From One-to-One Complexation to Multisite Binding: Analytical Transport Coefficients and Mechanistic Diagnostics in...

We develop a general analytical framework for reaction-drift-diffusion processes under arbitrary multisite complexation schemes. This framework explains the separation of chiral compounds in capillary electrophoresis (CE) experiments involving multiple complexes, thereby extending beyond the scope of classical one-to-one (1:1) models. By diagonalizing the reaction-drift-diffusion operator in Fourier-Laplace space, we obtain closed-form expressions for the effective electrophoretic mobility and diffusion coefficient in an $n$ -site mechanism. For 1:1 binding, the theory recovers the Wren-Rowe equation and exactly reproduces the diffusion coefficient obtained using the generating-function technique. Application to published data for Tyr-Arg-Phe-Phe-NH₂ stereoisomers interacting with DM- $\beta$ -cyclodextrin shows that a minimal two-site model reproduces the observed curve morphologies. These results provide a direct link between stochastic kinetics, continuum transport, and practical diagnostics for optimizing chiral CE.