Stochastic effects in cellular systems are usually modeled and simulated with Gillespie's stochastic simulation algorithm (SSA), which follows the same theoretical derivation as the chemical master equation (CME), but the low efficiency of SSA limits its application to large chemical networks.
To improve efficiency of stochastic simulations, Haseltine and Rawlings proposed a hybrid of ODE and SSA algorithm, which combines ordinary differential equations (ODEs) for traditional deterministic models and SSA for stochastic models. In this dissertation, accuracy analysis, efficient implementation strategies, and application of of Haseltine and Rawlings's hybrid method (HR) to a budding yeast cell cycle model are discussed.
Accuracy of the hybrid method HR is studied based on a linear chain reaction system, motivated from the modeling practice used for the budding yeast cell cycle control mechanism. Mathematical analysis and numerical results both show that the hybrid method HR is accurate if either numbers of molecules of reactants in fast reactions are above certain thresholds, or rate constants of fast reactions are much larger than rate constants of slow reactions. Our analysis also shows that the hybrid method HR allows for a much greater region in system parameter space than those for the slow scale SSA (ssSSA) and the stochastic quasi steady state assumption (SQSSA) method.
Implementation of the hybrid method HR requires a stiff ODE solver for numerical integration and an efficient event-handling strategy for slow reaction firings. In this dissertation, an event-handling strategy is developed based on inverse interpolation. Performances of five wildly used stiff ODE solvers are measured in three numerical experiments.
Furthermore, inspired by the strategy of the hybrid method HR, a hybrid of ODE and SSA stochastic models for the budding yeast cell cycle is developed, based on a deterministic model in the literature. Simulation results of this hybrid model match very well with biological experimental data, and this model is the first to do so with these recently available experimental data. This study demonstrates that the hybrid method HR has great potential for stochastic modeling and simulation of large biochemical networks. / Ph. D. / Stochastic effects in cellular systems play an important role under some circumstances, which may enhance the stability of the systems or damage their mechanism. To study the stochastic effects, Gillespie’s stochastic simulation algorithm (SSA) is usually applied to simulate the evolution of cellular systems. SSA can successfully mimic the behavior of a biochemical network consisting of elementary reactions, but it may spend a long time to complete a simulation of a complicated cellular system.
To improve efficiency of stochastic simulations, Haseltine and Rawlings proposed a hybrid stochastic simulation algorithm (HR) combining ordinary differential equations (ODEs) for deterministic models and SSA for stochastic models. Applications of the hybrid method HR show that when some conditions are satisfied, the hybrid method HR can provide results much close to that of SSA and the efficiency is largely improved, but till now little analysis for the accuracy and efficiency of the hybrid method HR has been proposed.
In this dissertation, accuracy of the hybrid method HR is studied based on a linear chain reaction system, a fundamental subsystem motivated from the modeling practice used for the budding yeast cell cycle control mechanism. The requirement for the application of the hybrid method HR is proposed according to mathematical analysis and numerical simulations. Our analysis also shows that the hybrid method HR is valid for a much larger region in system parameter space than those for some other methods. To efficiently implement the hybrid method HR, an event-handling strategy is developed based on inverse interpolation. Performances of the hybrid method HR with five wildly used ODE solvers are measured.
Furthermore, inspired by the strategy of the hybrid method HR, a hybrid of ODE and SSA stochastic models for the budding yeast cell cycle is developed. Simulation results of this hybrid model match very well with biological experimental data, and this model is the first to do so with these recently available experimental data. This study demonstrates that the hybrid method HR has great potential for stochastic modeling and simulation of large biochemical networks.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/82717 |
| Date | 06 October 2016 |
| Creators | Wang, Shuo |
| Contributors | Computer Science, Cao, Yang, Rathinam, Muruhan, Onufriev, Alexey V., Hoops, Stefan, Watson, Layne T. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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