional to its effective charge and the electric field strength. The translational movement of the ion is opposed by a retarding frictional force, which is proportional to the velocity of the ion and the friction coefficient. eF Q E= ⋅                                (1.2) 6fF f rπ η= − ⋅ = ⋅ ⋅ ⋅ ⋅v v         (1.3) where Q  is the net effective charge of the ion (coulombs), f is the frictional coefficient ( 1sg −⋅ ), r is the radius of the particle (cm), and η is the viscosity of the medium ( sPa ⋅ ). During electrophoresis, the ion can almost instantly reach a steady state velocity where the accelerating force Fe equals the Ff, as defined: e fF F= −                             (1.4)    6Q E rπ η⋅ = ⋅ ⋅ ⋅ ⋅v          (1.5) Rearranging eq. 1.5 gives, 6 Q E rπ η ⋅= ⋅ ⋅ ⋅v          (1.6) and the electrophoretic mobility of a spherical particle (or an ion), epμ , is also proportional to the charge of the ion, Q, and is inversely proportional to the friction coefficient,  f.    ep 6 Q E r μ π η= = ⋅ ⋅ ⋅ v         (1.7) The above equation implies that the electrophoretic mobility of each species in a solution depends only on its charge and size.  The fused silica capillary is made of fused silicon dioxide (Si-O-Si). The inner surface of a fused silica capillary is covered with silanol groups (Si-OH). Depending on the pH of the buffer solution, the inner wall of a fused silica capillary can have different amount of Si-O- 7  groups present at the surface. Surface silanol groups are deprotonated to negatively charged Si-O- groups at pH above 3. More silanol groups deprotonate as the pH increases up to 9. This ionization can be enhanced by first passing a basic solution through the capillary, followed by the background electrolyte. Figure 1.3 demonstrates the wall of the capillary with negatively charged Si-O- groups.                                           -SiOH ⇌-SiO- + H+                 Figure 1.3. Representation of the silanol groups inside of the capillary.     The layer of negatively charged ions on the silica capillary wall attracts the positively charged ions in the buffer solution. A portion of cationic counter ions attaches to the charged surface and gives rise to an immobilized compact layer called the Stern layer. The charge and potential distribution in the Stern layer are mainly determined by the ionic strength of the solution and the geometric restrictions of ions. Outer surface Capillary wall Inner surface 8  Since only part of the excessive charges at the capillary wall is neutralized in the Stern layer, the additional cations present in the adjacent area will be attracted to the residual negative charges at the capillary wall, forming a diffuse layer. The surface charge potential is linearly dissipated from the surface to the first layer of counter ions, and then exponentially dropped through the diffuse layer, approaching zero at the imaginary boundary of the double layer. The potential drop across the diffuse layer is called Zeta potential (ζ). When an electric field is applied to the capillary, the cations in the diffused layer will migrate towards the cathode. These cations drag the solvent molecules with them to produce electroosmotic flow (EOF). The electroosmotic velocity, veo, is defined by [6]  0eo eo rE E E ζ ε εζ εμ η η ⋅ ⋅⋅= − ⋅ = − ⋅ = − ⋅v        (1.8) where eoμ  is the electroosmotic mobility, ε is the static permittivity of the solution, εr is the relative static permittivity, ε 0 is the permittivity of vacuum, and ζ is the zeta potential at the capillary/solution interface.[6] The negative sign means that when ζ is negative, the electroosmotic flow is towards the cathode; this is defined as a positive flow which is also the direction of EOF. Zeta potential is largely dependent on the electrostatic nature of the capillary surface, and on the ionic nature of the buffer solution. In fused silica capillaries, the veo varies with pH of the background buffer solution. Below about pH 3, the fully protonated SiOH groups minimize veo; however, a maximal veo can be reached when pH value increases to about 9. The veo also decreases with increasing ionic strength, because more cations are present in the Stern layer, resulting in a smaller ζ. Electroosmotic flow can be reduced by coating the capillary with a material that suppresses ionization of the SiOH group, such as 9  polyacrylamide or methylcellulose. The structure of the double layer at the capillary wall and the change of Zeta potential is illustrated in Figure 1.4 [8].    Figure 1.4. Schematic representation of the electrical double layer formed at a negatively charged inner capillary wall in contact with an electrolyte solution [8].  The separations of charged ions in an electric field before and after EOF are demonstrated in Figure 1.5A and 1.5B.  The direction of the arrow indicates the direction of the motion. The length of the arrow indicates the magnitude of the velocity of corresponding 10  species in the same radius. According to eq. 6, with EOF, the most positively charged ion moves toward the cathode fastest, the mobility of the neutral ion is the same as the EOF and the most negatively charged ion moves the slowest.  EOF ++ + - - - - - - - - - + + + + + + ++ + - - - - - - - - - + + + + + + A B  Figure 1.5. The velocity of ions (A) with and (B) without the presence of electroosmotic flow.  1.1.2 Flow dynamics In chromatography techniques, such as gas and liquid chromatography, the driving force of the separation is pressure. This results in frictional forces building up where mobile phase is in contact with solid surfaces. These frictional forces result in drops of velocity in mobile phase at the interfaces and this creates a laminar or parabolic flow profile in an open tube capillary (Figure 1.6A). In the laminar flow, the velocity of the mobile phase is large in the centre but decreases to zero at the liquid-solid interface. The velocity gradient formed results in substantial band-broadening and reduced resolution of the separation; however, in a CE system, EOF, the driving force, is originated at the capillary wall and uniformly distributed across the entire length of the capillary [9]. As a result, there is no pressure drop, and flow velocity is uniform across the entire tubing diameter (Figure 1.6B). Because of the flat flow 11  profile formed in the capillary, CE system could offer much higher resolution than open tubular chromatography systems.    Figure 1.6. Cross section flow profile of liquid due to (A) hydrodynamic flow and (B) electroosmotic flow.      The efficiency of a CE system can be derived from fundamental principles.  The migration velocity, vep, is  totep ep ep LE V μ μ= ⋅ = ⋅v        (1.9)  in which  Ltot is the total length of a capillary and V is the voltage applied on the capillary. The migration time, t, is defined as  det tot det ep ep L L Lt Vμ= =v         (1.10) where Ldet is the capillary length to the detector. When molecules migrate through the capillary, molecular diffusion occurs, which leads to peak dispersion, σ2,  2 tot det22 ep DL LDt V σ μ= =        (1.11) 12  where D is  the diffusion coefficient of the solution ( 2 1cm s−⋅ ). The number of theoretical plates, N, is calculated as  tot det2 L LN σ=          (1.12) The dispersion, σ2, is assumed to be time-related diffusion only.  Substituting eq. 1.11 into eq. 1.12 yields  2 epVN D μ=          (1.13) The equation indicates that molecules with small diffusion coefficients, D, will generate high number of theoretical plates. Larger N value can be achieved when higher voltage is applied to the capillary; however, the maximum voltage can be used is 30 kV in today’s technology. The practical field strength is limited by Joule heating [9].  1.1.3 Joule heating  Joule heating is a consequence of the resistance of the buffer to the flow of current. The production of heat in CE is the inevitable result of the current flowing through the capillary during the CE process. The heat production can cause two major problems: temperature gradients across the capillary and temperature changes with time due to ineffective heat dissipation. The rate of heat generation in a capillary can be expressed as following  tot dH iV dt L A =           (1.14) where A is the cross-sectional area of the capillary. According to Ohm’s law, the current i is 13    Vi R =           (1.15) and  VR kA =          (1.16) Therefore,  2 2 2 tot dH kV kE dt L = =          (1.17) where k is the conductivity. Equation 1.17 indicates that the amount of heat generated is proportional to the square of the field strength. Increasing the length of the capillary, decreasing the voltage, or using low conductivity buffer can effectively reduce the heat generated [9].  High heat dissipation creates temperature gradients across the capillary. Since heat is dissipated by diffusion, the temperature at the center of the capillary is greater than that at the capillary walls. Viscosity of the solution decreases at higher temperature, thus, both the electroosmotic flow and electrophoretic mobility will increase at the center, which results a flow profile that is similar to the hydrodynamic flow profile shown in Figure 1.6A, and causes band broadening to occur.  Operating with narrow-diameter capillaries improves the situation. To avoid ineffective heat dissipation in narrow-diameter capillaries, cooling systems are required to ensure heat removal. To date, liquid cooling has been the most effective way of heat removal and capillary temperature control [9].   14  1.2 Dynamic Complexation in Capillary Electrophoresis (DCCE) The dynamic complexation of solutes migrates at different velocities in a single phase is a fundamental and crucial assumption in developing an appropriate theory to describe CE separations. The theory of dynamic complexation capillary electrophoresis (DCCE) [10, 11] can be applied to most situations where additives were used to induce or enhance differential migration of analytes. The migration behavior of all types of analytes and additives, such as protein-ligand, antigen-antibody, and chiral selectors and enatiomers or regeoisomers, whether charged or neutral, can all be described by DCCE theory [8]. Based on the type of complexation and the length of the injected sample plug, the presence of binding species in the injection plug and the background electrolyte (BGE) solution, five modes of DCCE have been developed, including affinity CE (ACE) [12-14], Hummel-Dreyer (HD) method [15-17], frontal analysis CE (FA-CE) [18], vacancy peak (VP) and vacancy affinity CE (VACE) method [12, 19-21]. These DCCE methods can all be used in the determination of binding parameters for specific types of interactions.  15   Figure 1.7. Illustration of initial conditions of different modes of dynamic complexation in capillary electrophoresis: (A) affinity CE, (B) vacancy affinity CE, (C) Hummel-Dreyer, (D) vacancy peak, and (E) frontal analysis method.  1.2.1 Affinity Capillary electrophoresis (ACE)  In affinity capillary electrophoresis (ACE), the capillary is filled with buffer containing the additive to be studied at various concentrations. The migration rate of a narrow plug of analyte is varied depending on the amount of additive present in the BGE (Figure 1.7A). When the analyte and the additive interact at a 1:1 stoichiometry, the equilibrium can be express as the following  A + P ⇌ C                                    (1.18) where A, P and C are the analyte, additive and the formed analyte-additive complex, respectively. A C E Analyte Additive Analyte-additive complex BGE D B 16  When the association/dissociation process between the analyte and the additive is relatively fast, the binding (or equilibrium) constant, K, can be written as   [ ] [ ] [ ]f f CK A P =          (1.19) in which [A]f, [P]f, and [C] are the concentrations of the free analyte, free additive and the complex, respectively. The net electrophoretic mobility of the analyte, represented by Aepμ , can be written as  Aep ep,A ep,C(1 )f fμ μ μ= + −        (1.20) where μep,A, μep,C and Aepμ represent the electrophoretic mobility of the free analyte, complex and the net electrophoretic mobility of the analyte, respectively, and f is the fraction of the free analyte. Substituting [ ] [ ] f t A f A =  into eq. 1.20 gives,  Aep ep,A ep,C [ ] [ ] [ ] [ ] f b t t A A A A μ μ μ= +                             (1.21) When the amount of additive in the BGE is changed, the value of f will change and the average mobility of the analyte, Aepμ , will shift between  μep,A and  μep,C as given in Figure 1.8. The positive peak represents the mixture of the free analyte and the analyte-additive complex, indicated by (•), and the negative peak represents vacancy of the free additive in the back ground electrolyte (BGE) solution, indicated by (*). Since the mobility of the free additive is kept constant, the negative peak will not shift when increasing amount of additive is present.  17  A D C B * * * TΔ  Figure 1.8. Schematic representation the ACE method. TΔ  reflects the change on the migration time of the free analyte and analyte-additive complex (•).    In a 1:1 analyte-additive interaction, the concentration of complex formed can be written either as the concentration of bound analyte or the bond additive ([ ] [ ] [ ]b bC A P= = ), and the free analyte concentration can be described as  [ ] [ ] [ ] [ ] [ ]f t b t bA A A A P= − = −        (1.22) Substituting eq. 1.22 in eq. 1.19 gives  [ ] ([ ] [ ] )[ ] b t b f PK A P P = −        (1.23) Rearranging eq. 1.23 yields  [ ] [ ] [ ] [ ] 1 [ ] t f b b f A K P P A K P ⋅= = +        (1.24) The net electrophoretic mobility of the analyte can be expressed as 18   Aep ep,A ep,C [ ]1 1 [ ] 1 [ ] f f f K P K P K P νμ μ μ= ++ +         (1.25) where ν is the correction factor that is defined as 0/ηη , η is the viscosity of the buffer with the additive and η0 is the viscosity of the buffer when [P]t is approaching zero. The use of the correction factor accounts for the changes of mobility caused by the viscosity change when additives are used [7].  Equation 1.25 can be rearranged to give  Aep ep,A ep,C ep,A [P] ( ) ( ) 1 [P] f f K K νμ μ μ μ− = −+      (1.26) In ACE, because the concentration of the additive is often much higher than that of the analyte, [P]f can be replaced by [P]t, or [P]. Finally, with Aepμ and ν  measured at different [P]t, the equilibrium constant and the electrophoretic mobility of the complex ( ,ep Cμ ) can be estimated using nonlinear regression method.  Equation 1.26 can then be linearized using one of the following three forms: [22, 23] A ep ep,A A ep ep,A ep,C ep,A( ) ( )[P] K K νμ μ νμ μ μ μ− = − ⋅ − + ⋅ −     (1.27) A ep ep,A ep,C ep,A ep,C ep,A [P] [P] 1 ( ) Kνμ μ μ μ μ μ= +− − − ⋅      (1.28) A ep ep,A ep,C ep,A ep,C ep,A 1 1 1 1 ( ) [P]Kνμ μ μ μ μ μ= +− − ⋅ −     (1.29) These three equations can be referred to as x-reciprocal (eq. 1.27), y-reciprocal (eq. 1.28), and double-reciprocal (eq. 1.29) regression equations, respectively [7, 24].  ACE has been mainly used to study 1:1 analyte-additive interactions.  19  1.2.2 Vacancy Affinity CE method  In vacancy affinity CE (VACE) method, the capillary is filled with buffer containing both binding species, and the injected sample is a small plug of plain buffer (Figure 1.7B). The concentration of one species, normally the analyte, is fixed and the concentration of the other species is varied. A schematic representation of the VACE experiment is demonstrated in Figure 1.9 in which the analyte and the complex migrate faster than the additive. The negative peak on the left arises due to a vacancy in the analyte-additive complex and the free analyte (•), and the other negative peak is due to the lack of free additive (*). In ACE and VACE, the binding constant is calculated based on the changes in electrophoretic mobility of the analyte due to complexation. Upon increasing the concentration of the additive in the BGE solution, the mobility of the free additive will shift as illustrated in eq. 1.30. A ep ep,A ep,C(1 )f fμ μ μ= + −        (1.30) where  μep,A and Aepμ are the electrophoretic mobility and the net electrophoretic mobility of the analyte. Similar to the ACE method, the binding constant, K, for a single analyte-additive interaction can be obtained using the change in the electrophoretic mobility of the additive.  Aep ep,A ep,C ep,A [A] ( ) ( ) 1 [A] f f K K νμ μ μ μ− = −+      (1.31) More details for higher order interaction are discussed in Chapter 3.  20  A D C B * * * * TΔ  Figure 1.9. Schematic representation of the VACE method. Peak identification: the mixture of the free analyte and analyte-additive complex (•) and free additive (*). TΔ represents the shift of the free additive trough.  1.2.3 Hummel-Dreyer method  The Hummel-Dreyer (HD) and ACE method have similar experimental set-up. In HD, a mixture of the analyte and the additive is injected into a capillary filled with separation buffer containing fixed concentration of the additive. By increasing the concentration of the additive in the sample mixture, and remaining the concentration of the analyte constant, internal calibration method can be used to calculate the equilibrium constant (Figure 1.7). In Figure 1.10, the positive peak marked with “•” represents the mixture of analyte-additive complex (C) and the free analyte (A), and the negative peak marked with “*” indicates vacancy of the free additive (P) in the separation buffer solution. The area of the negative peak is directly related to the amount of additive in free form, [A]f. With specific binding 21  stoichiometry between the selected analyte and additive, the number of drug molecule bound to the protein, [P]b, and can be calculated using internal calibration of the peak area [13]. In the internal calibration, when the amount of additive injected in the sample mixture is increased, the trough area will decrease as shown in Figure 1.10A and 1.10B. If the amount of P present in the sample mixture is sufficiently large, a positive peak may even appear as shown in Figure 1.10C and 1.10D. The concentration of the additive bound to the analyte, [P]b, can be calculated through interpolation.   Figure 1.10. Schematic representation of calibration procedure for the HD method.  1.2.4 Vacancy Peak method In vacancy peak (VP) method, the capillary is filled with buffer containing both binding species, and the sample is a small amount of plain buffer, which is similar to the set-up of the VACE method (Figure 1.7C). The schematic representation of the VP method is given in 22  Figure 1.11. The negative peak on the left hand side arises due to vacancy of the free analyte and the analyte-additive complex, indicated by (•), and the negative peak on the right hand side is due to the lack of free additive, indicated by (*). The concentration of free additive in each BGE solution can be determined using internal calibration, in which a series of buffer containing increasing concentration of the additive is injected into the capillary containing fixed concentration of both binding species., The trough area of the free additive peak decreases as higher concentration of additive is injected, and eventually it appears as a positive peak when the injected sample contains sufficiently large amount of the additive. Similar to the HD method, the [P]b can be determined through the interpolation.   Figure 1.11. Schematic representation of calibration procedure for the VP method.  23  1.2.5 Frontal Analysis method Unlike other DCCE formats, in frontal analysis (FA) method, the capillary is filled with plain buffer, and a relative large sample plug consisting of pre-equilibrated additive and analyte mixture is injected (Figure 1.7E). In order to use this method, two requirements have to be satisfied: (1) the mobility of the analyte and the analyte-additive complex are similar; (2) the mobility of the additive is different from that of the complex. Because of the difference in mobility, the free additive is separated from the injected sample plug (Figure 1.12). In this figure, two plateaus are seen, one is related to the mixture of the free analyte and analyte- additive complex (•), and the other one is related to the free additive (*). The height of the plateau is directly proportional to the concentration of corresponding species. The concentration of free additive can be calculated by comparison with a calibration curve, obtained by injecting a sample containing only the additive.  H A B L * * [ ] [ ] [ ] [ ] tot b b tot PL H P HP P L = =  Figure 1.12. Schematic representation of the calibration method for CE-FA method.   24  In the HD, VP and FA method, the average number of additive molecules bound per analyte molecule, I, can be obtained [13]:  [ ] [ ] b t LI P =          (1.32) For a 1:1 stoichiometry interaction, the following can be used to determine the binding constants in these methods. [ ][ ] [ ] 1 [ ] f tot f K PCI A K P = = +         (1.33) A more complex equation will be used to determine higher order binding equilibrium, which is discussed in Chapter 4. All methods mentioned so far are equilibrium CE methods that can be used in systems with fast association and dissociation rates.       If the dissociation of the complex is relatively slow compared to the time required to separate the free analyte from the complex, non-equilibrium CE methods can be used. In non- equilibrium CE, a small amount of pre-equilibrated additive and analyte mixture is injected into the capillary that is filled with plain buffer. When the high voltage is applied, the complex is separated form the free analyte and additive as they migrate at different velocities. Eventually, an irregularly shaped analyte band will pass through the detector window than generate a peak. The binding constant can be determined by measuring the areas of the free analyte signal and the complex signal. Berezovski et al. introduced a method to determine not only binding constants but also rate constants using nonequilibrium CE of equilibrium mixtures (NECEEM) [25, 26].  25  1.3 Simulation of Dynamic Complexation in Capillary Electrophoresis (SimDCCE) 1.3.1 Unified separation science Prof. John Calvin Giddings pointed out many of the common thermodynamic characteristics of different techniques in his book titled “Unified Separation Science” published in 1991. Two general forms of separative transport: bulk flow displacement and relative displacement were proposed [27].  As Giddings stated in his book, “in bulk flow displacement every component in a flowing medium is carried along nonselectively with the medium [27].” In many systems, flow plays an integral role in driving the separation process. One of the essential characteristics of the separation method therefore is determined by the existence, orientation, and nature of the bulk flow. The driving force to make bulk flow occur is different in different types of techniques. For instance, in gas chromatography, the pressure from an outside source, such as a high pressure gas from a tank, forces the gas phase flow through the column; in liquid chromatography, pumps are often used to force the liquid phase move along the column; in CE, electroosmotic flow is created by a high electrical potential.  Relative displacement causes the motion of a component through its surrounding medium, and the process is selective [27].  Relative displacement in separations is usually created by some force or gradient, such as intermolecular interactions with the surrounding medium and electrical fields. In chromatographic technique, the analyte is distributed between the stationary phase and the mobile phase, and its transport is determined by the amount of the analyte distributed in the two phases. In open tubular CE, the transport of each charged species is determined by their migration rates in the applied electric field. 26   Bulk flow displacement cannot be used alone to create separation because it is nonselective. All separation methods must rely on relative displacement alone or in conjunction with bulk flow displacement.  1.3.2 Mass balance equation  Mass balance equation was first used to establish an ideal model for chromatography by Wilson [28]. In 1997, Stanhlberg illustrated zone migration of analytes in electrochromatography using mass balance equations [7, 29]. Hjerten and co-worker were the first to point out that the initial stages of the derivation of mass balance equation make no assumption as to the separation technique [30, 31]. Therefore, mass balance equation is generally applicable to all separation techniques.  The flux density J  can be used to tell how solute moves across boundaries into and out of a region, and to detail the ebb and flow of concentration [27]. As demonstrated in Figure 1.13, over a period of time, the analyte moves from a fixed cross section S1, at position x , to cross section S2, at position x dx+ , with a linear velocity v,  27   Figure 1.13. Movement of solute across two cross sections S1 and S2 in the capillary at position x and x dx+ . Over a period of time, the solute moves from S1 to S2 at speed v.    The flux density of the analyte, the number of moles carried through a unit area in unit time, is related to the average velocity of the analyte, v, and its concentration, c.  J c= ⋅v          (1.34) S1 S2 x S1 S2 x V S1 S2 x  x + dx V V  x + dx x + dx 28   Assuming the cross-sectional area is unity, the amount of the analyte swept across the fixed cross section in the unit time equals the flux density, J. The average velocity, v, can be written as  1dx dX dt f dx ⎛ ⎞= = −⎜ ⎟⎝ ⎠v          (1.35) where X is the effective force, x is distance that the analyte moves along the column, and f is the friction coefficient.           Substituting v from eq. 1.35 into eq. 1.34 yields,  c dXJ f dx = −          (1.36) The general form of X  is given as [27]  int 0 lnext extX X X X X RT c= + = + +       (1.37) in which extX is the energy from external field, intX is energy from intermolecular interactions, and 0X is the standard state chemical potential. R is the gas constant and T is temperature. The substitution of eq. 1.37 into eq. 1.36 gives  0extc dX dX RT dcJ f dx dx f dx ⎛ ⎞= − + −⎜ ⎟⎝ ⎠       (1.38) A condensed form of eq. 1.38 can be written as  dcJ Uc D dx = −          (1.39) where U indicates the average velocity caused by external fields and internal effects in combination. It is expressed by  01 extdX dXU f dx dx ⎛ ⎞= − +⎜ ⎟⎝ ⎠        (1.40) 29  In the absence of external fields and internal forces, in which case 0U = ,  RT dcJ f dx = −          (1.41) Fick’s first law defines the flux density as  dcJ D dx = −          (1.42) Comparing eq. 1.41 and eq. 1.42 yields the diffusion coefficient, D, in terms of the basic parameters R, T, and f.  RTD f =           (1.43) When flux passing cross sections demonstrated in Figure 1.13, the flux entering at position x minus that leaving at position x dx+  represents the accumulation, moles gained/second, of the analyte between S1 and S2.  moles gained / secondx x dxJ J +− =       (1.44) Multiplying the right-hand side of eq. 1.44 by /dx dx , the change in flux density, J, can be written as  moles gained secondx x dx dx dcJ J dx dx dt+ − = =      (1.45) where dc dt  is the increment in concentration per second. The left-hand side of eq. 1.45 can also be expressed using Taylor’s expansion of x dxJ + around position x as x dx x dJJ J dx dx+ = +         (1.46) The substitution of eq.1.46 into eq. 1.45 gives 30   dc dJ dt dx = −          (1.47) This is known as the equation of continuity and can be applied to any form that J may take (mass flux, heat flux, etc.). The substitution of eq. 1.39 into eq. 1.47 yields  ( )dc d d dcUc D dt dx dx dx = − +        (1.48) When D and U are constant, this becomes  2 2 dc dc d cU D dt dx dx = − +         (1.49) In capillary electrophoresis, U, the average velocity of a component, is the product of net electrophoretic mobility, μ , and the electric field, E. The increment in concentration per second can be determined using  2 2 dc dc d cE D dt dx dx μ= − ⋅ +        (1.50)   1.3.3 Simulation of Dynamic Complexation in capillary electrophoresis (SimDCCE)  In 2005, a computer program Simulation of Dynamic Complexation in Capillary Electrophoresis (SimDCCE) was developed in our group by Ning Fang based on mass balance equation to provide insight into the detailed analyte migration and analyte-additive interaction processes in CE.  In SimDCCE, the electrophoretic migration and binding interaction are considered in two separate steps. To achieve an efficient and sufficiently accurate simulation result, a number of finite difference schemes were evaluated in the electrophoretic migration step [32]. As a result, a forward-time backward-space finite difference scheme (FDS) is used: 31   , , , , , , , , , , , , , , , , , 2 1[ (1 )( )] 2 2  ( ) z t t i z t i i z i z z t i z t i z t i z z t i z z t i z t i z z t i i C C E E tC C d d t z z C C C D z μ μ+Δ −Δ −Δ +Δ −Δ − Δ= − − + − −Δ Δ Δ − ++ Δ              (1.51) where Cz,t,i is the concentration of species in i at position z and time t, Ez is the local electric field strength, μi is the apparent mobility of i (μi = μep,i + μeo, where μep,i  is the electrophoretic mobility of i and μeo is the EOF), and Di is the symmetrical dispersion coefficient of i, which accounts for the dispersions caused by longitudinal diffusion and other factors. Δt and Δz are the time and space increments for the calculation, , ,z t id  and , ,z z t id −Δ are the concentration gradient at position Δz and z z− Δ , and  , , , , , , , , , , , , , , , , , , , , , , 2( )( )  = ( )            if ( )( ) 0 z t i z z t i z z t i z t i z t i z z t i z z t i z t i z z t i z z t i z t i C C C C d C C C C C C −Δ +Δ +Δ −Δ −Δ +Δ − − − − − >                  (1.52)  , , 0z t id =  otherwise [32].  The interaction process can be considered in the next step depend on the binding stoichiometry and whether the interaction is equilibrium or non-equilibrium.        32  1.4 Description of Research 1.4.1 Computer simulation of five common capillary electrophoresis methods  In chapter 2, several modes of the often used equilibrium CE methods are simulated based on the principle of dynamic complexation of interacting species in a capillary column. SimDCCE is used to provide insight into the detailed analyte migration and interaction processes in CE. Normal ACE, Hummel–Dreyer method, vacancy affinity CE, vacancy peak method, and CE frontal analysis are simulated based on typical ACE conditions. The simulation results were compared with the detector responses of real CE processes using BSA and warfarin as a model system. The resemblance between the simulated results and the experimental observations is studied for well-buffered ACE systems. 1.4.2 Behavior of interacting species in vacancy affinity capillary electrophoresis described by mass balance equation   Vacancy ACE (VACE), one of the affinity CE methods, has been used to study binding interactions between biomolecules. In VACE, the binding constants can be estimated with nonlinear regression methods. With a highly efficient computer simulation program (SimDCCE), the detailed behaviors of each species during the interaction process under different conditions are demonstrated. In this work, thirteen scenarios in four different combinations of migration orders of the free protein, free drug, and complex formed are studied. The detailed interaction process between proteins and ligands is discussed and illustrated based on the mass balance equation. By properly setting the parameters in the simulation model, the influence of different factors during the interaction process can be explained.  This work is presented in Chapter 3. 33  1.4.3 Using capillary electrophoresis-frontal analysis to characterize biomolecular interactions   In Chapter 4, capillary electrophoresis-frontal analysis (CE-FA) is used to investigate the specific binding characteristics of human αvβ3 integrins with an arginine-glycine-aspartic- acid (RGD) containing fluorescently labeled cyclic peptide. Due to the assumptions made in the commonly used Scatchard Plot method, a newly derived algorithm is proposed to calculate the binding affinity constants and binding stoichiometry. The new approach enables the determination of specific binding parameters in the presence of nonspecific binding. The αvβ3 integrin, a membrane protein, is studied in solution without the need of immobilization or any other kind of modification. An RGD containing fluorescently labeled cyclic pentapeptide is used as the ligand with both specific and nonspecific binding characteristics, and an arginine-alanine-aspartic-acid (RAD) containing peptide is used as the control for nonspecific binding. While a typical specific binding isotherm has a shape of a rectangular hyperbola, a nonspecific binding isotherm is linear in the same ligand concentration region. The specific binding stoichiometry of RGD with αvβ3 integrin is revealed through a comparison study.  