Rotational and translational dynamics of flexible macromolecules

Abstract

In two previous studies [J. Chem. Phys. 91, 1287 (1989); 95, 1234 (1991)] we had examined the dynamics of coupled, internal translational, and rotational motions in a rigid or pseudorigid N-sphere macromolecular model using the rotational–translational Brownian dynamics algorithm of Dickinson et al. [J. Chem. Soc. Faraday Trans. 2 81, 591 (1985)]. In the present study, those works are generalized to include all possible internal flexible motions in an N-sphere macromolecular model. In general, for the N-sphere system there are 6(N-1) degrees of configurational freedom, although not all modes may be active in any particular application. Using the language of small oscillation theory, the deviations in the generalized coordinates associated with the ‘‘joints’’ connecting the spheres to one another are described in terms of quadratic potentials. From these potentials, the components of the generalized forces (torques and forces) are obtained for subsequent use in the Brownian dynamics algorithm. The degree of flexibility for any particular mode in the N-sphere system can be controlled by a single constant in the associated quadratic potential function. By taking the appropriate limits of these constants, the complete range of flexibility, viz., from ‘‘torque (or force)-free’’ to ‘‘rigid’’ can be approximately realized at any point in the N-sphere system. The model given is, therefore, capable of simulating all types of macromolecular motions. As a specific example, we studied the linear elastic rotator, where all modes (translational and rotational) are constrained except for rotations about the line of center of the spheres. Brownian dynamics results expressed in terms of rotational correlation functions were in good agreement with analytical solutions obtainable for this highly symmetric system. The algorithm given here is believed to be particularly useful in the study of the dynamics of biological macromolecules where ‘‘flexibility’’ is often critical to the functionality of the macromolecule [J. Chem. Phys. 90, 3843 (1989); Macromolecules 16, 421 (1983); 15, 1544 (1982); Chem. Phys. 41, 35 (1979)].