Computer simulation and experimental validation of the electrophoretic behavior of proteins

Concentration and separation of proteins in microfluidic channels on the basis of transverse IEF

The use of microfluidic channels formed by two electrodes made of gold or palladium to perform transverse isoelectric focusing (IEF) is presented as a means for continuous concentration and fractionation of proteins. The microchannels were 40 mm long with an electrode gap of 1.27 mm and a depth of 0.354 mm. The properties of pH gradients formed as a result of the electrolysis of water were influenced by variation of parameters such as the initial pH, ionic strength, and flow rate. Transverse IEF in pressure-driven flow is demonstrated using bovine serum albumin in a single ampholyte buffer as well as in multiple-component buffers. Experimental results of protein focusing compare well to predictions of a mathematical model. Optimal conditions for efficient continuous fractionation of a protein mixture are summarized and discussed.

Formation of natural pH gradients in a microfluidic device under flow conditions: model and experimental validation

A new isoelectric focusing technique has been developed that incorporates natural pH gradient formation in microfluidic channels under flowing conditions. In conjunction, a one-dimensional finite difference model has been developed that solves a system of algebraic-ordinary differential equations that describe the phenomena occurring in the system, including hydrolysis at the electrodes, buffering effects of weak acids and bases, and mass transport due to both diffusion and electrophoresis. A quantitative, noninvasive, optically based method of monitoring pH gradient formation is presented, and the experimental data generated by this method are found to be in good agreement with model predictions. In addition, the model provides a theoretical explanation for initially unexpected experimental results. Model predictions are also shown to match well with experimental results of microfluidic isoelectric focusing of a single protein species. Accounting for the nonuniform velocity profile, characteristic of pressure-driven flow in microfluidic channels, is found to improve predictions of dynamic pH changes close to the electrodes and overall time required to reach steady state, but to reduce the accuracy of dynamic pH change predictions in other regions of the channel.

Dynamics of capillary isoelectric focusing in the absence of fluid flow: high-resolution computer simulation and experimental validation with whole column optical imaging

A 150-component, dynamic electrophoresis simulator was developed and applied to the description of capillary isoelectric focusing (CIEF) of amphoteric substances in quiescent solution. The simulator is shown to be capable of producing high-resolution pH 3-10 focusing data with 140 individual carrier ampholytes (20/pH unit) and at current densities that are used in CIEF, i.e., under conditions that were hitherto unaccessible by dynamic computer simulation. Having a focusing capillary of 5-cm length, the predicted focusing dynamics for amphoteric dyes obtained at a constant voltage of 1500 V (300 V/cm) are shown to qualitatively agree with data obtained by whole-column optical imaging. The simulation data provide detailed insight into the dynamics of the focusing process for the cases with the focusing column being sandwiched between 40 mM NaOH (catholyte) and 100 mM phosphoric acid (anolyte) or having the column ends only permeable for OH- and H+ at cathode and anode, respectively. Simulation data reveal that the number of sample boundaries migrating from the two ends of the column to the focusing positions is always equal to the number of sample components. The number of detectable migrating sample boundaries, however, can be lower. Whole-column optical imaging is demonstrated to be the method of choice for following the approach to equilibrium. With that detection format, transient sample peaks can be recognized and properly identified. This would also be possible with a scanning detector moving rapidly and repeatedly along the column but cannot be accomplished by a stationary detector placed at a specified location. The data presented demonstrate that the model together with imaging monitoring can be used to optimize the CIEF separation conditions.

The Effect of Protein Concentration on Electrophoretic Mobility

The electrophoretic mobility of haemoglobin was measured in a novel membrane-electrophoresis cell and by electrophoretic light scattering. The effect of protein concentration was investigated at different ionic strengths in two different buffer systems. The results indicated that although the effect of the concentration is weak, the mobility did decrease linearly with an increase in volume fraction throughout the range of volume fractions investigated (&phi;<0.06). This dependence is more pronounced at lower kappaa values where double-layer interactions between the particles are more significant. Protein contribution to the solution ionic strength alone cannot explain the observed reduction in electrophoretic mobility. The theory of Shugai et al. (Shugai, A. A., Carnie, S. L., Chan, D. Y. C., and Anderson, J. L., J. Colloid Interface Sci. 191, 357 (1997)) was found to be adequate in describing particle interactions. The agreement with Shugai's theory is somewhat surprising considering the polydispersed nature of the samples, uncertainties in protein size, changes in ionic strength at high protein concentrations, and possible membrane-protein interactions not accounted for in the theory. Copyright 2000 Academic Press.

