BROWNIAN DYNAMICS SIMULATION OF NEEDLE CHAINS

Polymers consisting of rigid segments connected by flexible joints (ne edle chains) constitute an important class of biopolymers. Using kinet ic theory as a starting point, we first derive the generalized coordin ate-space diffusion (Fokker-Planck) equation for the needle chain poly mer model. Next, the equivalent generalized coordinate Ito stochastic differential equation is established. Nonlinear transformations of var iables finally yield a stochastic differential equation for the needle chain spatial coordinates in the laboratory coordinate system where t he coefficients are expressed in terms of the chain constraint conditi ons. This latter equation constitutes the basis for our needle chain B rownian dynamics (BD) algorithm. The used needle chain model includes needle translation-translation and rotation-rotation hydrodynamic inte ractions, a homogeneous solvent flow field, external forces, excluded volume effects, and bending and twisting stiffness between nearest nei ghbor segments. For this chain model we find that by proper generaliza tion of the involved parameters the mathematical analysis of the polym er dynamics, in great detail, maps onto the analysis of the bead-rod-s pring polymer chain model with constraints presented by Ottinger in Ph ys. Rev. E 50, 2696 (1994). Preliminary numerical simulation data show that for a three segment needle chain, with needle axial ratio equal to five, our new needle chain BD algorithm is, in general, more than a bout 10(3) times more efficient than the bead-spring polymer chain BD algorithm commonly used as an approximation for studies of such polyme r chains, This efficiency ratio increases asymptotically proportional to approximately the fourth power of the needle axial ratio. In additi on to this major gain in efficiency, the needle chain model for segmen ted polymers, in general, incorporates a more realistic hydrodynamic d escription of the individual segments and, in particular, the joints b etween the segments than the bead-rod-spring models. (C) 1996 American Institute of Physics.