Detailed Balance [Formula: see text] Complex Balance [Formula: see text] Cycle Balance: A Graph-Theoretic Proof for Reaction Networks and Markov Chains.

Detailed Balance [Formula: see text] Complex Balance [Formula: see text] Cycle Balance: A Graph-Theoretic Proof for Reaction Networks and Markov Chains. Bull Math Biol. 2020 Sep 03;82(9):116 Authors: Müller S, Joshi B Abstract We further clarify the relation between detailed-balanced and complex-balanced equilibria of reversible chemical reaction networks. Our results hold for arbitrary kinetics and also for boundary equilibria. Detailed balance, complex balance, "formal balance," and the new notion of "cycle balance" are all defined in terms of the underlying graph. This fact allows elementary graph-theoretic (non-algebraic) proofs of a previous result (detailed balance = complex balance + formal balance), our main result (detailed balance = complex balance + cycle balance), and a corresponding result in the setting of continuous-time Markov chains. PMID: 32885279 [PubMed - in process]
Source: Bulletin of Mathematical Biology - Category: Bioinformatics Authors: Tags: Bull Math Biol Source Type: research