Accurate chemical master equation solution using multifinite buffers
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 steadystate and timeevolving 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 steadystate 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 6node toggle switch, 11node phagelambda epigenetic circuit, and 16node MAPK cascade network, the latter two withmore »
 Authors:

^{[1]}
;
^{[2]};
^{[2]}
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Univ. of Illinois, Chicago, IL (United States)
 Publication Date:
 Report Number(s):
 LAUR1627504
Journal ID: ISSN 15403459
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Multiscale Modeling & Simulation
 Additional Journal Information:
 Journal Volume: 14; Journal Issue: 2; Journal ID: ISSN 15403459
 Publisher:
 SIAM
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE Laboratory Directed Research and Development (LDRD) Program
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Computer Science; Mathematics; chemical master equation; stochastic biological networks; state space truncation; steady state probability landscape; timeevolving probability landscapes; first passage time distribu tion.
 OSTI Identifier:
 1358164
Cao, Youfang, Terebus, Anna, and Liang, Jie. Accurate chemical master equation solution using multifinite buffers. United States: N. p.,
Web. doi:10.1137/15M1034180.
Cao, Youfang, Terebus, Anna, & Liang, Jie. Accurate chemical master equation solution using multifinite buffers. United States. doi:10.1137/15M1034180.
Cao, Youfang, Terebus, Anna, and Liang, Jie. 2016.
"Accurate chemical master equation solution using multifinite buffers". United States.
doi:10.1137/15M1034180. https://www.osti.gov/servlets/purl/1358164.
@article{osti_1358164,
title = {Accurate chemical master equation solution using multifinite buffers},
author = {Cao, Youfang and Terebus, Anna and Liang, Jie},
abstractNote = {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 steadystate and timeevolving 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 steadystate 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 6node toggle switch, 11node phagelambda epigenetic circuit, and 16node MAPK cascade network, the latter two with no known solutions. We also show how probabilities of rare events can be computed from firstpassage times, another class of unsolved problems challenging for simulationbased 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.},
doi = {10.1137/15M1034180},
journal = {Multiscale Modeling & Simulation},
number = 2,
volume = 14,
place = {United States},
year = {2016},
month = {6}
}