Two-peak approximation in kinetic capillary electrophoresis

Abstract

Kinetic capillary electrophoresis (KCE) constitutes a toolset of homogeneous kinetic affinity methods for measuring rate constants of formation (k₊) and dissociation (k₋) of non-covalent biomolecular complexes, C, formed from two binding partners, A and B. A parameter-based approach of extracting k₊ and k₋ from KCE electropherograms relies on a small number of experimental parameters found from the electropherograms and used in explicit expressions for k₊ and k₋ derived from approximate solutions to mass transfer equations. Deriving the explicit expressions for k₊ and k₋ is challenging but it is justified as the parameter-based approach is the simplest way of finding k₊ and k₋ from KCE electropherograms. Here, we introduce a unique approximate analytical solution of mass transfer equations in KCE termed a “two-peak approximation” and a corresponding parameter-based method for finding k₊ and k₋. The two-peak approximation is applicable to any KCE method in which: (i) A* binds B to form C* (the asterisk denotes a detectable label on A), (ii) two peaks can be identified in a KCE electropherogram and (iii) the concentration of B remains constant. The last condition holds if B is present in access to A* and C* throughout the capillary. In the two-peak approximation, the labeling of A serves only for detection of A and C and, therefore, is not required if A (and thus C) can be observed with a label-free detection technique. We studied the proposed two-peak approximation, in particular, its accuracy, by using the simulated propagation patterns built with the earlier-developed exact solution of the mass-transfer equations for A* and C*. Our results prove that the obtained approximate solution of mass transfer equations is correct. They also show that the two-peak approximation facilitates finding k₊ and k₋ with a relative error of less than 10% if two peaks can be identified on a KCE electropherogram. Importantly, the condition of constant concentration of B is always satisfied in macroscopic approach to studying kinetics at equilibrium (MASKE) whether or not B is in excess to A* and C*, and, thus, the two-peak approximation is applicable to MASKE. It completes a toolset of fitting-free methods for processing MASKE data and makes MASKE a simple practical method for finding k₊ and k₋ of “fast”, “slow”, and “intermediate-rate” non-covalent interactions.