Continuous free-flow electrophoresis

This review evaluates the literature on continuous free flow electrophoresis, published during the last four years. Its aim is to serve not only experts in the field but also newcomers, and, therefore, it also briefly describes the principles of the method and the techniques used, referring to fundamental papers published earlier. The actual commercial instrumentation is briefly outlined. A substantial part of this review is devoted to the optimization of the performance of this method. Finally, diverse applications of fractionations of charged species in solution, ranging from small ions to biological particles and cells, are surveyed.

Amperometric pH regulation--a flexible tool for rapid and precise temporal control over the pH of an electrolyte solution

Temporal control over both pH and ionic strength of an electrolyte solution with high accuracy was achieved with a dynamic, computer feedback-controlled amperometric pH-stat device consisting of four pH-regulating electrodes placed in electrolyte reservoirs that are separated by dialysis membranes from a central compartment. Theoretical predictions of the behavior of this arrangement, obtained by computer simulation, were validated by running temporal pH programs such as step functions, oscillations, and linear pH gradients. Deviations from nominal values given by the computer program are within the limits of accuracy of the pH-measuring electrodes. No volume changes accompany a change of pH or conductivity since ions are forced to leave or enter the central compartment through the membranes by the electrical force applied between the pH-regulating electrodes. The device is flexible, easy to use and easily miniaturized. We discuss a wide range of possible applications in biochemistry and cell science. These include automated pH adjustment, isoelectric protein separation, amperometric measurement of enzyme kinetics and the response of cell cultures to well-defined pH changes.

Impact of electroosmosis on isotachophoresis in open-tubular fused-silica capillaries: analysis of the evolution of a stationary steady-state zone structure by computer simulation and experimental validation

A dynamic computer model for simulation of open-tubular capillary electrophoresis that includes in situ calculation of electroosmosis along the fused-silica capillary column has been applied to the characterization of an anionic isotachophoretic system in presence of a cathodic electroosmotic flow. For each column segment, electroosmosis is calculated with the use of a wall mobility, the voltage gradient and the degree of dissociation of the silanol surface groups of the capillary wall. Then, the bulk capillary flow is taken to be the average of all of the segment flows and considered to represent a plug flow. This simple approach enables the combined simulation of the temporal behavior of an isotachophoretic zone structure in presence of electroosmosis. For a model anionic isotachophoretic configuration at pH 6, simulation data reveal the asymptotic formation of a stationary steady-state zone configuration in which electrophoretic and electroosmotic zone displacements are opposite and of equal magnitude. The position of the stationary boundaries are predicted to be dependent on the selected wall pK and mobility values. For two different instruments, qualitative agreement between experimental data and simulation results obtained with a wall pK between 5 and 6 is demonstrated. However, for the two experimental setups, significant differences in electroosmotic pumping (i.e. wall mobility values) are noted.

Sample self-stacking and sample stacking in zone electrophoresis with major sample components of like charge: general model and scheme of possible modes

A theoretical study is presented of zone electrophoretic behavior of samples that contain one or more minor analytes and at least one major ionogenic component of like charge. Based on a simple model comprising weak univalent anionic electrolytes, conditions are derived under which analytes are temporarily focused isotachophoretically into very narrow zones by a sample self-stacking effect provided by the major sample components. Requirements for minimal/maximal mobility and a background coion concentration dependent minimal concentration of a major sample component (stacker) are presented. For systems in which sample self-stacking does not apply, an expression for the concentrating factor is derived that involves the effects of both nonselective (classical) and selective sample stacking, the latter being a consequence of electrophoretic separation of the minor analyte from the major component. The theory derived is discussed with selected model examples by using both numerical calculation and computer simulation.

