Mathematical Theory of Electrophoresis

ISBN-13: 9781461282259 / Angielski / Miękka / 2012 / 260 str.

V. G. Babskii; M. Yu Zhukov;V. I. Yudovich

Opis

The development of contemporary molecular biology with its growing tendency toward in-depth study of the mechanisms of biological processes, structure, function, and identification of biopolymers requires application of accurate physicochemical methods. Electrophoresis occupies a key position among such methods. A wide range of phenomena fall un der the designation of electrophoresis in the literature at the present time. One common characteristic of all such phenomena is transport by an elec tric field of a substance whose particles take on a net charge as a result of interaction with the solution. The most important mechanisms for charge generation are dissociation of the substance into ions in solution and for mation of electrical double layers with uncompensated charges on particles of dispersed medium in the liquid. As applied to the problem of separation, purification, and analysis of cells, cell organelles, and biopolymers, there is a broad classification of electrophoretic methods primarily according to the methodological charac teristics of the process, the types of supporting media, etc. An extensive literature describes the use of these methods for the investigation of differ ent systems. A number of papers are theoretical in nature. Thus, the mi croscopic theory has been developed rather completely 13] by considering electrophoresis within the framework of electrokinetic phenomena based on the concept of the electrical double layer."

Spis treści

I. Basic Equations.- 1. Mass Balance.- 2. Momentum Balance.- 3. Angular Momentum Balance.- 4. Equations of the Electromagnetic Field in Matter and Determination of the Ponderomotive Forces.- 5. Internal Energy Balance.- 6. Inequality for the Entropy of the Mixture Components.- 7. The Gibbs Relation and the Chemical Potential.- 8. Entropy Balance Equation for the Mixture.- 9. Description of the Behavior of Multicomponent Mixtures.- 10. Simplified Equations of Motion and the Entropy Balance Equation.- 11. Basic Model for a Multicomponent Mixture.- 12. Defining Relations for the Specific Dipole Moment.- 13. Linear Onsager Defining Relations.- 14. Complete System of Equations for Describing Multicomponent Mixtures.- 15. Infinite-Component Mixtures.- II. Chemical Subsystems.- 1. Integrals for the Chemical Kinetics Equations Describing Equilibrium Chemical Reactions.- 2. Integrals of the Chemical Kinetics Equations for “Slow” Variables for the Simplified System of Equations.- 3. Transition to Dimensionless Variables.- 4. Acidity of the Solution.- 5. Applicability of the Approximation of Local Chemical Equilibrium.- III. Electrophoresis Methods and Their Mathematical Models.- 1. Electrophoresis Methods.- 2. Additional Simplifications.- 3. Simplest Model for Isoelectric Focusing and Zone Electrophoresis: One-Component Buffer, One Sample.- 4. Model with One-Component Buffer and Several Samples.- 5. Simplified Models for the Case of Weak Electrolytes.- 6. Mobility and Molar Charge of an Amino Acid with Several Carboxyl and Amino Groups.- 7. Mathematical Model of Isoelectric Focusing and Zone Electrophoresis in the Case of a Two-Component Buffer.- 8. Mathematical Model of Isotachophoresis.- 9. Boundary Conditions for Models of Electrophoresis.- IV. Isotachophoresis.- 1. Models of Isotachophoresis for Weak and Strong Electrolytes.- 2. Riemann Invariants of the System of Quasilinear Equations.- 3. Motion of Two Zones with Arbitrary Concentration, Separated at the Initial Instant of Time.- 4. Case of Any Number of Zones of Pure Electrolytes.- 5. Case of Two Partially Mixed Electrolytes.- 6. Separation of Two-Component Mixtures by the Isotachophoresis Method.- 7. Temperature Distribution for Completely Separated Zones.- V. Model of Zone Electrophoresis.- 1. Electrophoresis in an Infinite Column.- 2. Reaction of the Zones with the Buffer.- 3. Radial Distortion of the Zone Profile.- VI. Creation of a pH Gradient in Infinite-Component Systems.- 1. Reactions Occurring in Aqueous Solutions of Boric Acid with Polyols.- 2. “Slow” Variables for Describing Borate—Polyol Systems.- 3. Mathematical Model for Creating pH Gradients in Borate—Polyol Systems.- 4. One-Dimensional Problem.- 5. Evolution of a Continuous Initial pH Gradient in the Boric Acid—Polyol System with Vanishing Diffusion.- 6. Principal Terms of the Asymptotic Expansion when ?? 0.- 7. Evolution of a Piecewise-Constant pH Profile in the Boric Acid—Polyol System for Vanishing Diffusion.- VII. Isoelectric Focusing in Infinite-Component Mixtures. Creation of a pH Gradient.- 1. Description of Infinite-Component Mixtures.- 2. Formulation of the Problem of Creation of the pH Gradient.- 3. Establishing the Principal Term in the Asymptotic Expansion for µ ? 0.- 4. Principal Term of the Asymptotic for a Mixture of Carrier Ampholytes.- 5. Creation of a Linear pH Profile (First Model).- 6. Creation of a Linear pH Profile (Second Model).- 7. Creation of a Linear pH Profile (Third Model).- 8. Results of Calculations.- 9. Temperature Distribution in an Infinite-Component Mixture.- VIII. Resolution of Isoelectric Focusing.- 1. Formulation of the Problem.- 2. Equations for Describing the Motion of the Mixture to be Separated in Isoelectric Focusing in a Specified pH Gradient.- 3. Basic Results.- 4. Conditions Imposed on the Difference Between Isoelectric Points for Components to be Separated.- 5. Shift in the Concentration Maximum Point Due to Thermal Diffusion.- IX. Zone Evolution in Isoelectric Focusing.- 1. One-Dimensional Case.- 2. Solution in the Case of Vanishing Diffusion.- 3. Asymptotic Solution for Low Diffusion.- Conclusion.- References.