Brownian dynamics simulation of diffusion to irregular bodies

An extension of the Monte Carlo algorithm for solving the three-dimensional Smoluchowski diffusion equation (Brownian dynamics) for an arbitrarily shaped target particle with a nonsymmetric force field is described. The algorithm uses extensive table lookups to describe the molecular shape and force field in order to reduce computation during the simulation. This also allows the algorithm to be vectorized. Dynamic adjustment of the step size is used to handle rapidly changing and nonlinear force fields. The accuracy of the approximations introduced due to the discrete representation of the field and particle shape is assessed by comparison with several cases where analytical solutions are available. An application to the diffusion of a substrate to an enzyme, where the enzyme's shape and electrostatic field are believed to be important, is described. The electric fields calculated by using different Coulombic potentials do not account for the ionic strength dependence of the enzyme rate. However, the field calculated numerically from the Poisson-Boltzmann equation, which includes the effects of the dielectric boundary between the protein and the solvent, correctly reproduces the ionic strength dependence of the enzyme.