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Accuracy Analysis of Hybrid Stochastic Simulation Algorithm on Linear Chain Reaction Systems.
Bull Math Biol 2019; 81(8):3024-3052BM

Abstract

Noise in cellular systems is often modeled and simulated with Gillespie's stochastic simulation algorithm (SSA), but the low efficiency of the SSA limits its application to large biochemical networks. To improve the efficiency of stochastic simulations, Haseltine and Rawlings (HR) proposed a hybrid algorithm, which combines ordinary differential equations for traditional deterministic models and the SSA for stochastic models. In this paper, accuracy of the HR hybrid method is studied based on a linear chain reaction system. Mathematical analysis and numerical results both show that the HR hybrid method is accurate if either the quantity of reactant molecules in fast reactions is above a certain threshold, or the reaction rates of fast reactions are much larger than those of slow reactions. This analysis also shows that the HR hybrid method approximates the chemical master equation well for a much greater region in system parameter space than the slow-scale SSA and the stochastic quasi-steady-state assumption methods.

Authors+Show Affiliations

Department of Computer Science, Virginia Tech, Blacksburg, VA, 24061, USA.Department of Computer Science, Virginia Tech, Blacksburg, VA, 24061, USA.Department of Computer Science, Virginia Tech, Blacksburg, VA, 24061, USA. ycao@cs.vt.edu.

Pub Type(s)

Journal Article
Research Support, U.S. Gov't, Non-P.H.S.

Language

eng

PubMed ID

29992454

Citation

Chen, Minghan, et al. "Accuracy Analysis of Hybrid Stochastic Simulation Algorithm On Linear Chain Reaction Systems." Bulletin of Mathematical Biology, vol. 81, no. 8, 2019, pp. 3024-3052.
Chen M, Wang S, Cao Y. Accuracy Analysis of Hybrid Stochastic Simulation Algorithm on Linear Chain Reaction Systems. Bull Math Biol. 2019;81(8):3024-3052.
Chen, M., Wang, S., & Cao, Y. (2019). Accuracy Analysis of Hybrid Stochastic Simulation Algorithm on Linear Chain Reaction Systems. Bulletin of Mathematical Biology, 81(8), pp. 3024-3052. doi:10.1007/s11538-018-0461-z.
Chen M, Wang S, Cao Y. Accuracy Analysis of Hybrid Stochastic Simulation Algorithm On Linear Chain Reaction Systems. Bull Math Biol. 2019;81(8):3024-3052. PubMed PMID: 29992454.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Accuracy Analysis of Hybrid Stochastic Simulation Algorithm on Linear Chain Reaction Systems. AU - Chen,Minghan, AU - Wang,Shuo, AU - Cao,Yang, Y1 - 2018/07/10/ PY - 2018/01/17/received PY - 2018/06/29/accepted PY - 2018/7/12/pubmed PY - 2018/7/12/medline PY - 2018/7/12/entrez KW - Accuracy analysis KW - Hybrid stochastic algorithm KW - Linear chain reaction systems KW - Next slow reaction firing time KW - SSA SP - 3024 EP - 3052 JF - Bulletin of mathematical biology JO - Bull. Math. Biol. VL - 81 IS - 8 N2 - Noise in cellular systems is often modeled and simulated with Gillespie's stochastic simulation algorithm (SSA), but the low efficiency of the SSA limits its application to large biochemical networks. To improve the efficiency of stochastic simulations, Haseltine and Rawlings (HR) proposed a hybrid algorithm, which combines ordinary differential equations for traditional deterministic models and the SSA for stochastic models. In this paper, accuracy of the HR hybrid method is studied based on a linear chain reaction system. Mathematical analysis and numerical results both show that the HR hybrid method is accurate if either the quantity of reactant molecules in fast reactions is above a certain threshold, or the reaction rates of fast reactions are much larger than those of slow reactions. This analysis also shows that the HR hybrid method approximates the chemical master equation well for a much greater region in system parameter space than the slow-scale SSA and the stochastic quasi-steady-state assumption methods. SN - 1522-9602 UR - https://www.unboundmedicine.com/medline/citation/29992454/Accuracy_Analysis_of_Hybrid_Stochastic_Simulation_Algorithm_on_Linear_Chain_Reaction_Systems_ L2 - https://dx.doi.org/10.1007/s11538-018-0461-z DB - PRIME DP - Unbound Medicine ER -