No description available.

In this thesis we study stochastic modeling and simulation methods for biochemical systems. The thesis is focused on systems with multi-state and multi-scale features and divided into two parts. In the first part, we propose new algorithms that improve existing multi-state simulation methods. We first compare the well known Gillespie\\\'s stochastic simulation algorithm (SSA) with the StochSim, an agent-based simulation method. Based on the analysis, we propose a hybrid method that possesses the advantages of both methods. Then we propose two new methods that extend the Network-Free Algorithm (NFA) for rule-based models. Numerical results are provided to show the performance improvement by our new methods. In the second part, we investigate two simulation schemes for the multi-scale feature: Haseltine and Rawlings\\\' hybrid method and the quasi-steady-state stochastic simulation method. We first propose an efficient partitioning strategy for the hybrid method and an efficient way of building stochastic cell cycle models with this new partitioning strategy. Then, to understand conditions where the two simulation methods can be applied, we develop a way to estimate the relaxation time of the fast sub-network, and compare it with the firing interval of the slow sub-network. Our analysis are verified by numerical experiments on different realistic biochemical models. / Ph. D.

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. / Ph. D.