ROTATIONAL AND TRANSLATIONAL DYNAMICS OF FLEXIBLE MACROMOLECULES

In two previous studies [J. Chem. Phys, 91, 1287 (1989); 95, 1234 (199 1)] we had examined the dynamics of coupled, internal translational, a nd rotational motions in a rigid or pseudorigid N-sphere macromolecula r 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 possi ble internal flexible motions in an N-sphere macromolecular model. In general, for the N-sphere system there are 6(N-1) degrees of configura tional freedom, although not all modes may be active in any particular application. Using the language of small oscillation theory, the devi ations in the generalized coordinates associated with the ''joints'' c onnecting the spheres to one another are described in terms of quadrat ic potentials. From these potentials, the components of the generalize d forces (torques and forces) are obtained for subsequent use in the B rownian dynamics algorithm. The degree of flexibility for any particul ar mode in the N-sphere system can be controlled by a single constant in the associated quadratic potential function. By taking the appropri ate limits of these constants, the complete range of flexibility, viz. , from ''torque (or force)-free'' to ''rigid'' can be approximately re alized at any point in the N-sphere system. The model given is, theref ore, capable of simulating all types of macromolecular motions. As a s pecific example, we studied the linear elastic rotator, where all mode s (translational and rotational) are constrained except for rotations about the line of center of the spheres. Brownian dynamics results exp ressed in terms of rotational correlation functions were in good agree ment with analytical solutions obtainable for this highly symmetric sy stem. The algorithm given here is believed to be particularly useful i n the study of the dynamics of biological macromolecules where ''flexi bility'' is often critical to the functionality of the macromolecule [ J. Chem. Phys. 90, 3843 (1989); Macromolecules 16, 421 (1983); 15, 154 4 (1982); Chem. Phys. 41, 35 (1979)].