turkmath.org

It is possible to consider biological processes as reaction systems that are formed by many different species interacting via multiple chemical reactions. It is a well-known fact that reaction types and also abundance of reactants in these processes cannot be classified in one category. To be more precise, they can have fast/slow reactions and reactants in these processes can have high/low copy-number of molecules. In other words, these processes have multi-scale nature. There are two well-established approaches to model the behaviour of reaction systems: deterministic approach which assumes that the behaviours of such processes are continuous, deterministic and stochastic approach which assumes that the behaviours of such processes are discrete, stochastic. Using only one of these approaches fails to account for this multi-scale nature of biological processes. Therefore, it is necessary to couple different approaches in one computational model. We developed an efficient diffusion approximation to capture this multi-scale nature. Briefly, in this study, we partitioned the reactions into two fast and slow groups. Then, we modelled fast reactions with Langevin equation while slow reactions were modelled with Continuous Time Markov Chains (CTMCs). The error bound of the model is used to construct dynamic partitioning algorithm which takes into account the fact that types of reactions can change during the course of time for simulation of multi-scale processes. The proposed algorithm is applied to Michaelis Menten model and MAPK signalling pathway. This presentation is based on the paper “Jump-diffusion approximation of stochastic reaction dynamics: Error bounds and algorithms” which is joint work with A. Ganguly, H. Koeppl and submitted to SIAM Journal of Multiscale Modelling and Simulations.