Stability of the Free and Bound Microstates of a Mobile Loop of α-Amylase Obtained from the Absolute Entropy and Free Energy.

Abstract

The hypothetical scanning molecular dynamics (HSMD) method is a relatively new technique for calculating the absolute entropy, S, and free energy, F, from a given sample generated by any simulation procedure. Thus, each sample conformation, i, is reconstructed by calculating transition probabilities that their product leads to the probability of i, hence to the entropy. HSMD is an exact method where all interactions are considered, and the only approximation is due to insufficient sampling. In previous studies HSMD (and HS Monte Carlo - HSMC) has been applied very successfully to liquid argon, TIP3P water, self-avoiding walks, and peptides in a α-helix, extended, and hairpin microstates. In this paper HSMD is developed further as applied to the flexible 7-residue surface loop, 304-310 (Gly-His-Gly-Ala-Gly-Gly-Ser) of the enzyme porcine pancreatic α-amylase. We are mainly interested in entropy and free energy differences ΔS = Sfree - Sbound (and ΔF=Ffree-Fbound) between the free and bound microstates of the loop, which are obtained from two separate MD samples of these microstates without the need to carry out thermodynamic integration. As for peptides, we find that relatively large systematic errors in Sfree and Sbound (and Ffree and Fbound) are cancelled in ΔS (ΔF) which is thus obtained efficiently with high accuracy, i.e., with a statistical error of 0.1-0.2 kcal/mol (T=300 K) using the AMBER force field and AMBER with the implicit solvation GB/SA. We provide theoretical arguments in support of this cancellation, discuss in detail the problems involved in the computational definition of a microstate in conformational space, suggest potential ways for enhancing efficiency further, and describe the next development where explicit water will replace implicit solvation.