Effect of pH and ionic strength of running buffer on peptide behavior in capillary electrophoresis: theoretical calculation and experimental evaluation

The effect of pH and ionic strength of running buffer on peptide behavior in capillary electrophoresis (CE) is studied. A system for predictions of peptide migration in CE (SPPMCE) developed in our laboratory has been tested in a wide range of pH and buffer concentrations. The SPPMCE consists of a computer program for calculating peptide pKa values, an equation which relates peptide structures to their electrophoretic mobilities and a coupled computer program for the prediction of electropherograms. More than 25 different buffers have been employed, covering a pH range of 2-11 and a concentration range of 5-100 mM. Results from experiments are compared with the theoretical predictions. Good agreement is observed, which confirms the utility of the SPPMCE and allows fast and easy optimization of peptide separations in CE, with nothing more than the amino acid sequence of the linear peptide as the input.

Computation of the electrophoretic mobility of proteins

A scheme is presented for computing the electrophoretic mobility of proteins in free solution, accounting for the details of the protein shape and charge distribution. The method of Teubner is implemented using a boundary integral formulation within which the velocity distribution, the equilibrium electrical potential around the molecule, and the potential distribution due to the applied field are solved for numerically using the boundary element method. Good agreement of the numerical result is obtained for spheres with the corresponding semi-analytical specialization of Henry's analysis. For protein systems, the method is applied to lysozyme and ribonuclease A. In both cases, the predicted mobility tensors are fairly isotropic, with the resulting scalar mobilities being significantly smaller than for spheres of equal volume and net charge. Comparisons with previously published experimental results for ribonuclease show agreement to be excellent in the presence of a net charge, but poorer at the point of zero charge. The approach may be useful for evaluating approximate methods for estimating protein electrophoretic mobilities and for using electrophoretic measurements to obtain insight into charge distributions on proteins.

Peptides as standards for denaturing isoelectric focusing

A set of commercially available peptides suitable for use as standards in denaturing isoelectric focusing (IEF) is described. The peptides N-procalcitonin fragment 1-57 (pI 3.98), Gln11-amyloid beta-protein fragment 1-28 (pI 5.76), gastric inhibitory polypeptide (pI 7.14), parathyroid hormone fragment 1-34 (pI 8.64) and human beta-endorphin (pI 9.49) can be focused to their isoelectric point in the presence of 8 M urea and 2% Nonidet P-40, and subsequently fixed and stained in polyacrylamide gels. The peptides give a linear standard curve in close agreement with a slope determined with a surface pH electrode. Under the same conditions some proteins focus to positions significantly at odds with their theoretical isoelectric point. The origins of these discrepancies and the implications for the determination of isoelectric points of unknown proteins by denaturing IEF are discussed.

Numerical simulation of protein separation by continuous-flow electrophoresis

Continuous-flow electrophoresis is a process for separating protein mixtures on a preparative scale. Its resolution is determined by the migration distance at the collection plane and by the fineness of the filament occupied by each protein species. Filaments undergo spreading due to a number of different phenomena, among which electrokinetics and electrohydrodynamics are known to be important. In the first of these, differences in migration velocity between the ionic species give rise to local variations in pH and electrical conductivity near the protein filament. In the second, the local change in electrical conductivity distorts the electric field, thus inducing shear stress in the liquid and creating a local flow pattern. A numerical model has been developed to describe these phenomena when two proteins are being separated.

Computer simulation of transient states in capillary zone electrophoresis and isotachophoresis

Transient states in the evolution of electrophoretic systems comprising aqueous solutions of weak monovalent acids and bases are simulated. The mathematical model is based on the system of nonstationary partial differential equations, expressing the mass and charge conservation laws while assuming local chemical equilibrium. It was implemented using a high resolution finite-difference algorithm, which correctly predicted the behavior of the concentration, pH and conductivity fields at low computational expense. Both the regular and the irregular modes of separation in capillary zone electrophoresis and isotachophoresis are considered. It is shown that the results of separation, particularly zone order, strongly depend on pH distribution. Simulation data as well as simple analytical assessments may help to predict and correctly interpret the experimental results.

Separation of natural and synthetic heparin fragments by high-performance capillary electrophoresis

The application of capillary electrophoresis (CE) for the analysis of natural and synthetic low-molecular-mass heparin fragments at low pH is described. It is demonstrated that under the applied conditions the separation is based on charge, charge distribution and molecular mass of the heparin molecules, yielding a high resolution. It is shown that the presence of sodium chloride in the sample solution has hardly any effect on the CE performance. However, the pH of the electrophoresis buffer is a critical parameter. The resolutions obtained with CE and high-performance anion-exchange chromatography (HPAEC) are compared for various heparin fragments and it is concluded that, at least for this type of molecule, CE forms an attractive alternative to HPAEC.