With the SimDCCE model, by setting up the simulation parameters using experimental conditions and calculated binding parameters for the selected system, the simulated and experimental electropherograms for the CE-FA runs are compared. Through a set of snapshots taken from a simulation run at selected moments, the SimDCCE model is also capable of demonstrating the interaction and concentration changes of each species during the electrophoresis process in the capillary.  34  1.4.4 Characterization of Epidermal Growth Factor Receptor binding with Panitumumab by Capillary Electrophoresis Frontal Analysis   Ligand-induced signaling from receptor tyrosine kinases (RTKs) of the epidermal growth factor receptor (EGFR) family regulates many cellular processes, including proliferation, cell motility, and differentiation. Perturbations in these cellular signals can lead to malignant transformation, and the EGFR pathway appears to play an important role in the development of a wide range of epithelial cancers, including those of the breast, colon, kidney, lung, pancreas, etc. Panitumumab is fully humanized monoclonal antibody specific to the epidermal growth factor receptor (EGFR). To study the specific interaction activity of panitumumab with EGFR rabbit Fc dimmer, CE-FA method was employed. With the newly derived algorithm, the specific binding affinity constants and binding stoichiometry of the studied interaction are calculated to help understand how the biological system work.  By setting up proper parameters, the real time separation process of species involved in the competitive dynamic complexation during CE is studied using the computer simulation model CoSiDCCE.  Chapter 5 describes this work. 1.4.5 Chiral separation of amino acids using experimental and simulation methods  Chiral separation is one of the most important areas in analytical separation. In the area of chiral analysis, there is a growing interest in the use of highly efficient separation techniques such as capillary electrophoresis. Comparing with chromatography, chiral separation in CE depends on more complex factors, such as the difference in the affinity of the enantiomers towards the chiral selectors and in the mobility of the complexes. 35     The studies by our first simulation model (SimDCCE) showed that one of the important uses of this computer program is to display in graphic format the concentration profiles of the analytes in real time or faster, which has helped to explain the interactions occurring between species during a CE process. In addition, it can be used to provide more detailed understanding on the information shown on the experimentally obtained electropherograms, such as elution order and peak shape. However, SimDCCE is only applicable in studies where a single analyte and a single additive are investigated with various CE modes. It is also limited by the software platform because only PCs can be used to run the program.      In order to overcome the limitations of the SimDCCE, and make the program capable of simulating more general cases, a new simulation program CoSiDCCE (computer simulation of dynamic complexation capillary electrophoresis) has been developed based on the well defined mass balance equation (or mass transfer equation) using a more universal computer programming language JAVA, in which more complicated systems can be studied, such as interactions of single drug with multiple proteins and multiple drugs competing with a single protein. Through the displayed concentration profile of the species involved in the interaction during a CE process, more understanding can be obtained on the binding mechanism between analyte(s) and additive(s). The program can also be used to visualize how the analytes are separated gradually in the capillary under a high voltage.  In Chapter 6, the JAVA based program CoSiDCCE is used to elucidate the determining factors that result in the separations of enantiomers, and predict the efficiency of the chiral selectors when used in other separation systems such as chromatography. In this work, two chiral selectors, α-cyclodextrin (α-CD) and hydroxypropyl-β-cyclodextrin (HP-β-CD), are used for the separation of amino acid enantiomers. The binding constants and complex mobilities are estimated using nonlinear regression methods. The results of the simulation 36  runs with various parameters are compared with real experiments. The simulated peaks with proper parameters for the equilibrium affinity CE experiment have shape and position similar to that of the experimental peaks, with which the accuracy and the prediction capability of the CoSiDCCE were evaluated. Our study showed that while some chiral CE separation is based on the difference in binding constants, others are based almost entirely on the difference in complex mobility. This work is presented in Chapter 6. 1.4.6 Separation of anti-carcinogenic flavonoids with micellar electrokinetic chromatography   The micellar electrokinetic chromatography (MEKC) was first introduced by Terabe and coworkers in 1984 [33].In MEKC, surfactant molecules can self-aggregate to form the micelles and acting as a pseudo stationary phase, and the analytes can be separated based on their differential partition between the micelles and the aqueous environment. In Chapter 8, an MEKC method was developed for the determination of potentially anti-carcinogenic flavonoids in various types of wines. Through the optimization of the factors affecting the separation and detection, including the concentration and pH of the running buffer, the injection time, the sodium dodecyl sulphate (SDS) concentration, and the wavelength of UV absorption monitored, six potentially anti-carcinogenic flavonoids were separated within 16 min in a borate buffer containing SDS at pH 9.0. The detection limits for the six analytes are in the range of 1.48 ×10-2 − 2.31 ×10-2 μg mL-1. With a relatively simple extraction procedure, this method is successfully used in the analysis of commercial wine samples.  The work is described in Chapter 7.  37  1.5 References [1] Michaelis, L., Biochemische Zeitschrift 1909, 16, 7. [2] Tiselius, A. W. K., Nova Acta Rgiae Soc. Sci. Upsa 1930, 4. [3] Tiselius, A. W. K., Nobel Lecture 1948, pp. 1-21. [4] Hjerten, S., Chromatogr Rev 1967, 9. [5] Jorgenson, J. W., Lukacs, K. D., Anal. Chem. 1981, 53, 1298-1302. [6] Rice, C. L., Whitehead, R., J. Phys. Chem. 1965, 69, 4017-4024. [7] Bowser, M. T., Chen, D. D. Y., Electrophoresis 1998, 19, 1586-1589. [8] Fang, N., Chemistry Department, University of British Columbia, Vancouver 2006, p. 190. [9] Coulter, B., Beckman Coulter 2000, p. 6. [10] Bowser, M. T., Bebault, G. M., Peng, X. J., Chen, D. D. Y., Electrophoresis 1997, 18, 2928-2934. [11] Peng, X. J., Bowser, M. T., Britz-McKibbin, P., Bebault, G. M., et al., Electrophoresis 1997, 18, 706-716. [12] Busch, M. H. A., Boelens, H. F. M., Kraak, J. C., Poppe, H., J. Chromatogr. A 1997, 775, 313-326. [13] Busch, M. H. A., Carels, L. B., Boelens, H. F. M., Kraak, J. C., Poppe, H., J. Chromatogr. A 1997, 777, 311-328. [14] Chu, Y. H., Avila, L. Z., Gao, J. M., Whitesides, G. M., Accounts Chem. Res. 1995, 28, 461-468. [15] Parsons, D. L., J. Chromatogr 1980, 193, 11. [16] Rundlett, K. L., Armstrong, D. W., Electrophoresis 1997, 18, 2194-2202. [17] Sun, S. F., Hsiao, C. L., J. Chromatogr 1993, 648, 325-331. [18] He, X. Y., Ding, Y. S., Li, D. Z., Lin, B. C., Electrophoresis 2004, 25, 697-711. [19] Gordon, M. J., Huang, X. H., Pentoney, S. L., Zare, R. N., Science 1988, 242, 224-228. [20] Schou, C., Heegaard, N. H. H., Electrophoresis 2006, 27, 44-59. [21] Soltes, L., Biomed. Chromatogr. 2004, 18, 259-271. [22] Bowser, M. T., Chen, D. D. Y., J. Phys. Chem. A 1998, 102, 8063-8071. [23] Bowser, M. T., Chen, D. D. Y., J. Phys. Chem. A 1999, 103, 197-202. [24] Bowser, M. T., Chen, D. D. Y., Electrophoresis 1998, 19, 383-387. [25] Berezovski, M., Krylov, S. N., J. Am. Chem. Soc. 2002, 124, 13674-13675. [26] Berezovski, M., Nutiu, R., Li, Y. F., Krylov, S. N., Anal. Chem. 2003, 75, 1382-1386. [27] Giddings, J. C., Unified Separation Science, John Wiley & Sons, Inc., New York 1991. [28] Wilson, J. N., J. Am. Chem. Soc. 1940, 62, 1583-1591. [29] Stahlberg, J., Anal. Chem. 1997, 69, 3812-3821. [30] Hjerten, S., Electrophoresis 1990, 11, 665-690. [31] Hjerten, S., Nucleosides Nucleotides 1990, 9, 319-330. [32] Fang, N., Chen, D. D. Y., Anal. Chem. 2005, 77, 840-847. [33] Terabe, S., Otsuka, K., Ando, T., Anal. Chem. 1985, 57, 834-841.     38                                                   Chapter 2   Computer Simulation of Different Modes of ACE Based on the Dynamic Complexation Model*                  * A version of this chapter has been published. Fang, N., Sun, Y. and Chen, D.D.Y. Computer simulation of different modes of ACE based on the dynamic complexation model, Electrophoresis, 2007, 28, 3214–3222. 39  2.1 Introduction   CE has been employed in numerous bioanalytical applications because it has a well- controlled physical and chemical environment [1]. A variety of affinity methods have been developed for CE to study equilibrium or kinetic properties of binding interactions [2–7], including affinity CE (ACE) [7–9],  Hummel–Dreyer (HD) method[10–12], vacancy affinity CE (VACE) [13–16] and vacancy peak (VP) method [16], and frontal analysis (CE-FA) method [17]. These CE modes are distinguished by the separation of free species from complex, the kinetics of association and dissociation processes, the length of the injected sample plug, or the combination of binding species present in the injection plug and in the BGE.  In ACE, HD, VACE, and VP methods, the free and complexed species are not completely separated, and the association and dissociation processes must be much faster than the separation time to ensure the validity known as equilibrium CE.  CE frontal analysis (CE-FA) uses a different scheme. This method requires that one binding species migrates closely with its complex, and the other binding species has a different mobility so that it can move out of the mixture plateau to form another plateau [6]. The binding constant can be determined from the heights of the plateaus. This method is applicable regardless of binding kinetics [18].  The final group is nonequilibrium CE methods, which are used to study slow-kinetics interactions when steady states cannot be reached. The common setup is to inject a small amount of pre-equilibrated mixture into a plain-buffer-filled capillary. When the dissociation rate is very slow, the free species separates completely from the complex, and the binding constant can be determined by measuring the peak areas of the free species and the complex: 40  this method is often called pre-equilibrium CZE. When the dissociation rate is not very slow, the dissociation of the complex gives rise to an exponential part of the analyte peak, which can be fitted with a single-exponential function to determine both binding constants and rate constants. This method was named nonequilibrium CE of equilibrium mixtures (NECEEM) [19, 20].  Because all of the aforementioned CE methods are based on the same principle of dynamic complexation of species migrating in a CE capillary, they are all described as dynamic complexation CE (DCCE) in this paper.  Several computer simulation models of CE have been developed [21–31]. In this work, we will discuss the feasibility of using the dynamic complexation model to simulate different modes of affinity CE. The principle calculation schemes and equations have been discussed previously [31]. The key assumption of the simulation model is the use of a well buffered system, which eliminates most deteriorating factors [32], e.g., electromigration dispersion and Joule heating, and assumes constant local electric field strength throughout the capillary. Stable physical and chemical environment is required for the determination of binding or dissociation constants. The simulation program has been used to study the behavior of interacting species in ACE experiments with various combinations of migration orders [33].  We have since improved the program and its user interface to animate the migrational and interacting behaviors of DCCE experiments in real-time or faster, which not only gives a comprehensive visual presentation, but also strengthens the understanding of various modes of DCCE.  The normal ACE method have been simulated using several methods, includes this model [31], Andreev et al.’s model [30], and Petrov et al.’s multigrid model [3]. Therefore, 41  the focus of this study is the simulation of other modes of ACE methods. The interaction between BSA and warfarin was chosen to provide experimental conditions for our program named SimDCCE. This interaction has been studied extensively by Busch et al. [6]. The advantage of using this pair of compounds is that it works for all equilibrium CE modes and the CE-FA method. The free BSA, free warfarin, and their complex are denoted P (for protein), L (for ligand), and C (for complex), respectively, throughout this paper. CE experiments were performed with the same conditions as used for the simulation to compare the effectiveness of the simulation program.             42  2.2 Experimental Section 2.2.1 Instrumentation  The experiments were carried out on a Beckman Coulter P/ACE Glycoprotein System (Beckman Coulter, Fullerton, CA) with a built-in UV detector. Uncoated fused-silica capillary (50 cm total length, 42 cm length to detector, 50 mm inner diameter, 360 mm outer diameter) (Polymicro Technologies, Phoenix, AZ) was used throughout. The capillary temperature was maintained at 25 oC. A voltage of 110 kV (anode is on the inlet side) was applied for CE runs. UVdetection was performed at 214 nm based on the structure of the molecules. The samples were always injected under a pressure of 0.5 psi or 3447 Pa. The experimental electropherograms were exported as ASCII files, then plotted and compared with the simulated electropherograms in SigmaPlot (Systat Software, Richmond, CA). 2.2.2 Chemicals and solutions  A pH 7.4 phosphate buffer with 1% v/v ACN was prepared by mixing 0.05 M potassium dihydrogenphosphate (Anachemia, Canada) with 0.05 M dipotassium hydrogenphosphate (Sigma–Aldrich Canada, Oakville, ON, Canada) and adding an appropriate amount of ACN (Fischer Scientific, Nepean, ON, Canada). All of the chemicals used are of analytical grade, and the buffer solution was prepared with purified water (NANOpure Infinity Reagent Grade Water System, Apple Scientific, Chesterland, OH).  BSA (B-4287, Sigma–Aldrich Canada) was dissolved in this phosphate buffer at approximately 40 mM. Warfarin (A2250, Sigma–Aldrich Canada) was dissolved in the same buffer at concentrations of 100, 200, and 400 mM. A series of solutions containing 40 mM of BSA and varying concentrations (100, 200, and 400 mM) of warfarin were also prepared. 43  In addition, 0.1% of mesityl oxide (tech., 90%, Sigma–Aldrich Canada) was added as a neutral EOF marker. 2.2.3 Determination of electrophoretic mobilities and viscosity correction factors The electrophoretic mobilities of free BSA (μep, P) and free warfarin (μep, L) were determined by the following procedure: the capillary was first filled with plain phosphate buffer, then a small plug of BSA or warfarin was injected for 3 s at 0.5 psi, and finally the migration time of the sample plug was measured while a voltage of 10 kV was applied across the capillary. The migration times of BSA were estimated at the center of the distorted peaks because the BSA peaks were not Gaussian-shaped due to the presence of different variations of BSA in the sample. This procedure was repeated 10 times on different days to include the instrumental and other errors, and the average free mobilities were determined for BSA and warfarin, respectively. The measured average μep, P was -1.423×10-4 cm2V-1s-1 with a standard deviation of 0.006×10-4 cm2V-1s-1, and the average μep, L was -1.809×10-4 cm2V-1s-1 with a standard deviation of 0.008×10-4 cm2V-1s-1. These values were used in all simulation runs.  The warfarin solutions were used as the BGEs in ACE and HD. The presence of large molecule additives in a buffer solution may change its viscosity, which in turn changes the electrophoretic mobilities of the binding species [34]. The viscosity measurement was taken by the following procedure: 300 mM warfarin solution was injected for 3 s at 0.5 psi into the capillary which was filled with plain phosphate buffer or a buffer containing a mixture of 40 mM BSA and 200 mM warfarin. By applying a low pressure (0.5 psi), the injected sample and buffer solution were pushed out slowly from the inlet side of the capillary to the detector. The procedure was repeated three times to obtain an average time for pushing out the sample plug with each separation buffer. The results showed that the viscosity correction was not 44  necessary in this case because the times for the plain phosphate buffer and the buffer containing the mixture were similar, with less than 1% difference. 2.2.4 Determination of relative UV intensity of BSA and warfarin  At 0.5 psi, a long (99-s injection) BSA or warfarin sample plug was introduced into the capillary filled with plain phosphate buffer. The length of the injected sample plug was 6.0 cm, calculated based on the injection parameters provided by Beckman Coulter. Such a long sample plug ensures the presence of a plateau with the height directly proportional to the injected sample concentration. At the same concentration, BSA’s UVsignal at the selected wavelength of 214 nm was measured 68 times higher than warfarin’s, and the BSA–warfarin complex was assumed to have roughly the same molar absorptivity as BSA. 2.2.5 Procedures for DCCE modes  Table 2.1 lists the experimental conditions for all DCCE runs. Each experiment was repeated three times. Before each measurement, the capillary was flushed for 4 min with 0.1 M NaOH, 2 min with water, and then 8 min with the respective BGE.  Table 2.1. The conditions for DCCE experiments  Injected Sample BGE Injection Time ACE BSA  warfarin (100, 200, 400 µM) 3 s HD BSA + warfarin (200 µM) warfarin (100, 200, 400 µM) 3 s VACE/VP Plain buffer BSA + warfarin (100, 200, 400 µM) 20 s CE-FA BSA + warfarin (100, 200, 400 µM) Plain buffer 30, 60, 90 s 45  2.3 Results and Discussion 2.3.1 DCCE simulation model 2.3.1.1 Electrophoretic migration Although different experimental conditions produce different patterns of peaks, the electrophoretic migration of species in any CE system can be described by the mass transfer equation [32, 36]: 2 ,, 2 ,,,, z C D z C E t C itz i itz zi itz ∂ ∂+∂ ∂−=∂ ∂ μ            (2.1) where itzC ,, is the concentration of species i at position z and time t, Ez is the local electric field strength, iμ  is the apparent mobility of i ( eo ep, μμμ += ii ), and Di is the symmetrical dispersion coefficient of i. Symmetrical dispersion accounts for dispersions caused by longitudinal diffusion and other factors. Ez can be calculated from local concentrations of all ions (free binding species, complex, and buffer ions, as well as H+ and OH-) and the global ion concentration profiles through the current [24]. However, in practice, H+, OH-, and buffer ion concentrations are often kept near constant, and are not the point of interest in a well buffered system where the concentrations of the binding species are much smaller than the electrolytes in the BGE. If only the binding species are monitored, Ez can be assumed constant throughout the capillary.  46  2.3.1.2 Evaluation of mass transfer equation The fundamental mass transfer equation (eq. 1) can be evaluated with finite difference schemes (FDS). The general idea is to divide the entire space and time domains into small steps (grids), and then to carry out calculations on these discrete points in space and time. Small steps in space are called “cells” in this paper. A number of FDS methods have been investigated in previous studies [22-26, 32, 37]. Stability and convergence are required for successful FDS applications. A good finite difference scheme must eliminate or minimize two major types of error: numerical dispersion (or phase errors) and numerical diffusion. The advective nature of CE systems can be better described by upwind finite difference scheme or one of its higher-order variations, in which only the information of current and “upwind”, cells in the previous time step is used for the calculation on the current cell in the current time step. More importantly, numerical dispersion is eliminated with the upwind schemes. In all simulation runs presented in this paper, the space increment (Δz) was set to 0.001 cm, and the time increment (Δt) was set to 0.001 s. These settings meet all the aforementioned requirements, and could indeed generate good simulation results within 10 minutes on a laptop computer (Intel Pentium Mobile 1.86 GHz, 1 GB RAM).  2.3.1.3 Association and dissociation processes The ligand-receptor binding and the complex dissociation take place at the same time as the species migrate in the electric field. A convenient way to handle both electrophoretic 47  migration and binding interaction is to separate them into two distinct steps. The change in concentration due to the electrophoretic migration is calculated first using eq. 1 for a short period of time (Δt) at any given position with a short length (Δz) along the capillary. Then the interaction takes place at that position, and the new concentrations of interacting species are calculated based on equilibrium or kinetic constants. The key factors to measuring the binding ability between two species are equilibrium constants and rate constants. If the interaction rate is much faster than the time scale of the analytical separation, the equilibrium is preserved at any position along the capillary, and equilibrium constants can be used to calculate the new concentrations of ions involved in the interaction. However, for slowly dissociating, strong binding complexes, the equilibrium cannot be reached fast enough. Therefore, rate constants (forward rate constant k+1, and reverse rate constant k-1) have to be used to obtain the new concentrations. No matter how the calculation is done, a small time step is usually required. If the time step is too big, the concentration changes due to electrophoretic migration and diffusion would be too large; this, in turn, would lead to significant overestimate or underestimate of the concentration changes due to interactions. The model interaction between BSA and warfarin is considered a fast association/dissociation process; therefore, the equilibrium constants were used in all simulation runs. The reported binding constants (Kb) of the BSA-warfarin interaction using different CE modes were in the range of 6.0×104 to 2.0×105  L⋅mol-1 [8]. Because no significant differences in the simulation results were found with different Kb values in this range, 7.0×104 L⋅mol-1 was chosen for all simulation runs.  48  2.3.1.4 Electrophoretic mobility of complex  Electrophoretic Mobility of Complex ( Cep,μ ) is another key parameter to describe DCCE systems. However, not under all circumstances can Cep,μ  be measured experimentally. For slowly dissociating, strong binding complexes, the binding species are usually mixed for a long enough time to establish equilibrium before being injected into the capillary. In this case, the remaining complex is often shown in the electropherogram as a visible peak at a time determined by its mobility. Therefore, Cep,μ  is measurable, but k+1 and k-1 are the unknown variables. For rapid association/dissociation interactions, the complex cannot be completely separated from the free species, and there is a peak of the mixture of the free and complexed compounds. The complex mobility can only be measured experimentally in ACE under some extreme conditions. In ACE, the mobility of the analyte plug is determined by the sum of the fractions of different species multiplied by their individual velocities migrating in a separation system. If a very high concentration of additive in the BGE is used, the fraction of the complex approaches 100%, and the complex mobility is approximately equal to the mobility of the analyte plug. However, this method is not always feasible because high concentrations of the additive are not practical for many systems. Therefore, Cep,μ  is another unknown variable in addition to the equilibrium constant.  The unknown variables can be determined using regression methods with various DCCE modes, or using the enumeration algorithm with computer simulation [38]. However, for the interaction of BSA and warfarin, the complex mobility is approximately equal to the free BSA mobility [8]. This was verified by a set of ACE 49  experiments: similar migration times of the BSA peak were obtained with different concentrations of warfarin in the BGE. The three mobilities are in the following order: ep,C ep,P ep,Lμ μ μ≈ > .  2.3.1.5 Initial experimental conditions Two major differences amid various DCCE modes are species present in the injected sample and the BGE, and the length of the injection plug. The injected sample solution and the BGE can be plain buffer, buffer containing one binding species, or buffer containing the pre-equilibrated mixture of both binding species. A large amount of sample is injected in CE- FA to maintain a sample plateau throughout the CE process; while in other modes, only a small amount of sample is injected to form a narrow injection plug. The simulation program must have the ability to handle all these initial conditions. Using SimDCCE, this requirement can be fulfilled by defining different initial conditions on SimDCCE’s user interface (Figure 2.1).          50    Figure 2.1. The user interface (UI) of SimDCCE. Region 1: Input for experimental conditions for simulation parameters; Region 2: Input for the animation of migrational processes; Region 3: Panel on which the animation is displayed.        51  2.3.1.6 Dispersion coefficients Longitudinal diffusion of all species contributes to peak broadening. According to the Stokes-Einstein equation for isolated hard spheres, diffusion coefficient depends on molecular size and shape, solvent viscosity, and interaction with the solvent. Diffusion coefficients of proteins in aqueous solution are usually on the order of 10-5 cm2s-1 or smaller [39]. The influence of longitudinal diffusion on the peak shape is not significant for protein binding interactions. In the simulation model, dispersion coefficients, rather than diffusion coefficients, are used to account for the effects of all symmetrical dispersion phenomena. Although wall adsorption is an asymmetrical phenomenon, its effect on the BSA peak shape can be approximated to symmetrical because the adsorption is rather weak. In nearly all simulation runs presented in this paper, the dispersion coefficients of free warfarin, free BSA, and complex were 1.0×10-6, 1.0×10-5, and 1.0×10-5 cm2s-1, respectively. These values were not measured directly from experiment, but were estimated from the simulation of one simple capillary zone electrophoresis (CZE) experiment: a plug of a single species migrates in the plain buffer. The value that could make SimDCCE generate a peak similar to the experimental one was chosen for that species. The complex is assumed to have the same dispersion coefficient as BSA.  2.3.2 Simulation output  On-line snapshots of the capillary at any given moment can be taken easily as the concentrations of all species in the active cells are stored in the computer’s memory. A series 52  of snapshots taken at proper moments of a simulation run can illustrate the detailed behavior of the CE process. The simulated result normally shows the concentration profiles of the species of interest. However, experimental electropherograms display the sum of signals generated by all species under either UV or fluorescence detectors. For ACE and VACE experiments, the additive does not have to provide significant signals to the detector because only the analyte peak is required for calculating binding constants. These methods are particularly useful for the additives with little or no UV absorption or fluorescence activity, such as cyclodextrins. On the other hand, for VP and HD experiments, the additive must give either UV or fluorescence signals to enable the quantification of bound additive (HD) or free additive (VP) for the determination of binding constants. Therefore, the simulation model needs to have the flexibility to generate simulated peaks based on each species’ ability to absorb UV light or emit laser induced fluorescence. This can be achieved by providing a multiplier to each species according to its UV absorption or fluorescence property. The simulated signal is the sum of the product of each species’ concentration and the multiplier. If a species does not give any signal, or its concentration is uniform throughout the capillary, its multiplier can be set to zero. Simulated electropherograms can be acquired by calculating the simulated signals from the concentrations of all species at the position of the detector.  These electropherograms are then compared with the experimental ones to validate the simulation model and the simulation parameters. SimDCCE is also able to display the snapshots of a simulation run at a given time interval on screen to animate the migration process. 53  2.3.3 Simulation results 2.3.3.1 Simulation of ACE/HD  SimDCCE has been used to study ACE where the experiments were categorized into six cases by the order of the three mobilities [34]. For the interaction between BSA and warfarin, the three mobilities are in the following order: ep,C ep,P ep,Lμ μ μ≈ > . Because ep,Pμ and ep,Cμ  are close in this case, the shift of the analyte migrating time due to complexation in ACE/HD is too small to be recognized.  The simulated and experimental electropherograms for one of the ACE runs are compared in Figure 2.2. The average EOF time is 690.3 s or 11.51 min. A three-second injection results in an estimated 0.18 cm sample plug. The experimental electropherogram is displaced as it is obtained, and the simulated electropherogram has been converted so that the height of the negative warfarin peak matches the height of the experimental warfarin peak. The experimental and simulated migration times and peak areas of the BSA and warfarin peaks are similar. However, there are some differences on the BSA peak shapes: the simulated peak has a symmetrical Gaussian shape, whereas peak broadening and splitting were observed on the elution peak. This phenomenon was probably associated with the different variations of BSA and wall adsorption.   54  Time (min) 18 20 22 24 26 28 30 A bs or ba ce  (m A U ) -40 -20 0 20 40 60 Experiment Simulation BSA and Complex Warfarin  Figure 2.2. Simulation of ACE/HD. BGE: 400 μM warfarin in 50 mM phosphate buffer. Injected sample: 40 μM BSA in 50 mM phosphate buffer. Injection time: 3 s. Separation voltage: 10 kV. Kb = 7.0 × 104 L⋅mol-1.         55  2.3.3.2 Simulation of CE-FA The CE-FA experimental conditions are also listed in Table 2.1. The EOF time was 630.6 s or 10.51 min. Figure 2.3A and 2.3B illustrate two experiments with different injection times (60 and 90 s). The generated peak on the left is the mixture of free BSA and BSA- warfarin complex, and the plateau region (right) indicates free warfarin. The height of the plateau is directly related to the concentration of warfarin in the BGE, which can be used for the determination of binding parameters in CE-FA. The experimental migration times, peak shapes, and plateau heights match closely with the simulated ones. With long sample plugs in CE-FA experiments, the electric field inside the capillary could become less consistent, which would cause molecules to travel at different velocities in different zones, which, in turn, would result in some distortions on peak shapes that have not yet been simulated by the current model. However, such distortions were usually not significant for well-buffered systems, as shown in Figure 2.3.      56  Time (min) 10 12 14 16 18 20 22 24 0 20 40 60 80 100 120 140 Experiment Simulation 1 Simulation 2 10 12 14 16 18 20 22 24 A bs or ba nc e (m A U ) 0 20 40 60 80 100 120 140 Experiment Simulation A B Warfarin Warfarin BSA and Complex BSA and Complex  Figure 2.3. Simulation of CE-FA experiments. BGE: 50 mM phosphate buffer. Injected sample: 40 μM BSA and 400 μM warfarin in the BGE. Injection time: (A) 60 s; (B) 90 s. The dispersion coefficients of BSA and the complex used for the solid simulation curves in (A) and (B) are 1.0×10-5 cm2s-1, and 1.0×10-4 cm2s-1 for the second simulation curve in (B). The larger diffusion coefficients can generate better-fitted peak profile, which indicates that wall adsorption and other factors play bigger role when a large sample plug is introduced in CE- FA experiments.   