Two-dimensional reaction of biological molecules studied by Weighted-Ensemble Brownian dynamics

Computer simulations offer critical insights into the reaction of biological macromolecules, especially when the molecular shapes are too complex to be amenable to analytical solution. In this work, the Weighted-Ensemble Brownian (WEB) Dynamics simulation algorithm is adapted to a reaction of two unlike biological molecules, with the interaction modeled by a two-parameter system: a spherical molecular depositing on a target region of an infinite cylinder with a periodic boundary conditions. The original algorithm of Huber and Kim is streamlined for this class of reactive models. The reaction rate constant is calculated as a function of relative sizes of the reactive to non-reactive regions of the cylindrical molecule. An analytical expression for the rate constant is also obtained from the solution of the diffusion equation for the special case of a constant-flux boundary condition. Good agreement between analytical and simulation results validates the applicability of WEB Dynamics to a reaction of molecules of complicated shape. On the other hand, the simple form of our analytical expression is useful as a testing case for other simulation and numerical techniques.