Monte Carlo calculations on polypeptide chains. 10. A study of the kinetics of the helix--coli transition.

A stochastic model of the kinetics of the helix--coil transition based on the equilibrium statistical mechanical theory of Lifson and Roig is presented. A Monte Carlo simulation of the kinetics based on the stochastic model was used to study the kinetics of the helix--coil transition. Kinetics simulations were conducted from several initial values of the fractional hydrogen bonding parameter theta to each equilibrium value of theta. A spectrum of relaxation times and characteristic weighting constants is reported for each kinetics simulation. The chain lengths used in this study were 15, 34, and 85 residues. It was found that at each chain length the relaxation times depend only on the equilibrium value of 0 while the characteristic weighting constants depend on both the initial and equilibrium values of theta. The mean relaxation time was calculated for several relaxations at chain lengths 15, 34, and 85. It was found that the mean relaxation time does not reflect the correct order of magnitude of the slowest relaxation process. In addition, it was found that pure random coil species do not survive long enough to be measured by nmr spectroscopy and therefore values of t greater than or equal to 10(-1)s do not reflect a relaxation time of the helix--coil transition.

Monte Carlo calculations on polypeptide chains. IX. A study of the effect of long-range interactions on the helix-coil transition.

A Monte Carlo statistical mechanical study of the helix-coil transition for a hard-sphere model of poly(L-alanine) has been conducted base on the theory of Lifson and Roig but including the effects of long-range interactions. A stochastic model of the kinetics of the helix-coil transition is presented, and a Monte Carlo stimulation of the kinetics based on this model was used to generate equilibrium chain samples, each chain of which consisted of Lifson-Roig weighted sequences of helix and coil residues. Each of the chains in this sample was then used many times by assigning at random specific sterically allowed coil states from a hard-sphere Ramachandran dipeptide map. Unperturbed properties were then calculated using this sample and perturbed properties by using only the non-self-conflicting subset. The properties calculated were the average degree of hydrogen bonding, the average length of a helical sequence, the mean-square end-to-end distance, the mean-square radius of gyration, and the distribution functions for the end-to-end distance and radius of gyration. This study was conducted at chain lengths 10, 34, and 85 residues. Helix-coil transition theory was fit to the perturbed transition curves in an attempt to ascertain if theory could then predict the perturbed values of the dimensions. For the hard-sphere model used in these calculations, it was found that current helix-coil transition theory does not predict the correct perturbed dimensions.

Monte Carlo calculations on polypeptide chains. VIII. Distribution functions for the end-to-end distance and radius of gyration for hard-sphere models of randomly coiling poly(glycine) and poly(L-alanine).

A Monte Carlo study of the distribution functions for the end-to-end distance and radius of gyration for hard-sphere models of poly(glycine) and poly(L-alanine) random coils has been conducted in the chain-length range n = 3 to 100 monomer units for both unperturbed chains and chains perturbed by long-range interactions (excluded volume effects). The distribution functions for the radius of gyration in all cases have been very precisely calculated, those for the perturbed end-to-end distance less precisely, and those for the unperturbed end-to-end distance least precisely. Empirical distribution functions of the form W(p) = ap-b exp(-cp-d) for the reduced end-to-end distance p = r/"r-2"-one-half and a similar form for the reduced radius of gyration could be least-squares fit to the Monte Carlo data. The expansion factors alpha-r and alpha-s were calculated vs. chain length and were used to test various versions of the two-parameter theory of the excluded volume effect. To be consistent with the chain-length dependence of alpha-r and alpha-s as determined by the Monte Carlo calculations, each of these theories required two different binary cluster integrals, a beta-r based on alpha-r and a beta-s based on alpha-s, both of which were strongly chain-length dependent. Both of these results suggest that the two-parameter theory is not applicable to the models used in this study. It was also found that, except for very short chain lengths, plots of ln alphs-r vs. ln n were linear, and thus that alpha-r could be estimated for long chain lengths. Comparison of these estimates with the experimental data on four polypeptide chains in one-earth solvents that the hard-sphere models used in this study yield expansion factors that do not seriously overestimate the magnitude of the excluded volume effect.