57  2.3.3.3 Simulation of the vacancy ACE/vacancy peak method The experimental setups for VACE and VP are similar. Three runs were carried out with a fixed BSA concentration and various warfarin concentrations in the separation buffer, as listed in Table 2.1. The average experimental EOF time was 630.6 s or 10.51 min. The length of the sample plug resulted from twenty-second injection was estimated to be 1.20 cm. The simulated concentration profiles and the experimental electropherograms were compared in Figure 2.4. All three VACE/VP experiments were simulated with identical conditions, except for the warfarin concentration in the BGE. The simulated profiles were converted so that the simulated BSA peak matches its experimental counterpart in height. 16 18 20 22 24 -70 -60 -50 -40 -30 -20 -10 0 10 Experiment Simulation 16 18 20 22 2416 18 20 22 24 Time (min) A bs or ba nc e (m A U ) A B C BSA and Complex Warfarin BSA and Complex Warfarin BSA and Complex Warfarin  Figure 2.4. Simulation of VACE/VP. BGE: 50 mM phosphate buffer containing 40 μM BSA and various concentrations of warfarin: (A) 100 μM; (B) 200 μM; (C) 400 μM. Injected sample: 50 mM phosphate buffer (no BSA or warfarin). Injection time: 20 s. 58  The first negative peak was detected due to a vacancy in free and complexed BSA. This peak was always Gaussian-shaped and passed the detector at nearly identical time because the mobilities of free and complexed BSA were similar. The second negative peak was created due to the lack of free warfarin. An increase in the negative peak area was observed as the warfarin concentration in the BGE was increased. This peak always had a sharp front edge and a large tail because the free warfarin migrated at the slowest velocity.  2.3.3.4 Simulation snapshot The experimental and simulated electropherograms showed remarkable resemblance in Figures 2-4. In addition, the ability of SimDCCE to display the detailed real-time (or faster) migrational and interacting behaviors makes it an even more valuable tool for studying affinity interactions in CE. SimDCCE opens a window for users to actually observe and understand the real-time separation process and the formation of different peak shapes, which are usually hard to accomplish with conventional CE instruments. ACE experiments were categorized by the order of the three mobilities in our earlier investigation [34], but scenarios with identical or similar free analyte and complex mobilities, such as the BSA-warfarin experiments, have not been discussed. The mechanism of the BSA- warfarin interaction will be demonstrated using a set of snapshots. Four snapshots taken from an ACE simulation run at selected moments were exported and analyzed in Figure 2.5. A small volume of 40 μM BSA (analyte) was introduced into the capillary filled with a buffer containing 100 μM warfarin (additive). After the sample is 59  injected, the complex formed at the front and back edges of the injection plug (Figure 2.5A). The BSA analyte then moves ahead of the additive and exits the vacancy of the additive from the front edge. To maintain the equilibrium condition in the buffer solution, more BSA and warfarin are dissociated from the complex as the complex migrates through the vacancy plug, which causes the formation of the unsymmetrical “V” shaped warfarin trough. As the analyte catches up with the additive in the front, more complex is formed as indicated in Figure 2.5B. Eventually, the entire analyte plug passes through the additive vacancy zone (Figure 2.5C), and a steady state condition is established throughout the capillary. Except for the small changes caused by diffusion, the length of the combined free and complexed BSA plug remains constant at 0.18 cm. The constant plug length is resulted from the nearly identical mobilities of free BSA and the complex, and is in contrast with the continuous reduction or expansion of the analyte plug when all three mobilities are significantly different [34]. The final concentration profiles are shown in Figure 2.5D. 60  0.00 .05 .10 .15 .20 C on ce nt ra tio n (μM ) -20 0 20 40 60 80 100 [BSA] [Complex] [Warfarin] .4 .5 .6 -20 0 20 40 60 80 100 1.2 1.4 1.6 1.8 -20 0 20 40 60 80 100 15 16 17 18 -20 0 20 40 60 80 100 A B C D On-capillary position (cm) 0.18 cm 0.18 cm   0.18 cm  Figure 2.5. Simulated concentration profiles for ACE. BGE: 100 μM warfarin in 50 mM phosphate solution.  Injected sample: 40 μM BSA in 50 mM phosphate buffer. Injection time: 3 s. Separation voltage: 10 kV. Kb = 7.0 × 104 L⋅mol-1.  The concentration profiles of the three species are displayed in time sequence: (A) 4.0 s; (B) 24.0 s; (C) 50.0 s; (D) 425.0 s. Detailed discussion can be found in the text.       61  2.4 Conclusion The traditional way of studying separation mechanisms and chemical behaviors was to carry out well-controlled experiments and then deduce, from observed detector response, the events happened between the initial and final states using existing knowledge and observations. In this paper, we demonstrated that more insights can be obtained by comparing results from experiment and computer simulation. The BSA-warfarin interaction was chosen as a model system. The computer program SimDCCE, which was designed based on the well- known mass transfer equation, enables the simulation of chemical interaction and migration behaviors of different ACE modes, and outputs the detailed processes efficiently in a graphic or digital format. All of the simulated electropherograms provided in this paper were completed in a few minutes with a laptop PC. The accuracy and efficiency of the model were demonstrated by comparing experimental and simulated results. By setting up proper parameters, the program can be utilized to simulate and predict experimental results for ligand-receptor binding systems with most modes of ACE. 62  2.5 References [1] Kraly, J., Fazal, M. A., Schoenherr, R. M., Bonn, R., et al., Anal. Chem. 2006, 78, 4097-4110. [2] Rundlett, K. L., Armstrong, D. W., Electrophoresis 1997, 18, 2194-2202. [3] Rundlett, K. L., Armstrong, D. W., Electrophoresis 2001, 22, 1419-1427. [4] Petrov, A., Okhonin, V., Berezovski, M., Krylov, S. N., J. Am. Chem. Soc. 2005, 127, 17104-17110. [5] Galbusera, C., Chen, D. D. Y., Curr. Opin. Biotechnol. 2003, 14, 126-130. [6] Heegaard, N. H. H., Nissen, M. H., Chen, D. D. Y., Electrophoresis 2002, 23, 815- 822. [7] Busch, M. H. A., Kraak, J. C., Poppe, H., J. Chromatogr. A 1997, 777, 329-353. [8] Busch, M. H. A., Carels, L. B., Boelens, H. F. M., Kraak, J. C., Poppe, H., J. Chromatogr. 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F., Krylov, S. N., Anal. Chem. 2003, 75, 1382-1386. [22] Saville, D. A., Palusinski, O. A., AIChE Journal 1986, 32, 207-214. [23] Palusinski, O. A., Graham, A., Mosher, R. A., Bier, M., Saville, D. A., AIChE Journal 1986, 32, 215-223. [24] Dose, E. V., Guiochon, G. A., Anal. Chem. 1991, 63, 1063-1072. [25] Ermakov, S., Mazhorova, O., Popov, Y., Informatica 1992, 3, 173-197. [26] Ermakov, S. V., Bello, M. S., Righetti, P. G., J. Chromatogr. A 1994, 661, 265-278. [27] Gaš, B., Vacík, J., Zelenský, I., J. Chromatogr. 1991, 545, 225-237. [28] Hruška, V., Jaroš, M., Gaš, B., Electrophoresis 2006, 27, 984-991. [29] Ikuta, N., Hirokawa, T., J. Chromatogr. A 1998, 802, 49-57. [30] Ikuta, N., Sakamoto, H., Yamada, Y., Hirokawa, T., J. Chromatogr. A 1999, 838, 19- 29. [31] Andreev, V. P., Pliss, N. S., Righetti, P. G., Electrophoresis 2002, 23, 889-895. [32] Fang, N., Chen, D. D. Y., Analytical Chemistry 2005, 77, 840-847. [33] Gaš, B., Kenndler, E., Electrophoresis 2000, 21, 3888-3897. [34] Fang, N., Chen, D. D. Y., Anal. Chem. 2006, 78, 1832-1840. [35] Rundlett, K. L., Armstrong, D. W., J. Chromatogr. A 1996, 721, 173-186. 63  [36] Giddings, J. C., Unified Separation Science, John Wiley & Sons, Inc., New York 1991. [37] Hawley, J. F., Smarr, L. L., Astrophysical Journal Supplement 1984, 55, 221-246. [38] Fang, N., Chen, D. D. Y., Anal. Chem. 2005, 77, 2415-2420. [39] Fang, N., Yeung, E. S. Anal. Chem. 2007, 79, 5343-5350.                   64      ` ` ` ``  ``  `` ```   ````                                             Chapter 3   Behavior of Interacting Species in Vacancy Affinity Capillary Electrophoresis Described by Mass Balance Equation*                 * A version of this chapter has been published. Sun, Y., Fang, N. and Chen, D.D.Y. Behavior of interacting species in vacancy affinity capillary electrophoresis described by mass balance equation, Electrophoresis, 2008, 29, 3333–3341.  65  3.1 Introduction   Characterizing interactions between biomolecules is one of the important areas in biochemical research [1]. CE has become an effective tool to study binding parameters under either equilibrium or nonequilibrium condition, and various CE methods, such as ACE [1–3], Hummel–Dreyer (HD) [4–6] method, frontal analysis (CE-FA) [7–9], vacancy ACE (VACE) [10–13], and vacancy peak (VP) method [12, 14–16], have been developed.  A similar experimental setup is used in the VP and VACE method in which a small volume of neat buffer is injected into the capillary filled with a buffer containing both binding species (e.g., protein and ligand). VP methods have been developed in HPLC, and have been used to study the binding of ligand and proteins [17, 18]. In the VP method, the VP area of the species added to the buffer is used to determine binding parameter. In the VACE method, the changes on the mobility of the component due to complexation are used [19]. To study the protein–ligand binding, the concentration of one species is fixed, while that of the other species is varied. Usually, the protein concentration is kept constant, and the ligand concentration is varied.  With CEFA, HD, VACE, and VP method, the binding constant and the exact number of binding sites can be determined. With ACE method, 1:1 binding stoichiometries have been studied [20, 21].   These five CE methods can be more useful if the detailed interaction mechanism inside the capillary during the CE process is better understood. In the past two decades, several simulation models of CE have been developed to study the interactions between species, the detailed migration behavior, and the reaction kinetics [20, 22–31]. In our previous work, the mechanisms of ACE experiments were studied based on the well-established mass  66  balance equation (also referred to as mass transfer equation) [32]. The concentration profiles of the interacting species can be simulated using a program based on dynamic complexation of interacting species in CE (SimDCCE).  In this work, we will provide an insight into the migration behaviors of the protein and the ligand along the capillary column in the VACE method. Four possible cases will be discussed in more detail and used to demonstrate that not only the order of three mobilities but also the difference between the three mobilities, the concentrations of the protein and ligand can be a factor to determine the peak shapes. A computer simulation program (SimDCCE) is used to simulate VACE experiments with various experimental conditions. BSA and warfarin was selected as a model for simulation because their interaction has been well characterized by many other techniques [33].           67  3.2 Experimental Section The experiments were performed on a Beckman Coulter P/ACE MDQ automated CE system (Beckman Coulter Inc., Fullerton, CA). The build-in UV-Visible absorption detector was used to monitor absorbance at 214 nm based on the maximum absorption of the analytes. Uncoated fused silica capillaries (50-μm inner diameter, 360-μm outer diameter) (Polymicro Technologies, Phoenix, AZ) were used for all experiments. The total length of the capillary was 50 cm, and the length from the injection end to the detector was 40.2 cm. The capillary temperature was maintained at 25 °C. A voltage of +10 kV in the normal polarity mode was applied for CE runs. Low pressure (0.5 psi or 3447 Pa) was applied for all sample injections. The data were converted to ASCII files and exported to produce the electropherograms presented with SigmaPlot 10.0 (Systat Software Inc., Richmond, CA). BSA (>96%, essential amino acid free) and a racemic mixture of R- and S-warfarin (A2250) were purchased from Sigma-Aldrich, Canada. All samples were prepared in deionized water. A phosphate buffer was prepared by mixing 0.05 M potassium dihydrogenphosphate (Anachemia, Canada) and dipotassium hydrogenphosphate (Sigma- Aldrich, Canada). Acetonitrile (Fischer Scientific, Nepean, ON, Canada) was added to the phosphate buffer to make 1% v/v concentration. The pH of the buffer solution was adjusted to 7.4 with 1 M NaOH (BDH Chemicals, Toronto, ON, Canada). BSA and warfarin were dissolved in the aforementioned phosphate buffer to prepare 40 μM BSA and 100, 200, 400 and 600 μM warfarin solutions. In addition, 0.1% of mesityl oxide (tech., 90%, Sigma- Aldrich Canada) was added as a neutral electroosmotic flow (EOF) marker. All of the solutions were filtered through 0.22 μm sterile, Nylon filters prior to use for the CE experiments.  68  New capillaries were first rinsed with 1.0 M NaOH (15 min, 20 psi), followed by methanol for 15 min, 0.1 M NaOH for 15 min, deionized water for 15 min, and finally the BGE for 15 min, before being used. Prior to each run, the capillary was rinsed with 1 M NaOH (5 min), 0.1 M NaOH (5 min), H2O (5 min), and the corresponding BGE (5 min). Samples were introduced using a 20s pressure injection (0.5 psi or 3447 Pa). A voltage of +10 kV was used for the electrophoresis process.   Proteins can adsorb to the uncoated fused silica capillary wall [34]. With no exception, the adsorption of BSA on the capillary was observed. However, since the resulted BSA peak broadening and tailing have no significant effects on the protein-ligand interaction, the uncoated fused-silica capillary was still usable for this study.                           69  3.3 Results and Discussion In VACE method, the capillary, as well as the inlet and outlet vials are filled with a background electrolyte (BGE) containing a pre-equilibrated mixture of BSA and warfarin. The presence of these species in the BGE causes a high background absorption signal. When a small volume of plain buffer is injected and the voltage is applied to the capillary, because the mobility difference, negative peaks caused by the protein and the ligand vacancies are formed and separated in the electropherogram. The height of the vacancy peak is directly related to the concentration of corresponding species, while the position of the negative peak (mobility) holds the information about the binding interaction. Both VACE and VP methods can be used to estimate the binding parameters. In the following discussion, the protein (BSA), ligand (warfarin), and complex will be denoted as P, L, and C, respectively, to be consistent with our earlier papers on ACE [33, 35]. As the concentration of warfarin changes, migration time of the negative peaks varies because of the changes on the average mobilities of protein at the presence of ligand ( , ( )ep P Lμ ) and the average mobilities of ligand at the presence of protein ( , ( )ep L Pμ ), which can be calculated using the following equations: , ( ) , ,(1 )ep P L P ep P P ep Cf fμ μ μ= + −             (3.1)  , ( ) , ,(1 )ep L P L ep L L ep Cf fμ μ μ= + −            (3.2) where Pf  and Lf  are the fractions of free P and free L, respectively, and μep,P,  μep,L, and μep,C are the electrophoretic mobilities of free P, free L and the formed complex. When the concentration of L in the BGE is low, only a small portion of P is complexed with L, and the change on , ( )ep P Lμ  is not significant as compared to μep,P. However, as the amount of L present in the BGE is sufficiently large, more complex are formed, and Pf  decreases significantly. As  70  a result, μep,C  becomes the major contributor to , ( )ep P Lμ . , ( )ep L Pμ  is affected in a similar manner.  The average mobilities of the individual species in the BSA-warfarin system were measured experimentally with VACE method. The electrophoretic mobility of the protein and the ligand was measured from 15 CE runs with normal CE method to avoid typical instrumental and experimental errors. The mobility of free BSA (μep,P) is -1.423 ( ± 0.006) × 10-4 cm2/V⋅s, and the mobility of free warfarin (μep,L) is -1.809 ( ± 0.008) × 10-4 cm2/V⋅s . Due to the small difference between μep,C and μep,P, μep,C cannot be measured directly from the experiments. The average electroosmotic flow (EOF) time of these runs was 630.6 ( ± 0.5) s. Therefore, the mobility order of BSA, warfarin and BSA-warfarin complex is μep,P ≈ μep,C >μep,L.  Figure 3.1 demonstrates the migration of the injected neat buffer plug during CE and the formation of the negative peaks Figure 3.1(d). From the experiments, two negative peaks were detected in the VACE method, as shown in Figure 3.2. The negative peak on the left is resulted from the vacancy of unbound BSA and BSA-warfarin complex, and the negative peak on the right indicates the vacancy of unbound warfarin. By comparing a set of experimental electropherograms, obvious shifts on the free drug vacancy peaks can be observed, and the detailed experimental conditions are listed in Table 3.1. The measured mobility of 40 μM BSA and 100 μM warfarin are given in the first and the second rows of the Table. From Case (a) to Case (c) listed in the table, the concentration of free BSA in the buffer was kept at 40 μM, and the concentration of warfarin in the buffer was increased from 100 to 400 μM. As a result, when [L]o >> [P]o (in Case (c)), more warfarin remain unbound in the buffer, and the average mobility of warfarin, , ( )ep L Pμ  is mainly affected by the mobility of the free warfarin  71  (μep,L). Since the mobility of free BSA and the complex are similar, no obvious shift on the BSA peak is seen through Case (a) to Case (c) with the increasing amount of warfarin in the BGE. Therefore, the changes on the average mobility of warfarin were chosen for the use of determination of the binding parameter. Eq. 3.2 can be expressed as: , ( ) , , [ ] [ ] [ ] [ ] f b ep L P ep L ep C t t L L L L μ μ μ= +              (3.3) where [L]f, [L]b and [L]t are the free, bound, and total ligand concentration in the buffer. [L]t is known, and , ( )ep L Pμ  and ,ep Lμ  can be measured. For neutral ligands, ,ep Cμ  is approximately equal to , ( )ep P Lμ . This assumption is also valid for small drug molecules, because the mobility of the protein will be barely affected as drugs bound to the large protein molecules [13]. With eq. 3.3, [L]f can be calculated. The binding parameters and the exact number of binding sites can be estimated by the following approach: 1 1 [ ] [ ] [ ] 1 [ ] N n n f b n N nt n f n nK L LI P K L = = = = + ∑ ∑                   (3.4) where I is the average number of the ligand molecules bound per protein molecule, N is the maximum number of binding sites on each protein molecule, and K is the binding constant which is generally calculated as the product of the binding constants of each step [35].     72    Figure 3.1. Illustration of migration of the injection zone along the capillary and the formation of the negative peaks. (a) Small volume of neat buffer is injected into the capillary filled with pre-equilibrated mixture of BSA and warfarin. High background signal is caused by the presence of BSA and warfarin in the BGE. (b) When a voltage is applied to the capillary, BSA and the formed BSA-warfarin complex co-migrate with a higher mobility compared to free warfarin. The vacancy of the ligand migrates at the same velocity as the ligand, while the vacancy of the protein and the complex migrates at the same velocity of the protein and the complex, and the distance between the two vacancies increases after certain amount of time. (c) Once the mixture of free BSA and complex catch up with warfarin at the front edge of sample plug, the two zones with the deficiency of corresponding species are separated. The migration profile of each component along the capillary is given in (d).   73  time (min) 0.0 5.0 10.0 15.0 20.0 25.0 Ar ib itr ar y U ni t ( AU ) -200 -150 -100 -50 0 Experiment Simulation a b c 1 2 3 1 1 2 2 3 3   Figure 3.2. Comparison study of experimental and simulated electropherogram for CE- VACE method. The dash line indicates the experimental obtained electropherogram, and the simulated results are indicated by the solid line. Injection sample: 50 mM neat phosphate buffer. Injection time: 20 s. Separation voltage, 10 kV. BGE: 50 mM phosphate containing 40 μM BSA and various concentrations of warfarin. Case (a), 100 μM; Case (b), 200 μM; Case (c), 400 μM warfarin. Kb,total, 6.640 × 108 M-2. Peaks: (1) system peak; (2) vacancy of BSA and BSA-warfarin complex; (3) vacancy of warfarin.      74  Table 3.1. Experimental obtained results for Case (a), (b) and (c) where the concentration of the BSA is fixed, and the concentration of the warfarin is varied. The mobilities are calculated from the experimental electropherograms. The electrophoretic mobility of free BSA and warfarin are listed in the first and the second cases.  Concentration Mobility  Exp. No. of BSA [P]o (μΜ) of warfarin [L]o (μΜ) of BSA, , ( )ep P Lμ (× 104 cm2/V⋅s) of Warfarin, , ( )ep L Pμ (× 104 cm2/V⋅s) Mobility difference , ( )ep P Lμ  − , ( )ep L Pμ (cm2/V⋅s)  40 0 -1.4123 0 0  0 100 0 -1.8091 0 Case a  40 100 -1.4058 -1.7143 0.3085 Case b 40 200 -1.4036 -1.7653 0.3617 Case c 40 400 -1.4012 -1.7805 0.3793    The typical binding curve for BSA and warfarin interaction can be obtained using conventional ACE or other CE methods as investigated by Busch and co-workers [2]. In our study, the BSA concentration was kept constant at 40 μM and the warfarin concentrations used in the BGE were 50, 100, 150, 200, 250, 300 and 350 μM. Eq. 3.4 was used to estimate the binding constant with non-linear regression. The estimated overall binding constants was 6.640 × 108 M-2 for the two binding sites on each BSA molecules. As the experimental conditions vary, the shape and position of the vacancies for each corresponding component appeared on the elution profiles can be significantly different. Using SimDCCE, these experimental observations can be fully understood through detailed illustrations of migration behaviours of each components during the CE processes [36]. SimDCCE was built on the well-established mass balance equation [37-40]. More details of  75  the mathematical approach were discussed in our earlier publications [32, 33, 36, 41, 42]. The space increment (Δz) is set to 0.001 cm, and the time increment (Δt) is set to 0.001 s for all simulation runs to maintain fast and accurate simulation of the CE system [37, 41]. Each simulation run can be completed in a few minutes on a laptop computer (Intel Pentium Mobile 1.86 GHz, 1 GB RAM), which is faster than the real-time separation with a commercial CE instrument. Three experimental and simulated electropherograms are compared in Figure 3.2 (a)- (c). The similarities on the peak shape, peak area, and migration time for the corresponding components are shown in the figure. One of these three experimental conditions was selected to demonstrate the progression of the CE process. The capillary was filled with the BGE containing 40 μM BSA and 200 μM warfarin, and a plug of neat buffer was injected (Case (b)). The total binding constant is set to 6.640 × 108 M-2 (second order). The diffusion coefficients of BSA, warfarin, and complex were set to 1.0 × 10-5, 1.0 × 10-6 and 1.0 × 10-5 cm2s-1, respectively. Although the experimental measurements show that the UV absorbance of BSA and the complex is about 68 times higher than that of warfarin at 214 nm, the signal multiplier was set to 1 in Fig. 4 for all components to make this a general case. The VACE experiments can be categorized into four cases based on the relative mobilities of individual species. In each case, the relative migration behaviours of the species are different. Table 3.2 lists the detailed information for 13 possible scenarios from the four possible orders of migration. The initial concentration of the protein and ligand are denoted correspondingly as [P]o and [L]o. The computer program SimDCCE can display the changes in concentration vs. on-capillary position continuously in a graphic format. The typical peak  76  shapes at selected moment were recorded and exported as a series of snapshots to illustrate the migration process.  3.3.1 Case I, μep,P ≈ μep,C > μep,L The concentration-position profiles of free protein, free ligand, and the complex generated by SimDCCE depict the interaction and migration behaviours in VACE analysis. Because the mobilities of BSA, warfarin and the complex formed fit the mobility order described in Case I, this system is used to produce real experimental results to compare with the simulated ones. Initially, a plug of neat buffer (1.20 cm long), which will be referred to as the first negative peak throughout the discussion, is introduced into the capillary filled with a buffer containing pre-equilibrated mixture of P and L. When a +10 kV potential is applied across the capillary, P and C move ahead of L and enter the injected buffer plug (the frist negative peak) from the rear edge as shown in Figure 3.3 (a). Due to the lack of L, C dissociates into P and L toward a new equilibrium. As a result, the first negative peak is filled gradually, and a mild slope is formed on the back (left) side of the zone. On the front (right) side, the zone lacking of P and C moves forward at a faster speed, and eventually form the second negative peak (Figure 3.3 (b)). In the end, the two negative peaks are separated by a distance of over 13 cm (Figure 3.3 (c)). Through the entire migrating process, the front edge of the first negative peak remains sharp. The length of the first negative peak extends from 1.2 cm to 2.4 cm due to the complexation and diffusion processes. The concentration profiles are determined not only by the mobility order of the species, but also by the concentration of the species, and the differences between their mobilities. The effect of the latter two factors can be studied in four additional scenarios. The three steps ((a),  77  (b) and (c)) remain unchanged for scenario I-2 to I-5, however, the resulted peak shapes are different as seen in Figure 3.4.  1.0 1.5 2.0 2.5 C on ce nt ra tio n (M ) 0.0 4.0e-5 8.0e-5 1.2e-4 1.6e-4 2.0e-4 Protein Complex Ligand On capillary position (cm) 3.0 4.0 5.0 20.0 24.0 28.0 32.0 36.0 2.4 cm1.4 cm1.2 cm a b c 1.2 cm 1.0 cm 0.8 cm ep, P ep, C ep, LCase I: μ μ μ≈ >  Figure 3.3. Simulated concentration profiles for Case I, μep,P = μep,C > μep,L. The three curves are free protein (solid), free ligand (dashed), and complex (dotted). The concentration profiles recorded at different stages of a CE process are listed as a, b and c.    The influence of different [L]o is demonstrated through Scenario I-2 and I-3. The detailed conditions of these two scenarios are listed also in Table 3.2, and the comparison of the simulated electropherograms is given in Figure 3.4A.  In scenario I-2, [L]o is decreased from 200 μM to 100 μM, and all other conditions remain the same as that in scenario I-1. As described in eq. 3.1, , ( )ep L Pμ  is increased when significant amount of L is consumed in the complex formation, and , ( )ep L Pμ  will be significantly effected by ,ep Cμ . With a fixed [P]o, the area of the L trough is directly associated to the concentration of free L present in the BGE. As a result, a slightly smaller trough is observed in I-2 comparing to I-1.  78   In contrast, when [L]o increases from 200 μM to 600 μM in scenario I-3, [L]o >> [P]o and a large amount of ligand would remain unbound to generate a larger vacancy of free L. 16.0 18.0 20.0 22.0 24.0 26.0 28.0 30.0 32.0 34.0A u -50.0 -40.0 -30.0 -20.0 -10.0 0.0 Scenario I-1 Scenario I-2 Scenario I-3 Free P and C Free L 4A Time (min) 15.0 20.0 25.0 30.0 -15.0 -10.0 -5.0 0.0 Scenario I-1 Scenario I-4 Scenario I-5 4B Free P and C Free L Free L 20.12 min 30 .9 6 m in   Figure 3.4. (A) Simulated electropherograms for scenario I-1, I-2 and I-3. (B) Simulated electropherograms for scenario I-1, I-4 and I-5. In scenario I-1 and scenario I-4, the migration time of the free L is 30.96 min and 20.12 min, respectively.  79   Scenario I-4 and I-5 show the effects of the differences between three mobilities.  The [P]o, [L]o and other conditions are kept the same as those in scenario I-1, except for the differences between ,ep Lμ , ,ep Pμ  (or ,ep Cμ ). When ,ep Lμ  is increased from -2.20 × 10-4 cm2/V⋅s to -1.6 × 10-4 cm2/V⋅s (Scenario I-4), not only the migration time of free L is significantly decreased from 30.96 min to 20.12 min, but also the free L trough becomes narrower comparing to that in scenario I-1 due to the faster mobility of free L (Figure 3.4B).  In scenario I-5, when μep,P  and μep,C  are increased from -1.40 × 10-4 cm2/V⋅s to -0.80 × 10-4 cm2/V⋅s, a larger distance between the vacancy of free P and that of free L and a significant broadening on the vacancy of free L are observed when compared to I-4. It is obvious that the shape of the vacancy of the ligand can be affected by the mobility difference between the free protein and the ligand. Narrower trough can be resulted when the difference between ,ep Pμ  and ,ep Lμ is relative small.  .8 1.2 1.6 2.0 2.4 C on ce nt ra tio n (M ) 0.0 4.0e-5 8.0e-5 1.2e-4 1.6e-4 2.0e-4 On capillary position (cm) 4.0 5.0 6.0 24.0 28.0 32.0 1.2 cm 1.4 cm 2.3 cma b c 1.2 cm 0.5 cm 0.7 cm ep, P ep, C ep, LCase II: μ μ μ> > Protein Complex Ligand  Figure 3.5. Simulated concentration profiles for Case II, μep,P > μep,C > μep,L. The three curves are free protein (solid), free ligand (dashed), and complex (dotted). The concentration profiles recorded at different stages of a CE process are listed as a, b and c.  80  Time (min) 18.0 20.0 22.0 24.0 26.0 28.0 30.0 32.0 34.0 Au -50.0 -40.0 -30.0 -20.0 -10.0 0.0 Scenario II-1 Scenario II-2 Scenario II-3 Free P and C Free L  Figure 3.6. Simulated electropherograms for scenario II-1 to II-3.   3.3.2 Case II, μep,P > μep,C > μep,L  The concentration profiles of each species generated by SimDCCE are demonstrated in Figure 3.5. Although the electropherograms produced at the end are similar with characteristics of VACE, the detailed processes are quite different. The conditions of scenario II-1, as given in Table 3.2, are created to illustrate the analyte migration process of this case. Same amount of plain buffer plug was injected into the capillary. When the voltage was applied to the capillary, the species started to migrate toward the outlet. Initially, free P migrated toward the detector faster than C and L. As C and P enter the vacancy region from the back (left), because of the lack of free L, P and L dissociate from C as shown in Figure 3.5 (a). This process resulted in a mild slop at the back (left) side of the first negative peak. The  81  generated P in the vacancy keeps migrating forward. When unbound P catches up with free L at the front, complex formation occurs (Figure 3.5 (b)). In addition, due to the relatively faster movement of P and C, the zone lack of P and C is separated from the first negative peak, resulting in the appearance of the second negative peak. Because μep,P > μep,C, the second negative peak is no longer symmetrical. When the steady state is achieved, the final concentration profiles of each species are given in Figure 3.5 (c). Eventually, two negative peaks are generated and separated by a distance of over 7.0 cm. As described in Case I, the shape of the first negative peak remains as an unsymmetrical “V” shape through the entire process. The length of the first negative peak extends from 1.2 cm to 2.3 cm. The final simulation results are shown in Figure 3.6, scenario II-1.  Scenario II-2 and II-3 are studies on designed to study the effect of different [L]o and the mobility difference between three components. As listed in Table 3.2, low [L]o (100 μM) is used in scenario II-2. The lower concentration of L in the BGE solution decreases the amount of C formed in the pre-equilibrated buffer, which causes the observation of a smaller C trough on the final simulation results.  In Scenario II-3, a relative larger C trough is generated based on the relative higher [L]o (600 μM) used in the simulation. The different [L]o added to the buffer solution also effect the migration time of free L vacancy as illustrated in Case I. In scenario II-2 and II-3, μep,P and μep,C are changed to -0.80 × 10-4 cm2/V⋅s and -1.60 × 10-4 cm2/V⋅s, respectively, resulting an increased separation time between free P and L as demonstrated in Figure 3.6.     