Volume 29, Issue 2
Transitions States of Stochastic Chemical Kinetic Systems

Jun DuDi Liu

Commun. Comput. Phys., 29 (2021), pp. 606-627.

Published online: 2020-12

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  • Abstract

Based on Transition Path Theory (TPT) for Markov jump processes [1, 2], we develop a general approach for identifying and calculating Transition States (TS) of stochastic chemical reacting networks. We first extend the concept of probability current, originally defined on edges connecting different nodes in the configuration space [2], to each sub-network. To locate sub-networks with maximal probability current on the separatrix between reactive and non-reactive events, which will give the Transition States of the reaction, constraint optimization is conducted. We further introduce an alternative scheme to compute the transition pathways by topological sorting, which is shown to be highly efficient through analysis.

  • Keywords

Transition path theory, Markov chain, reacting network.

  • AMS Subject Headings

00A69, 92B05, 37L55, 60J35, 60J75

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-29-606, author = {Du , Jun and Liu , Di}, title = {Transitions States of Stochastic Chemical Kinetic Systems}, journal = {Communications in Computational Physics}, year = {2020}, volume = {29}, number = {2}, pages = {606--627}, abstract = {

Based on Transition Path Theory (TPT) for Markov jump processes [1, 2], we develop a general approach for identifying and calculating Transition States (TS) of stochastic chemical reacting networks. We first extend the concept of probability current, originally defined on edges connecting different nodes in the configuration space [2], to each sub-network. To locate sub-networks with maximal probability current on the separatrix between reactive and non-reactive events, which will give the Transition States of the reaction, constraint optimization is conducted. We further introduce an alternative scheme to compute the transition pathways by topological sorting, which is shown to be highly efficient through analysis.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0014}, url = {http://global-sci.org/intro/article_detail/cicp/18476.html} }
TY - JOUR T1 - Transitions States of Stochastic Chemical Kinetic Systems AU - Du , Jun AU - Liu , Di JO - Communications in Computational Physics VL - 2 SP - 606 EP - 627 PY - 2020 DA - 2020/12 SN - 29 DO - http://doi.org/10.4208/cicp.OA-2019-0014 UR - https://global-sci.org/intro/article_detail/cicp/18476.html KW - Transition path theory, Markov chain, reacting network. AB -

Based on Transition Path Theory (TPT) for Markov jump processes [1, 2], we develop a general approach for identifying and calculating Transition States (TS) of stochastic chemical reacting networks. We first extend the concept of probability current, originally defined on edges connecting different nodes in the configuration space [2], to each sub-network. To locate sub-networks with maximal probability current on the separatrix between reactive and non-reactive events, which will give the Transition States of the reaction, constraint optimization is conducted. We further introduce an alternative scheme to compute the transition pathways by topological sorting, which is shown to be highly efficient through analysis.

Jun Du & Di Liu. (2020). Transitions States of Stochastic Chemical Kinetic Systems. Communications in Computational Physics. 29 (2). 606-627. doi:10.4208/cicp.OA-2019-0014
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