Mutual Linearity of Complexes in Chemical Reaction Networks
Abstract
Exact statements about how a system far from equilibrium responds to changes in its rate constants are scarce beyond linear response, yet they are central to the control of biochemical networks. A notable exception is mutual linearity: in a jump process, controlling the rates of a single transition makes any two stationary probabilities obey an exact affine relation, arbitrarily far from equilibrium. With nonlinear mass-action kinetics, and conservation laws in place of a normalization, chemical reaction networks seem to defy mutual linearity since species concentrations obey no such relation. We show that it was there all along, in the complexes' activities (mass-action monomials) rather than in the concentrations of species. For zero-deficiency networks with a single linkage class, controlling one reaction makes any three stationary activities obey a linear relation whose coefficients are independent of the controlled rate constants, the conserved quantities (hence the initial state), and even of the stoichiometry of complexes. This predicts hidden activities and bounds the activity ratios the control can reach, while a violation signals nonzero deficiency or multiple linkage classes.
Related
- Joint Neural Posterior Estimation and Model Selection for Chemical Reaction Networks
- Optimal Control of Chemical Reaction Networks with Thermodynamic Cost
- Large-deviations theory for growing chemical reaction networks
- Generative discovery of chemical reaction networks
- Hierarchical models for large chemical reaction networks
BibTeX
@misc{harunari2026mutual,
title = {{Mutual Linearity of Complexes in Chemical Reaction Networks}},
author = {Pedro E. Harunari and Guilherme Fiusa and Matteo Polettini},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11970},
eprint = {2610.11970},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11970},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mutual Linearity of Complexes in Chemical Reaction Networks
AU - Pedro E. Harunari
AU - Guilherme Fiusa
AU - Matteo Polettini
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11970
UR - https://arxiv.org/abs/2610.11970
AB - Exact statements about how a system far from equilibrium responds to changes in its rate constants are scarce beyond linear response, yet they are central to the control of biochemical networks. A notable exception is mutual linearity: in a jump process, controlling the rates of a single transition makes any two stationary probabilities obey an exact affine relation, arbitrarily far from equilibrium. With nonlinear mass-action kinetics, and conservation laws in place of a normalization, chemical reaction networks seem to defy mutual linearity since species concentrations obey no such relation. We show that it was there all along, in the complexes' activities (mass-action monomials) rather than in the concentrations of species. For zero-deficiency networks with a single linkage class, controlling one reaction makes any three stationary activities obey a linear relation whose coefficients are independent of the controlled rate constants, the conserved quantities (hence the initial state), and even of the stoichiometry of complexes. This predicts hidden activities and bounds the activity ratios the control can reach, while a violation signals nonzero deficiency or multiple linkage classes.
ER -