Steady-state electrophoresis

Early experiments in the development of isoelectric focusing, a high-resolution steady-state electrophoresis method, occurred in 1912, with an electrolytic cell that was used to isolate glutamic acid from a mixture of its salts.1 A simple U-shaped cell, such as that used for moving-boundary electrophoresis (Chapter 9), with two ion-permeable membranes equidistant from the center, created a central compartment that separated anodic and cathodic chambers, as shown in Figure 11.1. Redox reactions occurring in the anodic (Eq. 11.1) and cathodic (Eq. 11.2) electrolyte compartments generated H+ and OH ions in the respective chambers ... 

Fawcett, JS Sullivan, SV Chrambach, A, Toward a Steady-State Pore Limit Electrophoresis Dimension for Native Proteins in Two-Dimensional Polyacrylamide Gel Electrophoresis, Electrophoresis 10, 182, 1989. 

Shimao, K, Mathematical Simulation of Steady State Isoelectric Eocusing of Proteins using Carrier Ampholytes, Electrophoresis 8, 14, 1987. 

If the electric field E is applied to a system of colloidal particles in a closed cuvette where no streaming of the liquid can occur, the particles will move with velocity v. This phenomenon is termed electrophoresis. The force acting on a spherical colloidal particle with radius r in the electric field E is 4jrerE02 (for simplicity, the potential in the diffuse electric layer is identified with the electrokinetic potential). The resistance of the medium is given by the Stokes equation (2.6.2) and equals 6jtr]r. At a steady state of motion these two forces are equal and, to a first approximation, the electrophoretic mobility v/E is... 

In electric-field driven separations an electric field causes ions to travel through a matrix, such as a gas, liquid, or gel. The movement is retarded by frictional forces from interaction with the matrix and the ions almost instantly reach a steady-state velocity. This velocity depends on properties of both the sample molecules and the surrounding matrix. The two main types of electric-field driven separations are ion mobility spectrometry where the matrix is a gas and electrophoresis where the matrix is a liquid or gel. 

Isotachophoresis. In isotachophoresis (ITP), or displacement electrophoresis or multizonal electrophoresis, the sample is inserted between two different buffers (electrolytes) without electroosmotic flow. The electrolytes are chosen so that one (the leading electrolyte) has a higher mobility and the other (the trailing electrolyte) has a lower mobility than the sample ions. An electric field is applied and the ions start to migrate towards the anode (anions) or cathode (cations). The ions separate into zones (bands) determined by their mobilities, after which each band migrates at a steady-state velocity and steady-state stacking of bands is achieved. Note that in ITP, unlike ZE, there is no electroosmotic flow and cations and anions cannot be separated simultaneously. Reference 26 provides a recent example of capillary isotachophoresis/zone electrophoresis coupled with nanoflow ESI-MS. 

During electrophoresis, a steady state establishes where the vector sum of electrical force and frictional force is zero therefore, a constant migration velocity v is attained, given by ... 

One of the most successful models for gel electrophoresis is the reptation theory of Lumpkin and Zimm for the migration of double-stranded DNA (Lumpkin, 1982). An in-depth discussion can be found in Zimm and Levene (1992) for a synopsis see Bloomfield et al. (2000). The velocity v of a charged particle in a solution with an electric field E depends on the electrical force Fei = ZqE, in which Z is the number of charges and q is the charge of a proton, and the frictional force l fr = —fv, in which/is the frictional coefficient. At steady state, these forces balance and the velocity is v = ZqE/f. The electrophoretic mobility fi is the velocity relative to the field strength, fi = vE = Zq/f. 

The most common classification scheme in electrophoresis focuses on the nature of electrolyte system. Using this scheme, electrophoretic modes are classified as continuous or discontinuous systems. Within these groupings the methods may be further divided on the basis of constancy of the electrolyte if the composition of the background electrolyte is constant as in capillary zone electrophoresis, the result is a kinetic process. If the composition of the electrolyte is not constant, as in isoelectric focusing, the result is a steady-state process. 

In an experiment done to separate proteins by electrophoresis at 20°C, the voltage is switched on at time t = 0. At what time does serum albumin, for which D = 5.94xl0 7 cm2/s and MW = 66,000, reach 99% of its terminal (steady-state) average velocity (See Exercises 3.1 and 3.2.)... 

It could be argued, of course, that the differences and similarities cited above stem from the fact that solvent extraction is essentially a steady-state (equilibrium) process while electrophoresis and sedimentation are transient (rate) processes. However, such an argument would overlook the fact (to be explained later) that the different forms of the chemical potential profile determine which systems can be run successfully in the steady-state mode and which in the transient mode. Thus the chemical potential profile and associated flow structure emerge as dominant influences that should be classified at the very beginning of any attempt to organize separation phenomena into a cohesive discipline. 

Peak capacity nc, like resolution, can be calculated in a straightforward manner for both isoelectric focusing and isopycnic sedimentation. However, it is most interesting to cast ne in a form such that these steady-state methods can be related to the analogous transient methods, namely, zone electrophoresis and rate-zonal sedimentation. To do this we substitute a from Eq. 8.42 into the basic peak capacity expression nc = L/4o-, Eq. 5.59. Then using D = 9177/, we get... 

Shimao, K. (1987). Mathematical simulation of steady state isoelectric focusing of proteins using carrier ampholytes. Electrophoresis 8, 14-19. 

Stoyanov, A. V., and Righetti, P. G. (1998). Steady-state concentration distribution of ampholytes in isoelectric focusing in a linear immobilized pH gradient. Electrophoresis 19, 1596-1600. 

Patton, W. F. (2004). Gharacterization of dynamic and steady-state protein phosphorylation using a fluorescent phosphoprotein gel stain and mass spectrometry. Electrophoresis 15, 2526-2532. 

In real cells, multiple transmembrane pumps and channels maintain and regulate the transmembrane potential. Furthermore, those processes are at best only in a quasi-steady state, not truly at equilibrium. Thus, electrophoresis of an ionic solute across a membrane may be a passive equilibrative diffusion process in itself, but is effectively an active and concentra-tive process when the cell is considered as a whole. Other factors that influence transport across membranes include pH gradients, differences in binding, and coupled reactions that convert the transported substrate into another chemical form. In each case, transport is governed by the concentration of free and permeable substrate available in each compartment. The effect of pH on transport will depend on whether the permeant species is the protonated form (e.g., acids) or the unprotonated form (e.g., bases), on the pfQ of the compound, and on the pH in each compartment. The effects can be predicted with reference to the Henderson-Hasselbach equation (Equation 14.2), which states that the ratio of acid and base forms changes by a factor of 10 for each unit change in either pH or pfCt ... 

The concentration depends only on that of the leading ion it is independent of the initial concentration in the sample. Therefore, ITP can act as an enrichment method, analogous to displacement chromatography and in contrast to zone electrophoresis and elution chromatography. The concentration in the steady state is adjusted to the value given in Eq. (2). If the concentration of the analyte species is lower in the initial sample, the higher steady-state concentration is established. This concentration is independent of the migration distance there is no dilution with a BGE as there is in capillary zone electrophoresis (CZE). 

Explain the fundamental difference between zone electrophoresis as discussed in Chapters 9 and 10, and the steady-state technique of isoelectric focusing. Why do some IEF gels exhibit time-dependent behavior ... 

Recycling isoelectric focusing, like its parent method lEF, is an equilibrium process in which each component migrates to a steady-state position and remains there. By contrast, zone electrophoresis is a rate process in which each component moves at a steady-state velocity. In order to convert ZE to a recycle system, it is necessary to provide a counterflow to offset electromigration of the solutes. 

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