Stream broadening in free flow affinity electrophoresis

Complexation plays a vital role in a variety of chemical and biological systems. Thus, our ability to reliably measure the equilibrium and kinetic parameters governing complexation reactions is crucial to comprehending important natural and artificial processes. Free-Flow Affinity Electrophoresis or FFAE offers a simple and powerful approach to measuring complexation parameters at high throughputs over a wide range of experimental conditions. However, the range and accuracy of analytical information that can be extracted from these affinity measurements remains limited due to significant knowledge gaps in our understanding of analyte transport in FFAE systems. To fill this gap in knowledge, the current article describes a mathematical formulation for quantitating stream broadening in FFAE assays. A closed-form expression has been derived for the stream width based on this formulation in the Taylor-Aris dispersion limit assuming fast analyte-ligand binding kinetics. It has been shown that the effects of affinity interactions on the stream dispersion in FFAE devices can be described using four terms that are additive to the contributions observed in conventional free-flow electrophoresis. Notably, all these additional terms were determined to scale with the square of the distance migrated by the analyte stream in the lateral direction. Moreover, they were shown to vary inversely with the Damköhler number in the system computed as the ratio of the rate of reaction over that of diffusive mass transfer.