Nature often colocalizes successive steps in a metabolic pathway. Such organization is predicted to increase the effective concentration of pathway intermediates near their recipient active sites and to enhance catalytic efficiency. Here, the pathway of a two-step reaction is modeled using a simple spherical approximation for the enzymes and substrate particles. Brownian dynamics are used to simulate the trajectory of a substrate particle as it diffuses between the active site zones of two different enzyme spheres. The results approximate distances for the most effective reaction pathways, indicating that the most effective reaction pathway is one in which the active sites are closely aligned. However, when the active sites are too close, the ability of the substrate to react with the first enzyme was hindered, suggesting that even the most efficient orientations can be improved for a system that is allowed to rotate or change orientation to optimize the likelihood of reaction at both sites.

Diffusion is often the rate determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. This paper proposes a new hybrid diffusion method that couples the strengths of each of these two methods. The method is derived for a general multidimensional system, and is presented using a basic test case for 1D linear and radially symmetric diffusion systems.