Band broadening in mobility shift affinity capillary electrophoresis due to pressure-driven flow

Abstract

Mobility Shift Affinity Capillary Electrophoresis (msACE) presents a simple and powerful approach to determining the equilibrium and kinetic parameters governing the interaction between a variety of analyte and ligand molecules. These determinations often rely on measuring the elution peak profile for the analyte zone when migrated with a steady electric field. However, pressure-gradients applied intentionally or generated due to unwanted differences in the hydrostatic heads at the capillary/channel ends and/or a variation in the electroosmotic flow rate along the analysis column can significantly alter this peak profile introducing error in the estimated parameter values. To account for these alterations, this article describes a mathematical formulation for quantitating band broadening in msACE systems due to a steady pressure-driven flow in the Taylor–Aris dispersion limit with fast analyte-ligand binding kinetics. The current analysis shows that the additional zone dispersion under such conditions can be quantitated using four terms that scale with the square of the Péclet number calculated based on the pressure-driven flow velocity. While the first term among these quantitates the Taylor–Aris dispersion experienced by a neutral tracer advected by the pressure-gradient, the other three terms are proportional to the square of the difference in the diffusion coefficients for the analyte and analyte-ligand complex. Moreover, these latter terms also vary inversely with the Damköhler number computed as the ratio of the rate of reaction over that of diffusive mass transfer with the coefficient for each of the four terms shown to be dependent on the cross-sectional shape of the analysis column.