Title: Approximate Method for Stochastic Chemical Kinetics with Two-time Scales by Chemical Langevin Equations
Abstract: For stochastic chemical kinetics with two-time scales, the quasi-steady-state assumption (QSSA) based on chemical master equation (CME) and the corresponding modified stochastic simulation algorithm (SSA) effectively reduce the computational complexity by reducing the number of molecular species and reactions in which the fast reactions are removed. While for the chemical reaction processes involving a large of molecular species and reactions, the rest slow reactions may still include a large number molecular species and reaction, so it is still computational expensive. Because theτ-leaping, expressed by the CLE (Chemical Langevin Equations), is an efficient approximation strategy for the SSA, it is interesting and important to establish the reduction method based on the CLE similar to the QSSA and the modified SSA. By the stochastic averaging principle (see Khasminskii and Yin [37–40]), this paper establishes the reduction of complexity for the CLE with two-time scales. This reduction method deduces a limit averaging system, which is an approximation of the slow-reacting subsystem. Since in the stochastic chemical kinetics, the CLE is seen as the approximation of the SSA, the limit averaging system can be treated as the approximation of the slow-reaction process. As an application, this paper establishes the reduction of complexity for the gene regulatory networks with two-time scales driven by intrinsic noise. For linear and nonlinear protein production functions, the simulations shows that the expectation of the limit averaging system is close to the expectation of the slow-reaction process based on the SSA, which demonstrates that the limit averaging
system is an approximation of the slow-reacting variables in the CLE with two-time scales in the sense of the weak convergence.
吴付科，教授，1976年11月生于河南邓州，2003年博士毕业于华中科技大学数学与统计学院。主要从事随机微分方程以及相关领域的研究，2011年入选教育部新世纪优秀人才支持计划，2012年入选华中科技大学“华中学者”，2014年获得基金委优秀青年基金资助。近年来，在SIAM J. Appl. Math., SIAM J. Numer. Anal., SIAM J. Control Optim., Numer. Math., J. Differential Equations, Automatica和IEEE TAC等国际权威期刊发表论文60余篇，全部为SCI收录。截止2014年，共主持3项国家自然科学基金和一项教育部新世纪优秀人才基金，出版一部专著(与胡适耕教授和黄乘明教授合著:随机微分方程,科学出版社, 2008)和一部译著(与刘金山副教授合译：随机微分方程：导论与应用, 科学出版社, 2012年).先后应邀访问英国、德国、美国、澳大利亚的国家的学术机构.