82  Table 3.2. Simulation conditions for 13 scenarios. [P]o and [L]o are the initial protein and drug concentrations, respectively, μep,P, μep,L and μep,C are the mobilities of free protein, free ligand and the complex. Mobility (× 10-4 cm2/V⋅s) Scenarios [P]o (μM) [L]o (μM)          μep,P       μep,L          μep,C I-1 40 200 -1.40 -2.20 -1.40 I-2 40 100 -1.40 -2.20 -1.40 I-3 40 600 -1.40 -2.20 -1.40 I-4 40 200 -1.40 -1.60 -1.40 I-5 40 200 -0.80 -2.20 -0.80 II-1 40 200 -1.40 -2.20 -1.80 II-2 40 100 -0.80 -2.20 -1.60 II-3 40 600 -0.80 -2.20 -1.60 III-1 40 200 -1.80 -2.20 -1.40 III-2 20 200 -1.80 -2.20 -1.40 III-3 20 100 -1.80 -2.20 -1.40 IV-1 40 200 -1.80 -1.40 -2.20 IV-2 40 200 -1.80 -0.80 -2.20    3.3.3 Case III, μep,C > μep,P > μep,L  This is one of two cases where the mobility of the free P is between the mobility of the free L and C. The condition for scenario III-1, III-2 and III-3 are also listed in Table 3.3. Relative to the movement of the free L, C enters the injected buffer zone from the left hand side of the zone, dissociates and generates more P and L (Figure 3.7 (a)). Because μep,C > μep,P, more C dissociates in free L vacancy zone (the first negative peak) and generates relatively larger amount of P. As depicted in Figure 3.7 (b), C starts forming as free P catches up free L  83  in the front, and keeps migrating forward. Similar to aforementioned cases, the generated second negative peak is separated from the first negative peak due to the different mobility of the species. Figure 3.7(c) gives the concentration profiles of the three components at the steady state. Through the entire migration process, the vacancy on free L profile remains a sharp front (right) and a mild slop on the back (left). The simulated results are given in Figure 3.8. The negative peak on the left is the vacancy of free P and C, and the bigger trough on the right is the vacancy of free L in the BGE at the steady state. 1.0 1.5 2.0 2.5 3.0 C on ce nt ra tio n (M ) 0.0 4.0e-5 8.0e-5 1.2e-4 1.6e-4 2.0e-4 On capillary position (cm) 3.0 4.0 5.0 6.0 7.0 20.0 24.0 28.0 32.0 36.0 1.2 cm 1.4 cm 2.2 cm cba 1.2 cm 1.4 cm 2.2 cm ep, C ep, P ep, LCase III: μ μ μ> > Protein Complex Ligand   Figure 3.7. Simulated concentration profiles for Case III, μep,C > μep,P > μep,L. The three curves are free protein (solid), free ligand (dashed), and complex (dotted). The concentration profiles recorded at different stages of a CE process are listed as a, b and c.    84  Time (min) 18.0 20.0 22.0 24.0 26.0 28.0 30.0 32.0 34.0 A u -16.0 -12.0 -8.0 -4.0 0.0 Scenario III-1 Scenario III-2 Scenario III-3 Free L Free P and C  Figure 3.8. Simulated electropherograms for scenario III-1 to III-3.   In scenario III-2, the only condition changed is [P]o, which is reduced from 40 μM to 20 μM. As free P present in BGE is much less, it is seen that the vacancy of free P is reduced to half comparing to III-1(Figure 3.8). On the other hand, the vacancy of free L trough is increased significantly as less amount of C dissociates in the first negative peak.  In scenario III-3, [P]o and [L]o are both reduced. [P]o is decreased from 40 μM to 20 μM, and [L]o present in the separation buffer is decreased to 100 μΜ. All other conditions remained the same as those in Scenario III-1. The same [P]o present in the BGE in Scenario III-2 and III-3 brings a similar P trough in both cases. A smaller L trough is observed in Scenario III-3 (Figure 3.8) due to the relative low [P]o (100 μΜ ).    85  3.3.4 Case IV, μep,L > μep,P > μep,C  In Case IV, the mobility order of the interacting species is completely opposite to that in Case III. The created condition of Case IV-1 is also listed in Table 3.2. Free L migrates ahead of free P and C. As the L vacancy catches up the free P and C at the front edge (right), due to the lack of L in the plug zone, C starts to dissociate into P and L to maintain the equilibrium in the buffer solution as demonstrated in Figure 3.9 (a). At this selected moment, the concentration of the formed complex, [C], decreased, [L] and [P] are increased gradually. In other words, the first negative peak is filled up gradually, and a mild slop is generated at the front edge (right). Since no change occurs at the back edge of the free L vacancy, a sharp edge remains. The complex formation takes place when free L meets the free P in the front (Figure 3.9 (b)). The collection of the final concentration profiles of P, L and C are listed in Figure 3.9 (c). Comparing to Case III, the observed order of the negative peaks is reversed, and the rear slop of the L vacancy becomes the front slope in Case IV due to the change on the mobility order. Therefore, the concentration profile of each component can be understood similar to Case III.     86  1.0 1.5 2.0 2.5 C on ce nt ra tio n (M ) 0.0 4.0e-5 8.0e-5 1.2e-4 1.6e-4 2.0e-4 On capillary position (cm) 3.0 4.0 5.0 6.0 20.0 24.0 28.0 32.0 1.2 cm 1.4 cm 2.2 cma b c 1.2 cm 1.4 cm 2.2 cm ep, L ep, P ep, CCase IV: μ μ μ> > Protein Complex Ligand  Figure 3.9. Simulated concentration profiles for Case IV, μep,L > μep,P > μep,C. The three curves are free protein (solid), free ligand (dashed), and complex (dotted). The concentration profiles recorded at different stages of a CE process are listed as a, b and c.  Time (min) 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0 28.0 30.0 32.0 34.0 A u -16.0 -12.0 -8.0 -4.0 0.0 Scenario IV-1 Scenario IV-2 Free P and C Free LFree L  Figure 3.10. Simulated electropherograms for scenario IV-1 and IV-2.   87   Scenario IV-2 illustrates the influence of the different mobilities of the three species. As listed in Table 3.2, in scenario IV-2, μep,L is altered from -1.40 × 10-4 cm2/V⋅s to -0.80 × 10- 4 cm2/V⋅s, other conditions remain the same as those in scenario IV-1. As depicted in Figure 3.10, the fast migration speed causes two major variations on the simulated electropherograms. One is the migration time of free L, and the other difference is the shoulder generated on the vacancy of free P and C.                   88  3.4 Conclusion  We have demonstrated the migration behaviour of each species, as well as the vacancy peaks of interacting molecules in VACE method based on the mass balance equation. With the SimDCCE simulation program, detailed separation and migration processes of each component inside the capillary become visible in a graphic format. Through the comparison of the experimental and simulated results for the interaction between BSA and warfarin in VACE analysis, reasonable accuracy and efficiency are obtained by the simulation program. 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[42]  Jouyban, A., Kenndler, E., Electrophoresis 2006, 27, 992-1005.        91                                         Chapter 4   Capillary Electrophoresis Frontal Analysis for Characterization of αvβ3 Integrin Binding Interactions*                   * A version of this chapter has been published. Sun, Y., Cressman, S, Fang, N., Cullis, P.R and Chen, D.D.Y. Capillary Electrophoresis Frontal Analysis for Characterization of Alpha-v Beta-3 Integrin Binding Interactions, Analytical Chemistry, 2008, 80(9), 3105-3111.   92 4.1 Introduction Binding affinity and interaction stoichiometry are essential characteristics for understanding biological processes. A variety of methods have been developed to characterize biomolecular interactions, such as equilibrium dialysis, ultrafiltration, ultracentrifugation, gel filtration, calorimetry, microdialysis, spectroscopy, high performance liquid chromatography (HPLC), surface plasmon resonance (SPR), and capillary electrophoresis (CE) [1-5]. CE has many advantages over other techniques, because of the relatively short analysis time, low sample consumption, ease of automation, and high separation efficiency. Integrins are a large family of heterodimeric integral membrane proteins that function to sense and respond to the extracellular environment [6].  High levels of αvβ3 integrin are expressed in vascular endothelial cells involved in pathological angiogenesis that supports tumour growth, making this class of integrin an attractive anti-cancer target [7, 8]. Studies have shown that arginine-glycine-aspartic-acid (RGD) containing peptides can compete with the natural ligands of αvβ3 integrins. Potent and specific αvβ3 antagonists have been discovered from NMR structural studies [9].  This has led to the development of Merck’s drug candidate, Cilengitide™ (cyclic arginine-glycine-aspartic-acid-d-phenylalanine- (N-methyl)-lysine (cRGDf[N(Me)]V)).  Second generation conjugates that are similar to Cilengitide™ have broadened the application of these ligands from just being integrin antagonists to drug delivery and tumour imaging agents [10, 11]. Despite extensive efforts towards finding integrin antagonists and the existence of high resolution structural data of the integrin, our understanding of the mechanisms that govern the integrin’s switch from an inactive to high-affinity active state is far from complete   93 [12].  In an effort to obtain further insight into the binding of RGD-peptides to the integrin, we used solubilized αvβ3 integrin and measured RGD binding using CE-FA. Currently, several CE methods are available to study the equilibrium and kinetic binding properties [13-18] such as normal affinity CE (ACE), Hummel-Dreyer method (HD), vacancy affinity CE (VACE), vacancy peak method (VP) and frontal analysis (CE-FA) [19- 21]. The most suitable method can be chosen based on the characteristics of the binding interaction, namely, the speed of the association/dissociation processes, the mobilities of the free species and the complex, each species’ ability to absorb UV light or emit laser induced fluorescence, and the availability of the interacting species. In ACE and VACE methods, measurable differences in electrophoretic mobilities between free ligand and the complex are required, and the measurements are based on the changes in electrophoretic mobility of free protein or ligand due to complex formation [18, 21-23].  In HD and VP methods, the mobilities of free protein and the complex have to be similar, and the measurements are mainly based on the changes of the free ligand concentration. The method chosen for use in this study is CE-FA. In CE-FA, a relatively large amount (~ 100 nL) of pre-equilibrated mixture of protein and ligand is injected into the capillary filled with background electrolyte (BGE). The injection of a large volume of sample plug leads to the appearance of plateaus in the observed electropherogram. Partial separation of the binding species can be achieved based on the differences in their mobilities. The compound with a unique mobility in the capillary is separated from the mixture plateau to form another plateau. In the study of protein and ligand interaction, the mobility of the free ligand is usually different from the protein and the protein-ligand complex. The height of the   94 plateau is directly related to the concentration of corresponding species, therefore, the binding parameters can be determined by comparing the heights of the plateaus. Different data analysis methods have been utilized to estimate binding parameters in CE [22]. With the papers published to date, a complex equilibrium model based on Scatchard analysis has been the most commonly used in CE-FA [24]. According to the assumptions used in this approach, binding parameters can be obtained in cases where the binding stoichiometry is 1:1, and where non-cooperative binding occurs on multiple identical binding sites. However, there are many other cases relevant to biomolecules that do not fit the interaction model described [25]. Specific binding and non-specific binding often co-exist in protein-ligand interactions, and methods need to be developed to differentiate the different types of binding because, in many occasions, only specific bindings trigger the cascade of biochemical processes. In this study, we have found new information about the binding of cRGDfK-448 to the αvβ3 integrin as measured by the CE-FA method. This behavior was characterized by a set of refined equations for determining the parameters of higher order binding.            95 4.2 Theory Currently, the most often used approach to determining the binding characteristics for interactions with higher order stoichiometry is to evaluate the changes of a physical parameter of the system with a Scatchard Plot [4]. For a Scatchard Plot to provide meaningful information, certain conditions have to be satisfied. The ligand should have only one active site, and the multiple binding sites on the protein should be identical, distinguishable, and independent. However, in practice, these conditions may not be easily met. Specific binding events often differ from non-specific ones, and the binding of the first ligand often affects the second binding, favorably or adversely, depending on the function of the protein. To properly address these properties, the following equations are derived and used to process the data used in this work. 4.2.1 Single binding stoichiometry  As the binding of the species (protein-ligand) occurs with a 1:1 stoichiometry, the equilibrium is given by:                                                                                      (4.1)  [ ] [ ][ ]b PLK P L =                                                                                                (4.2)  where [P], [L] and [PL] are the concentrations of the protein, the ligand and the protein-ligand complex, respectively. The binding constant, Kb, is given by eq. 4.2. The fraction of the protein bound, fb,P, is an important factor that can be used to determine the affinity between the protein and the ligand: , [ ] [ ] [ ] [ ] [ ] b b P t f P PLf P P PL = = +                         (4.3) P + L PL   96 The subscripts b, f, and t denote bound, free, and total concentrations of corresponding species in the solution, respectively. In CE-FA, the injected sample plug contains pre-equilibrated protein and ligand. The total concentration of protein present in the sample mixture, [P]t, is kept constant, and the total ligand concentration, [L]t, is varied in each CE process. As species start to migrate through the capillary under a high voltage, the free ligand molecules are partially separated from the protein and the protein-ligand complex. As shown in Figure 4.1A, the free ligand concentration can be calculated by using a common calibration curve, obtained by injecting samples containing only the ligand. The calculated [L]f can be used to estimate the binding parameters. In CE-FA, [P]b is always hard to measure because the mobilities of free protein and protein-ligand complex are often very close. Therefore, the average number of ligand molecules bound per protein molecule, I, is introduced as [L]b/[P]t base on the relation of [P]b and [L]b in different interaction stoichiometries. For a 1:1 binding, I is defined as [ ][ ] [ ] [ ] [ ] [ ] 1 [ ] b fb t f b f K LL PLI P P PL K L = = =+ +                                    (4.4) With a plot of [L]b/[P]t vs. [L]f, the binding constant, Kb, can be determined by a non-linear curve fit.    97  Figure 4.1. Ideal and experimental CE-FA profiles. (A) Ideal electropherograms from a set of CE frontal analysis experiments. The height of the rectangular signal is directly related to the concentration of corresponding species. The solid curve (a) is for sample containing ligand only, and the dash curve (b) represents the sample containing pre-equilibrated mixture of protein and ligand. When a portion of the ligand was used to form the complex in the pre- equilibrated sample plug, the height of plateau resulted from the unbound peptide, [L]f, decreases. The increased migration time of the free peptide is caused by the reduced electroosmotic flow when a large plug of protein and ligand mixture is present during CE process. (B) The plateau height (dash-dot curve) is resulted from a free cRGDfK-488 peptide plug at 2.40 µM with a 90 s injection under a pressure of 0.5 psi. The other two curves resulted from the injection of the pre-equilibrated mixture of integrin (0.295 µM) and peptide (2.40 µM) but with different injection time: 90 s (solid) and 50 s (dash).   98 4.2.2 Higher order binding stoichiometry  Specific binding of small molecules to macromolecules, such as enzymes and other proteins, poly-nucleic acids, and synthetic polymers, is an important area that often requires consideration of multiple binding sites [26]. Scatchard plots (I vs. [L]f) have been used to process data obtained in several CE methods, such as CE-FA, HD, and VP [23, 27, 28]. Because the assumptions used in the Scatchard method are often not valid for biological molecules, a more general model should be developed. For a 1:2 interaction, eq. 4.1 and eq. 4.2 can be used to describe the first binding step, with Kb1, replacing Kb as the binding constant. The following steps can be expressed as the following:                                                    (4.5) 2 2 [ ] [ ][ ]b f PLK PL L =               (4.6) and                                                        (4.7) 1 [ ] [ ][ ] n bn n f PLK PL L− =               (4.8) The overall binding constant, K, is generally calculated as the product of binding constants of each step: 1 2 1 [ ] [ ] [ ] N n bn b b bn n n f f PLK K K K K P L= = = ⋅ ⋅⋅ ⋅ =∏                                        (4.9) In this study, we will focus on the specific interaction with a small number of binding sites (i.e., n = 2 and/or 3), which is common for binding of macromolecules in real biological systems. For a protein-ligand binding with 1:2 or 1:3 stoichiometry, inserting [PL], [PL2] and [PL3] into eq. 4.9, the I value for 1:2 binding is obtained from: PL + L PL2 PLn-1 + L PLn   99 2 1 1 22 2 2 1 1 2 [ ] 2 [ ][ ] [ ] 2[ ] [ ] [ ] [ ] [ ] 1 [ ] [ ] b f b b fb t f b f b b f K L K K LL PL PLI P P PL PL K L K K L ++= = =+ + + +                        (4.10) and the I value for 1:3 binding is obtained from: 2 3 2 3 2 3 1 1 2 1 2 3 2 3 1 1 2 1 2 3 [ ] [ ] 2[ ] 3[ ] [ ] [ ] [ ] [ ] [ ] [ ] 2 [ ] 3 [ ]  1 [ ] [ ] [ ] b t f b f b b f b b b f b f b b f b b b f L PL PL PLI P P PL PL PL K L K K L K K K L K L K K L K K K L + += = + + + + += + + +                               (4.11) For the case of multiple types of binding sites, the overall I can be defined as: 1 m t i i I I = =∑                                                                                       (4.12) Most commonly, i is 1 or 2 as reported in the literature. If non-specific binding also exists, I is the sum of Ispecific and Inon-specific, and eq. 4.4, 4.10 and 4.11 still describe the specific binding process, if the non-specific binding can be accounted for. Thus, the appropriate isotherm describing higher order equilibrium for each type of sites is generalized: 1 1 [ ] 1 [ ] N n n f n N n n f n nK L I K L = = = + ∑ ∑                                                                            (4.13) Most of the parameters in eq. 4.13 are defined earlier, except for N, which is the maximum number of binding sites available on each protein molecule. The individual binding constant for each step, Kbn, can be determined by plotting [L]b/[P]t vs. the free ligand concentration, [L]f, and the number of binding sites can be determined by fitting the experimental results with the nth order equation, such as eq. 4.10, 4.11 and 4.13. It should be noted that the unit of the binding constant obtained from Scatchard Plots is always in M-1, forcing all multiple bindings to a pseudo 1:1 stoichiometry. The overall binding constant obtained by eq. 4.4, 4.10 and 4.11 have units of M-1, M-2, or M-3, depending on the overall stoichiometry. Strictly   100 speaking the binding constants are unitless. The units are used in this work only to follow the conventions practiced in most current literature. There are also cases where the concentration of ligand present in the BGE is much greater than that of protein in BGE ([L]t >> [P]t), in which case the binding sites on the protein molecules are saturated, and the concentration of the unsaturated species ([PL], [PL2], …, [PLn-1]) are negligible. Eq. 4.13 can be simplified in these situations as the following: [ ] 1 [ ] n n f n n f nK L I K L = +                                                                                            (4.14) Due to the similarities of the CE techniques, these equations can be also applied to Hummel-Dreyer (HD) and vacancy peak (VP) methods for the determination of binding parameters in either cooperative or non-cooperative multiple-site protein-ligand interactions [21].              101 4.3 Experimental Section 4.3.1 Peptide synthesis All peptides were made on 2-Cl2trt resin (EMD Biosciences, San Diego, CA), using 9- fluorenylmethyloxycarbonyl (FMOC) strategy solid phase peptide synthesis. O- Benzotriazole-N,N,N’,N’-tetramethyl-uronium-hexafluoro-phosphate (HBTU) (Advanced Chemtech, Louisville, KT) and N-hydroxybenzotriazole (HOBT) (Advanced Chemtech, Louisville, KT) activating agents were used and the pH was adjusted with triethylamine (TEA) (Aldrich Milwaukee, WI). All solvent were from Fisher Scientific (Nepean, ON, Canada). Linear peptides were cleaved in a solution of 0.1% TFA (Aldrich, Milwaukee, WI)/DCM with triisopropyl silane (TIS) (Adrich, Milwaukee, WI) and H2O scavengers. Lyophilized linear peptides were cyclised at a concentration of 0.5 mM in dimethylformamide (DMF) using benzotriazol-1-yl-oxytripyrrolidinophosphonium hexafluorophosphate (PyBop) (Aldrich, Milwaukee, WI) and HOBT activating agent, activated in situ with TEA. Cyclisation yields were typically over 95% and occurred within thirty minutes as indicated by an increase in retention to C18 when analyzed by Reverse Phase High Performance Liquid Chromatography (HLPC). Electrospray Ionization-Mass Spectroscopy (ESI-MS) data showed a loss of one water molecule providing evidence of head-to-tail cyclisation. 1H NMR assignments for all amide bonds confirmed a cyclic compound. Selective deprotection of lysine side chain amines was achieved by hydrogenation with a Pd/C catalyst under normal pressure. Conjugation to the Alexa Fluor-488 pre-formed PFP ester (Invitrogen, Burlington, Ontario Cat. No., A-30005) was performed in mildly basic conditions, and purified by RP HPLC on a C18 semi-prep column (Vydac, 214TP510) with a gradient of 0 – 65% aqueous   102 acetonitrile containing 0.1% TFA. Deprotection of the final peptide was done using a solution of 95% TFA, 2.5% TRIS, 2.5% H2O and purified by RP HPLC using the same gradient as for the protected and labeled peptide. The final product was eluted from a C18 semi-prep column at 21% aqueous acetonitrile for both cRADfK-488 and cRGDfK-488. All peptides were used with > 95% purity, as justified by analytical HPLC and CE. Product identification was validated by ESI-MS. Peptides were lyophilized, weighed, and a standard curve for peptide quantification was established using HPLC peak areas. 4.3.2 Chemicals and solutions Purified human integrin αvβ3 in 20 mM Tris-HCl, pH 7.5, 150 mM NaCl, 2 mM MgCl2, and 0.2% Triton X-100 was purchased from Chemicon International (Temecula, CA), catalog #CC1019. The initial concentration was 210 µg⋅mL-1. Integrin αvβ3 was aliquoted into portions of 10 µL, and stored at -80 ºC. For each CE-FA experiment, the integrin was used at a concentration of 0.295 μM.  The same buffer solution was prepared and used as the background electrolyte (BGE) throughout the CE experiments. The following chemicals were used in buffer preparation: trizma base (T-8404, Sigma-Aldrich, St. Louis, MO), sodium chloride (37,886-0, Aldrich, Milwaukee, WI), magnesium chloride (Fisher Scientific, Fair Lawn, NJ), triton X-100 (T- 9284, SigmaUltra, St. Louis, MO), and hydrochloric acid (Fisher Scientific, Nepean, ON, Canada).  Purified peptides were re-dissolved in the aforementioned BGE at 36.03 μM, and then diluted to required concentrations.     103 4.3.3 CE Conditions and procedures  The experiments were performed on a Beckman Coulter P/ACE Glycoprotein System (Beckman Coulter Inc., Fullerton, CA) with a laser induced fluorescence (LIF) detector (488 nm excitation and 520 nm emission). Uncoated fused-silica capillary (Polymicro Technologies, Phoenix, AZ) was used with inner diameter of 50 μm, outer diameter of 360 μm, and length of 50 cm. The capillary length from the injection end to the detector (effective length) was 40.2 cm. Prior to use, the new capillary was rinsed with 1 M NaOH (30 min), methanol (30 min), purified water (30 min), and finally the separation BGE (30 min), and was conditioned with the BGE overnight. At the beginning of each run, the capillary was rinsed with 1 M NaOH (5 min), followed by methanol (5 min) and then with water (5 min) and with the BGE (8 min). The capillary temperature was maintained at 25°C. A voltage of +10 kV (anode is on the inlet side) was applied for CE runs. All experimental electropherograms were exported as ASCII files, and then plotted with SigmaPlot 10.0 (Systat Software Inc., Richmond, CA). The calibration curve of fluorescence signal vs. Alexa Fluor-488 labeled peptide concentration was first constructed. The initial peptide solution (36.03 μM) was diluted to 24.02, 4.80, 2.40, 1.20, 0.48, 0.24, 0.12, 0.08 µM. To construct the calibration curve, a relative long plug of one of the diluted peptide solutions was injected under a pressure of 0.5 psi (3447 Pa) for 90 s. Then a voltage of +10 kV was applied across the entire capillary, and the fluorescence signals were recorded. Each peptide solution was tested at least three times to minimize the instrumental errors. Proper amounts of the peptide solution and the BGE were added into one aliquot of integrin solution (10 μL), and then mixed thoroughly but gently. The mixture was placed into   104 the sample tray of the CE instrument, and the temperature was maintained at 37 ºC for one hour. The pre-equilibrated mixture of integrin and peptide was injected into a neat-BGE-filled capillary under a pressure of 0.5 psi (3447 Pa) for 50 s to 90 s, and then a voltage of +10 kV was applied when both inlet and outlet vials contained the BGE.                105 4.4 Results and Discussion 4.4.1 CE frontal analysis  A good linear relationship was obtained for fluorescence signals and peptide concentrations, as proved by the R-square value (> 0.999). The calibration curve is used to determine peptide concentrations from fluorescence signals. No signal for αvβ3 was recorded with LIF detection since the integrin is not fluorescently labeled. A schematic illustration of the CE-FA signal and a set of real electropherograms generated from CE-FA experiments are given in Figure 4.1A and 4.1B, respectively. Figure 4.1A depicts the ideal signals from the free or bound peptide measured from electropherograms. Due to the amount of complex formed in the pre-equilibrated sample, the concentration of free peptide, [L]f, decreases, and the height of the free peptide plateau also decreases compared to the plateau obtained for the sample containing peptide only. In Figure 4.1B, the higher narrow plateau (dash-dot curve) was generated from a sample containing cRGDfK-488 (2.40 μM) only. The electropherograms shown with lower and broader plateaus (solid curve and short-dash curve) in the figure were obtained from the separation of the pre- equilibrated mixture of αvβ3 integrin and cRGDfK-488. The two CE-FA curves containing broader plateaus have similar plateaus on the right side, generated by the free peptide from the mixture. With a longer plug length (90 s injection), a significant amount of complex still existed in the plug at the end of the run, giving rise to a peak on the left side. When a shorter plug length (50 s injection) was used, almost all of the complex in the mixture was dissociated during the migration, resulting in a slope on the left. The obtained electropherogram also shows that the complex migrates at nearly the same velocity as the free (unbound) αvβ3, but   106 faster than the free peptide. In addition, as depicted in Figure 4.1B, a fairly fast dissociation rate of the αvβ3-peptide complex is observed.  4.4.2 Binding parameters To determine specific binding of cRGDfK-488 to human integrin αvβ3, another cyclic peptide, cRADfK-488, which is known to have no specific affinity to αvβ3, was used as a negative control. The alanine side chain of RAD in place of glycine in RGD diminishes the antagonistic ability while retaining non-specific interactions of the peptide with the integrin [29].  It is important to note that it is necessary to have a ligand with similar structure but without the specific binding affinity as a control in order to differentiate specific binding from non-specific binding.  For nonspecific binding the [L]b/[P]t increases linearly with [L]f. When the curve of [L]b/[P]t vs. [L]f of another ligand shows characteristics of a rectangular hyperbola in the linear concentration range of the non-specific binding ligand, it is a result of specific binding.  The binding isotherms of cRGDfK-488 to the integrin αvβ3 and the non- specific binding of cRADfK-488 are shown in Figure 4.2. To only account for the specific binding, Ispecific for cRGDfK-488 was calculated using the difference between the number of cRGDfK-488 bound per integrin and that of cRADfK-488, and [L]f is taken from [L]t - [L]b. This assumption is only valid if the Inon-specific for cRGDfK-488 is similar to Inon-specific for cRADfK-488.   107 [L]f (M) 0.0 5.0e-6 1.0e-5 1.5e-5 2.0e-5 2.5e-5 [L ] b/ [P ] t 0.0 2.0 4.0 6.0 8.0 cRGDfK-488 cRADfK-488   Figure 4.2. Binding isotherms of cRGDfK-488 and cRADfK-488 to αvβ3 integrin. Closed circles represent total binding of cRGDfK-488.  Open circles represent the linear non-specific binding of cRADfk-488 to the same amount of αvβ3.    A series of comparison studies were done as various interaction stoichiometries were assumed, and the binding isotherms constructed for integrin-RGD interaction are demonstrated in Figure 4.3. Eq. 4.13 was used to fit 1:1, 1:2 and 1:3 binding isotherms of protein-ligand interaction. Binding isotherm (a) (dash-dot line) in Figure 4.3 is generated with an assumed 1:1 protein-ligand stoichiometry. The curve only fits the data points where the concentration of ligand in the buffer is low, because 1:1 interaction is dominant in these   108 conditions. However, values higher than 1 for I at higher ligand concentrations suggest that higher order interactions become important at higher ligand concentrations. Curve (b) (the solid line) is fitted with eq. 4.10 when assuming two different binding sites present on each αvβ3 integrin molecule. The information provided by non-linear regression suggests that, during CE process, two different binding sites on each αvβ3 integrin molecule can be detected with different affinities. The estimated binding constants for the two sites, Kb1 and Kb2, are 2.1 × 105 M-1 and 1.3 × 106 M-1, respectively. The two sites on the αvβ3 molecules are saturated gradually as ligand concentration in the sample mixture increases in free solution. It is obvious that the equation considering step by step two-site binding better describes the experimental data for the interaction of αvβ3 integrin and cRGDfK-488. To further confirm the binding stoichiometry of the system, the data is also fitted with a 1:3 binding stoichiometry. With eq. 4.11, the generated isotherm (c) (the short dash line) presented in Figure 4.3 gives a similar fitting as curve (b); The estimated binding constants for the three sites are 2.4 × 105 M-1, 1.1 × 105 M-1 and 2.3 × 103 M-1, respectively. Because the third binding constant is two orders of magnitude lower than the first two, it can be attributed to the slightly increased non-specific binding at higher ligand concentrations.  Therefore, it is concluded that the affinities of the two specific binding sites to the ligand are similar, reflected by the similar values of the binding constants for the first and the second steps.   In theory CE-FA can be used for characterizing interactions with both strong and weak interactions, and is not particularly limited by fast and slow kinetics.  It is required, however, that the mobility of the complex has to be similar to either the mobility of the free protein or the free ligand to avoid significant errors in the obtained constants. In addition, because it can   109 be difficult to differentiate the boundaries between the frontal zones of the complex and the ligands when the binding constant is below 103 M-1, ACE may be a better method for characterizing those interactions [22, 24]. Because Figure 4.3 only shows the maximum number of bound ligands to be smaller than 2, and the value for Kb3 is rather small, the error on Kb3 has to be ration large.  [L]f (M) 0.0 5.0e-6 1.0e-5 1.5e-5 2.0e-5 [L ] b / [ P ] t  0.0 .5 1.0 1.5 2.0 One-site Two-site Three-site c a b   Figure 4.3. Specific binding isotherms of cRGDfK-488 to αvβ3 integrin. The open squares represent the specific response of cRGDfK-488. Different stoichiometries are fitted based on the experimental obtained data for (a) 1:1, (b) 1:2 and (c) 1:3 binding interactions.        