Hybrid spatial Gillespie and particle tracking simulation

Motivation: Cellular signal transduction involves spatial-temporal dynamics and often stochastic effects due to the low particle abundance of some molecular species. Others can, however, be of high abundances. Such a system can be simulated either with the spatial Gillespie/Stochastic Simulation Algorithm (SSA) or Brownian/Smoluchowski dynamics if space and stochasticity are important. To combine the accuracy of particle-based methods with the superior performance of the SSA, we suggest a hybrid simulation. Results: The proposed simulation allows an interactive or automated switching for regions or species of interest in the cell. Especially we see an application if for instance receptor clustering at the membrane is modeled in detail and the transport through the cytoplasm is included as well. The results show the increase in performance of the overall simulation, and the limits of the approach if crowding is included. Future work will include the development of a GUI to improve control of the simulation.