Effect of total percent polyacrylamide in capillary gel electrophoresis for DNA sequencing of short fragments. A phenomenological model

Polyacrylamide capillary gels were prepared with constant (5% C) cross-linker concentration and with total acrylamide concentration ranging from 2.5 to 6% T. At each acrylamide concentration, peak spacing was constant for DNA sequencing fragments ranging from 25 to 250 nucleotides in length. Peak spacing increased linearly with the total acrylamide concentration. The intercept of the retention time vs. fragment length plot was independent of % T. Ferguson plots were constructed for short DNA fragments; the polyacrylamide pore size falls in the 2.5 to 3.5 nm range for the gels studied. Theoretical plate count is independent of total acrylamide concentration; longitudinal diffusion, and not thermal gradients, limit the plate count. A phenomenological model is presented that predicts retention time, plate count, and resolution for sequencing fragments ranging in size from 25 to 250 bases and gels that range from 2.5 to 6% total acrylamide.

High speed electrophoresis simulation for optimization of continuous flow electrophoresis and high performance capillary techniques: Part I. Computer model

A computer program for high-speed simulation and optimization of electrophoretic processes has been developed for carrier-free systems of all kinds. The calculations are based on the one-dimensional dynamic (transient-state) model. The three-dimensional geometry of the simulation space can be chosen deliberately. With a highly efficient transport algorithm instead of complicated integration schemes for the transport equations, the calculation time can be effectively spent on various important parameters such as ionic strength, temperature, Joule heat, activity coefficients and concentration changes due to membranes. The parameter set of any carrier free electrophoretic method (i.e., continuous-flow electrophoresis, capillary isotachophoresis and high performance capillary zone electrophoresis) can be imported directly into the computer program by means of a graphic user interface. The program performs overnight-simulation of any electrophoretic system containing up to 15 components.

Innovative developments in isotachophoresis (displacement electrophoresis)

This Mini Review is aimed at characterizing the innovative developments in isotachophoresis (ITP) during the past few years, discussing in turn new theoretical, analytical, preparative and applicative aspects of this unique separation method. Examples given from our laboratory include the study of the detailed dynamics of the ITP separation of four components by computer simulation and experimental validation in a capillary-type instrument with multiple sensors along the separation trough; the anionic ITP analysis in presence of a strong cathodic electroosmotic flow using an open-tubular fused-silica capillary with on-column multiwavelength detection, and the fractionation of proteins in a screen-segmented, rotating column as well as by recycling ITP.

Recycling and screen-segmented column isotachophoresis, two free-fluid approaches for fractionation of proteins

Recycling and screen-segmented column isotachophoresis (ITP), two approaches for the milligrams to grams preparative-scale purification of proteins, are discussed and compared. Recycling ITP was performed in a recycling free-flow focusing apparatus. In this process, fluid flows rapidly through a narrow channel and the effluent from each channel is reinjected into the electrophoresis chamber through the corresponding input port. The residence time in the cell is of the order of 1 s per single pass, which does not allow complete separation, so recycling is essential to attain the steady state. Immobilization of the advancing zone structure is obtained via a controlled counterflow. Thirty fractions of about 4 ml each are obtained. Column ITP was executed in a Rotofor apparatus and in a similar column operated vertically and without rotation. These instruments feature a screen-segmented annular separation space with twenty subcompartments of about 2 ml each. With both approaches, the collected fractions were analysed separately for conductivity, pH and UV absorbance. Selected fractions were characterized by analytical electrophoretic methods. Examples presented include the cationic and anionic ITP behaviour of model proteins, including bovine serum albumin, ovalbumin and ribonuclease A, and the ITP removal of the major impurities from a commercial ovalbumin sample. These examples revealed that the screen-segmented column is suitable for ITP protein purification and operates optimally in a horizontal rotating mode and without internal cooling. The recycling experiments showed that counterflow improves separation and the steady-state patterns are dependent on the fluid layer thickness in the separation cell but, with a given gap, essentially independent of applied current and recycling pump rate.

