Recent advances in biology have shown that proteins and genes often interact probabilistically. The resulting effects that arise from these stochastic dynamics differ significantly than traditional deterministic formulations, and have biologically significant ramifications. This has led to the development of computational models of the discrete stochastic biochemical pathways found in living organisms. These include spatial stochastic models, where the physical extent of the domain plays an important role; analogous to traditional partial differential equations.
Simulation of spatial stochastic models is a computationally intensive task. We have developed a new algorithm, the Diffusive Finite State Projection (DFSP) method for the efficient and accurate simulation of stochastic spatially inhomogeneous biochemical systems. DFSP makes use of a novel formulation of Finite State Projection (FSP) to simulate diffusion, while reactions are handled by the Stochastic Simulation Algorithm (SSA).
Further, we adapt DFSP to three dimensional, unstructured, tetrahedral meshes in inclusion in the mature and widely usable systems biology modeling software URDME, enabling simulation of the complex geometries found in biological systems. Additionally, we extend DFSP with adaptive error control and a highly efficient parallel implementation for the graphics processing units (GPU).
In an effort to understand biological processes that exhibit stochastic dynamics, we have developed a spatial stochastic model of cellular polarization. Specifically we investigate the ability of yeast cells to sense a spatial gradient of mating pheromone and respond by forming a projection in the direction of the mating partner. Our results demonstrates that higher levels of stochastic noise results in increased robustness, giving support to a cellular model where noise and spatial heterogeneity combine to achieve robust biological function. This also highlights the importance of spatial stochastic modeling to reproduce experimental observations.