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. Therefore, traditional approaches only based on Ordinary Differential Equations (ODEs) and Continuous Time Markov Chains (CTMCs) fail to account this nature. Therefore, to gain system level understanding, it is necessary to couple different approaches in one computational model. We develop a hybrid approximation that couples the two regimes. In this study, we partition the reactions into two groups which are fast reactions and slow reactions. Then, we model fast reactions with ODEs or Diffusion equation while slow reactions are modelled with CTMCs. Given a principled way of how to reduce such complex CTMC models into a manageable mathematical representation, the error bounds of the path-wise representation of the state vector are used to construct dynamic partitioning algorithms for simulation of multi-scale processes. We call them as dynamic partitioning algorithms because they take into account the fact that the fast reactions could change to slow reactions or vice versa during the process. We implement our algorithms to different biochemical systems.