The aim of this work is to develop efficient and flexible methods for accurate modeling and simulation of intracellular biochemical processes, with target applications in biology  and medicine .
It has been established that traditional deterministic differential equation-based models may fail to capture important dynamics of biochemical systems due to the inherent randomness of the processes. The stochastic simulation algorithm (SSA) derived by Gillespie  faithfully captures the behavior of well-mixed systems by tracking the discrete copy number of each species and by simulating every reaction event.
In collaboration with Dan Gillespie, we have developed several multiscale stochastic simulation algorithms that take advantage of timescale separation of systems. Tau-leaping  is a method that allows larger time-steps by simulating multiple reactions in each time step. The slow-scale SSA (ssSSA)  accelerates simulations where fast reactions involve chemical species that are present in small numbers, and the slow-scale tau-leaping method  incorporates aspects of both the tau-leaping and ssSSA methods.
However, some systems do not satisfy the well-mixed condition, thus requiring a more detailed level of simulation. For such systems, spatial effects can be taken into account by either considering an extension of the SSA to a spatially heterogeneous setting (the next sub volume method (NSM) ), or even more fine-grained particle-tracking models.
Unfortunately, simulating systems with high spatial resolution is computationally intensive, and to make large computations feasible we are developing multiscale methods, taking advantage of separation of scales. Parts of a simulation can be carried out at a level with less spatial resolution, while other parts are carried out at a more fine-grained level .
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