The Art of Modeling and Simulation of Multiscale Biochemical Systems
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In this thesis we study modeling and simulation approaches for multiscale biochemical systems. The thesis addresses both modeling methods and simulation strategies. In the first part, we propose modeling methods to study the behavior of the insulin secretion pathway. We first expand the single cell model proposed by Bertram et. al. to model multiple cells. Synchronization among multiple cells is observed. Then an unhealthy cell model is proposed to study the insulin secretion failure caused by weakening of mitochondria function. By studying the interaction between the healthy and unhealthy cells, we find that the insulin secretion can be reinstated by increasing the glucokinase level. This new discovery sheds light on antidiabetic medication. In order to study the stochastic dynamics of the insulin secretion pathway, we first apply the hybrid method to model the discrete events in the insulin secretion pathway. Based on the hybrid model, a probability based measurement is proposed and applied to test the new antidiabetic remedy. In the second part, we focus on different simulation schemes for multiscale biochemical systems. We first propose a partitioning strategy for the hybrid method which leads to an efficient way of building stochastic cell cycle models. Then different implementation methods for the hybrid method are studied. A root finding method based on inverse interpolation is introduced to implement the hybrid method with three different ODE solvers. A detailed discussion of the performance of these three ODE solvers is presented. Last, we propose a new strategy to automatically detect stiffness and identify species that cause stiffness for the Tau-Leaping method, as well as two stiffness reduction methods. The efficiency is demonstrated by applying this new strategy on a stiff decaying dimerization model and a heat shock protein regulation model.
- Doctoral Dissertations