110 These binding constants are in accordance with the apparent specific affinity (Kd) of cRGDfK-488 to αvβ3 integrins on the cell surface, which was calculated to be 0.2 μM [30]. Because of the complexity of the cellular activities that account for this binding, it is difficult to assign stoichiometry constants using cell-based assays, while CE-based assays simplify the system to only account for the effect of binding. It was also found in the cell-based assays that non-specific effects by the RAD-containing peptide did not stimulate endocytosis while the RGD peptide did. Although it is not currently possible to explain the entire binding mechanism of this pair of reactions, the shape of the electropherograms can be explained by using our simulation program [31]. To understand the interaction process of the species during electrophoresis process, a dynamic complexation capillary electrophoresis simulation program (SimDCCE) is used to study the migration of the species in a graphic format during the CE process [31]. The electrophoretic mobility of free RGD (μep, L) was determined by the following procedure: the capillary was first filled with plain buffer, then a small plug of RGD was injected for 3 s at 0.5 psi, and finally the migration time of the sample plug was measured while a voltage of 10 kV was applied across the capillary. This procedure was repeated 10 times on different days to include the instrumental and other errors, and the average free mobility was determined for cRGDfK-488. The measured average electrophoretic mobility was 2.441 ± 0.003 × 10-4 cm-2V-1s-1. The mobilities of the αvβ3 integrin and integrin-RGD complex are not measurable; however, they can be estimated by using the SimDCCE model. The mobilities of the integrin and complex are similar but greater than μep, L. Four snapshots taken from a CE-FA simulation run at selected moments were exported and analyzed in Figure 4.4 to demonstrate the interaction and concentration changes   111 of each species during CE process. A relatively large volume of pre-equilibrated mixture of 0.297 μM αvβ3 integrin and 2.40 μM RGD in the buffer was introduced into the capillary filled with neat buffer in the simulation program. As demonstrated in Figure 4.4A, the injected pre-equilibrated sample mixture plug is 6.4 cm, which contains 1.893 × 10-7 μM integrin-cRGDfK-488 complex formed during pre-equilibrium and remaining free αvβ3 integrin and peptide. Due to the mobility order of species (μep, P ≈ μC > μep, L), integrin and complex move ahead of RGD and exit the sample plug from the front edge (Figure 4.4B). To maintain the equilibrium condition in the buffer solution, more cRGDfK-488 and integrin are dissociated from the complex when the complex migrates through the cRGDfK-488 plug. As the species migrate along the capillary, they are further separated and the amount of free peptide and integrin dissociated from the complex increase as indicated in Figure 4.4C. Eventually, the concentrations of each species no longer change, and a steady state condition is established throughout the capillary. Due to the mobility difference of the species and diffusion effects, the length of the sample plug increases to 15.1 cm. The final concentration profiles are shown in Figure 4.4D. With SimDCCE, the final simulation result is generated as the summation of the concentration profiles of each species. With the consideration of different fluorescence intensities for each species, the simulated and experimental electropherograms for one of the CE-FA runs are compared in Figure 4.5. The experimental electropherogram is displayed as it is obtained, and the simulated electropherogram has been converted so that the height of the plateau matches the height of the experimental peak. The experimental and simulated migration profiles and the areas of the plateau are similar.   112 4.0 6.0 8.0 10.0 12.0 0.0 .5 1.0 1.5 2.0 On-capillary distance (cm) 20.0 24.0 28.0 C on ce nt ra tio n (μM ) 0.0 .5 1.0 1.5 2.0 28.0 32.0 36.0 40.0 0.0 .5 1.0 1.5 2.0 0.0 2.0 4.0 6.0 0.0 .5 1.0 1.5 2.0 Integrin αvβ3 Complex fRGDcK-448 A B C D 6.4 cm 15.1 cm   Figure 4.4. Simulated concentration profiles for CE-FA. Injected sample: pre-equilibrated mixture of 0.297 μM integrin αvβ3 and 2.402 μM RGD in the buffer. Injection time: 90 s. Separation voltage: 10 kV. Kb,total = 2.629 × 1011 M-2.  The concentration profiles of the three species are displayed in time sequence: (A) 4.0 s; (B) 100.0 s; (C) 400.0 s; (D) 755.0 s. Detailed discussions can be found in the text.   113   Figure 4.5. Comparison of the experimental result (solid line, a) with the simulation result (short dash line, b) for one of the CE-FA runs. BGE: freshly prepared buffer pH 7.5. Injected sample: 0.297 μM integrin αvβ3 and 2.402 μM RGD in the buffer. Injection time:  90 s. Separation voltage: 10 kV. Kb,,total =  2.629 × 1011 M-2. The injection time for the simulation is adjusted to account for the parabolic flow profile at the front of the real injection plug generated during the pressure injection.              114 4.5 Conclusions Our CE-FA studies propose for the first time that the specific binding of human integrin αvβ3 to cRGDfK-488 is a 1:2 interaction. Several existing studies have demonstrated that the binding process between integrins and RGD ligands is complex. For example, studies on the association of the natural α5β1 ligand, fibronectin, suggest that a synergy site exists to facilitate binding to the RGD site [32]. It has also been shown that initial RGD-ligand binding causes a major change in the integrin’s structure in order to form a high affinity complex [33]. The existence of another binding site may also help to explain why multivalent RGD-containing imaging agents are more effective at binding to their cell target than monovalent RGD-containing agents [11, 34].  CE provides a unique advantage for the study of membrane proteins which are inherently difficult to solubilize without disturbing the protein’s tertiary structure. It is of interest to overcome these handling problems since the most accessible targets for intravenous drug delivery reside at the surface of a cell. Perhaps more importantly, we demonstrated a new approach to processing data obtained from one of the simplest CE method, CE-FA, to deduce important binding characteristics of biomolecules. To understand the binding of membrane proteins with complex biological behavior, non-perturbing analytical methods such as CE-FA may prove to be increasingly useful.           115 4.6 References [1] Bertucci, C., Domenici, E., Curr. Med. Chem. 2002, 9, 1463-1481. [2] Sebille, B., Zini, R., Madjar, C. V., Thuaud, N., Tillement, J. P., J. Chromatogr.-Biomed. Appl. 1990, 531, 51-77. [3] Harding, S. E., Chowdhry, B. Z., Protein-Ligand Interactions: Hydrodynamics and Colorimetry, oxford University Press, oxford 2001. [4] Connors, K. A., Binding Constant. The Measurement of Molecular Complex Stability, John Wiley & Sons, New York 1987. [5] Oravcova, J., Bohs, B., Lindner, W., J. Chromatogr. B-Biomed. Appl. 1996, 677, 1-28. [6] Giancotti, F. G., Ruoslahti, E., Science 1999, 285, 1028-1032. [7] Brooks, P. C., Clark, R. A. F., Cheresh, D. A., Science 1994, 264, 569-571. [8] Folkman, J., J Natl Cancer Inst 1990, 82, 4-6. [9] Dechantsreiter, M. A., Planker, E., Matha, B., Lohof, E., et al., J Med Chem 1999, 42, 3033-3040. [10] Beer, A. J., Haubner, R., Sarbia, M., Goebel, M., et al., Clin Cancer Res 2006, 12, 3942- 3949. [11] Wu, Y., Cai, W., Chen, X., Mol Imaging Biol 2006. [12] Puklin-Faucher, E., Gao, M., Schulten, K., Vogel, V., J Cell Biol 2006, 175, 349-360. [13] Rundlett, K. L., Armstrong, D. W., Electrophoresis 1997, 18, 2194-2202. [14] Rundlett, K. L., Armstrong, D. W., Electrophoresis 2001, 22, 1419-1427. [15] Petrov, A., Okhonin, V., Berezovski, M., Krylov, S. N., J. Am. Chem. Soc. 2005, 127, 17104-17110. [16] Galbusera, C., Chen, D. D. Y., Curr. Opin. Biotechnol. 2003, 14, 126-130. [17] Heegaard, N. H. H., Nissen, M. H., Chen, D. D. Y., Electrophoresis 2002, 23, 815-822. [18] Busch, M. H. A., Kraak, J. C., Poppe, H., J. Chromatogr. A 1997, 777, 329-353. [19] Kraak, J. C., Busch, S., Poppe, H., Journal of Chromatography 1992, 608, 257-264. [20] Busch, M. H. A., Boelens, H. F. M., Kraak, J. C., Poppe, H., J. Chromatogr. A 1997, 775, 313-326. [21] Busch, M. H. A., Carels, L. B., Boelens, H. F. M., Kraak, J. C., Poppe, H., J. Chromatogr. A 1997, 777, 311-328. [22] Tanaka, Y., Terabe, S., J. Chromatogr. B 2002, 768, 81-92. [23] Rundlett, K. L., Armstrong, D. W., Electrophoresis 2001, 22, 1419-1427. [24] Ostergaard, J., Heegaard, N. H. H., Electrophoresis 2003, 24, 2903-2913. [25] Bowser, M. T., Chen, D. D. Y., Anal. Chem. 1998, 70, 3261-3270. [26] Scatchard, G., Ann, N. Y., Acad. Sci. 1949, 51. [27] Fanali, S., J. Chromatogr. A 1997, 792, 227-267. [28] Colton, I. J., Carbeck, J. D., Rao, J., Whitesides, G. M., Electrophoresis 1998, 19, 367- 382. [29] Pfaff, M., Tangemann, K., Muller, B., Gurrath, M., et al., J. Biol. Chem. 1994, 269, 20233-20238. [30] Cressman, S., Sun, Y., Maxwell, E. J., Chen, D. D. Y., Cullis, P. R., Unpublished Work. [31] Fang, N., Chen, D. D. Y., Anal. Chem. 2005, 77, 840-847. [32] Takagi, J., Strokovich, K., Springer, T. A., Walz, T., Embo J 2003, 22, 4607-4615. [33] Mould, A. P., Barton, S. J., Askari, J. A., McEwan, P. A., et al., J Biol Chem 2003, 278, 17028-17035.   116 [34] Montet, X., Funovics, M., Montet-Abou, K., Weissleder, R., Josephson, L., J Med Chem 2006, 49, 6087-6093.      117                                          Chapter 5   Characterization of Epidermal Growth Factor Receptor Binding with Antibody by Capillary Electrophoresis-Frontal Analysis*              * A version of this chapter has been accepted by a company as a collaborative research project report. Sun, Y., Chen, D.D.Y. Characterization of Epidermal Growth Factor Receptor binding with antibody by Capillary Electrophoresis Frontal Analysis, 2008.   118 5.1 Introduction  The study on the specific interactions between species has become one of the major focuses in chemical and biochemical research. Parameters describing binding interactions and interaction stoichiometries are essential for translation of experimental data into an understanding of how biological systems work. A variety of different approaches have been developed to quantify molecular interactions [1, 2].  Among the available CE methods, capillary electrophoresis-frontal analysis (CE-FA) is the most commonly used for determination of unbound ligand concentration in protein binding equilibrium [3]. Ligand-induced signaling from receptor tyrosine kinases (RTKs) of the epidermal growth factor receptor (EGFR) family regulates many cellular processes, including proliferation, cell motility, and differentiation [4]. Recent studies show that perturbations in these cellular signals can lead to malignant transformation, and the EGFR pathway appears to play an important role in the development of a wide range of epithelial cancers, including those of the breast, colon, kidney, lung, pancreas, etc. According to finding from the early 1980s, EGFR signaling and cellular proliferation could be blocked by antibodies that interact with the extracellular region of the receptor and prevent the binding of activating ligands, such as EGF and other transforming growth factors [4]. Shiqi and co-workers illustrated the possible mechanism of EGFR activation and proposed that the antigen binding partially occlude the ligand binding region on this domain and sterically prevent the receptor from adopting the extending conformation required for EGFR activation. In Shiqi’s work, SPR was employed to study the inhibition of EGFR by antibodies. However, binding of EGFR to the sensor surface might sterically hinder the active sites on EGFR. In this work, to further clarify   119 the actual interaction process, the binding of EGFR with a fully human monoclonal antibody was evaluated in free solution through capillary electrophoresis.                      120 5.2 Experimental Section 5.2.1 Instrumentation All CE experiments were performed using a Beckman P/ACE MDQ capillary electrophoresis instrument (Beckman Coulter Inc., Fullerton, CA) with a built-in photodiode array (PDA) detector.  Uncoated fused-silica capillary (50 cm total length, 40.2 cm length to detector, 50 μm inner diameter, 360 μm outer diameter) (Polymicro Technologies, Phoenix, AZ) was used as a separation capillary. The capillary cassette temperature was set at 25.0 oC and the CE voltage at +20 kV. PDA detection was performed in the range 190 nm to 400 nm for all samples. The electropherograms were generated at 280 nm from the PDA data array based on the maximum absorption of the analytes. All solutions were degassed in an Elma ultrasonic bath (Transsonic 310, Germany) prior to use. A Beckman Φ 350 pH meter (Fullerton, CA) was used to adjust the pH of the separation buffer.  5.2.2 Chemicals and solutions Buffer solution was prepared by mixing 10mM HEPES (Sigma-Aldrich Canada) with 150 mM NaCl (Fischer Scientific, Nepean, ON, Canada), 3mM EDTA (Fischer Scientific, Nepean, ON, Canada), and 0.005% Tween 20 (HBS-EP8, Sigma-Aldrich Canada).  All of the chemicals used are analytical grade, and the buffer solution was prepared with purified water (NANOpure Infinity Reagent Grade Water System, Apple Scientific Inc., Chesterland, OH). The buffer was filtered prior to use through 0.45 μm pore size nylon membranes (Micron Separation, West-borough, MA, USA). The antibody and epidermal growth factor receptor   121 (EGFR) rabbit Fc dimmer were provided by a company. The initial EGFR (20.3 μM) solution was diluted to 3.38 μM with the HEPES buffer. The initial antibody (68.0 μM) was diluted in the same buffer to concentrations of 4.53, 5.67, 7.55, 9.06, 11.3, 15.1, 22.7 μM. A series of solutions containing 3.38 μM of EGFR and increasing concentrations (4.53, 5.67, 7.55, 9.06, 11.3, 15.1, 22.7 μM) of the antibody were also prepared, and then mixed thoroughly but gently.  5.2.3 Capillary conditioning New capillaries were first flushed with 1.0 M NaOH (15 min, 20 psi), followed by methanol for 15 min, 0.1 M NaOH for 20 min, deionized water for 15 min, and finally the background electrolyte (BGE) for 15 min, before being used. The samples were always injected under a pressure of 0.5 psi (or 3447 Pa) for 90 s. A voltage of +20 kV (anode is on the inlet side) was applied for CE runs. In order to achieve better reproducibility, the capillary was conditioned every day prior to use, with 0.1 M NaOH for 5 min followed by methanol for 5 min, deionized water for 5 min, and finally the BGE for 5 min. Between runs, the capillary was rinsed for 2 min with 0.1 M NaOH, followed by water for 2 min and then equilibrated with running buffer for 2 min. The running buffer used in all CE experiments was freshly prepared buffer solution at pH 7.4. The mixture was placed into the sample tray of the CE instrument and thermostated at 25.0 oC for at least one hour. The pre-equilibrated mixture of antibody and EGFR was injected into a neat-buffer-filled capillary under a pressure of 0.5 psi (3447 Pa) for 90 s in the normal mode, and then a voltage of +20 kV was applied when both inlet and outlet vials contained the BGE, and the UV signals of species during CE process were recorded.   122 A good linear relationship was obtained for UV signals and antibody concentrations, as proved by the R-square value 0.9986 shown in Figure 5.1. The calibration curve is used to determine antibody concentrations from the UV signals. Each solution is measured at least three times to minimize instrumental errors. [Antibody]  (M) 5.0e-6 1.0e-5 1.5e-5 2.0e-5 m A u 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Y=299074x+0.217 R2=0.9986 F Figure 5.1. Calibration curve of the antibody.            123 5.3 Results and Discussion  The binding parameters of antibody-receptor were determined by the following equation: 1 1 [ ] [ ] [ ] 1 [ ] N n n f b n N nt n f n nK L LI P K L = = = = + ∑ ∑         (5.1) 1 2 1 [ ] [ ] [ ] n n n m n n m f f PLK K K K K P L= = = ⋅ ⋅⋅ ⋅ =∏       (5.2) where I is the average number of the ligand molecules bound to one protein molecule, and P, L and PL are the protein, ligand and protein-ligand complex of interest, respectively. N is the exact number of binding sites present on each protein molecule. The overall binding constant, Kn, is generally calculated as the product of binding constants of each step. With eq. 1, either identical independent binding type or dependent binding can be studied. According to the mechanism of EGFR-antibody binding reported by Ferguson [5], the experimental obtained data were analyzed for different binding stoichiometries. Binding parameters were estimated by non-linear regression using the SigmaPlot 10.0 (Systat Software Inc., Richmond, CA) software package. The applicability of CE-FA in the study of the interactions of antibody with protein EGFR at near physiological concentrations was evaluated in free solution format. For this reason, mixtures containing a fixed EGFR concentration (3.38 μM) and increasing concentrations of antibody (from 4.53 to 22.7 μM) were prepared. The EGFR concentration and antibody concentration range studied were selected according to the detection limit of the   124 CE instrument. One of the criteria of using CE-FA is that the mobilities of the protein and ligand are different. The electrophoretic mobilities of free EGFR (μep, P) and free antibody (μep, L) were determined by the following procedure: the capillary was first filled with plain buffer, then a small plug of EGFR or antibody was injected for 3 s at 0.5 psi, and finally the migration time of the sample plug was measured while a voltage of 20 kV was applied across the capillary. This procedure was repeated 10 times on different days to include the instrumental and other errors, and the average free mobilities were determined for EGFR and antibody, respectively. The measured average μep, P, was -9.062 ± 0.063 × 10-5 cm2V-1 s-1, and the average μep, L, was -8.039 ± 0.034 × 10-5 cm2V-1s-1. The mobility of the EGFR-antibody complex is not measurable; however, it can be estimated by using a computer simulation program for capillary electrophoresis (SimDCCE).  The mobility of the complex is smaller than μep, L but greater than μep, P. The free antibody concentration in each mixture was determined relative to the plateau height of pure antibodies. Due to the small difference between the free antibody mobility and the complex formed, the plateau of the free antibody remaining in the sample is not completely separated from the plateau of the complex. However, the concentration of the free antibody can be estimated by the height of the partial plateau on the left hand side of the signal shown in Figure 5.2. Data from the PDA confirmed that only free antibodies are present in this region. Figure 5.2 contains two electropherograms. Electropherogram A was observed from the injection of a sample containing 9.06 μM antibody only, and electropherogram B was obtained from a mixture containing 3.38 μM EGFR and 9.06 μM   125 antibody. Based on the estimated mobility order of the species (μep, L > μC > μep, P), increasing free antibody migration time and decreasing free EGFR migration time were observed.   Figure 5.2. A set of representative electropherograms of antibody and antibody binding to EGFR. Sample mixture injected contained 9.06 μM antibody (A) and pre-equilibrated 3.38 μM EGFR with 9.06 μM antibody (B). The background electrolyte was the freshly prepared buffer solution at pH 7.4. Capillary temperature, 25.0 oC. PDA detection was performed at 280 nm for both runs. An uncoated fused-silica capillary with 50.0 cm total length was used. The sample is injected by a low pressure (0.5 psi) for 90s and a separation voltage of +20 kV was performed.            126  Eq. 5.3, 5.4 and 5.5 are used to fit 1:1, 1:2 and 1:3 binding isotherms of protein-ligand interaction, respectively. With a plot of [L]b/[P]t vs. [L]f, the binding constant, Kbn, can be easily determined through a non-linear regression method. [ ][ ] [ ] [ ] [ ] [ ] 1 [ ] b fb t f b f K LL PLI P P PL K L = = =+ +        (5.3) 2 1 1 22 2 2 1 1 2 [ ] 2 [ ][ ] [ ] 2[ ] [ ] [ ] [ ] [ ] 1 [ ] [ ] b f b b fb t f b f b b f K L K K LL PL PLI P P PL PL K L K K L ++= = =+ + + +     (5.4) 2 3 2 3 2 3 1 1 2 1 2 3 2 3 1 1 2 1 2 3 [ ] [ ] 2[ ] 3[ ] [ ] [ ] [ ] [ ] [ ] [ ] 2 [ ] 3 [ ]  1 [ ] [ ] [ ] b t f b f b b f b b b f f b b f b b b f L PL PL PLI P P PL PL PL K L K K L K K K L K L K K L K K K L + += = + + + + += + + +     (5.5) All parameters are defined as in Eq. 5.1 and 5.2. A series of comparison studies were done as various interaction stoichiometries were assumed, and the binding isotherms constructed for EGFR-antibody interaction are demonstrated in Figure 5.3. Eq. 5.3 is used for an assumed 1:1 interaction. The generated binding isotherm does not fit the actual data as shown in Figure 5.3 A, suggesting that more than one active site must exist on each EGFR molecule. The y-axis used to generate the binding isotherm is the average number of ligand bound per protein molecule. With a 1:1 interaction, the I value, which is the ratio of the bound ligands and the total protein, cannot exceed 1. It is obvious that the average number of ligands bound per protein molecule exceeds 1 as the concentration of antibody in the sample increases. Curve B (the solid line) is a typical binding isotherm fitting with Eq. 5.4 when assuming two different binding sites present on the receptor. The information provided by the non-linear regression suggests that, during CE process, two different binding sites on each EGFR molecule can be detected with different affinity to the antibody. The estimated binding constants for the two   127 sites, Kb1 and Kb2, are 49.873 10×  M-1 and 52.007 10×  M-1, respectively. The value of Kb1 is less than Kb2, showing that the second binding process is somewhat cooperative to the first binding. The two sites on the receptor molecule are saturated gradually as ligand concentration in the sample mixture increases in free solution circumstance. To further ensure the actual binding stoichiometry of the system of interest, the data is also fitted with a 1:3 stoichiometry. With Eq. 5.5, the generated isotherm C (the long dash line) presented in Figure 5.3 gives a similar fitting as curve B; however, the estimated three binding constants, 7.2287×104 M-1, 3.0258×105 M-1and 4.5419×103 M-1, imply that the assumed 1:3 interaction process is not likely to happen. This also shows that non-specific binding is minimal in this binding pair.       128 [Antibody]free (M) 0.0 5.0e-6 1.0e-5 1.5e-5 2.0e-5 [A nt ib od y] bo un d / [ E G FR ] to ta l ( fra ct io n bo un d) 0.0 .2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 One-site Two-site Three-site A B C   Figure 5.3. Binding isotherms of EGFR to antibody. Different stoichiometries are used to fit the experimental data. (A). With eq. 5.3, a 1: 1 stoichiometry is assumed, the estimated binding constant, K, is 58.649 10×  M-1. (B). A 1:2 binding is assumed, the estimated binding constant, K, on each individual site is 49.873 10×  M-1 and 52.007 10×  M-1, respectively. (C). A 1:3 binding is assumed, the determined binding constants are 7.2287×104 M-1, 3.0258×105 M-1 and 4.5419×103 M-1.    Although it is not currently possible to explain the entire binding mechanism of this pair, the shape of the electropherograms can be explained by using our simulation program. To understand the interaction process of the species during electrophoresis process, the simulation model of dynamic complexation capillary electrophoresis (SimDCCE) is employed to simulate the actual motion of the species in a graphic format during CE process.   129 Four snapshots taken from a CE-FA simulation run at selected moments were exported and analyzed in Figure 5.4 to demonstrate the interaction and concentration changes of each species during CE process. A relatively large volume of pre-equilibrated mixture of 3.38 μM EGFR and 9.06 μM antibody in the buffer was introduced into the capillary filled with neat buffer. As demonstrated in Figure 5.4 A, the injected pre-equilibrated sample mixture plug is 6.4 cm, which contains 1.54 × 10-6 μM EGFR-antibody complex formed during pre- equilibrium and remaining free EGFR and antibody. Due to the mobility order of species (μep, L > μC > μep, P), the antibody moves ahead of complex and EGFR and exits the sample plug from the front edge (Figure 5.4 B). To maintain the equilibrium condition in the buffer solution, more antibody and EGFR are dissociated from the complex as the complex migrates through the EGFR plug, which causes the formation of the protuberates at the front edge of antibody plug, and at the back edge of EGFR plug. As the species migrate along the capillary, they are further separated and the amount of free antibody and EGFR dissociated from the complex increases as indicated in Figure 5.4C. Eventually, the concentrations of each species no longer change, and a steady state condition is established throughout the capillary. Due to the mobility difference of the species and diffusion effects, the length of the sample plug increases to 10.4 cm. The final concentration profiles are shown in Figure 5.4 D. With SimDCCE, the final simulation results generated is the summation of the concentration profiles of each species. With the consideration of different UV absorptivity for each species, the simulated and experimental electropherograms for one of the CE-FA runs are compared in Figure 5.5. The experimental electropherogram is displaced as it is obtained, and the simulated electropherogram has been converted so that the height of the plateau matches the   130 height of the experimental plateau. The experimental and simulated migration times and the areas of the plateau are similar. 0.0 2.0 4.0 6.0 C on ce nt ra tio n (μM ) 0.0 2.0 4.0 6.0 EGFR Complex Antibody On-capillary distance (cm) 22.0 24.0 26.0 28.0 30.0 0.0 2.0 4.0 6.0 34.0 36.0 38.0 40.0 42.0 44.0 0.0 2.0 4.0 6.0 A C D 8.0 10.0 12.0 14.0 0.0 2.0 4.0 6.0 B   Figure 5.4. Simulated concentration profiles for CE-FA. BGE: freshly prepared buffer solution.  Injected sample: pre-equilibrated mixture of 3.38 μM EGFR and 9.06 μM antibody in the buffer. Injection time: 90 s. Separation voltage: 20 kV. Kb = 2.34 × 1010 M-2.  The concentration profiles of the three species are displayed in time sequence: (A) 4.0 s; (B) 160.0 s; (C) 450.0 s; (D) 725.0 s. Detailed discussion can be found in the text.     131   Figure 5.5. Comparison of the experimental result (solid line) with simulation result (short dash line) for one of the CE-FA runs. BGE: freshly prepared buffer pH 7.4. Injected sample: 3.38 μM EGFR and 9.06 μM antibody in the buffer. Injection time:  90 s. Separation voltage: 20 kV. Kb,total = 2.34 × 1010 M-2.                  132 5.4 Conclusion  The CE-FA data shows that the EGFR binds towards the antibody with a 1:2 stoichiometry. The second binding process is somewhat co-operative to the first binding event, as the second binding constant doubles the first binding constant. The result of fitting the CE-FA data with a 1:3 stoichiometry suggests that non-specific binding of the two analytes is not significant. Because the proteins are studied in a solution, all possible binding sites are exposed to interact with the ligands.                   133 5.5 References [1] Connors, K. A., Binding Constant. The Measurement of Molecular Complex Stability, John Wiley & Sons, New York 1987. [2] Harding, S. E., Chowdhry, B. Z., Protein-Ligand Interactions: Hydrodynamics and Colorimetry, oxford University Press, oxford 2001. [3] Ostergaard, J., Heegaard, N. H. H., Electrophoresis 2003, 24, 2903-2913. [4] Li, S. Q., Schmitz, K. R., Jeffrey, P. D., Wiltzius, J. J. W., et al., Cancer Cell 2005, 7, 301-311. [5] Ferguson, K. M., Berger, M. B., Mendrola, J. M., Cho, H. S., et al., Mol. Cell 2003, 11, 507-517.          134                      Chapter 6   Computer Assisted Investigation into Principles of Chiral Separation in Capillary Electrophoresis*                 * A version of this chapter has been submitted. Sun, Y. and Chen, D.D.Y. Computer Assisted Investigation into Principles of Chiral Separation in Capillary Electrophoresis, 2010   135 6.1 Introduction Chiral separation is becoming increasingly critical in research and manufacturing activities in life sciences and drug development [1-3]. Quality control of enantiomerically pure drugs and pharmacokinetic studies of each enantiomer require chiral separation. A variety of analytical techniques have been used extensively for the separation of chiral compounds, such as high performance liquid chromatography (HPLC) [4-6], gas chromatography (GC) [7, 8], supercritical fluid chromatography (SFC) [1], thin layer chromatography (TLC) [9] and capillary electrophoresis (CE) [10-12]. In recent years, the use of CE has proven to be extremely valuable over other techniques due to its high separation efficiency and low sample and reagent consumptions [3, 13-17].  In chromatography, chiral stationary phase (CSP) packed columns are commonly used for enantiomeric separations.  While in CE, without switching to a new column, chiral selectors can be changed by using another additive in the background electrolyte (BGE), which not only makes the separation easier, but also dramatically lowers the experimental cost. Amongst the wide selection of different commercially available chiral selectors used in CE, cyclodextrins (CDs) and their derivatives are the most frequently used BGE additives due to their molecular recognition properties [18-22]. It was believed that the interactions between the enantiomers and the CDs with different binding affinities are the main driving forces for enantiomeric separations. The aim of this work is to provide further understanding into the mechanism of CD- mediated chiral separations in CE. The driving forces of separation for tryptophan (Trp)   136 enantiomers and dansyl-derivatives of phenylalanine enantiomers were investigated to illustrate the distinctly different separation mechanism between CE and other techniques.                                    137 6.2 Experimental Section 6.2.1 Chemicals and solutions L- and D-tryptophan (98.0%), dansyl-L and D-phenylalanine, α-cyclodextrin (α-CD), hydroxypropyl-β-cyclodextrin (HP-β-CD), sodium phosphate monobasic (99.0%), sodium phosphate dibasic (99%), and thymidine were purchased from Sigma-Aldrich (Oakville, ON, Canada). All samples were prepared in double deionized water. An appropriate amount of α-CD or HP-β-CD was dissolved in 0.1 M phosphate buffer to make 150 mM and 100 mM of corresponding cyclodextrin stock solutions, and the pH of the BGE was adjusted to 2.5 with 1M HCl (BDH Chemicals, Toronto, ON, Canada). The α- CD stock solution was diluted to 140, 130, 120, 110, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10 mM with the 0.1 M phosphate buffer, and the concentrated HP-β-CD solution was diluted to make a series of solution ranging from 90 mM to 10 mM. Other solutions were prepared by dissolving appropriate amounts of  L- or D-tryptophan (Trp) enantiomers in deionized water to make a solution of 10 mM. The 1 mM L and D-Trp mixture was made by mixing an aqueous solution of the enantiomers with 0.1 M phosphate buffer. A racemic mixture of dansyl-L and D-phenylalanine was dissolved in deionized water to make a 1 mM solution. All of the solutions were sonicated for 10 minutes and filtered through 0.22 μm sterile, Nylon filters prior to use for CE experiments.  6.2.2 CE Conditions and procedures Electrophoretic experiments were performed on a P/ACE MDQ automated CE system (Beckman Coulter Inc., Fullerton, CA, USA) with the build-in UV-Vis detector (214 nm).   138 Uncoated fused silica capillaries (75-μm inner diameter, 360-μm outer diameter) (Polymicro Technologies, Phoenix, AZ) were used in all experiments. The total length of the capillary was 50 cm, and the length from the injection end to the detector was 42 cm. The capillary temperature was maintained at 25 °C, and a voltage of +22.5 kV in the normal polarity mode was applied for CE separations. A low pressure (0.5 psi or 3447 Pa) was used for all sample injections. The sample storage temperature was maintained at 20 °C. ASCII files were collected and exported to produce the electropherograms with SigmaPlot 10.0 (Systat Software Inc., Richmond, CA). New capillaries were pre-conditioned prior to their use, with 1M NaOH rinse for 15 min at 20 psi, followed by methanol for 15 min, deionized water for 15 min, and finally the BGE to be used for 15 min. At the beginning and end of each working day and prior to each run, the capillary was rinsed with 0.1 M NaOH (2 min, 20 psi), followed by methanol (2 min), deionized water (2 min) and corresponding BGE solution (3 min). With the capillary filled with α-CD or HP-β-CD solution at various concentrations, a small amount of racemic mixture or individual enantiomer was injected by a pressure of 0.5 psi (or 3447 Pa) for 3 s to form a 0.5 cm analyte plug. The length of the analyte plug was calculated based on Backman P/ACE injection parameters provided by the manufacturer. 