Evaluating the conformational entropy of macromolecules using an energy decomposition approach

We have developed a novel method to compute the conformational entropy of any molecular system via conventional simulation techniques. This method only requires that the total energy of the system is available and that the Hamiltonian is separable, with individual energy terms for the various degrees of freedom. Consequently the method, which we call the energy decomposition (Edcp) approach, is general and applicable to any large polymer in implicit solvent. Edcp is applied to estimate the entropy differences due to the peptide and ester groups in polyalanine and polyalanil ester. Ensembles over a wide range of temperatures were generated by replica exchange molecular dynamics, and densities of states were estimated using the weighted histogram analysis method. The results are compared with those obtained via evaluating the P ln P integral or employing the quasiharmonic approximation, other approaches widely employed to evaluate the entropy of molecular systems. Unlike the former method, Edcp can accommodate the correlations present between separate degrees of freedom. In addition, the Edcp model assumes no specific form for the underlying fluctuations present in the system, in contrast to the quasiharmonic approximation. For the molecules studied, the quasiharmonic approximation is observed to produce a good estimate of the vibrational entropy, but not of the conformational entropy. In contrast, our energy decomposition approach generates reasonable estimates for both of these entropy terms. We suggest that this approach embodies a simple yet effective solution to the problem of evaluating the conformational entropy of large macromolecules in implicit solvent.