Calculation of Configurational Entropy with a Boltzmann–Quasiharmonic Model: The Origin of High-Affinity Protein–Ligand Binding

Abstract

Accurate assessment of configurational entropy remains a large challenge in biology. While many methods exist to calculate configurational entropy, there is a balance between accuracy and computational demands. Here we calculate ligand and protein conformational entropies using the Boltzmann-quasiharmonic (BQH) method, which treats the first-order entropy term by the Boltzmann expression for entropy while determining correlations using the quasiharmonic model. This method is tested by comparison with the exact Clausius expression for entropy on a range of test molecules ranging from small ligands to a protein. Using the BQH method, we then analyze the rotational and translational (R/T) entropy change upon ligand binding for five protein complexes to explore the origins of extremely tight affinity. The results suggest that in these systems such affinity is achieved by a combination of simultaneously maintaining good protein-ligand contacts while allowing significant residual R/T motion of the ligand through suitable protein motions.

Will molecular dynamics simulations of proteins ever reach equilibrium?

“…In most cases, the conformational entropy shows a similar logarithmic time-dependence as in Figures 2-4 and a questionable convergence. 15,25,22,32,35,79,80,81,82,83 For example, a 1.1 µs simulation of a 15-peptide was not enough to reach convergence of the entropy. 35 As longer and longer MD simulations are published, it also becomes more and more apparent that proteins show extensive dynamics at the ns and µs time scales.…”

Mechanical properties of symmetric and asymmetric DNA A-tracts: implications for looping and nucleosome positioning

“…Besides that, it is also desirable to characterize the flexibility in an overall manner by one simple parameter. To this end we propose to use the conformational entropy (61), defined by the Gibbs formula \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}\begin{equation*} S_c = - k_B \int {p({\bf w})\ln } p({\bf w})d{\bf w} \end{equation*}\end{document}…”

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