A Computational Resolution of the Inverse Problem of Kinetic Capillary Electrophoresis (KCE)

Abstract

Determining kinetic rate constants is a highly relevant problem in biochemistry, so various methods have been designed to extract them from experimental data. Such methods have two main components: the experimental apparatus and the subsequent analysis, the latter often dependent on mathematical theory. Thus the theoretical approach taken influences the effectiveness of constant determination. A computational inverse problem approach is hereby presented, which does not merely give a single rough approximation of the sought constants, but is inherently capable of determining them from exact signals to arbitrary accuracy. This approach is thus not merely novel, but opens a whole new category of solution approaches in the field, enabled primarily by an efficient direct solver.

A fast stable discretization of the Constant–Convection–Diffusion–Reaction equations of Kinetic Capillary Electrophoresis (KCE)

“…The KCE system of convection-diffusion-reaction equations includes kinetic rate constants in the reaction term, which can be viewed as parameters that the solution functions of this system of partial differential equations depend on. The efficient and accurate generation of such parametric solutions to the direct problem is necessary for the evaluation of the error target function at each iteration of some optimization algorithm, which minimizes this target function to resolve the inverse problem of determining the parameters that induce a given target signal [30].…”

“…The inverse problem of our research requires fast and accurate simulation of the solutions to the KCE equations for varying k on , k off values, modeling experimental electropherogram signals [30]. Thus we analyze our direct solver in terms of both runtime and error below.…”