Numerical simulation of protein separation by continuous-flow electrophoresis

A review of the zone broadening contributions in free-flow electrophoresis

The broadening of analyte streams, as they migrate through a free-flow electrophoresis (FFE) channel, often limits the resolving power of FFE separations. Under laminar flow conditions, such zonal spreading occurs due to analyte diffusion perpendicular to the direction of streamflow and variations in the lateral distance electrokinetically migrated by the analyte molecules. Although some of the factors that give rise to these contributions are inherent to the FFE method, others originate from non-idealities in the system, such as Joule heating, pressure-driven crossflows, and a difference between the electrical conductivities of the sample stream and background electrolyte. The injection process can further increase the stream width in FFE separations but normally influencing all analyte zones to an equal extent. Recently, several experimental and theoretical works have been reported that thoroughly investigate the various contributions to stream variance in an FFE device for better understanding, and potentially minimizing their magnitudes. In this review article, we carefully examine the findings from these studies and discuss areas in which more work is needed to advance our comprehension of the zone broadening contributions in FFE assays.

Controlling Dispersion during Single-Cell Polyacrylamide-Gel Electrophoresis in Open Microfluidic Devices

New tools for measuring protein expression in individual cells complement single-cell genomics and transcriptomics. To characterize a population of individual mammalian cells, hundreds to thousands of microwells are arrayed on a polyacrylamide-gel-coated glass microscope slide. In this "open" fluidic device format, we explore the feasibility of mitigating diffusional losses during lysis and polyacrylamide-gel electrophoresis (PAGE) through spatial control of the pore-size of the gel layer. To reduce in-plane diffusion-driven dilution of each single-cell lysate during in-microwell chemical lysis, we photopattern and characterize microwells with small-pore-size sidewalls ringing the microwell except at the injection region. To reduce out-of-plane-diffusion-driven-dilution-caused signal loss during both lysis and single-cell PAGE, we scrutinize a selectively permeable agarose lid layer. To reduce injection dispersion, we photopattern and study a stacking-gel feature at the head of each <1 mm separation axis. Lastly, we explore a semienclosed device design that reduces the cross-sectional area of the chip, thus reducing Joule-heating-induced dispersion during single-cell PAGE. As a result, we observed a 3-fold increase in separation resolution during a 30 s separation and a >2-fold enhancement of the signal-to-noise ratio. We present well-integrated strategies for enhancing overall single-cell-PAGE performance.

An analytic description of electrodynamic dispersion in free-flow zone electrophoresis

The present work analyzes the electrodynamic dispersion of sample streams in a free-flow zone electrophoresis (FFZE) chamber resulting due to partial or complete blockage of electroosmotic flow (EOF) across the channel width by the sidewalls of the conduit. This blockage of EOF has been assumed to generate a pressure-driven backflow in the transverse direction for maintaining flow balance in the system. A parallel-plate based FFZE device with the analyte stream located far away from the channel side regions has been considered to simplify the current analysis. Applying a method-of-moments formulation, an analytic expression was derived for the variance of the sample zone at steady state as a function of its position in the separation chamber under these conditions. It has been shown that the increase in stream broadening due to the electrodynamic dispersion phenomenon is additive to the contributions from molecular diffusion and sample injection, and simply modifies the coefficient for the hydrodynamic dispersion term for a fixed lateral migration distance of the sample stream. Moreover, this dispersion mechanism can dominate the overall spatial variance of analyte zones when a significant fraction of the EOF is blocked by the channel sidewalls. The analysis also shows that analyte streams do not undergo any hydrodynamic broadening due to unwanted pressure-driven cross-flows in an FFZE chamber in the absence of a transverse electric field. The noted results have been validated using Monte Carlo simulations which further demonstrate that while the sample concentration profile at the channel outlet approaches a Gaussian distribution only in FFZE chambers substantially longer than the product of the axial pressure-driven velocity and the characteristic diffusion time in the system, the spatial variance of the exiting analyte stream is well described by the Taylor-Aris dispersion limit even in analysis ducts much shorter than this length scale.

Analysis of geometry effects on band spreading of microchip electrophoresis

The geometry and the flow field conditions in the separation microchannel of an electrophoresis chip system may have important impact on the system's separation efficiency. Understanding the geometry effect on the flow field physics in the separation microchannel is beneficial to the design or operation of an electrophoresis system. The turns in a microfabricated separation microchannel generally results in degraded separation quality. To avoid this limitation, channels are constructed with different types of turns to determine the optimum design that minimizes turn-induced band broadening. We have designed and tested various geometric bend ratios to greatly reduce this so-called "racetrack" effect. The effects of the separation channel geometry, fluid velocity profile and bend ratio on the band distribution in the detection area are discussed. Results show that the folded square U-shaped channel is better for miniaturization and simplification. The band tilting was corrected and the racetrack effect reduced in the detection area when the bend ratio is 4:1. The detection time obtained from the present numerical solution matches very well with the experimental data.

