COMPUTER-SIMULATION OF THE ENTROPY OF POLYPEPTIDES USING THE LOCAL STATES METHOD - APPLICATION TO CYCLO-(ALA-PRO-D-PHE)2 IN VACUUM AND IN THE CRYSTAL

The local states (LS) method is an approximate technique proposed by Meirovitch (Chem. Phys. Lett. 1977, 45, 38) for estimating the entropy from a sample of conformations. The method is further developed and extended here to molecular dynamics samples of the cyclic peptide cyclo-(Ala-Pro-D-Phe)2 in vacuum and in the crystal environment. This is the first time the LS method has been applied to a peptide with side chains which is described by flexible geometry. The method enables one to obtain an approximation P(i) of the sampling probability of conformation i where P(i) is expressed as a product of transition probabilities, which relate a dihedral or a valence angle to a number of preceding angles in the chain. This set of angles is called a local state. The values of P(i) define approximations for the entropy S (S approximately ln P(i)) which together with the energy lead to upper and lower bounds for the free energy. The LS method is general; i.e., it can be applied to samples of any conformational state (e.g., a random coil) and is not restricted to a molecule undergoing small harmonic conformational fluctuations. Thus, the relative stability of states of considerable structural difference can be obtained from the corresponding free energies. In this work we investigate some effects of environment on cyclo-(Ala-Pro-D-Phe)2 and, in particular, calculate the reduction in entropy, DELTA-S, in going from vacuum to the crystal. We find that T-DELTA-S = T[S(vacuum) - S(crystal)] = 9.4 +/- 0.8 kcal/mol where T approximately 300 K is the absolute temperature. Calculation of DELTA-S is important in biological processes such as the binding of a peptide to a receptor, which involves a change of environment. We argue that under certain conditions the method is expected to be efficient even for large proteins.