Brownian dynamics simulation of needle chains

Polymers consisting of rigid segments connected by flexible joints (needle chains) constitute an important class of biopolymers. Using kinetic theory as a starting point, we first derive the generalized coordinate–space diffusion (Fokker–Planck) equation for the needle chain polymer model. Next, the equivalent generalized coordinate Ito stochastic differential equation is established. Nonlinear transformations of variables finally yield a stochastic differential equation for the needle chain spatial coordinates in the laboratory coordinate system where the coefficients are expressed in terms of the chain constraint conditions. This latter equation constitutes the basis for our needle chain Brownian dynamics (BD) algorithm. The used needle chain model includes needle translation–translation and rotation–rotation hydrodynamic interactions, a homogeneous solvent flow field, external forces, excluded volume effects, and bending and twisting stiffness between nearest neighbor segments. For this chain model we ...