6.2.3 Viscosity correction factor measurement The viscosity of each BGE solution, η , was measured by injecting a plug of 10 mM thymidine into the inlet of a capillary filled with corresponding BGEs and applying a constant pressure (20 psi) to push the sample plug through the capillary [23]. In the measured α- and HP-β- CD concentration range, the calibration curves obtained are η  = 0.0145x + 0.9823 and   139 η  = 0.0276x + 0.9611 where x is the concentration of corresponding α-CD and HP-β-CD solutions, respectively, and the R2 values are 0.9957 and 0.9931, respectively.                140 6.3 Simulation Procedure Several computer simulation models of CE (or ACE) have been developed to study the separation of analytes in CE [24-35]. However, none of them are suitable for this study, which involves multiple analyte-single additive or multiple additive-single analyte interactions, either because of the complexity of the interactions or because of the extended simulation time required. With an efficient algorithm, we have developed a program named CoSiDCCE (Computer Simulation of Dynamic Complexation Capillary Electrophoresis). This program was used to simulate the detailed migration and interaction behavior of all species involved in DCCE experiments through a comprehensive visual presentation, and to predict the migration times and the peak shapes.  More details on this program are given in the Supporting Material. All simulation conditions were the same as those used in the real experiments described in this work.  Throughout this paper, the free L-, D- enantiomer, free CDs (α-CD or HP-β-CD) and their complexes are denoted as L, D, C, LC and DC, respectively. When the same condition and parameters are used for simulation, the effectiveness of the CoSiDCCE is evaluated. We have previously developed a SimDCCE program to simulate the migration and distribution behavior of various species of an analyte during a CE process, including systems with more than one additive and higher than 1:1 stoichiometry [28], [36, 37]. The aim of developing the CoSiDCCE is to build a more efficient tool to simulate more complicated dynamic complexation systems, such as interactions of a single analyte with multiple additives (e.g., a drug with multiple proteins) and multiple analytes with a single additive (e.g., multiple ligands competing with a single protein).  The use of JAVA language ensures that the program can be used by all types of personal computers.   141 As in SimDCCE, the  CoSiDCCE program is based on the mass balance equation, and the electrophoretic migration for all species can be described by the following equation [28, 38]: 2 ,, 2 ,,,, z C D z C E t C itz i itz zi itz ∂ ∂+∂ ∂−=∂ ∂ μ        (6.1) where Cz,t,i is the concentration of species i at position z and time t, Ez is the local electric field strength, and Di is the symmetrical dispersion coefficient of i, including the dispersion caused by longitudinal diffusion and other factors, μi is the apparent mobility of i which is the sum of the electrophoretic mobility of i (μep,i) and the electroosmotic mobility (μeof). The concentrations of each species in a chiral separation system with one chiral selector have to be calculated by solving individual cubic equations. The detailed procedure in solving these more complicated equations is presented in the Supporting Material. With the knowledge of the concentrations of each species at any given time and location, the apparent mobility for each compound can be calculated with the following equations: , ,(1 ) L ep L ep L L ep LCf fνμ μ μ= + −        (6.2) , ,(1 ) D ep D ep D D ep DCf fνμ μ μ= + −       (6.3) where v is the viscosity correction factor; fL and fD are the fraction of free L- and D- enantiomers, ,ep Lμ , ,ep Dμ , ,ep LCμ and ,ep DCμ are the electrophoretic mobilities of free enantiomers and the complex LC and DC, respectively. The binding constants and complex mobilities were calculated using a non-linear regression method, and the values were used in the simulation program to predict the migration and separation of the chiral compounds at different chiral selector concentrations, even when some of the conditions cannot be achieved in real experiments. The detailed   142 procedure in calculating the binding constants and complex mobilities is also presented in the Supporting Material.                      143 6.4 Results and Discussion A low-pH background electrolyte (BGE) (pH = 2.5) was used to minimize the EOF generated during the CE process. At pH higher than 3, a gradual increase in EOF was observed, but no enantiomeric separation took place. Both α- and HP-β-CDs used in the experiments are nonionic, and the electrophoretic mobility of the native CDs is zero ( , 0ep Cμ = ) in these experimental conditions.  6.4.1 Case I, tryptophan enantiomers The electrophoretic mobilities of the free tryptophan enantiomers, ,ep Lμ  and ,ep Dμ , were measured without the presence of the CDs. The electropherograms showed that when the L/D-Trp racemic mixture was injected into the capillary filled with only phosphate buffer (0.1 M), the enantiomers migrate toward the outlet of the capillary with essentially the same mobility, thus no separation was observed. Five replicate measurements were carried out to estimate the systematic errors, and the measured values for ,ep Lμ  and ,ep Dμ  were both (1.076±0.009)×10-4 cm2V-1s-1. α-CD concentrations ranging from 10 to 150 mM were used to obtain the binding constants. When more α-CD was added into the BGE, the difference between the net mobilities of L-Trp and D-Trp increased and the resolution also increased from 0.36 to 2.79. Through non-linear regression, the calculated binding constants for L-Trp and D-Trp, KLC and KDC, were determined to be 8.15±0.73 M-1 and 11.82±0.96 M-1, respectively, and the mobilities for the complex LC and DC, ,ep LCμ and ,ep DCμ , are (1.911±0.001)×10-5 cm2V-1s-1 and (2.302±0.003)×10-5 cm2V-1s-1, respectively. The calculated K values indicate that, when   144 α-CD was dissolved in the BGE acting as a pseudo-stationary phase, the enantiomers of tryptophan were separated with two distinctive mechanisms, and the D- enantiomer had a greater ability to bind α-CD than the L- enantiomer. Two peaks were detected, as shown in Figure 6.1. The peak on the left is the L-Trp, and the peak on the right is the D-Trp. The migration order (or elution order) of the two enantiomers was identified by adding 25% more of pure L-Trp to the racemic mixture. When increasing the amount of chiral selector in the BGE, obvious shifts in migration times of the L- and D- enantiomers were observed. Time (min) 15.0 20.0 25.0 30.0 Ar bi tra ry  U ni t ( AU ) -4.0e+4 -2.0e+4 0.0 2.0e+4 4.0e+4 Experiment Simulation A B C L-Tryptophan D-tryptophan   Figure 6.1. Experimental and simulated results for the separation of 1 mM L/D- Trp racemic mixture with α-CD: (A) 20 mM α-CD; (B) 50 mM α-CD; (C) 100 mM α-CD in 0.1 M phosphate buffer.      145 Another set of data was collected from the HP-β-CD mediated separations and fitted using non-linear regression method. The estimated binding constants for HP-β-CD with L- and D- Trp are 17.20±1.23 M-1 and 16.89±1.56 M-1, respectively, and ,ep LCμ and ,ep DCμ  are (2.019±0.004)×10-5 cm2V-1s-1 and (2.058±0.006)×10-5 cm2V-1s-1, respectively. Because of the small differences between two complex mobilities and binding affinity constants of HP-β-CD with tryptophan enantiomers, no chiral separation was observed even when 100 mM concentration was used, as shown in Figure 6.2. Time (min) 15.0 20.0 25.0 30.0 35.0 40.0 Ar bi tra ry  U ni t ( AU ) -4.0e+4 0.0 4.0e+4 8.0e+4 1.2e+5 1.6e+5 Experiment Simulation A B C L/D-tryptophan  Figure 6.2. Chiral separation of L- and D-Trp with HP-β-CD. BGE: (A) 20 mM; (B) 50 mM; (C) 100 mM HP-β-CD in 0.1 M phosphate buffer. Injected sample: 1 mM L/D-Trp racemic mixture.     146  Athough it is impossible to achieve complete separations experimentally, the simulation program could determine the conditions required if the solubility of the additive was not the limiting factor.  Figure 6.3 shows the improved resolution with the increase of the HP-β-CD concentration. Time (min) 30.0 35.0 40.0 45.0 50.0 55.0 Ar bi tra ry  U ni t ( AU ) 0.0 2.0e+4 4.0e+4 6.0e+4 8.0e+4 1.0e+5 1.2e+5 110mM HPβ−CD 120mM HPb-CD 130mM HPb-CD 140mM HPb-CD 150mM HPb-CD 160mM HPb-CD 170mM HPb-CD 180mM HPb-CD 190mM HPb-CD 200mM HPb-CD  Figure 6.3. Simulated electropherograms for the separation of 1 mM L/D-Trp mixture with HP-β-CD ranging from 110 mM to 200 mM in 0.1 M phosphate buffer. Detailed conditions are provided in the Supporting Material.      147 6.4.2 Case II, dansyl-phenylalanine The separation of dansyl-phenylalanine (dansly-Phe) enantiomers using α- and HP-β- CDs was also investigated. Figures 6.4A to 6.4E demonstrate the migration behaviour of the pair in a plain buffer and with α-CD and HP-β-CD in the BGE. As observed, no separation was seen when 0 mM, 50 mM and 100 mM α-CD were added in the phosphate buffer solution (Figure 6.4A, 6.4B and 6.4C). The unresolved L- and D- enantiomers passed the detector at 10.60, 12.79 and 17.06 min, respectively. In contrast, when the HP-β-CD concentration increased from 50 mM to 100 mM, the enantiomer peaks were completely separated as presented in Figure 6.4D and 6.4E. The elution order of the enantiomers was also identified by adding 25% of pure dansyl-L-phenylalanine to the racemic mixture. Comparing with typtophan, the analyte used in Case II is much bulkier. In Case I, good enantiomeric separation was achieved with α-CD, but no separation was seen with HP-β-CD. As the size of the analyte increases, within the same concentration range of CDs, better separation was achieved with HP-β-CD. Significantly shorter migration times were seen with α-CD (runs B and C), which indicates that the hydrophobic group of dansyl-Phe does not favour the inside of the cavity of α-CD and the interaction between α-CD and dansyl-Phe is minimal.  With one more unit of glucose the hydrophobic cavity of the β-form cyclodextrin can accommodate bulkier groups than the indole groups on tryptophan molecules.  In other words, with α-CD, the gradually decreased mobility of the enantiomers is mainly due to the increasing viscosity of the BGE. With HP-β-CD, while the mobility of the enantiomers is also affected by the viscosity change of the buffer solution, the main reason for the mobility change is the interactions between HP-β-CD and the analyte in runs D and E.   148 The measured electrophoretic mobility of free dansyl-Phe enantiomers, , ,ep fμ is (1.377±0.001)×10-4 cm2V-1s-1. Binding parameters for HP-β-CD with dansyl-L(D)-Phe were obtained using non-linear regression method described in the Supporting Material. The estimated binding constants for L- and D- enantiomers with HP-β-CD, KLC and KDC, are -154.35 2.66 M± and -153.66 1.32 M ,±  respectively, and the calculated ,ep LCμ and ,ep DCμ  are (1.814±0.004)×10-5 cm2V-1s-1 and (2.219±0.004)×10-5 cm2V-1s-1. Although the estimated KLC and KDC are similar, the enantiomer peaks were well resolved, which indicates that both the difference in binding affinity and complex mobility contribute to the separation. The estimated K values suggest that, with a slightly greater binding affinity, dansyl-D-Phe-HP-β- CD complexes tend to be more stable than dansyl-L-Phe-HP-β-CD complexes. The obtained binding affinity for dansyl-Phe with HP-β-CD is slightly higher than that for tryptophan with HP-β-CD, suggesting that the variations in amino acid side chain and derivatives at the amino terminals has an effect on the interactions with the cyclodextrin, and thus affect their migration behaviour.   149 10.5 11.0 11.5 12.0 12.5 13.0 13.5 0.0 2.0e+4 4.0e+4 6.0e+4 8.0e+4 1.0e+5 1.2e+5 1.4e+5 15.0 16.0 17.0 18.0 19.0 0.0 2.0e+4 4.0e+4 6.0e+4 8.0e+4 1.0e+5 1.2e+5 Time (min) 30.0 32.0 34.0 0.0 1.0e+4 2.0e+4 3.0e+4 4.0e+4 5.0e+4 6.0e+4 50.0 52.0 54.0 56.0 58.0 60.0 0.0 1.0e+4 2.0e+4 3.0e+4 4.0e+4 5.0e+4 6.0e+4 10 11 12 13 Ar bi tra ry  U ni t 0.0 3.0e+4 6.0e+4 9.0e+4 1.2e+5 A rb itr ar y U ni t ( A U ) B C D E A 12 .7 9 m in 17 .0 2 m in 30 .6 9 m in 32 .8 1 m in 52 .8 1 m in 57 .8 2 m in 10.60 min Dansyl-L/D-Phe Dansyl-L/D-Phe Dansyl-L-Phe Dansyl-D-Phe  Figure 6.4. Electropherograms for the separation of dansyl-L/D-Phe racemic mixture with no chiral selector (A), α-CD concentration of 50 mM (B), 100 mM (C) and HP-β-CD concentration of 50 mM (D) and 100 mM (E).          150 6.4.3 Selector concentrations To understand the influence of CD concentrations on the separation of enantiomers, CoSiDCCE was used to describe the concentration changes of the free and complexed enantiomers as various amounts of α-CD or HP-β-CD were added to the BGE (Figure 6.5). Six snapshots were taken at the same on-capillary position, 15 cm, for each case studied. Figure 6.5 I-A to I-F describe the changes in the concentrations of L- and D- tryptophan and the formed diastereomeric complexes when various α-CD concentrations were used. In Figure 6.5 I-A, when the α-CD concentration was 20 mM, only a small amount of the enantiomers were complexed with the selector. When the α-CD concentration was increased to 50 and then 100 mM (Figure 6.5 I-B and I-C), more complexes were formed and the L- and D- tryptophan enantiomer peaks were better separated. With 500 mM α-CD, significantly decreased resolution was observed for the two enantiomers, and less than 30 % of free enantiomer remained in the solution as described in Figure 6.5 I-D. As the amount of chiral selector was increased to 1M, the migration order was reversed (Figure 6.5 I-E). The low concentration of the free analyte was due to the very large amount of α-CD used, and the reversed migration order can be explained by the mobility values of the L- and D- Trp-α-CD complexes. In this case, D-Trp has a greater affinity to bind α-CD, and the complex (DC) moves with a faster speed than the L-Try-α-CD complex. When a sufficient amount of selector was added to the separation buffer, the fraction of complex became much greater than that of the free enantiomer. As described in eq. 2 and 3, with an extremely small fraction of free enantiomer, the apparent mobility is mainly determined by the complex mobility, , L ep ep LCμ μ≈  and ,Dep ep DCμ μ≈ . Although KLC > KDC, ,ep DCμ is larger than ,ep LCμ , resulting in a reversed migration order of L- and D- Try-α-CD when most of the analytes are present in   151 complexed form.   This phenomenon is similar to that described in a paper by Kranack et al., except that in this case, the binding isotherms start at the same mobility when the additive concentration is zero [39]. In the case of extremely large amount of α-CD (50 M), the amount of free enantiomer remaining in the solution was reduced to almost zero (Figure 6.5 I-F). Because of the mobility difference between L-Try-α-CD and D-Try-α-CD complexes, the peaks were better separated at such a high selector concentration. In fact, the resolution would increase to a maximum and then become constant. A parallel study was done with the same range of HP-β-CD concentrations used in the separation of dansyl-phenylalanine enantiomers. Because of the relatively higher binding affinity constants of HP-β-CD with dansyl-Phe, KDC = 53.6 and KLC = 54.3, with 20 mM HP- β-CD, about 50% of the enantiomers were complexed with the chiral selector (Figure 6.5 II- A). Similarly, more enantiomer-selector complexes were formed as an increasing amount of chiral selector was added into the BGE. When very high selector concentrations were used, almost 100% of enantiomers existed in the complexed form (Figure 6.5 II-B to II-F). With the noticeable difference in the binding affinity constants of the L- and D- enantiomers and the difference in mobilities of the complex formed, enantiomer peaks were well resolved and no decrease of the resolution was seen in the simulated concentration range. Since the D- enantiomer tends to form a stronger complex with HP-β-CD, and the dansyl-D-Phe-HP-β-CD complex also migrates slower than the dansyl-L-Phe-HP-β-CD complex, no switching of the migration order was found in this case.  It is apparent that both differences in binding   152 affinities and differences in the complex mobilities, as well as the concentration of chiral selector can affect the chiral separation.  15 16 17 C on ce nt ra tio n (m M ) 0.0 0.2 0.4 0.6 0.8 1.0 On-capillary position (cm) 15 16 17 0.0 0.2 0.4 0.6 0.8 15 16 17 18 0.0 0.2 0.4 0.6 15 16 17 0.0 0.3 0.6 0.9 1.2 15 16 17 0.0 0.3 0.6 0.9 1.2 1.5 15 16 17 18 19 0.0 0.4 0.8 1.2 1.6 2.0  [Free L]  [Free D]  [Complex LC] [Complex DC] Case I: Enantiomeric separation of tryptophan with α-CD Case II: Enantiomeric separation of dansyl-phenylalanine with HP-β-CD 15 16 17 C on ce nt ra tio n (m M ) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 15 16 17 18 0.0 0.2 0.4 0.6 0.8 15 16 17 18 0.0 0.2 0.4 0.6 0.8 15 16 17 18 19 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 15 16 17 18 19 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 15 16 17 18 19 0.0 0.3 0.6 0.9 1.2 1.5 1.8 20 mM 50 mM 100 mM 500 mM 1 M 50 M 20 mM 50 mM 100 mM 500 mM 1 M 50 M A B C D E F A B C D E F On-capillary position (cm) LC DC DC LC LC DC LC DC  Figure 6.5. CoSiDCCE simulated concentration profiles for tryptophan enantiomers and their complexes with α-CD (Case I) and for dansyl-phenylalanine enantiomers and complexes with HP-β-CD (Case II).  Concentration of chiral selectors: (A) 20 mM; (B) 50 mM; (C) 100 mM; (D) 500 mM; (E) 1 M; (F) 50 M.      153   With the estimated binding constants, complex mobilities, and experimental conditions, the enantiomeric separation for tryptophan using 50 mM α-CD was also studied.  A good agreement was obtained when the simulation result (the short dash line) was compared with the electropherogram (the solid line) in Figure 6.6A. While assuming identical mobilities of the formed tryptophan-α-CD complexes, decreased resolution was observed (Figure 6.6B). In Figure 6.6C, zero complex mobility was used to mimic the case when a chiral stationary phase is used in chromatography. The apparent mobility of the enantiomers was greatly reduced, thus resulting in a longer retention time for tryptophan. The slightly increased resolution of the two peaks was a result of the longer retention time. 19 20 21 22 23 Ar bi tra ry  U ni t ( AU ) 0 1e+4 2e+4 3e+4 4e+4 5e+4 Experiment Simulation Time (min) 19 20 21 22 23 0 1e+4 2e+4 3e+4 4e+4 5e+4 22 23 24 25 26 0 1e+4 2e+4 3e+4 4e+4 5e+4 A B C  Figure 6.6. Experimental and CoSiDCCE simulated electropherograms for the separation of tryptophan enantiomers with 50 mM α-CD when (A) different (B) identical and (C) zero complex mobilities are used. In (A), the experimental results are compared with the simulated data when calculated complex mobilities are used in the simulation ( ,ep LCμ  = 1.911×10-5 cm2V-1s-1 and  ,ep DCμ  = 2.302×10-5 cm2V-1s-1). In case (B), ,ep LCμ = ,ep DCμ = 1.911×10-5 cm2V- 1s-1; and in case (C), ,ep LCμ  = ,ep DCμ = 0, which is the case when chiral stationary phase is used in chromatography.   154  The simulated results suggest that either the mobility difference between two complexes or the differences in binding constants can result in successful enantiomeric separations.  The separation of dansyl-Phe enantiomers using 50 mM HP-β-CD was also investigated.   The comparison of the experimental (solid line) and simulated (dashed line) results was shown in Figure 6.7A. When identical complex mobilities were used, 5 2 -1 -1 , , 1.814 10 cm V sep LC ep DCμ μ −= = × , as in Figure 6.7B, the enantiomer peaks were no longer separated, and the peak area was doubled. The slightly increased migration time was due to the smaller complex mobility used in the simulation. In Figure 6.7C, the simulation data was presented assuming no movement of the complexes, , , 0ep LC ep DCμ μ= = . Significantly reduced apparent mobility of the enantiomers caused a much longer migration time for the racemic mixture. The broader peak generated was due to the longer separation time.  This case is essentially the same as the separations performed in a chiral chromatography column.       155 28 30 32 34 36 Ar bi tra ry  U ni t ( AU ) 0 1e+4 2e+4 3e+4 4e+4 5e+4 Experiment Simulation 28 30 32 34 36 0 2e+4 4e+4 6e+4 8e+4 Time (min) 42 44 46 48 0 1e+4 2e+4 3e+4 4e+4 5e+4 6e+4 A B C  Figure 6.7. Experimental and CoSiDCCE simulated electropherograms for the separation of dansyl-Phe enantiomers with 50 mM HP-β-CD when (A) ,ep LCμ = 1.814×10-5 cm2V-1s-1and ,ep DCμ  = 2.219×10-5 cm2V-1s-1; (B) ,ep LCμ = ,ep DCμ = 1.814×10-5 cm2V-1s-1; (C) ,ep LCμ = ,ep DCμ = 0, which is the case when chiral stationary phase is used in chromatography.    The simulation data given in Figure 6.7 indicates that separation of dansyl-Phe enantiomers is based almost entirely on the difference in complex mobility.  This conclusion suggests that if a chiral column with immobilized β-CD was used it would be impossible to separate dansyl-Phe enantiomers with HPLC or GC.  Another immobilized chiral selector, which has differential binding abilities to the enatiomers would have to be used.       156 6.5 Conclusions Two types of CD-mediated enantiomeric separation of tryptophan and dansyl-Phe enantiomers using affinity CE method were presented. The binding constants of the amino acids with chiral selectors and the mobilities of the complexes are obtained using non-linear regression. The estimated values indicate that the separation of tryptophan enantiomers with α-CD is based on the difference in binding affinities between α-CD and L- and D- enantiomers, while the separation of dansyl-phenylalanine enantiomers using HP-β-CD is mainly driven by the difference in the complex mobilities. With the assistance of the computer program CoSiDCCE, the detailed migration behaviors of the analyte involved in the enantiomeric separation during the CE process can be quantitatively described using the dynamic complexation model. The effectiveness and accuracy of CoSiDCCE were evaluated through the comparison of the experimentally obtained CE separation results with a series of simulated enantiomeric separations. It was concluded that CoSiDCCE, which was written based on the well-established mass transfer equation, enables the simulation of two analytes interacting with a single additive. When proper parameters are used, CoSiDCCE is capable of predicting the migration time, peak shape and peak order of a pair of analytes, as well as facilitating the design of BGE compositions in CE separation systems.         157 6.6 References  [1] Ward, T. J., Baker, B. A., Analytical Chemistry 2008, 80, 4363-4372. [2] Fanali, S., J. Chromatogr. A 1996, 735, 44. [3] Chankvetadze, B., J. Chromatogr. A 2007, 1168, 45-70. [4] Ahuja, A., Chiral Separations by Chromatography, ACS, New York 2000. [5] Debowski, J., Jurczak, J., Sybilska, D., J. Chromatogr. 1983, 282, 6. [6] Cavazzini, A., Nadalini, G., Dondi, F., Gasparrini, F., Ciogli, A., Villani, C., 2004, 1031, 16. [7] Molnar-Perl, I., J. Chromatogr. A 2003, 987, 291-309. [8] Jung, M., Mayer, S., Schurig, V., , LC. GC-Mag. Sep. Sci. 1994, 12, 9. [9] Altria, K., Marsh, A., Sanger-van de Griend, C., Electrophoresis 2006, 27, 2263-2282. [10] Goodnough, D. B., Lutz, M. P., Wood, P. L., J. Chromatogr. B-Biomed. Appl. 1995, 667, 223-232. [11] Hashimoto, A., Oka, T., Nishikawa, T., Eur. J. Neurosci. 1995, 7, 1657-1663. [12] Mayer, S., Schurig, V., J. Liq. Chromatogr. 1993, 16, 17. [13] de Boer, T., de Zeeuw, R. A., de Jong, G. J., Ensing, K., Electrophoresis 2000, 21, 3220- 3239. [14] Fanali, S., J. Chromatogr. A 1996, 735, 77-121. [15] Ward, T. J., Analytical Chemistry 2002, 74, 10-16. [16] Scriba, G. K. 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[29] Fang, N., Sun, Y., Zheng, J. Y., Chen, D. D. Y., Electrophoresis 2007, 28, 3214-3222. [30] Gaš, B., Vacík, J., Zelenský, I., J. Chromatogr. 1991, 545, 225-237. [31] Hruška, V., Jaroš, M., Gaš, B., Electrophoresis 2006, 27, 984-991. [32] Ikuta, N., Hirokawa, T., J. Chromatogr. A 1998, 802, 49-57. [33] Ikuta, N., Sakamoto, H., Yamada, Y., Hirokawa, T., J. Chromatogr. A 1999, 838, 19-29. [34] Palusinski, O. A., Graham, A., Mosher, R. A., Bier, M., Saville, D. A., Aiche J. 1986, 32, 215-223. [35] Saville, D. A., Palusinski, O. A., Aiche J. 1986, 32, 207-214. [36] Fang, N., Chen, D. D. Y., Anal. Chem. 2005, 77, 2415-2420. [37] Fang, N., Chen, D. D. Y., Anal. Chem. 2006, 78, 1832-1840. [38] Giddings, J. C., Unified Separation Science, John Wiley & Sons, Inc., New York 1991.   158 [39] Kranack, A. R., Bowser, M. T., Britz-McKibbin, P., Chen, D. D. Y., Electrophoresis 1998, 19, 388-396.    159                                               1. Introduction    Chapter 7   Determination of Potentially Anti-carcinogenic Flavonoids in Wines by Micellar Electrokinetic Chromatography*             * A version of this chapter has been published. Sun, Y., Fang, N., Chen, D.D.Y. and Donkor, K.K. Determination of potentially anti-carcinogenic flavonoids in wines by micellar electrokinetic chromatography, Food Chemistry, 2008, 106, 415–420.  160 7.1 Introduction  Flavonoids are a large group of phenolic compounds and constitute one of the largest groups of secondary metabolites in plants [1]. The basic structure of flavonoids contains a phenolic ring with a 2-phenylbenzopyrone [2]. Their derivatives differ in the substituents, the number and position of hydroxyl and methoxy groups, and the type and position of sugar moieties in the molecules [3]. Frequently, one or more of the hydroxyl groups are methylated, acetylated, prenylated or sulphated [1]. Flavonoids exhibit important health benefits and pharmacological activities, such as anti-inflammatory, anti-allergy, anti-viral [4], anti-cancer [5, 6], anti-oxidant [7-9] and anti-microbial [9, 10]. Other proven important properties of flavonoids include metal ion-chelation, enzyme inhibition, anti-proliferation, regulation of cell signaling and gene expression [11, 12]. Flavonoids are also associated with a low incidence of osteoporosis and menopausal vasomotor symptoms such as hot flashes and night sweats [13]. Auxins are hormones which are a critical determinant in controlling plant growth, and flavonoids have been found to act as auxin transport inhibitors [14]. In addition, flavonoidic constituents are responsible for the astringency, colour, bitterness [15] and general organoleptic characteristics of wine. As a consequence, research interest in flavonoids has intensified due to their numerous health benefits and its relationship to the benefits of wine consuming in human diet. Analytical methods for flavonoids include HPLC [16-20], thin-layerchromatography [21], and gas chromatography–mass spectrometry [22]. However,  in recent years, the popularity of capillary electrophoresis (CE) has increased dramatically since it offers several advantages, including excellent separation efficiency for complex samples, rapid analysis, minimum use of samples and organic solvents, much simpler and robust instrumentation, as well as various separation modes suitable for widely different  161 analytes [23, 24]. Micellar electrokinetic capillary chromatography (MEKC), or surfactant mediated CE, is one of the most important modes of CE in which surfactants are added to the buffer solution at concentrations that form micelles. In MEKC, the separation principle is based on a differential partition between the micelle and the mobile phase, which offers superb selectivity in the analysis of complex substances [25-27]. Flavonoids in plants are complex and usually appear as mixtures, often with varied amount and quality [15]. Several flavonoids have been determined by CE in different plant matrices [15, 28, 29]; However, not that many analyses for flavonoids in wines have been carried out using capillary electrophoresis. Therefore, the general objective of this work is to characterize flavonoids by MEKC. The information obtained can be used to fingerprint wines and thus determine the botanical and geographical origin of the grapes used to make these wines. In an attempt to achieve this goal, we have focused on a selected number of flavonoids in wines that might have anti-carcinogenic effects [16]. The structures of these flavonoids are shown in Figure 7.1.      162  Figure 7.1. The chemical structures of the investigated flavonoids.              163 7.2 Experimental Section  7.2.1 Standards and reagents  Flavonoid standards, i.e., catechin, naringenin, quercetin, apigenin, kaempferol and myricetin were purchased from Sigma Chemical Co. (St. Louis, MO, USA). The stock standard solutions of 200 mg L of each analyte were prepared by dissolving the appropriate mass of the flavonoid in 20 mL of 1-propanol and then diluted with doubly deionized water to 100 mL. Resorcinol, sodium dodecyl sulphate (SDS) and sodium tetraborate (Borax) were also obtained from Sigma Chemical Co. (St. Louis, MO). 1-propanol was purchased from Fischer Scientific, Nepean, ON, Canada. All reagents were analytical-reagent grade and used without further purification. The background electrolyte (BGE) was prepared by dissolving the appropriate amounts of SDS and sodium tetraborate in doubly deionized water to obtain the final concentration. The samples and running buffers contained 20% 1-propanol. The pH of the running buffer was adjusted with either 1.0 M NaOH (BDH Chemicals, Toronto, ON, Canada) or 2.0 M HCl (Fischer Scientific, Nepean, ON, Canada) within a range of 8.0–10.0. All solutions were filtered through 0.22 μm sterile, Nylon filters prior to use for the CE experiments.  7.2.2 Instrumentation and electrophoretic procedure   All CE experiments were performed using a Beckman P/ACE MDQ capillary electrophoresis instrument (Beckman Coulter Inc., Fullerton, CA) equipped with a UV absorbance detector. Uncoated fused-silica capillaries (Polymicro Technologies, Phoenix, AZ) with inner diameters of 75 μm and total lengths of 60 cm (52 cm to the detector) were used.  164 New capillaries were first rinsed with 1.0 M NaOH (30 min, 20 psi), followed by methanol for 20 min, 0.1 M NaOH for 20 min, deionized water for 10 min, and finally the BGE for 30 min, before being used. Sample injections were done by hydrodynamic pressure at 0.5 psi (3447 Pa). An injection time of 5 s was used for all analyses. UV absorption was monitored at 214 nm based on the maximum absorption of the analytes. The separation voltage was 15 kV at a constant temperature of 25 oC. The capillary was conditioned every day prior to use, with 0.1 M NaOH for 30 min followed by deionized water for 10 min, and finally the BGE for 30 min. Before each injection, the capillary was rinsed for 5 min with 0.1 M NaOH, followed by water for 2 min and then equilibrated with running buffer for 8 min. The pH of solutions was measured using a Beckman U 350 pH meter (Fullerton, CA).  7.2.3 Sample preparation  A total of 10 wines (6 red and 4 white) were obtained from a local liquor store. The flavonoids were extracted from the wine samples before analysis. In the extraction, wine samples (15 mL) were mixed with 45 mL diethyl ether in a separatory funnel. The mixture was shaken for about 30 min and after extraction the ether layer was collected. The remaining aqueous layer was mixed with 45 mL ethyl acetate and was shaken again for several minutes to ensure complete extraction of flavonoids. After extraction, the ethyl acetate layer was collected and combined with the diethyl ether portion previously collected. The combined extract was dried with 5 g of anhydrous sodium sulphate for about 30 min. The dried solution was concentrated with rotary evaporation and taken to dryness under high vacuum. The dried extract was dissolved in 2 mL of 1-propanol/water (1:1) and then filtered with a 0.22 μm filter.   165 7.3 Results and Discussion  7.3.1. Optimization of the MEKC separation conditions  The flavonoids were analyzed using a borate buffer containing sodium dodecyl sulfate (SDS). Borate was employed because it can complex with the flavonoids to form more soluble complex anions (Volpi, 2004). The optimization and separation was achieved by optimizing the wavelength of UV detection, the pH of the buffer, borate concentration, organic solvent, and SDS concentration. Using a photodiode array detector, UV spectra of the flavonoids were obtained. Based on the spectra, the UV detection was investigated at 214 nm, 254 nm, and 280 nm for the flavonoids studied. The measurement at 214 nm yielded the best signal and a more stable background as well as the best separation for the flavonoids studied. Thus, 214 nm was chosen as the optimum UV detection wavelength throughout the experiment.  The acidity (pH) of the running buffer affects the electroosmotic flow (EOF) as well as the overall charge of the analytes, which determine the migration time and affect the separation of the analytes. The pH of the running buffer was varied from pH 8.0 to 10.0 in increments of 0.5. The optimum resolution was achieved when the running buffer pH is 9.0. Using 20% 1-propanol gave the best results for the analysis. The use of 1-propanol did not interfere with the analysis. The borate concentration was also studied and 40 mM was found to be the optimum concentration for the separation.  