Method optimization in capillary zone electrophoretic analysis of hGH tryptic digest fragments

The mobile phase composition was optimized for the separation of tryptic digest fragments of human growth hormone by capillary zone electrophoresis. The effect of pH (pH 2.4, 6.1, 8.1 and 10.4) was evaluated since pH determines the relative charge of species, the prime contributor to selectivity; pH 8.1 was selected for the optimization studies. Tricine (buffer), sodium chloride (ionic strength adjustor), and morpholine (mobile phase additive) concentrations were systematically varied a pH 8.1. All three exhibited major effects on the electroosmotic flow velocity and current, and minor effects on selectivity. Tricine was the most crucial for good resolution, although addition of morpholine helped to resolve closely eluting species. The optimum separation conditions were found to be pH 8.1 with 0.1 M tricine, 0.02 M morpholine and no salt.

Steady state electrolysis and isoelectric focusing

The properties of pH gradients formed by stationary electrolysis of weak mobile or fixed electrolytes are analyzed. The model uses the appropriate balance equations and those of chemical equilibria. It is shown how the equation of the current density has to be modified for considering that fraction of current that is associated with the diffusion of neutral buffer molecules within a pH gradient. Furthermore it is shown that the pH gradients themselves give rise to water production within the gradient and that essential properties of the steady state are related to chemical reactions between the electrolyte constituents. The differential equations describing the gradients of the concentration of a given component, the pH, conductivity and potential are explicitly formulated in relation to those reactions. The equations are solved numerically and the significance of the results for isoelectric focusing is discussed. The experimental conditions to reach shallow and smooth pH gradients exhibiting sufficient ionic strength are formulated.

Free flow electrophoresis for the purification of proteins: I. Zone electrophoresis and isotachophoresis

The principles and some applications of free flow zone electrophoresis and isotachophoresis are described. The influence of (i) carrier electrolyte conductivity on the migration velocity and (ii) band shape on zone electrophoresis was investigated. The technique was found convenient for studying the effect of pH on the mobility of proteins to create a mobility curve. The purification of alcohol dehydrogenase from a crude yeast extract revealed the separation power of zone electrophoresis for complex protein mixtures. Without additional steps, a purification factor of 5.4, with a recovery of 97% alcohol dehydrogenase, was achieved. Free flow isotachophoresis was applied to the purification of immunoglobulins from human serum. Disadvantages of this technique are the time-consuming development of an optimized separation system and the empirical search for suitable spacers. Also, reaching of the steady state becomes increasingly difficult as the number of sample components increases.

Experimental and theoretical description of the isotachophoretic behavior of serum albumin

The isotachophoretic behavior of serum albumin is examined for three anionic and one cationic electrolyte systems by (i) computer simulation, (ii) capillary isotachophoresis (ITP) and (iii) continuous flow ITP. The theoretical relationship between pH of the leading electrolyte and the steady state protein plateau concentration is presented for one of the anionic systems. With leading ion concentrations of the order of 10 mM, experimental protein plateau concentrations of 1.3-2.3% w/v are obtained. The computer predictions are approximately half these values.

Isotachophoretic zone formation of serum albumin in different free fluid electrophoresis instruments

The isotachophoretic behavior of a model protein, serum albumin, was examined (i) by computer simulation, (ii) by capillary isotachophoresis in HPE 100 and Tachophor 2127, (iii) by continuous flow isotachophoresis in Elphor VaP 22 and the BIO-STREAM Separator and (iv) by recycling isotachophoresis in an apparatus of our own design. Variations in monitored zone shapes can be explained by differences in engineering aspects and fluid stabilization principles of the instruments.

The impact of boundary conditions in free flow field step electrophoresis

The impact of the type of membrane used to separate the electrolyte compartments from the separation cell for continuous flow field step electrophoresis is examined using both experimental and computer simulation data. It is shown that the distinct transport characteristics of ion exchange membranes and dialysis membranes may have an effect on the stability of the pH and conductivity gradients created by the buffer system. These effects are interpreted using computer simulation data. The limitations of the model used to portray the transport characteristics of ion exchange membranes are discussed as are the experimental conditions which provide the greatest stability for field step electrophoresis.