Brownian dynamics of bead–rod–nugget–spring polymer chains with hydrodynamic interactions

Abstract

With Brownian dynamics simulations of solutions containing complex biological macromolecules in mind we have formulated a polymer chain model consisting of a selectable sequence of spherical subunits (beads) and nonspherical subunits of arbitrary shapes (nuggets) connected by rigid rods, rigid ball–socket joints, or springs. Many physical properties of both subunits and connections are selectable. First a very general diffusion equation of polymer kinetic theory is employed. Next the equivalent Itô stochastic differential equation of motion is established and finally an effective Brownian dynamics simulation algorithm is presented. In all these steps it is assumed that the numerical values of the subunit steady state mobility tensor are obtainable. The important and previously unanswered question of how to include translational–rotational hydrodynamic interactions in Brownian dynamics simulations of polymer chains containing nonspherical subunits linked by rigid constraints is resolved rigorously here. This means that during the formal derivation of the presented Brownian dynamics simulation algorithm all subunit hydrodynamic interactions of the proposed bead–rod–nugget–spring polymer chain model have in principle been taken fully into account. In addition the model includes rigid constraints to fixed points in the laboratory coordinate system, solvent flow, external forces, excluded volume effects, and bending and torsional stiffness between polymer chain subunits. Bead–spring, bead–rod–spring, needle–spring, needle polymer chains and liquid crystals are all special cases of the bead–rod–nugget–spring polymer chain model. The validity of the algorithm presented is limited to the diffusion time domain.