Stability of polypeptide conformational states as determined by computer simulation of the free energy

A method is developed to extract the entropy of polypeptides and proteins from samples of conformations. It is based on techniques suggested previously by Meirovitch, and has the advantage that it can be applied not only to states in which the molecule undergoes harmonic or quasiharmonic conformational fluctuations, but also to the random coil, as well as to mixtures of these extreme states. In order to confine the search to a region of conformational space corresponding to a stable state, the transition probabilities are determined not by “looking to the future,” as in the previous method [H. Meirovitch and H. A. Scheraga (1986) J. Chem. Phys. 84, 6369–6375], but by analyzing the previous steps in the generation of the chain. The method is applied to a model of decaglycine with rigid geometry, using the potential energy function ECEPP (Empirical Conformational Energy Program for Peptides). The model is simulated with the Metropolis Monte Carlo method to generate samples of conformations in the α‐helical and hairpin regions, respectively, at T = 100 K. For the α‐helix, the four dihedral angles of the N‐ and C‐terminal residues are found to undergo full rotational variation. The results show that the α‐helix is a more stable structure than the hairpin. Both its Helmholtz free energy F and energy E are lower than those of the hairpin by ΔF ∼ 0.4 and ΔE ∼ 0.3 kcal/mole/residue, respectively. It should be noted that the contribution of the entropy ΔS to ΔF is significant (TΔS ∼ 0.1 kcal/mole/residue). Also, the entropy of the α‐helix is found to be larger than that of the hairpin. This is a result of the extra entropy arising from the rotational freedom about the four terminal single bonds of the α‐helix.

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