Mathematical theory of isoelectric focusing.

Abstract

A mathematical model describing transient processes in isoelectric focusing (IEF) of M biprotic ampholytes is proposed. The problem consists of nonlinear partial differential equations and algebraic equations under nonlinear boundary conditions. Different models of IEF have been studied. For each model problem, we investigated the qualitative properties such as the local existence, global boundedness, stabilizations, and steady-state structures of its solutions. We have shown that, for all models the solutions of the evolution problem stabilize to the steady-state solutions, which have separate peaks at a certain point (the so-called isoelectric point). This means that for transient IEF processes, the concentrations of ampholytes will focus on their isoelectric points as time goes on. All these analytic results showed good agreement with the laboratory experiments and computer simulations.