Simulation of electrophoretic separations by the flux-corrected transport method

Electrophoretic separations at typical experimental electric field strengths have been simulated by applying the flux-corrected transport (FCT) finite difference method to the transient, one-dimensional electrophoresis model. The performance of FCT on simulations of zone electrophoresis (ZE), isotachophoresis (ITP), and isoelectric focusing (IEF) has been evaluated. An FCT algorithm, with a three-point, central spatial discretization, yields numerical solutions without numerical oscillations or spurious peaks, which have plagued previously-published second-order solutions to benchmark ZE and ITP problems. Moreover, the FCT technique captures sharp zone boundaries and IEF peaks more accurately than previously-published, first-order upwind schemes.

Optimization of protein separation by continuous-flow electrophoresis: influence of the operating conditions and the chamber thickness

The separation of protein by continuous-flow electrophoresis is disturbed by a number of effects which cause spreading of the protein streams with a loss of resolution. Two numerical models have been used to describe the coupling between the various spreading phenomena. A simple model takes into account molecular diffusion, electroosmosis and residence time gradients; the main model differs from the simple one by taking account of electrohydrodynamics. The influence of the separation chamber thickness, the radius of the sample filament, the field strength, and the residence time is explored. The simulations show that each dispersive effect has its own range of predominance, so that an optimum is found for the thickness of the separation chamber.

Purification of bioproducts by free-flow zone electrophoresis: choice of processing parameters

Free-flow zone electrophoresis may be used to purify biological samples, due to differences in electrophoretic mobility, in absence of a matrix--most frequently a gel--thus enabling the biological integrity of even fragile molecules to be preserved. However, the process is more complicated than its principle suggests due to different transport phenomena interfering with electrophoretic migration, with the resultant separation depending both on separation effects and dispersive phenomena. The physical origin of the main effects involved was identified. Mathematical expressions were proposed to estimate the influence of the crescent effect and electrohydrodynamics on the process. In this paper, these equations are used to determine the minimum difference in electrophoretic mobility required for a separation to be achieved with respect to the processing parameters. A methodology is proposed which defines the conditions under which the difference in electrophoretic mobilities equals that calculated when considering the influence of dispersive phenomena. Optimized separations of the whey proteins lactoferrin and albumin, known to interact strongly, and the purification of a monoclonal antibody from a mouse ascitic fluid illustrate the approach.

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.

Protein separation by electrophoresis in a nonsieving amphoteric medium

A numerical model has been used to study the separation of protein mixtures by zone electrophoresis in a nonsieving amphoteric medium. An amphoteric buffer fixes the pH of the solution close to its isoelectric point, where the buffer molecules are unchanged: they thus contribute very little to the conductivity of the solution. This means that high field strengths can be used for rapid separation without sacrificing resolution. The numerical study shows that in this process the band spreading that can reduce resolution is essentially due to differences in migration rate between protein-rich and low-protein zones: both differences in solution conductivity and in protein mobility are involved. Rules for judging the buffer capacity of amphoteric molecules are presented and it is shown how, for a given protein, the effectiveness of this technique varies with the range of pH in which it is applied.

Protein microheterogeneity and crystal habits: the case of epidermal growth factor receptor isoforms as isolated in a multicompartment electrolyzer with isoelectric membranes

A purified, soluble form of the epidermal growth factor receptor (sEGFR) was found, by isoelectric focusing in immobilized pH gradients, to consist of three major isoforms (with pI values 6.45, 6.71 and 6.96, respectively) and ca. a dozen minor components. This wild-type sEGFR, while producing crystals, has so far defied any attempt at decoding the structure, due to the very poor diffraction pattern. When the wild-type sEGFR was purified in a multicompartment electrolyzer with isoelectric Immobiline membranes, it yielded the three major isoforms as single-pI components, collected in three separate chambers of the recycling electrolyzer. The pI 6.71 and the pI 6.96 isoforms produced large crystals of apparent good quality. However, while the former produced a high-quality diffraction pattern, which may lead to decoding of three-dimensional structure, the pI 6.96 produced crystals which did not diffract at all. It is concluded that, in the case of "tough" proteins (large size, heterogeneous glycosylation, high water content of crystals), purification to single-charge components might be an essential step for growing proper crystals. The unique advantage of purification via isoelectric membranes is that the protein is collected both isoelectric and isoionic, i.e. uncontaminated by soluble buffers (such as the carrier ampholytes used in conventional focusing).