Molecular dynamics with internal coordinate constraints

Abstract

The method of Ryckaert, Ciccotti, and Berendsen [J. Comp. Phys. 23, 327 (1977)] for integrating the Cartesian equations of motion of a system with holonomic constraints, has been extended to allow the independent constraint of arbitrary internal coordinates. To illustrate this new methodology, and to investigate the effects of dihedral angle constraints on the equilibrium and dynamical properties of macromolecules, we have carried out parallel sets of molecular dynamics simulations and normal mode analyses of a small dipeptide: one without constraints, and one with a single backbone dihedral angle constrained. We find that the averages and the fluctuations of the energies, and of the internal degrees of freedom are not significantly modified by the constraint. However, in the region between 100 and 1400 cm−1 of the normal mode spectrum, the constraint shifts the frequencies of the modes, and modifies their contributions to the spectra of the internal coordinates. Except for the lowest frequency torsional modes, in which anharmonic effects are significant, the behavior of the molecular dynamics power spectra is similar to that of the normal mode spectra. We also illustrate the use of a dihedral angle constraint, in conjunction with a recently developed thermodynamic perturbation method, to calculate the torsional potential of mean force for gas phase n-butane. These results are in good agreement with those obtained in previous studies, and they suggest that the combined internal coordinate constraint/thermodynamic perturbation method is well suited for computing free energy surfaces. As an application of this combined approach, we investigate the role of thermal bond and angle fluctuations on the relative free energies of the three lowest energy conformers of N-methylalanylacetamide. The results indicate that the contribution to the free energy from these fluctuations can be significant, and that care must be taken when models with rigid bonds and angles are used to calculate free energy surfaces.

Keywords

Affiliated Institutions

• Carnegie Mellon University US

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