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Sensitivity of chemical reaction networks: a structural approach. 2. Regular monomolecular systems
Author(s) -
Fiedler Bernold,
Mochizuki Atsushi
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3436
Subject(s) - transitive relation , reaction rate , monotone polygon , perturbation (astronomy) , mathematics , chemical reaction , graph , steady state (chemistry) , sensitivity (control systems) , statistical physics , chemistry , physics , discrete mathematics , combinatorics , electronic engineering , engineering , biochemistry , geometry , quantum mechanics , catalysis
M. Otani Dedicated to Messoud Efendiev on the occasion of his 60th birthday For the deceptively innocent case of monomolecular reactions, only, we embark on a systematic mathematical analysis of the steady‐state response to perturbations of reaction rates. Our structural sensitivity analysis is based on the directed graph structure of the monomolecular reaction network, only. In fact our function‐free approach does not require numerical input. We work with general, not necessarily monotone reaction rate functions. Based on the graph structure alone, we derive which steady‐state concentrations and reaction fluxes are sensitive to, and thus affected by, a rate change—and which are not. Moreover we establish a transitivity property for the influence of a rate perturbation, at any reaction, on all reaction fluxes. The results and concepts developed here, from a mathematical view point, are of applied relevance including metabolic networks in biology; see our companion paper quoted below. Copyright © 2015 John Wiley & Sons, Ltd.