On balance relations for irreversible chemical reaction networks
File(s)
Accepted version
Author(s)
Levien, Ethan
Bressloff, Paul C
Type
Journal Article
Abstract
We investigate a class of irreversible networks whose chemical species
can be partitioned into two disjoint sets S1 and S2, resulting in a weakly
reversible subnetwork G2 involving only the species S2, and a semi-weaklyreversible network G1; the latter reduces to a weakly reversible network on
formally eliminating the chemical species S2. We introduce a generalized flux
balance condition that can be understood as the natural analogue of the complex
balance condition for weakly reversible networks, and which serves as a tool for
investigating how irreversible networks differ from reversible ones. We also make a
connection between the generalized balance condition and the theory of multiscale
networks by taking S1 to consist of high copy number species (O(N)), where N
is the system size, and S2 to consist of low copy number species (O(1)). We show
how the generalized balance condition of the full stochastic model is related to a
moment balance condition of the corresponding piecewise deterministic Markov
process (PDMP) obtained in the thermodynamic limit N → ∞.
can be partitioned into two disjoint sets S1 and S2, resulting in a weakly
reversible subnetwork G2 involving only the species S2, and a semi-weaklyreversible network G1; the latter reduces to a weakly reversible network on
formally eliminating the chemical species S2. We introduce a generalized flux
balance condition that can be understood as the natural analogue of the complex
balance condition for weakly reversible networks, and which serves as a tool for
investigating how irreversible networks differ from reversible ones. We also make a
connection between the generalized balance condition and the theory of multiscale
networks by taking S1 to consist of high copy number species (O(N)), where N
is the system size, and S2 to consist of low copy number species (O(1)). We show
how the generalized balance condition of the full stochastic model is related to a
moment balance condition of the corresponding piecewise deterministic Markov
process (PDMP) obtained in the thermodynamic limit N → ∞.
Date Issued
2017-11-24
Date Acceptance
2017-10-09
Citation
Journal of Physics A: Mathematical and Theoretical, 2017, 50 (47)
ISSN
1751-8113
Publisher
IOP Publishing
Journal / Book Title
Journal of Physics A: Mathematical and Theoretical
Volume
50
Issue
47
Copyright Statement
Copyright © 2017 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/1751-8121/aa91de
Identifier
http://dx.doi.org/10.1088/1751-8121/aa91de
Publication Status
Published
Article Number
475004
Date Publish Online
2017-11-01