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

Abstract

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.protein-ligand binding | molecular docking M otivated by the search for efficient small-molecule blockers of "virulent" transmembrane channels (1-3), we investigated the temperature behavior of the blockage reaction. The temperature dependence of the equilibrium constant of blocker association with the pore, that is, the reaction blocker(bulk) + channel(empty) ⇄ channel − blocker, was found to be surprisingly weak, with the temperature coefficient jQ 10 j ' 1.08. Applying the standard linear van't Hoff analysis to evaluate the enthalpy of an association reaction (4) to that of channel blockage (5), we arrive at an estimated enthalpy for the channel-blocker interaction of about 1 kcal/mol. However, examination of blocker partitioning between the bulk and the channel interior gives an estimate for the depth of the potential well for the blocker in the pore of at least 8 kcal/mol. Although these two estimates generally do not have to coincide, this impressive difference compelled us to take a detailed look at the assumptions that are often used in the thermodynamic analysis of blocking reactions as well as at the possible physical forces involved in the channel-blocker interaction. Our analysis is based on consideration of a simple model of particle interaction with the channel (6-8), which allows an explicit calculation of the involved thermodynamics. As might be expected, in the case of the temperatureindependent flat potential well, the enthalpy of the bindin...

Lipid nanodomains change ion channel function

“…It is worth mentioning here that the slopes of the temperature dependences allow only for evaluation of an “effective” height of the barrier. Indeed, the approach assumes a temperature-independent ΔG 27 while there are at least two factors suggesting that the actual situation is more complex. The first one is the temperature-induced change of the membrane mechanical parameters, such as thickness and bending rigidity, 28 the phenomenon that is presumably quite general and applies to both single-phase and two-phase bilayers.…”

Stochastic detection of Pim protein kinases reveals electrostatically enhanced association of a peptide substrate

“…Our method might also be coupled with high-throughput single-channel recording methods (62)(63)(64)(65). Finally, it is possible to estimate the entropic and enthalpic contributions to the change in free energy upon binding by measuring the temperature dependence of the equilibrium dissociation constant according to the van't Hoff equation (66)(67)(68).…”

Forces and Dynamics of Glucose and Inhibitor Binding to Sodium Glucose Co-transporter SGLT1 Studied by Single Molecule Force Spectroscopy

“…Thermal fluctuations of proteins are in general important for biological activity (55); thus the temperature changes in this work may modulate the protein flexibility, and folding and orientation of substructures within the membrane can be affected or accessibility to the sugar binding residues. Finally the interaction forces between ligands and proteins (hydrogen bonding and Coulomb and van der Waal forces) are temperature-dependent (56). At 10°C, which is below the transition point of the membrane lipids, SGLT1 is probably constrained in its structural movements and trapped in non-transporting conformational states.…”