Calculation of Configurational Entropy Differences from Conformational Ensembles Using Gaussian Mixtures

We present a novel, conceptually simple approach to calculate the configurational entropy difference between two conformational ensembles of a molecular system. The method estimates the full-dimensional probability density function of the system by a Gaussian mixture, using an efficient greedy learning algorithm with a cross-validation-based stopping criterion. An evaluation of the method on conformational ensembles corresponding to substates of five small peptide systems shows that excellent agreement is found with the exact entropy differences obtained from a full enumeration of conformations. Compared with the quasiharmonic method and two other, more recently developed methods, the Gaussian mixture method yields more accurate results at smaller sample sizes. We illustrate the power of the method by calculating the backbone torsion angle entropy difference between disulfide-bonded and nondisulfide-bonded states of tachyplesin, a 17-residue antimicrobial peptide, and between two substates in the native ensemble of the 58-residue bovine pancreatic trypsin inhibitor.