Revealing Equilibrium and Rate Constants of Weak and Fast Noncovalent Interactions

Rate and equilibrium constants of weak noncovalent molecular interactions are extremely difficult to measure. Here, we introduced a homogeneous approach called equilibrium capillary electrophoresis of equilibrium mixtures (ECEEM) to determine k_on, k_off, and K_d of weak (K_d > 1 μM) and fast kinetics (relaxation time, τ < 0.1 s) in quasi-equilibrium for multiple unlabeled ligands simultaneously in one microreactor. Conceptually, an equilibrium mixture (EM) of a ligand (L), target (T), and a complex (C) is prepared. The mixture is introduced into the beginning of a capillary reactor with aspect ratio >1000 filled with T. Afterward, differential mobility of L, T, and C along the reactor is induced by an electric field. The combination of differential mobility of reactants and their interactions leads to a change of the EM peak shape. This change is a function of rate constants, so the rate and equilibrium constants can be directly determined from the analysis of the EM peak shape (width and symmetry) and propagation pattern along the reactor. We proved experimentally the use of ECEEM for multiplex determination of kinetic parameters describing weak (3 mM > K_d > 80 μM) and fast (0.25 s ≥ τ ≥ 0.9 ms) noncovalent interactions between four small molecule drugs (ibuprofen, S-flurbiprofen, salicylic acid and phenylbutazone) and α- and β-cyclodextrins. The affinity of the drugs was significantly higher for β-cyclodextrin than α-cyclodextrin and mostly determined by the rate constant of complex formation.