Characterization of Conformational Equilibria Through Hamiltonian and Temperature Replica-exchange Simulations: Assessing Entropic and Environmental Effects

Molecular dynamics simulations based on the replica-exchange framework (REMD) are emerging as a useful tool to characterize the conformational variability that is intrinsic to most chemical and biological systems. In this work, it is shown that a simple extension of the replica-exchange method, known as Hamiltonian REMD, greatly facilitates the characterization of conformational equilibria across large energetic barriers, or in the presence of substantial entropic effects, overcoming some of the difficulties of REMD based on temperature alone. In particular, a comparative assessment of the HREMD and TREMD approaches was made, through computation of the gas-phase free-energy difference between the so-called D(2d) and S(4) states of tetrabutylammonium (TBA), an ionic compound of frequently used in biophysical studies of ion channels. Taking advantage of the greater efficiency of the HREMD scheme, the conformational equilibrium of TBA was characterized in a variety of conditions. Simulation of the gas-phase equilibrium in the 100-300 K range allowed us to compute the entropy difference between these states as well as to describe its temperature dependence. Through HREMD simulations of TBA in a water droplet, the effect of solvation on the conformational equilibrium was determined. Finally, the equilibrium of TBA in the context of a simplified model of the binding cavity of the KcsA potassium channel was simulated, and density maps for D(2d) and S(4) states analogous to those derived from X-ray crystallography were constructed. Overall, this work illustrates the potential of the HREMD approach in the context of computational drug design, ligand-receptor structural prediction and more generally, molecular recognition, where one of the most challenging issues remains to account for conformational flexibility as well for the solvation and entropic effects thereon.