To improve the resolution, the sodium dodecyl sulfate (SDS) concentration present in the borate buffer was optimized. The SDS concentration was varied from 10 mM to 80 mM in a 40 mM borate running buffer.  166  A typical electropherogram for the six flavonoids separated using the selected optimum conditions is shown in Figure 7.2. It can be seen that satisfactory separation is achieved within 16 min.   Figure 7.2. Electropherogram obtained from a standard mixture of six flavonoid compounds of 3.3× 10-5 g mL-1 of catechin (1), naringenin (2), kaempferol (3), apigenin (4), myricetin (5), and quercetin (6). Optimized separation condition was 40 mM borate solution containing 40 mm SDS at pH 9.0.        167 7.3.2 Regression equations, detection limits, recovery, and reproducibility for MEKC  Calibration curves for catechin (1), naringenin (2), kaempferol (3), apigenin (4), myricetin (5), and quercetin (6), ranging from 1.7 μg mL-1 to 200.0 μg mL-1 were established using the optimum separation conditions. In some cases, resorcinol was added in the separation as an internal standard to ensure the CE system is in proper conditions during these analyses. The detection limit is evaluated on the basis of S/N of 3. The results of the regression equations of calibration curves and detection limits for the six flavonoids are summarized in Table 7.1.  Table 7.1. Regression analysis on calibration curves, recovery, and detection limits Compound Regression equation Correlation coefficient (%) Linear range (μg mL-1) Detection limit (μg mL-1) Catechin  y =724.6x + 4687.9 99.4 1.7-200.0 0.0226 Naringenin  y = 708.4x – 198.4  99.6 1.7-200.0 0.0231 Kaempferol  y = 825.7x – 2246.1  99.8 3.3-200.0 0.0198 Apigenin  y = 1104.2x – 4746.0 99.3 3.3-200.0 0.0148 Myricetin  y = 814.4x – 13268.0 99.0 10-200.0 0.0201 Quercetin  y = 734.5x – 2729.3  99.6 6.7-200.0 0.0223           168 Table 7.2. Results of the recovery for this MEKC method (n = 3) Compound Original amount (μg mL-1) Added amount (μg  mL-1) Found (μg mL-1) Recovery (%) Catechin 15.3 60.0 69.7 93.0 Naringenin 8.0 40.0 41.0 85.0 Kaempferol 13.0 10.0 15.6 68.0 Apigenin 7.8 20.0 20.3 73.0 Myricetin 20.8 20.0 37.0 91.0 Quercetin 10.3 20.0 27.9 92.0    The flavonoids were identified by spiking the wine sample with a known amount of each flavonoid standard. The recoveries obtained for a typical red wine are shown in Table 7.2.  The reproducibility of the MEKC analysis was established by injecting three injections of the same standard mixture. The coefficient of variation (CV) for the migration times and the peak areas were calculated and the results are listed in Table 7.3. The CV for the retention times of all the peaks of the six flavonoid standards was <2% and the CV for the peak area was <5%. Reproducibility obtained using repeated injections of the wine samples also gave comparable results. This indicates that this MEKC method is highly reproducible.         169 Table 7.3.  Reproducibility of the studied flavonoids using MEKC (n = 3) Flavonoid Migration time (min) Migration time, CV (%) Peak area, CV (%) Catechin 10.1 1.3 2.8 Naringenin 10.9 1.5 2.2 Kaempferol 11.9 1.6 0.9 Apigenin 12.6 1.4 0.4 Myricetin 14.8 1.6 6.1 Quercetin 15.4 1.4 4.8   7.3.3 Wine sample analysis  Under the optimum conditions, flavonoids were determined in several red and white wine samples. Typical electropherograms for a red wine and a white wine are shown in Figure 7.3. By comparing the migration time of analytes with the electropherogram of a standard mixture, and by spiking of the wine samples, the six flavonoids can be determined. Analyzing the original wine directly did not yield accurate results as the electropherogram had a large background. It was therefore difficult to quantify accurately the peak areas of the analytes. The background improved dramatically following the extraction procedure used in this study and made quantification possible. The assay results for extracted samples of 6 red wines (labeled R1–R6) and 4 white wines (labeled W1–W4) are listed in Table 7.4. Three injections were made for each wine sample. The actual concentrations of the six flavonoids in the original wines would be 2/15 of the concentration values of the wine extracts listed in Table 7.4.   170 Table 7.4. Assay results for the flavonoids in 10 wine samples in μg mL-1(n = 3). Data in the  table are the means of three replicates; ND: not detected.  Catechin Naringenin Kaempferol Apigenin Myricetin Quercetin R1 56.7 78.6 32.0 22.4 30.3 26.0 R2 68.9 162.4 42.4 46.4 190.7 35.0 R3 121.7 70.6 13.5 ND 33.7 27.6 R4 24.4 88.8 111.1 33.3 63.3 33.1 R5 63.3 30.7 94.0 32.7 27.3 ND R6 22.2 83.5 61.3 ND 85.4 50.0 W1 85.4 17.0 ND 30.0 30.9 14.6 W2 77.2 7.9 24.6 17.5 58.8 46.2 W3 78.3 52.6 28.7 ND 60.9 80.0 W4 39.9 7.7 33.9 24.5 61.2 46.3         171    Figure 7.3. (a) and (b) are electropherograms obtained from diluted extracts of a red wine and a white wine respectively under optimum conditions.     172 7.4 Conclusions  An MEKC method was developed for the analysis of flavonoids with possible anti carcinogenic effects. The compounds were separated in 16 min in the BGE consisting of 40 mM borate containing 40 mM SDS and 20% v/v 1-propanol. This paper describes a practical method that can be used to compare the amount of potentially anti-carcinogenic flavonoids, and can be used for fingerprinting of wines from different regions.                   173 7.5 References  [1] De Rijke, E., Out, P., Niessen, W. M. A., Ariese, F., et al., Journal of Chromatography A 2006, 1112, 33. [2] Santornsuk, L., Journal of Pharmaceutical and Biomedical Analysis 2002, 27, 10. [3] Michael, G. L., Hertog, P. H., Hollman, P., Dini, P., J. Agric. Food Chem 1992, 40, 9. [4] Miean, K. H., Mohamed, S., J. Agric. Food Chem. 2001, 49, 7. [5] Bayard, V., Chamorro, F., Motta, J., Hollenberg, N. K., International Journal of Medical Sciences 2007, 4, 6. [6] Mak, P., Leung, Y.-K., Tang, W.-Y., Harwood, C., Ho, S.-M., Neoplasia 2006, 8, 9. [7] Furusawa, M., Tanaka, T., Ito, T., Nishikawa, A., et al., Journal of Health Sciences 2005, 51, 3. [8] Georgetti, S. R., Casagrande, R., Di Mambro, V. M., Azzolini, A. E., Maria, J., American Association of Pharmaceutical Scientists Journal 2003, 5, 4. [9] Proestos, C., Boziaris, I. S., Nychas, G.-J. E., Komaitis, M., Food Chemistry 2006, 95, 8. [10] Ielpo, M. T. L., Basile, A., Miranda, R., Moscatiello, V., et al., Fitoterapia 2000, 71, 10. [11] Havsteen, B. H., Pharmacol. Ther 2002, 96, 135. [12] Middleton Jr, E., Kandaswami, C., Theoharides, T. C., Pharmacol. Rev. 2000, 56, 78. [13] Powles, T., Breast Cancer Research 2004, 6, 3. [14] Brown, D. E., Rashotte, A. M., Murphy, A. S., Normanly, J., et al., Plant Physiology 2001, 126, 12. [15] Wang, S.-P., Huang, K.-J., J. Chromatogr. A. 2004, 1032, 7. [16] Da Queija, C., Queiros, M. A., Rodrigues, L. M., J. Chem. Ed. 2001, 78, 2. [17] Bilbao, M. d. L. M., Andres-Lacueva, C., Jauregui, O., Lamuela-Raventos, R. M., Food Chemistry 2007, 101, 6. [18] Fang, F., Li, J.-M., Pan, Q.-H., Huang, W.-D., Food Chemistry 2007, 101, 6. [19] Rehova, L., Skerikova, V., Jandera, P., Journal of Separation Science 2004, 27, 15. [20] Wang, S.-P., Huang, K.-J., Journal of Chromatography A 2004, 1032, 7. [21] Soczewinski, E., Hawryl, M. A., Hawryl, A., Chromatographia 2001, 54, 6. [22] Fiamegos, Y. C., Nanos, C. G., Vervoort, J., Stalikas, C. D., Journal of Chromatography A 2004, 1041, 8. [23] Weinberger, R., Practical Capillary Electrophoresis, Academic Press, New York 2000. [24] Molnar-Perl, I., Fuzfai, Z., Journal of Chromatography A 2005, 1073, 27. [25] Dadakova, E., Prochazkova, E., Krizek, M., Electrophoresis 2001, 6. [26] Rodriguez-Delgado, M. A., Perez, M. L., Corbella, R., Gonzalez, G., Montelongo, F. J., J. Chromatogr. A. 2000, 871, 12. [27] Tonin, F. G., Jager, A. V., Micke, G. A., Farah, J. P. S., Tavares, M. F. M., Electrophoresis 2005, 26, 9. [28] Suntornsuk, L., Journal of Pharmaceutical and Biomedical Analysis 2002, 27, 20. [29] Volpi, N., Electrophoresis 2004, 25, 7.       174                                             Chapter 8   Concluding Remarks                 175  Two computer simulation models of dynamic complexation capillary electrophoresis (DCCE) are presented in this thesis. The SimDCCE model was used to study single analyte- additive equilibrium (Chapter 2 and 3), whereas CoSiDCCE was developed to simulate multiple-additive, multiple-analyte, and multiple-stoichiometry equilibria (Chapter 6). Both simulation models were developed based on well defined mass transfer equation using finite difference scheme, which can simulate migration behaviors of all species efficiently. SimDCCE was written in C++ [1], whereas CoSiDCCE was developed using JAVA, which makes the simulation model more portable and versatile. While assuming a well-controlled physical and chemical environment and constant local electric field strength throughout the capillary, the simulation model can be utilized to demonstrate the interaction mechanism of species in various types of DCCE experiments (Chapter 2). The accuracy and efficiency of the program was examined through the simulation of real biomolecular interactions. With the SimDCCE program, detailed separation and migration processes of each component inside the capillary become visible in graphic formats, which provide better understanding on the separation mechanism of the interacting activity in vacancy ACE. The study of the thirteen scenarios demonstrated that the simulation model is capable of studying the Vacancy ACE in a comprehensive manner. Capillary electrophoresis-frontal analysis experiments were developed to study the binding characteristics of two protein-ligand interactions (Chapter 4 and 5). A new regression algorithm was introduced to determining binding constants and binding stoichiometry for higher order specific receptor-ligand interactions, which overcome the assumptions used in other commonly used regression methods. 176  The recently developed CoSiDCCE model has been used to simulate the enantiomeric separation of amino acids enantiomers (Chapter 6). The animation display of the concentration profile of each component explained how the enantiomer with similar physical and chemical properties and mobilities were separated gradually using chiral selectors in the capillary under a high voltage. With the high efficiency and accuracy of the CoSiDCCE model, the information provided by the simulation can be either used to design experiments for various CE modes, or to verify the experimental results in much more complex CE or microfluidic systems. The next step in developing simulation models of DCCE is to simulate more complex systems where the local electric field strength cannot be assumed constant. Protons and hydroxide ions should be included in the calculations and the effects of organic contents on the equilibrium constants and solution viscosity should also be considered. The simulation program will hopefully be able to handle multiple-step separation procedures. The MEKC experiment described in Chapter 7 is more complicated than ACE experiments because of the formation of micelles from SDS in the running buffer. This method has been used successfully in quantifying flavonoids at as low as 14.8 ng/ml (14.8 ppb). Appling an online sample concentration technique, such as sweeping-MEKC method, an even lower limit of detection (LOD) can possibly be achieved in analyzing and quantifying trace amounts of analytes in biological matrices. The method of MEKC and other online concentration techniques have been used extensively for various types of samples [2-4]. Once the future model is developed with the ability to simulate complex conditions mentioned earlier, it can be used to provide more detailed information on MEKC and related methods, and the many types of sample preconcentration techniques. 177  8.1 References  [1] Fang, N., Chen, D. D. Y., Anal. Chem. 2005, 77, 840-847. [2] Dadakova, E., Prochazkova, E., Krizek, M., Electrophoresis 2001, 6. [3] Rodriguez-Delgado, M. A., Perez, M. L., Corbella, R., Gonzalez, G., Montelongo, F. J., Journal of Chromatography A 2000, 871, 11. [4] Tonin, F. G., Jager, A. V., Micke, G. A., Farah, J. P. S., Tavares, M. F. M., Electrophoresis 2005, 26, 9.     178                          Appendix A   Supporting Material                 179      Scheme A.1. Chiral compounds used in this study.  The chiral centres are marked by “*”.  A.1 Calculation of Analyte Concentration Distribution and Analyte Mobilities In CE, each analyte-additive interaction consists of two simultaneous processes: electrophoretic migration and association/dissociation process. To obtain an accurate estimate on the concentration changes for each species during the entire process, the capillary was divided into thousands of narrow cells, and the migration flux of all species between adjacent cells is considered sequentially. First, the changes in concentrations due to the electrophoretic displacement were calculated. In the next step, based on the nature of the interaction (e.g., equilibrium, kinetics, stoichiometry), the association/dissociation process of the analyte(s), additive(s) and the complex(es) was considered. The changes in concentrations of all species in each cell were calculated before each species was allowed to migrate in the next time increment, and into the next cell. In CoSiDCCE, the electrophoretic migration is described by mass transfer equation   180  (or mass balance equation) [1, 2]: 2 ,, 2 ,,,, z C D z C E t C itz i itz zi itz ∂ ∂+∂ ∂−=∂ ∂ μ        (A.1) where i refers to one of the following species: free L- or D- enantiomer, chiral selector α-CD or HP-β-CD, or any enantiomer-chiral selector complexes. Through the electrophoresis process, the environment in the capillary is assumed to be well buffered and the local electric field strength is constant throughout the capillary. The time increment, Δt, defines the time interval between calculations. The space increment, Δz, defines the length of a cell that the capillary was divided into. With μ, E, D and selected Δt and Δz, the partial differential equation (eq. A.1) can be evaluated. In currently available CE simulation models, electrophoretic migration process was often described with finite difference schemes (FDS) [3-5]. Fang et al. compared the advantages and limitations of various FDS techniques.  The forward-time backward-space FDS method was reported to be the most accurate and robust algorithm for describing the analyte migration in CE with significantly reduced computing time, and our program also used this strategy [1]. In the next step, the association/dissociation processes were considered, and the concentration of each species in each cell was calculated when the new equilibrium is established. In this study, the interactions of two analytes, L- and D- enantiomers, with a single additive (i.e. chiral selector), α-CD or HP-β-CD, were investigated. Each of the studied amino acid enantiomer interacts with selected CDs at a 1:1 stoichiometry [6]. Since the binding process between the analytes and the chiral selector is relatively rapid and can be reached within very short time (Δt), the binding constant (K) is used in the calculation. The equilibria are described as the following:   181 L + C ⇌ LC          (A.2) D + C ⇌ LC                    (A.3) * * * , , [ ]  [ ] [ ] j LC f j f j LC K L C =          (A.4) * * * , , [ ] [ ] [ ] j DC f j f j DC K D C =          (A.5) Ktotal = KLC⋅KDC         (A.6) KLC and KDC are the binding constants for the individual analyte-selector interactions (1:1). The concentrations denoted as * ,[ ] f jL , * ,[ ] f jD , * ,[ ] f jC , *[ ] jLC  and *[ ] jDC  are equilibrium concentrations  at the current cell, j,  and are used to calculate the amount of each species migrating to the next cell. Ktotal is the overall binding constant for the interaction.  Rearrange eq. A.4 and A.5 by replacing * ,[ ] f jL , * .[ ] f jD , * .[ ] f jC  with the total concentrations of L, D and C ([L]T,j, [D]T,j and [C]T,j) which were obtained from the calculations for the electrophoretic migration process and remain constant at the equilibrium stage, the following cubic equation (eq. A.7) can be used to solve * ,[ ] f jC .The subscript “T” denotes the total concentration of a species, which includes the free and complexed species for L, D, and C, respectively.  Dividing eq. A.4 by eq. A.5, the following equation is obtained: * 3 * 2 , , , , , * , , , , , , , , [ ] ( ([ ] [ ] [ ] )[ ]       ( ([ ] [ ] [ ] ) [ ] [ ] [ ] 1)[ ] [ ] 0 LC DC f j LC DC LC DC T j T j T j f j DC T j T j T j DC T j LC T j LC T j f j T j K K C K K K K L C D C K L C D K L K C K L C C + + + − + + − + − − + + − =       (A.7) Since 0LC DCK K ≠ , without losing  generality, eq. A.7 can be divided by LC DCK K , giving   182 , , ,* 3 * 2 , , , , , , , , ,* , ([ ] [ ] [ ] [ ] [ ] ([ ] [ ] [ ] ) [ ] [ ] [ ] 1 [ ]       [ ] 0 LC DC LC DC T j T j T j f j f j LC DC DC T j T j T j DC T j LC T j LC T j T j f j LC DC LC DC K K K K L C D C C K K K L C D K L K C K L C C K K K K + + − ++ − + − − + ++ − =      (A.8) eq. A.8 can be written as:  * 3 * 2 *, 2 , 1 , 0[ ] [ ] [ ] 0f j f j f jC a C a C a+ + − =       (A.9) where  , , ,2 ([ ] [ ] [ ]LC DC LC DC T j T j T j LC DC K K K K L C D a K K + + − +=     (A.10)  , , , , , ,1 ([ ] [ ] [ ] ) [ ] [ ] [ ] 1DC T j T j T j DC T j LC T j LC T j LC DC K L C D K L K C K L a K K − + − − + +=  (A.11)    ,0 [ ]T j LC DC C a K K =          (A.12) Solving a cubic equation is more difficult than solving a quadratic equation. One way to make the cubic equation more solvable is to eliminate the 2a  term [7, 8],  and thus transferring the general cubic equation (eq. A.9) to a depressed cubic equation form as  * 3 *, ,[ ] 3 [ ] 2 0f j f jC Q C R+ − =        (A.13) by letting  2 1 23 9 a aQ −=          (A.14)  3 2 1 0 29 27 2 54 a a a aR − −=        (A.15) While calculating * ,[ ] f jC ,  the polynomial discriminant, d, was used to determine which roots are real and which are complex, where  3 2d Q R= +          (A.16)   183 The determination can be accomplished by noting that if  d > 0, one root is real and two are complex conjugates; if d = 0, all roots are real and at least two are equal; and if d < 0, all roots are real and unequal. In our study, * ,[ ] f jC  has to be a real number which is greater than or equal to zero and smaller than ,[ ]t jC , therefore only real roots were considered.  As d > 0, the real solution is  * 3 2 3 22 3 3,[ ] 3f j aC R Q R R Q R= − + + + + − +     (A.17) In the case of d = 0, the real solutions can be calculated as  * 30, ,1[ ] 23f j aC R= − +         (A.18)  * * 30, ,2 , ,3[ ] [ ] 3f j f j aC C R= = − −        (A.19) When d < 0, the three real solutions are of the form  * , ,1 2 1[ ] 2 cos( ) 3 3f j C Q aθ= − −        (A.20)  * , ,2 2 2 1[ ] 2 cos( ) 3 3f j C Q aθ π+= − −       (A.21)  * , ,2 2 4 1[ ] 2 cos( ) 3 3f j C Q aθ π+= − −       (A.22) where θ was defined as  1 3 cos ( )R Q θ −= −         (A.23)  Once * ,[ ] f jC  was calculated, by rearranging eq. A.4 and A.5 and replacing *[ ] jLC  and *[ ] jDC  with ([L]T,j - * ,[ ] f jL ) and ([L]T,j - * ,[ ] f jD ),  the concentrations of the free L and D after equilibrium process can be obtained.   184  ,* , * , [ ] [ ] [ ] 1 T j f j LC f j L L K C = +         (A.24)  ,* , * , [ ] [ ] [ ] 1 T j f j DC f j D D K C = +        (A.25)  At this moment, the calculations on concentration changes of all species in both the electrophoretic and the association/dissociation process at cell j were completed.  In each time interval tΔ , the calculation started at cell 0 of the loop, and ended when the last cell m ( /capillarym L z= Δ ) was reached (Table S1). After the entire loop was completed, it then moved on to the next step ( t t+ Δ ). The calculated final concentration of each species, such as * ,[ ] f jL , * .[ ] f jD , *[ ] jLC , and * ,[ ] f jDC in each cell at current time interval were saved and would be used in the calculation carried in the next time interval ( t t+ Δ ).  Table A.1.  Cell arrangement in the memory of a PC.  cell 0 cell 1 cell 2 cell 3 … cell j cell j+1 … cell m-1 cell m  t Cz-Δz,t,i Cz,t,i Cz+Δz,t,i Cz+2Δz,t,i … t+Δt Cz-Δz, t+Δt,i Cz,t+Δt,i Cz+Δz,t+Δt,i t+2Δt t+3Δt      Table A.1 shows the cell arrangement in the memory of a PC.  Cell 0 is the starting point. Cell m is the last cell allocated in each calculation loop. When the analyte passed this cell, it means the calculation in the current time interval t is completed, and thus it moves to …  …   185 the next step t t+ Δ . The last cell allocated in the memory is Cell m at step t+nΔt where n is the number of calculation loops required to complete the simulation run.   Once all interested species passed the position of the defined detection point on the capillary, the simulation process is stopped. In the collected simulation data file, the concentration of each species is converted by multiplying the experimentally measured UV absorption factor of corresponding species in order to match the experimental electropherograms.                  186 A.2 Implementation Unlike the C++ language based SimDCCE program, CoSiDCCE is developed with a universal programming language JAVA, which allows the simulation to be run on most personal computers running Microsoft Windows or other operating systems, such as those used in Macintosh computers. The user interface of the model is divided into three regions (Figure A.1). Region 1 is the simulation control panel. The function icons are listed in the first row. In the second row, the analytes involved in the interaction, as well as the overall UV absorbance signal are listed and can be selected by the user as needed for the animation display. Region 2 is the parameter panel in which experimental conditions and simulation parameters can be entered. The Reaction Mode Selector is located at the top of the panel, which contains ten analyte-additive reaction modes, including equilibrium and non- equilibrium 1:1, 1:2 analyte-additive interaction, single analyte-multiple additive interaction, and multiple analyte-single additive interaction. In addition to these analyte-additive interactions, simple separation of multiple analytes is also available in the program. In this work, only the equilibrium-multiple-analyte-single-additive-interaction mode was used. The graphic format of concentration changes for all species throughout the capillary is displayed in Region 3 in real time or faster.   187   Figure A.1. User interface of CoSiDCCE. Region 1: control panel for the simulation process. Region 2: selector for the simulation modes and input for experimental conditions for simulation parameters. Region 3: simulation animation display window.   To run a simulation with CoSiDCCE, the user is required to input all experimental conditions into the program, including the total length of the capillary, the length of the capillary from the injection end to the detector, the voltage and temperature used for the separation, the concentration and electrophoretic mobility of each analyte and additive, the calculated mobility of each formed complex, the calculated binding constants for each interaction (i.e. the interaction of α-CD with L- or D- enantiomers), the value of viscosity correction factors (v), and experimentally measured relative UV intensities of each species. Most of these conditions can be obtained from the experimental results, however, the binding parameters and the complex mobilities need to be calculated through a non-linear regression   188 method using the concentration of the additive and the apparent mobility of each analyte measured from a set of experiments. In the present work, the apparent mobility of a series of L- and D- enantiomers, ep Lμ and ep Dμ , can be measured directly from the electropherograms when small amount of recamic mixture is injected into the capillary filled with various concentrations of α- or HP-β- CD in the present study.  The apparent mobility of the analyte enantiomer is a reflection of the proportion of the analyte in their form the proportion that are complexed to the chiral selector, as expressed in the following: , ,(1 ) L ep L ep L L ep LCf fνμ μ μ= + −        (A.26)  , ,(1 ) D ep D ep D D ep DCf fνμ μ μ= + −       (A.27) [ ] [ ] [ ] [ ] [ ] f f L T f L L f L L LC = = +            (A.28) [ ] [ ] [ ] [ ] [ ] f f D T f D D f D D DC = = +          (A.29) where fL and fD are the fraction of free L- and D- enantiomers; ,ep Lμ , ,ep Dμ , ,ep LCμ and ,ep DCμ are the electrophoretic mobilities of free enantiomers and the formed diastereomeric complexes LC and DC, respectively. Rearranging eq. A.4 and eq. A.5, the concentration of respective complexes can be described as: [ ] [ ] [ ]LC f fLC K L C=          (A.30) [ ] [ ] [ ]DC f fDC K D C=         (A.31) and thus eq. A.26 and A.27 can be rewritten as:   189 , , [ ]1 1 [ ] 1 [ ] LC fL ep ep L ep LC LC f LC f K C K C K C νμ μ μ= ++ +      (A.32) , , [ ]1 1 [ ] 1 [ ] DC fD ep ep D ep DC DC f DC f K C K C K C νμ μ μ= ++ +     (A.33) When the amount of chiral selector (i.e. cyclodextrin) present in the BGE is very low, only small portion of free enantiomer is complexed with the selector, the apparent mobility of the enantiomer is approximately the same as its electrophoretic mobility (i.e. , L ep ep Lμ μ≈ and , D ep ep Dμ μ≈ ). Because , ,ep L ep Dμ μ= , no separation can be achieved.  In the case of an extremely large amount of additive being present in the running buffer, the fractions of free enantiomers, fL and fD, are minimal and the apparent mobilities are similar to the complex mobility. When the enantiomer-selector complexes migrate with different speed in free solution, with different binding affinity and complex mobility, , ,ep LC ep DCμ μ≠  and LC DCK K≠ , the enantiomer peaks can be resolved by simply adding sufficient amounts of chiral selector in the BGE. However, when the complexes are attached to the chiral recognition stationary phase, or migrate with identical speed in free solution, the enantiomeric separation can be achieved only if the binding affinity of chiral selector with each enantiomer is significantly different. In earlier studies of the CD-mediated enantiomeric CE separations, all binding parameters were calculated with the following equation through multivariant curve fitting [9, 10]: , ,[ ] [ ] 1 [ ] 1 [ ] f ep LC LC f ep DC DCL D ep ep L D K C K C K C K C μ μ μ μμ μ + +− = −+ +      (A.34)   190 The left hand side of the equation is the difference in the apparent mobility of the L- and D- enantiomers. fμ  is the mobility of the analyte enantiomers in the free form when assuming the electrophoretic mobilities of a pair of free enantiomers are identical. [C] is the concentration of the chiral selector. KLC, KDC, ,ep LCμ  and ,ep DCμ  are as defined earlier. This approach has applied in two separate situations: (1) when the mobilities of the diastereomeric complexes are the same, the separation is achieved in the case of different binding constants ( LC DCK K≠ ) (eq. A.35), such as HPLC enantiomeric separation using immobilized chiral selectors; (2) when the binding constants are the same, the separation is achieved based on the different complex mobilities ( . .ep LC ep DCμ μ≠ ) (eq. A.36). ( )( )[ ] 1 ( )[ ] [ ] f C L DL D ep ep L D L D K K C K K C K K C μ μμ μ − −− = + + +       (A.35)   , , [ ]( ) 1 [ ] ep LC ep DCL D ep ep K C K C μ μμ μ −− = +       (A.36) However, the cases where the binding constants and the complex mobilities are both different were never considered. In CE enantiomeric separations, without using an immobilized molecular recognizing stationary phase, the equilibrium constants and the complex mobilities can be both different. In our study, the concentration of CDs present in the BGE has an influence on the viscosity of the buffer solution, therefore, a viscosity correction factor, v ( 0/ν η η= ), should be considered to ensure the correct mobility values used in further calculation. Rearranging eq. A.32 and eq. A.33, the following equations should be used to obtain more accurate binding parameters for respective enantiomers.   191 , [ ] 1 [ ] f ep LC L fL ep L f K C K C μ μνμ += +          (A.37) , [ ] 1 [ ] f ep DC D fD ep D f K C K C μ μνμ += +         (A.38) As fμ is known, to be able to fit the data with non-linear regression method, eq. A.37 and A.38 can be transferred to: , , , ( ) [ ] 1 [ ] ep LC ep L LC fL ep ep L L f K C K C μ μνμ μ −− = +       (A.39) , , , ( ) [ ] 1 [ ] ep DC ep D DC fD ep ep D D f K C K C μ μνμ μ −− = +                 (A.40) The values of v at different CD concentrations were calculated based on the measurement of η  [11].  [C]f is the concentration of free chiral selector or additive. In all experiments, the concentration of the selector is much greater than that of the analytes, thus, the [C]f is assumed to be the same as the total concentration of the selector in the BGE. Regardless of the enantiomeric separation is based upon differences of binding affinity constants and/or the mobilities of diastereomeric complexes, eq. A.39 and A.40 can be applied.             192 A.3 Simulation Results CoSiDCCE was utilized to simulate the two types of CD-mediated enantiomeric separations. The relative mobility order is ( ) ( )L D LC DC Cμ μ μ μ μ> > . All experimental conditions were used in the simulation. The eletroosmotic flow (EOF) was assumed to be 0 s at pH 2.5. The estimated sample plug injected was 0.488 cm. The reported symmetrical dispersion coefficient, D, for tryptophan enantiomers and their complexes are on the order of 10-10 m2s-1[12]. In the studied case, the influence of the longitudinal diffusion on the peak shape was not significant in amino acid-selector interactions; therefore, in all simulations, the dispersion coefficients for all species were set to be 1×10-10 m2s-1, instead, measured experimentally. In CoSiDCCE, space (Δz) and time (Δt) increments are the two most important parameters. As discussed in our earlier study, in general, smaller Δz and Δt can generate more accurate results, but longer computing time is required. To ensure an accurate simulation with a reasonable computing speed, 22 /( ) 1D t zΔ Δ ≤  and | |i zz E tμΔ ≥ Δ  must be satisfied [1, 13]. In all simulation runs presented in this paper, the space increment was set to 0.001 cm, and the time increment was 0.01 s. The settings meet all the aforementioned requirements, and could indeed generate good simulation results within a few minutes on the laptop computer (Intel Centrino Duo 1.60 GHz, 1GB RAM).  The simulated and experimental electropherograms for series of chiral separations with α- and HP-β- CD are compared. The experimental migration times, peak shapes and peak areas match closely with the simulated results. To understand the interaction process of the species during CE, CoSiDCCE was used to simulate the migration behaviour of the interested analytes in a graphic format throughout   193 the process. Four snapshots taken from an ACE run at selected moments were exported and analyzed in Figure A.2 to demonstrate the interaction and concentration changes of each species in capillary. A relative small volume of 1 mM L/D-Trp mixture was introduced to the capillary filled with a buffer containing 20 mM α-CD (Figure A.2 A). As voltage is applied to the capillary, the tryptophan enantiomers move ahead of the α-CD and exit the vacancy of the chiral selector from the front edge. Without EOF, the native α-CDs will not migrate toward the outlet, but acting as a pseudo stationary phase in the capillary. When the analyte enantiomers catch up the α-CDs in front of the injected plug, the enantiomer-selector complexes start to form (Figure A.2 B). Since the mobility of free enantiomer is greater than that of the complex, to maintain the equilibrium condition in the buffer solution, small amount of L- and D- enantiomers and α-CD are dissociated from the complex as the L- and D- enantiomers migrated through the vacancy plug, which causes the formation of the curved front edge of the α-CD trough and minor tail at the back edge of the analyte plug (Figure A.2 C). Once the sample plug passes through the vacancy zone of α-CD, the steady state condition is established throughout the capillary. In the studied case, because the vacancy zone does not migrate during CE process, the steady state can be reached in very short time. The final concentration profiles of free α-CD, L- and D- enantiomers and complexes at 96 s are shown in Figure A.2 D. More details on the concentration profile of the free L- and D- enantiomers and the corresponding enantiomer-selector complexes are given in the interior figure where the unsymmetrical peak shape for the L- and D-Trp plug is more obvious. Due to the relative low concentration of α-CD and small binding affinity of α-CD to tryptophan, the amount of enantiomer remained in free form is much higher than that in the complexed form.   194 0.0 0.1 0.2 0.3 0.4 0.5 C on ce nt ra tio n (m M ) 0 5 10 15 20 0.0 0.2 0.4 0.6 0.8 0 5 10 15 20 On-capillary position (cm) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0 5 10 15 20 [L-Trp-α-CD] [D-Trp-α-CD] [L-Trp] [D-Trp] [α-CD] 0.0 10.0 15.0 0 5 10 15 20 14.0 14.5 15.0 15.5 16.0 0.0 0.4 0.8 1.2 A B C D 0.488 cm 0.488 cm 0.488 cm 1.12 cm  Figure A.2. Simulated concentration profiles for the separation of 1mM L/D-Trp in 0.1 M phosphate solution with 20 mM α-CD in 0.1 M phosphate solution. Sample injection time: 3s, 0.5 psi. Separation voltage: +22.5 kV, KLC = 8.15 M-1 and KDC = 11.82 M-1. The concentration profiles of the five species are displayed in time sequence: (A) 0 s (before the injected sample start migrating toward the outlet); (B) 4.0 s; (C) 10.0 s; (D) 96.0 s.   195 Time (min) 30.0 35.0 40.0 45.0 50.0 55.0 Ar bi tra ry  U ni t ( AU ) 0.0 2.0e+4 4.0e+4 6.0e+4 8.0e+4 1.0e+5 1.2e+5 110mM HP-β−CD 120mM HP-β-CD 130mM HP-β-CD 140mM HP-β-CD 150mM HP-β-CD 160mM HP-β-CD 170mM HP-β-CD 180mM HP-β-CD 190mM HP-β-CD 200mM HP-β-CD   Figure A.3. Simulated electropherograms for the separation of 1mM L/D-Trp recamic mixture, with HP-β-CD ranging from 110 mM to 200 mM in 0.1 M phosphate buffer.   