Browsing by Author "Chen, Minghan"
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- Analysis and remedy of negativity problem in hybrid stochastic simulation algorithm and its applicationChen, Minghan; Cao, Yang (2019-06-20)Background The hybrid stochastic simulation algorithm, proposed by Haseltine and Rawlings (HR), is a combination of differential equations for traditional deterministic models and Gillespie’s algorithm (SSA) for stochastic models. The HR hybrid method can significantly improve the efficiency of stochastic simulations for multiscale biochemical networks. Previous studies on the accuracy analysis for a linear chain reaction system showed that the HR hybrid method is accurate if the scale difference between fast and slow reactions is above a certain threshold, regardless of population scales. However, the population of some reactant species might be driven negative if they are involved in both deterministic and stochastic systems. Results This work investigates the negativity problem of the HR hybrid method, analyzes and tests it with several models including a linear chain system, a nonlinear reaction system, and a realistic biological cell cycle system. As a benchmark, the second slow reaction firing time is used to measure the effect of negative populations on the accuracy of the HR hybrid method. Our analysis demonstrates that usually the error caused by negative populations is negligible compared with approximation errors of the HR hybrid method itself, and sometimes negativity phenomena may even improve the accuracy. But for systems where negative species are involved in nonlinear reactions or some species are highly sensitive to negative species, the system stability will be influenced and may lead to system failure when using the HR hybrid method. In those circumstances, three remedies are studied for the negativity problem. Conclusions The results of different models and examples suggest that the Zero-Reaction rule is a good remedy for nonlinear and sensitive systems considering its efficiency and simplicity.
- Stochastic Modeling and Simulation of Multiscale Biochemical SystemsChen, Minghan (Virginia Tech, 2019-07-02)Numerous challenges arise in modeling and simulation as biochemical networks are discovered with increasing complexities and unknown mechanisms. With the improvement in experimental techniques, biologists are able to quantify genes and proteins and their dynamics in a single cell, which calls for quantitative stochastic models for gene and protein networks at cellular levels that match well with the data and account for cellular noise. This dissertation studies a stochastic spatiotemporal model of the Caulobacter crescentus cell cycle. A two-dimensional model based on a Turing mechanism is investigated to illustrate the bipolar localization of the protein PopZ. However, stochastic simulations are often impeded by expensive computational cost for large and complex biochemical networks. The hybrid stochastic simulation algorithm is a combination of differential equations for traditional deterministic models and Gillespie's algorithm (SSA) for stochastic models. The hybrid method can significantly improve the efficiency of stochastic simulations for biochemical networks with multiscale features, which contain both species populations and reaction rates with widely varying magnitude. The populations of some reactant species might be driven negative if they are involved in both deterministic and stochastic systems. This dissertation investigates the negativity problem of the hybrid method, proposes several remedies, and tests them with several models including a realistic biological system. As a key factor that affects the quality of biological models, parameter estimation in stochastic models is challenging because the amount of empirical data must be large enough to obtain statistically valid parameter estimates. To optimize system parameters, a quasi-Newton algorithm for stochastic optimization (QNSTOP) was studied and applied to a stochastic budding yeast cell cycle model by matching multivariate probability distributions between simulated results and empirical data. Furthermore, to reduce model complexity, this dissertation simplifies the fundamental cooperative binding mechanism by a stochastic Hill equation model with optimized system parameters. Considering that many parameter vectors generate similar system dynamics and results, this dissertation proposes a general α-β-γ rule to return an acceptable parameter region of the stochastic Hill equation based on QNSTOP. Different objective functions are explored targeting different features of the empirical data.