THEORY OF LONG-TIME PEPTIDE DYNAMICS - TEST OF VARIOUS REDUCED DESCRIPTIONS AND ROLE OF INTERNAL VARIABLES

We extend our recent theory of the long time dynamics for peptide molecules in solution to include side chain motions, interresidue interactions, the influence of solvent motions, and the relaxation correlation functions for arbitrary vector directions in the molecule. The theory represents a reduced statistical mechanical description of the system, in which several models are introduced to probe the relevant slow variables governing the long time peptide dynamics. The solution of the dynamical equations requires only the rather trivial diagonalization of matrices, but the complicated portion involves the computation of equilibrium averages for the bond vector correlation and hydrodynamic matrices. The latter are evaluated here using molecular dynamics simulations (including the solvent molecules) that are performed with the CHARMm package. The three models considered here take as relevant slow variables (a) the positions of the alpha-carbons (the virtual bond model), (b) the positions of all backbone bonds (the backbone bonds model), and (c) both the positions in (b) and those along the side group chains. Ignoring memory functions and using an additivity model for group friction coefficients, calculations with all three models are performed of the orientational relaxation correlation functions and correlation times for a variety of local bonds and directions in the peptide. Comparisons are made between the predictions of the three models (and with experiment) to assess the relative importance of retaining in the reduced description various categories of degrees of freedom and the importance of the neglected memory functions.