期刊
MULTISCALE MODELING & SIMULATION
卷 15, 期 4, 页码 1376-1403出版社
SIAM PUBLICATIONS
DOI: 10.1137/16M1099443
关键词
biochemical reaction networks; stochastic system; continuous-time Markov chain; multiscale approximation; singular perturbation theory; timescale separation
资金
- National Science Foundation [DMS-0931642, DMS-1318886, DMS-1620403]
- National Foundation of Korea [N01160447]
- KAIST Research Allowance grant [604150020]
- TJ Park Science Fellowship of POSCO TJ Park Foundation
- UMBC KAN3STRT
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1620403] Funding Source: National Science Foundation
Biochemical reaction networks frequently consist of species evolving on multiple timescales. Stochastic simulations of such networks are often computationally challenging and therefore various methods have been developed to obtain sensible stochastic approximations on the timescale of interest. One of the rigorous and popular approaches is the multiscale approximation method for continuous time Markov processes. In this approach, by scaling species abundances and reaction rates, a family of processes parameterized by a scaling parameter is defined. The limiting process of this family is then used to approximate the original process. However, we find that such approximations become inaccurate when combinations of species with disparate abundances either constitute conservation laws or form virtual slow auxiliary species. To obtain more accurate approximation in such cases, we propose here an appropriate modification of the original method.
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