The experimental results show that chiral separation cannot be achieved when using HP-β-CD ranging from 10 mM to 100 mM, but obvious shifts on migration time, peak broadening and gradually decreased UV intensity were observed, which suggests that the enantiomer peaks might be resolved if sufficient HP-β-CD was added in the separation buffer (or BGE). To avoid tedious sample preparations and relative time-consuming CE experiments, CoSiDCCE was used to predict the migration time and peak shape for enantiomer analytes when up to 200 mM HP-β-CD was added to the BGE. The viscosity   196 correction factor, v, used for the simulation was calculated based on the linear relation obtained on the measurement for the HP-β-CD solutions. As demonstrated in Figure A.3, the racemic mixture peak started splitting at higher HP-β-CD concentration; however, it was still impossible to resolve the two enantiomer peaks completely even when 200 mM HP-β-CD was used. As Melta and co-works reported [12],  with one more glucose unit on cyclodextrin, in the studied concentration range of CDs (10 mM to 100 mM) the tryptophan enantiomers have similar ability to bind HP-β-CD when migrating along the capillary during electrophoresis and no enantiomeric separation can be achieved.                  197 A.4 References [1] Fang, N., Chen, D. D. Y., Anal. Chem. 2005, 77, 840-847. [2] Giddings, J. C., Unified Separation Science, John Wiley & Sons, Inc., New York 1991. [3] Bier, M., Palusinski, O. A., Mosher, R. A., Saville, D. A., Science 1983, 219, 1281-1287. [4] Ermakov, S., Mazhorova, O., Popov, Y., Informatica 1992, 3, 173-197. [5] Ermakov, S. V., Bello, M. S., Righetti, P. G., J. Chromatogr. A 1994, 661, 265-278. [6] Zhu, Y. S., Tu, C. Y., Gu, W., Wei, P., Ouyang, P. K., Chinese Journal of Analytical Chemistry 2007, 35, 127-130. [7] Berndt, B. C., Ramanujan's Notebooks, Springer-Verlag, New York 1994. [8] Spanier, J., Oldham, K. B., An Atlas of Functions, Hemisphere, Washington, DC 1987, pp. 131-147, . [9] Scriba, G. K. E., J. Sep. Sci. 2008, 31, 1991-2011. [10] Wren, S. A. C., Rowe, R. C., Journal of Chromatography 1992, 603, 235-241. [11] Peng, X. J., Bebault, G. M., Sacks, S. L., Chen, D. D. Y., Can. J. Chem.-Rev. Can. Chim. 1997, 75, 507-517. [12] Malta, L. F. B., Cordeiro, Y., Tinoco, L. W., Campos, C. C., et al., Tetrahedron- Asymmetry 2008, 19, 1182-1188. [13] Fang, N., Sun, Y., Zheng, J. Y., Chen, D. D. Y., Electrophoresis 2007, 28, 3214-3222.        198                                                    Appendix B                   CoSiDCCE User Guide    199  B.1 Introduction to User Interface The computer simulation program CoSiDCCE was written in Java. This program runs on Microsoft Windows and the operating systems installed on Macintosh computers without installation.     Figure B.1. The user interface of CoSiDCCE is divided into three regions: 1. the simulation control panel; 2. the simulation setting panel defines experimental conditions and simulation parameters; 3. the display panel displays the animation of the simulated concentration profiles of the analytes.  B.2 Tutorial for CoSiDCCE  CoSiDCCE has two functions: (1) simulating the interaction mechanism between species; (2) determining interaction binding constant, K, using enumeration algorithm. 200  B.2.1 Simulate the Interaction Mechanism for Species B.2.1.1 Step 1: Select the reaction type for the analyte-additive interaction   CoSiDCCE can be used to simulate up to ten types of DCCE interactions, including equilibrium and non-equilibrium 1:1, 1:2 analyte-additive interaction, single analyte-multiple additive interaction, multiple analyte-single additive interaction (Table B.1), with real or hypothetical experimental conditions.  Table B.1. The type of reactions that can be studied in the CoSiDCCE program. 1 Equilibrium single analyte-additive interaction 2 Non-equilibrium single analyte-additive interaction 3 Equilibrium 1:2 analyte-additive interaction 4 Non-equilibrium 1:2 analyte-additive interaction 5 Equilibrium 2:1 analyte-additive interaction 6 Non-equilibrium 2:1 analyte-additive interaction 7 Equilibrium single analyte-multiple additive interaction 8 Non-equilibrium single analyte-multiple additive interaction 9 Equilibrium multiple analyte-single additive interaction 10 Non-equilibrium multiple analyte-single additive interaction    Before starting a simulation run, the user is required to select the type of the reaction that will be simulated from the “Reaction Type Selector” (Figure B.2).  201                      Figure B.2. Screenshot of the extended Reaction Type Selector panel.   B.2.1.2 Step 2: Set experimental conditions In this tutorial, CoSiDCCE is used to simulate a real equilibrium multiple analyte-single additive ACE experiment, consisting of the analyte tryptophan enantiomers that interacts with the additive α-cyclodextrin (α-CD). The experimental conditions are listed in Table B.2. Figure B.3 demonstrates the CoSiDCCE setting panel containing all these conditions.  Table B.2. The list of the experimental conditions used to simulate the interaction of tryptophan with α-CD. Length of the capillary  Ltotal = 50 cm Length to the detector Ldetection 40 cm Inner diameter of the capillary i.d. = 75 μm Length of the injected sample plug Lsample = 0.488 cm Voltage V = +22.5 kV Temperature of the capillary T = 25 oC Ramp time 10.2 s Idle time 20 s Detector type UV Detection wavelength 214 nm Electroosmotic flow 0 s Time of EOF marker 0 s 202  [A] in the injected sample plug [A] = 1 mM [B] in the injected sample plug [B] = 1 mM [C] in the injected sample plug [C] = 0 mM [A] in the BGE [A] = 0 mM [B] in the BGE [B] = 0 mM [C] in the BGE [C] = 50 mM Mobility of the free analyte A μep,A = 1.076×10-4 cm2/V ⋅s Mobility of the free analyte B μep,B = 1.076×10-4 cm2/V ⋅s Mobility of the free additive C μep,C = 0 for neutral α-CD Estimated complex mobility AC μep,AC = 1.911×10-5 cm2/V ⋅s Estimated complex mobility BC μep,BC = 2.302×10-4 cm2/V ⋅s Diffusion coefficients 10-10 cm2s-1 for all species Viscosity correction factor  ν = 1.08 for all species Space increment  Δz = 0.01 cm Time increment  Δt = 0.01 s Signal multiplier of the analyte A 6.0×107 Signal multiplier of the analyte B 6.18×107 Signal multiplier of the additive C 0 for α-CD Signal multiplier of the complex AB 0 Signal multiplier of the complex BC 0 Estimated binding constant K1 = 8.15 M-1 Estimated binding constant K2 = 11.82 M-1    203    Figure B.3. Screenshot of the parameter panel after all the experimental conditions were set in.   Experimental conditions: 1. The length of the injected sample plug was estimated using Beckman CE Expert software provided by the manufacturer of the CE instrument. 2. The idle and ramp time are default parameters from the CE instrument used. 3. Detector type and wavelength used for the detection are defined by the user. 4. The mobility of the free analyte ( ep,Aμ ) was measured from CE experiments, during which no additive was present in the separation buffer (or background electrolyte solution). 5. The binding constants (K1 and K2) and the complex mobilities ( ep,ACμ  and ep,BCμ ) were determined using the regression methods. These values are required to run a single simulation to show the mechanism. 204  6. The interaction between the analyte and the additive in this experiment occurs very quickly, so the system can be assumed to be equilibrated at any given position and moment. Consequently, this experiment is an equilibrium CE experiment in which the equilibrium constant is used in the calculation. 7. The diffusion coefficients for all species were set at 10 2 -110 cm s−  in this tutorial. No real values were obtained from either experiments or the literature. 8. The viscosity correction factors of each BGE solution, v, was measured by injecting a plug of 10 mM thymidine into the inlet of a capillary filled with corresponding BGEs and applying a constant pressure (20 psi) to push the sample plug through the capillary. To obscure the effect of the shift in equilibrium on the measured mobilities, the viscosity correction factor (ν ) of various concentrations of BGE solution can be obtained. 9. The values of the Length of a Cell (Δz) and Time Increment (Δt) is directly related to the accuracy and speed of the simulation. For this simulation run, Δz and Δt were set at 0.01 cm and 0.01 s, respectively. 10. The signal multiplier value of each species can be measured at selected wavelength. More details were illustrated in Chapter 1. In CoSiDCCE electropherograms are generated in a similar fashion as the real CE instrument. The concentration of each species in the detector cell multiplies the signal multiplier of the corresponding species yields the same value as UV or LIF signals. 11. The small panel located at the bottom of the setting panel provides more details on the selected condition.  205  B.2.1.3 Step 3: Save and open a simulation parameter file   Click on the “Save Para File” button (Figure B.4), all parameters that have been set in the parameter panel are saved in a simulation parameter file. Click the “Open Para File” button to open a saved simulation parameter file for a simulation run. All parameter files are given a default “.sce” extension. Because multiple interaction types are included in this model, it will be helpful if the user specifies the correct interaction type in the name of parameter file.  Figure B.4. Screenshot of the control panel in “Interaction” tab.   B.2.1.4 Step 4: Choose interested item for the animation   To observe the detailed separation and migration activity of each species inside the capillary, select your interested item(s) listed in the control panel, including “free A” (analyte A in free form), “free B” (analyte B in free form), “free C” (additive C in free from), “complex AC”, “complex BC”, “total A” (analyte A including free and complexed form), “total B” (analyte B including free and complexed form), “total C” (additive including free and complexed form), and “overall signal”  as listed in Figure B.5. The square bracket indicates concentration of corresponding species. The “overall signal” profile is the converted concentration profile that can be used to generate the final electropherogram. All items can be selected or deselected at anytime during a simulation run.  206   Figure B.5. Screenshot of the Control Panel.    B.2.1.5 Step 5: Inject the sample plug    When double clicking on the “Initial” button, colorful curves will subsequently evolve on the display panel, which demonstrates the concentration profile of the selected item before a CE simulation starts as given in Figure B.6.  Figure B.6. Screenshot of the CoSiDCCE program at the initial stage of the simulation.     B.2.1.6 Step 6: Start a simulation run  Click on the “Start” button, the colorful curves start moving on the display panel (Figure B.7), which allows the user to observe the real-time change on the concentration profile of each species that has been selected in the control panel.  207   Figure B.7. Screenshot of the CoSiDCCE program during a simulation run.   The simulation can be paused or stopped at any time. Once the “Pause” button is clicked during a run, the “Pause” button turns into the “Restart” button, and the “Stop & Clear” button becomes available.  B.2.1.6 Step 6: Save simulated data file   Click on the “Save Current Data File” button to capture a snapshot (Figure B.8A). A window pops up asking the user for a location in which to save the snapshot data file, which assumes a “.txt” extension. After the data file is saved, a message window pops up and shows “File saved” (Figure B.8B). A snapshot can be taken when the simulation is running or paused, but not when the simulation is stopped.  208    Figure B.8. Screenshot of the CoSiDCCE program when (A) the “Save Current Data” button is clicked, and (B) the file is successfully saved.    Once the analyte plug reach the distance that set up for the detector window, click the “Save Electropherogram” button (Figure B.7A), a window pops up asking the user for a location in which to save the final simulation result. The file can be opened with various types of data processing software, such as Microsoft Excel and SigmaPlot 10.0.  B.2.2 Determine binding constant, K, using enumeration algorithm  Click on the “Binding Constant” tab on the CoSiDCCE program to open the binding constant determination function. This function also consists of control panel and simulation parameter panel as shown in Figure B.9.  209    Figure B.9. The user interface of the “Binding Constant” determination function is divided into two regions: 1. Control Panel; 2. Simulation Parameter Panel.   B.2.1.2 Step 2: Set experimental and scan conditions   The “Binding constant” function of this program will not generate the shape of the entire analyte peak; instead, only the migration times of the peak maximums (Tsim) are generated.  To calculate the binding constant using the enumeration algorithm, in addition to all experimental conditions, the user is required to define the experimental migration time of the formed complex (Texp), and a range for binding constant, K, and the complex mobility, μep,C, with a user-defined interval, ΔK and Δμep,C, to be scanned by CoSiDCCE. An example is given in Figure B.10.  210   Figure B.10. Screenshot of the settings panel on the User Interface of “Binding Constant” determination function after experimental migration time Texp, estimated binding constant Kmin and Kmax, complex mobility μep,C, min and μep,C, max, and interval ΔK and Δμep,C were set in.  B.2.2.2 Step 2: Process a scan   Click the “Start” button (Figure B.11A), the program begins scanning the assigned range for K and μep,C. Once the calculation is completed, a window pops up and confirms the “Calculation is done” as demonstrated in figure B.9B. Click “Ok” to close the message window.    Figure B.11. Screenshot of the message window.  B.2.2.3 Step 3: Save the generated 2-D and 3-D data files  One can use the “Save 3D” button to save the 3-D data file (Figure B.12). Again, when clicking on the button, the program will ask the user for a location in which to save the 211  data file, which assumes a “.txt” extension. After the data file is saved, a window pops up and shows “File saved”. By default, the first, second and third columns of a 3-D data file contains entire range of the scanned complex mobility, μep,C, binding constant, K, and the generated migration time, Tsim, respectively as given in Figure B. 13.   Figure B.12. Screenshot of the Control Panel of the Binding Constant tab.     Figure B.13. The sample of a 3-D and 2-D data file generated.  212   When the generated migration time, Tsim, agrees with the assigned experimental migration time, Texp, the pair of K and μep,C values are collected to generate a 2-D curve as given in Figure B.14.   Figure B.14. A 3-D surface which is cut through by a plane to produce a 2-D curve, which is then projected onto the bottom plane: (1) The 3-D surface, (2) the cutting planes, (3) the intersection between 1 and 2, and (4) the projected intersection curve. Reprinted with permission [1].   Similar as the “Save 3D” function, click the “Save 2D” button to save the extracted 2- D date file (Figure B.12). By default, the first, second and the third columns of a 2-D data file corresponding to the scanned complex mobility, μep,C, μep,A/μep,C and the K values, respectively (Figure B. 13). Because μep,C values are normally very small, the μep,A/μep,C can be used instead with the user’s choice. The sample of a 3-D and 2-D data files is given in Figure B.13. 213   When another ACE experiment is performed with identical conditions except for the initial concentration of the analyte or additive, Tsim resulting from the same K and μep,C values will be different from the previous one, creating a different 3-D surface. A new 2-D curve can be obtained on the basis of the new Texp. Because the two experiments used the same analyte and additive, the binding constant and the complex mobility should have the same values. Therefore, the two 2-D curves have to intersect. The coordinate of the intersection gives the values for the binding constant and the complex mobility (or μep,A/μep,C with the user’s choice). If more experiments are performed, the 2-D curves extracted from all 3-D surfaces should all intersect at one point (Figure B.15), because there is only one true binding constant for a given binding interaction under specified conditions [1].    Figure B.15. 2-D graph generated from the simulation program with μep,A/μep,C as the x axis. [p-Nitrophenol]) 2mM. Each curve is composed of data points. Each color of the curves corresponds to one additive (α-cyclodextrin) concentration. Three shapes (circle, square, and triangle) in one color correspond to three ACE runs under identical experimental conditions. The red rectangle indicates the intersection of eight sets of curves. Reprinted with permission.1 214  B.2.2.4 Step 4: Obtain the coordinates of the intersection of the curve data sets  The 3-D and 2-D data file can be processed with Microsoft Excel or SigmaPlot. Each set of the 2-D data can be fitted with a xy b cx += +  using commercial software, such as SigmaPlot, or the “curve fitting” function found in the CoSiDCCE program.  Copy the generated regression data to a new worksheet. If another 2-D data is fitted with the non-linear regression, copy the regression data set to the same worksheet and list them side by side as demonstrated in Figure B.16.   Figure B.16. Two sets of generated regression data for the 2-D curve, (x1, y1) and (x2, y2), are listed side by side in a new SigmaPlot worksheet.  215   Highlight all the data on the worksheet and export it into a “Comma Delimited” (.csv) file.  Click the “Open curve file” button found in the Control Panel. A window pops up and asks the user to provide the location of the curve file. Find the file name and click “Open”, a small message window pops up and displays the coordinates of the intersection of the curve data sets contained in the file. The X value indicates the estimated complex mobility μep,C or the ratio of μep,A over μep,C as the user’s preference, and the Y value indicates the estimated binding constant K.                216  B.3 Ten Type of DCCE Binding Interactions B.3.1 Evaluation of mass transfer equation In CoSiDCCE, the electrophoretic migration can be described by mass transfer equation. To achieve an efficient and sufficiently accurate simulation result, in CoSiDCCE, eq. B.1 is transferred into a finite difference equation as discussed in Chapter 1. 2 ,, 2 ,,,, z C D z C E t C itz i itz zi itz ∂ ∂+∂ ∂−=∂ ∂ μ      (B.1) B.3.2 Association and dissociation processes  The new concentrations of all species in each cell are obtained after the electrophoretic migration process is completed. The association/dissociation processes are then considered. The concentration of each species in each cell is calculated when the new equilibrium is established. Based on the interaction stoichiometry and speed of association/dissociation process between species, in the CoSiDCCE,  ten DCCE modes can be studied, including the equilibrium and non-equilibrium 1:1 and 1:2 analyte-additive interactions, multiple analyte-single additive or multiple additive-single analyte interactions. Each type of the interactions is different and thus requires its own set of equation to calculate the new concentration for each species involved in the binding process.  B.3.2.1 Equilibrium and non-equilibrium single analyte-additive interaction (1:1)  When the equilibrium single analyte-additive interaction is studied, the binding equilibrium can be described as: A + P ⇌ AP           (B.2) 217  As the binding process between the analyte (A) and the additive (P) is relatively fast, the binding constant (or complex constant), K, can be written as * * * , , [ ]  [ ] [ ] j AC f j f j AP K A P =        (B.3) whre the equilibrium concentrations of the free analyte, the free additive and the complex at the current cell, j, are denoted as * ,[ ] f jA , * ,[ ] f jP , * ,[ ] f jAP , respectively.  By replacing *[ ] jAP  and * ,[ ] f jP with the total concentrations of A and P ([A]T,j and [P]T,j) which were obtained from the calculations for the electrophoretic migration process and remain constant at the equilibrium stage,  The following quadratic equation can be used to solve * ,[ ] f jA ,  * 2 *, , , , ,[ ] ( [ ] [ ] 1)[ ] [ ] 0f j t j t j f j t jK A K P K A A A+ − + − =         (B.4) The subscript “T” denotes the total concentration of a species, which includes the free and complexed species for A and P, respectively. The concentration of the complex formed, *[ ] jAP , and free additive, * ,[ ] f jP are calculated from the following:  * *, ,[ ] [ ] [ ]j T j f jAP A A= −        (B.5)  * *, ,[ ] [ ] [ ]f j T j jP P AP= −        (B.6)   When slower association/dissociation interactions are studied with CE, the forward and reverse rate constant, k+1 and k-1, are used. The concentration of the free analyte, the free additive and the complex after the electrophoretic migration process in the current step (j) are denoted as [A]f,j, [P]f,j and [AP]f,j. After the binding processing is complete, the final 218  concentration of the free analyte, the free additive and the complex, * ,[ ] f jA , * ,[ ] f jP  and * ,[ ] f jAP ,in current cell j can be calculated as,  * , , 1 , , 1[ ] [ ] ( [ ] [ ] [ ] )f j f j f j f j jA A k A P k AP t+ −= − − Δ             (B.7)  * , , 1 , , 1[ ] [ ] ( [ ] [ ] [ ] )f j f j f j f j jP P k A P k AP t+ −= − − Δ    (B.8)  * *, ,[ ] [ ] [ ]j T j f jAP A A= −        (B.9)  B.3.2.2 Equilibrium and non-equilibrium higher order analyte-additive interaction (1:2) When higher order equilibrium analyte- additive interactions are investigated, binding affinity constant, K, is used in the calculation. The equilibrium can be described as, A + 2P ⇌ AP2         (B.10) ( )2 * 2 2* * , , [ ]  [ ] [ ] j AP f j f j AP K A P =        (B.11) 2AP K is the overall binding affinity constant for the 1:2 analyte-additive interaction, and the concentration of the free analyte, the free additive, and the complex AP2 after the electrophoretic migration process in the current cell,  j, are denoted as * ,[ ] f jA , * ,[ ] f jP , and * 2[ ] jAP .      Replacing *2[ ] jAP  and * ,[ ] f jP with the total concentrations of A and P ([A]T,j and [P]T,j) which are obtained from the calculations for the electrophoretic migration process yields, * * 2 , ,[ ] [ ] [ ]j T j f jAP A A= −         (B.12)  * *, , , ,[ ] [ ] 2([ ] [ ] )f j T j T j f jP P A A= − −      (B.13)  2 2 2 * 3 * 2 , , , , 2 * , , , , 4 [ ] 4 ([ ] 2[ ] )[ ]                              ( ([ ] 2[ ] ) 1) [ ] [ ] 0 AP f j AP T j T j f j AP T j T j f j T j K A K P A A K P A A A + − + − + − =  (B.14) 219  * ,[ ] f jA  can be solved from the cubic eq. B.14, and the concentration of the complex ( * 2[ ] jAP ) and the free additive ( * ,[ ] f jP ) after binding process are calculated from the following:  * *2 , ,[ ] [ ] [ ]j T j f jAP A A= −       (B.15)  * *, , 2[ ] [ ] 2[ ]f j T j jP P AP= −       (B.16)  In the non-equilibrium 1:2 analyte-additive interaction, forward and reverse rate constant, k+1 and k-1, are used. The concentration of the free analyte, the free additive and complex after the electrophoretic migration process of the current step (j) are denoted as [A]f,j, [P]f,j and [AP2]f,j. The final concentration of  A, P, and AP2, after binding process can be calculated using the following set of equation.  * 2, . 1 , , 1 2[ ] [ ] ( [ ] [ ] [ ] )f j f j f j f j jA A k A P k AP t+ −= − − Δ    (B.17)  * 2, , 1 , , 1 2[ ] [ ] 2( [ ] [ ] [ ] )f j f j f j f j jP P k A P k AP t+ −= − − Δ    (B.18)  *2 , ,[ ] [ ] [ ]T j f jAP A A= −        (B.19)  B.3.2.3 Equilibrium and non-equilibrium higher order analyte-additive interaction (2:1) To study the equilibrium interaction of analyte with additive at a 2:1 stoichiometry, the binding equilibrium is given as  A + 2P ⇌ A2P        (B.20)  2 * 2 2 * * , , [ ]  [ ] [ ] j A P f j f j A P K A P =        (B.21) 220  Rearranging eq. B.21 by replacing *2[ ] jA P  and * ,[ ] f jP with the total concentration of A and P ([A]T,j and [C]T,j) which were obtained from electrophoresis migration process, * ,[ ] f jA  can be solved from the following cubic equation.  2 2 * 3 * 2 * , , , , , ,[ ] (2[ ] [ ] )[ ] [ ] [ ] 0AP f j AP T j T j f j f j T jK A K P A A A A+ − + − =   (B.22) After * ,[ ] f jA  is calculated, the concentration of A2P and P after binding process can be calculated from the following equations.  * *2 , ,[ ] ([ ] [ ] ) / 2j T j f jA P A A= −       (B.23)  * , , 2[ ] [ ] [ ]f j T j jP P A P= −       (B.24)  In the non-equilibrium 2:1 analyte-additive interaction, with the forward and backward rate constants,  k+1 and k-1, the final concentration of the analyte, the additive and the complex can be calculated using [A]f,j, [P]f,j and [AP2]f,j obtained from the electrophoretic migration process in same cell, j.  * 2, , 1 , , 1 2[ ] [ ] ( [ ] [ ] [ ] )f j f j f j f j jP P k A P k A P t+ −= − − Δ    (B.25)  * 2, , 1 , , 1 2[ ] [ ] 2( [ ] [ ] [ ] )f j f j f j f j jA A k A C k A P t+ −= − − Δ    (B.26)  *2 , ,[ ] [ ] [ ]j t j f jA P P P= −       (B.27)   B.3.2.4 Equilibrium and non-equilibrium single analyte-multiple additive  interaction  In the case of equilibrium single analyte (A) with multiple additives (P and D) at a 1:1 stoichiometry, the equilibrium is described as,  A + P ⇌ AP         (B.28) 221   A + D ⇌ AD                  (B.29)  * * * , , [ ]  [ ] [ ] j AP f j f j AP K A P =         (B.30)  * * * , , [ ] [ ] [ ] j AD f j f j AD K A D =        (B.31)  and  total AP ADK K K=        (B.32)  where KAP and KAD are the binding affinity constants for each single analyte-additive interaction (1:1), and Ktotal is the overall binding constant.  Rearrange eq. B.30 and B.31 by replacing * ,[ ] f jA , * .[ ] f jP , * .[ ] f jD  with the total concentrations of A, P and D ([A]T,j, [P]T,j and [D]T,j) obtained from the electrophoretic migration process, eq. B.33 can be used to solve * ,[ ] f jA .  * 3 * 2 , , , , , * , , , , , , , , [ ] ( ([ ] [ ] [ ] ))[ ]      ( ([ ] [ ] [ ] ) [ ] [ ] [ ] 1)[ ] [ ] 0 AP AD f j AP AD AP AD T j T j T j f j AD T j T j T j AD T j AP T j AP T f f j T j K K A K K K K D A P A K D A P K P K A K P A A + + + − + + − + − − + + − = (B.33)  After * ,[ ] f jA  is calculated, by rearrange eq. B.30 and B.31, the concentration of the free P and the free D after equilibrium process can be obtained using the following set of equation.  * , , ,[ ] [ ] /( [ ] 1)f j T j AP f jP P K A= +      (B.34)  * , , ,[ ] [ ] /( [ ] 1)f j T j AD f jD D K A= +      (B.35) Eventually, the concentration of the complex AP and AD are calculated as  * *, ,[ ] [ ] [ ]j T j f jAP P P= −        (B.36)  * *, ,[ ] [ ] [ ]j T j f jAD D D= −       (B.37) 222   In the study of slower interaction of analyte with multiple additives using CE, forward and reverse rate constant, k+1,  k+2, k-1, and k-2, are used. The final concentration of the analyte, the two additives and the complexes in cell j are calculated from the following: * , , 1 , , 2 , , 1 2[ ] [ ] ( [ ] [ ] [ ] [ ] [ ] [ ] )f j f j f j f j f j f j j jA A k A P k A D k AP k AD t+ + − −= − + − − Δ  (B.38)  * , , 1 , , 1[ ] [ ] ( [ ] [ ] [ ] )f j f j f j f j jP P k A P k AP t+ −= − − Δ    (B.39)  * , , 2 , , 2[ ] [ ] ( [ ] [ ] [ ] )f j f j f j f j jD D k A D k AD t+ −= − − Δ    (B.40)  * *, ,[ ] [ ] [ ]j T j f jAP P P= −        (B.41)  * *, ,[ ] [ ] [ ]j T j f jAD D D= −        (B.42)  B.3.2.5 Equilibrium and non-equilibrium multiple analyte-single additive interaction Similar as other equilibrium interactions, when each analyte (A and B) interacts with the additive (P) at a 1:1 stoichiometry, the following equilibrium is applied.  A + P ⇌ AP        (B.43)  B + P ⇌ BP                   (B.44)  * * * , , [ ]  [ ] [ ] j AP f j f j AP K A P =         (B.45) * * * , , [ ] [ ] [ ] j BP f j f j BP K B P =         (B.46) and  total AP BPK K K=        (B.47) * 3 * 2 , , , , , * , , , , , , , , [ ] ( ([ ] [ ] [ ] )[ ]       ( ([ ] [ ] [ ] ) [ ] [ ] [ ] 1)[ ] [ ] 0 AP BP f j AP BP AP BP T j T j T j f j BP T j T j T j BP T j AP T j AP T j f j T j K K P K K K K A P B P K A P B K A K P K A P P + + + − + + − + − − + + − =   (B.48) 223  The concentration of the free analyte, * ,[ ] f jP , is calculated from eq. B.48, and the concentrations of the free analytes and the formed complex, * ,[ ] f jA , * ,[ ] f jB , * ,[ ] f jAP , and * ,[ ] f jBP , are calculated as,  * , , ,[ ] [ ] /( [ ] 1)f j T j AP f jA A K P= +      (B.49)  * , , ,[ ] [ ] /( [ ] 1)f j T j BP f jB B K P= +      (B.50)  * *, ,[ ] [ ] [ ]j T j f jAP A A= −        (B.51)  * *, ,[ ] [ ] [ ]j T j f jBP B B= −        (B.52) where , , , , ,[ ] ,  [ ] ,  [ ] ,  [ ] ,  and [ ]T j f j T j f j f jA A B B P are the concentration of corresponding species obtained from electrophoresis migration process.  Similar as other non-equilibrium interaction, in the study where the interaction between each analyte and the additive is relative slow with CE, the forward and reverse rate constant, k+1,  k+2, k-1, and k-2, are used to solve the final concentration of the free analyte, additive and the complexes in current cell, j.  * , , 1 , , 2 , , 1 2 [ ] [ ] ( [ ] [ ] [ ] [ ] [ ]                        [ ] ) f j f j f j f j f j f j j j P P k A P k B P k AP k BP t + + − − = − + − − Δ     (B.53)  * 2, , 2 , 2[ ] [ ] ( [ ] [ ] )f j f j f j jB B k B k BP t+ −= − − Δ     (B.54)  * , , 1 , , 1[ ] [ ] ( [ ] [ ] [ ] )f j f j f j f j jA A k A P k AP t+ −= − − Δ    (B.55)  * *, ,[ ] [ ] [ ]j T j f jAP A A= −        (B.56)  * *, ,[ ] [ ] [ ]j P j f jBP B B= −        (B.57)    224  B.4 References [1] Fang, N., Chen, D. D. Y., 18th International Symposium on MicroScale Bioseparations, New Orleans, LA USA 2005.                 225                                                           Appendix C                         Publication List                226 Publications   Portions of the following chapters have been previously published, accepted for publication, or submitted for publication elsewhere. Chapter 2: Fang, N.; Sun, Y.; Chen, D.D.Y. Computer simulation of different modes of ACE based on the dynamic complexation model, Electrophoresis, 2007, 28, 3214–3222. Chapter 3: Sun, Y.; Fang, N; Chen, D.D.Y. Behavior of interacting species in vacancy affinity capillary electrophoresis described by mass balance equation, Electrophoresis, 2008, 29, 3333–3341. Chapter 4: Sun, Y.; Cressman, S.; Fang, N.; Cullis, P.R.; Chen, D.D.Y. Capillary electrophoresis frontal analysis for characterization of alpha-v beta-3 integrin binding interactions, Analytical Chemistry, 2008, 80(9), 3105-3111.  Chapter 5: Sun, Y.; Chen, D.D.Y. Characterization of epidermal growth factor receptor binding with Cetuximab by capillary electrophoresis frontal analysis. Research report to Amgen Inc., 2008, Seattle, USA. Chapter 6: Sun, Y.; Chen, D.D.Y. Computer assisted investigation into principles of chiral separation in capillary electrophoresis, submitted. Chapter 7: Sun, Y.; Fang, N.; Chen, D.D.Y.; Donkor, K.K. Determination of potentially anti- carcinogenic flavonoids in wines by micellar electrokinetic chromatography, Food Chemistry, 2008, 106, 415–420. Other publications: Cressman S.; Sun, Y.; Fang, N.; Chen, D.D.Y.; Cullis P. R. Targeting ligands stimulate endocytosis following binding to the αvβ3 integrin, International Journal of Peptide Research & Therapeutics, 2009, 15, 49-59.  227 Fang, N.; Meng, P.J.; Hong, Z.; Sun, Y.; Chen, D.D.Y. Systematic optimization of exhaustive electrokinetic injection combined with micellar sweeping in capillary electrophoresis, The Analyst, 2008, 132 , 127-134.    

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