Kinetics and thermodynamics of binding reactions as exemplified by anthrax toxin channel blockage with a cationic cyclodextrin derivative.

The thermodynamics of binding reactions is usually studied in the framework of the linear van't Hoff analysis of the temperature dependence of the equilibrium constant. The logarithm of the equilibrium constant is plotted versus inverse temperature to discriminate between two terms: an enthalpic contribution that is linear in the inverse temperature, and a temperature-independent entropic contribution. When we apply this approach to a particular case-blockage of the anthrax PA(63) channel by a multicharged cyclodextrin derivative-we obtain a nearly linear behavior with a slope that is characterized by enthalpy of about 1 kcal/mol. In contrast, from blocker partitioning between the channel and the bulk, we estimate the depth of the potential well for the blocker in the channel to be at least 8 kcal/mol. To understand this apparent discrepancy, we use a simple model of particle interaction with the channel and show that this significant difference between the two estimates is due to the temperature dependence of the physical forces between the blocker and the channel. In particular, we demonstrate that if the major component of blocker-channel interaction is van der Waals interactions and/or Coulomb forces in water, the van't Hoff enthalpy of the binding reaction may be close to zero or even negative, including cases of relatively strong binding. The results are quite general and, therefore, of importance for studies of enzymatic reactions, rational drug design, small-molecule binding to proteins, protein-protein interactions, and protein folding, among others.