Accurate chemical master equation solution using multi-finite buffers

Cao, Youfang; Terebus, Anna; Liang, Jie

doi:10.1137/15M1034180

Title: Accurate chemical master equation solution using multi-finite buffers

Journal Article · Wed Jun 29 00:00:00 EDT 2016 · Multiscale Modeling & Simulation

DOI:https://doi.org/10.1137/15M1034180· OSTI ID:1358164

^[1]; Terebus, Anna ^[2]; Liang, Jie ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. of Illinois, Chicago, IL (United States)

Here, the discrete chemical master equation (dCME) provides a fundamental framework for studying stochasticity in mesoscopic networks. Because of the multiscale nature of many networks where reaction rates have a large disparity, directly solving dCMEs is intractable due to the exploding size of the state space. It is important to truncate the state space effectively with quantified errors, so accurate solutions can be computed. It is also important to know if all major probabilistic peaks have been computed. Here we introduce the accurate CME (ACME) algorithm for obtaining direct solutions to dCMEs. With multifinite buffers for reducing the state space by $O(n!)$, exact steady-state and time-evolving network probability landscapes can be computed. We further describe a theoretical framework of aggregating microstates into a smaller number of macrostates by decomposing a network into independent aggregated birth and death processes and give an a priori method for rapidly determining steady-state truncation errors. The maximal sizes of the finite buffers for a given error tolerance can also be precomputed without costly trial solutions of dCMEs. We show exactly computed probability landscapes of three multiscale networks, namely, a 6-node toggle switch, 11-node phage-lambda epigenetic circuit, and 16-node MAPK cascade network, the latter two with no known solutions. We also show how probabilities of rare events can be computed from first-passage times, another class of unsolved problems challenging for simulation-based techniques due to large separations in time scales. Overall, the ACME method enables accurate and efficient solutions of the dCME for a large class of networks.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1358164

Report Number(s):: LA-UR-16-27504

Journal Information:: Multiscale Modeling & Simulation, Vol. 14, Issue 2; ISSN 1540-3459

Publisher:: SIAMCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 29 works

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