Hierarchical models for large chemical reaction networks
Abstract
The quest for the origin of life, especially in the metabolism-first scenario inspired by the celebrated Miller-Urey experiment, has triggered a research program dedicated to studying the emergence of complex dynamical behaviors in large chemical mixtures. Though autocatalysis, understood as the capacity of a reaction network to grow exponentially, has been recognized as a potential driver of instability and multistability, no quantitative theory has yet emerged, partly because of the lack of available kinetic data. We introduce a computational tool for large chemical reaction networks based on a scale-splitting algorithm inspired by Wilson's renormalization group. We focus on dilute regimes, where species of interest have low concentration, non-unimolecular reactions may be neglected, and the dynamics is close to linear. Depending on parameter thresholds, such networks can exhibit autocatalytic behavior. Our algorithm takes as input a network structure and outputs (1) a simplified effective graph containing the dominant reaction pathways, obtained through recursive coarse-graining; and (2) analytical formulas for the dynamics in terms of kinetic rates, called hierarchical formulas. These formulas are approximate but interpretable, accurate when scale separation is effective, and provide a reliable multiscale description of the dynamics. Their domains of validity define kinetic phases, each typically associated with a distinct pattern of chemical composition. We show on a simple example that this approach enables fast and reliable inference of kinetic rates from concentration time series. Hierarchical formulas have been implemented as a Python package and are illustrated on a simplified model of the formose reaction.
Related
- Large-deviations theory for growing chemical reaction networks
- Joint Neural Posterior Estimation and Model Selection for Chemical Reaction Networks
- Mutual Linearity of Complexes in Chemical Reaction Networks
- Optimal Control of Chemical Reaction Networks with Thermodynamic Cost
- Generative discovery of chemical reaction networks
BibTeX
@misc{unterberger2026hierarchical,
title = {{Hierarchical models for large chemical reaction networks}},
author = {Jeremie Unterberger and Ulysse Herbach and Roxane Cellier},
howpublished = {HAL},
year = {2026},
month = jun,
eprint = {2606.24246},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05783234v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Hierarchical models for large chemical reaction networks
AU - Jeremie Unterberger
AU - Ulysse Herbach
AU - Roxane Cellier
PY - 2026
DA - 2026/06/24
PB - HAL
UR - https://hal.science/hal-05783234v1
AB - The quest for the origin of life, especially in the metabolism-first scenario inspired by the celebrated Miller-Urey experiment, has triggered a research program dedicated to studying the emergence of complex dynamical behaviors in large chemical mixtures. Though autocatalysis, understood as the capacity of a reaction network to grow exponentially, has been recognized as a potential driver of instability and multistability, no quantitative theory has yet emerged, partly because of the lack of available kinetic data. We introduce a computational tool for large chemical reaction networks based on a scale-splitting algorithm inspired by Wilson's renormalization group. We focus on dilute regimes, where species of interest have low concentration, non-unimolecular reactions may be neglected, and the dynamics is close to linear. Depending on parameter thresholds, such networks can exhibit autocatalytic behavior. Our algorithm takes as input a network structure and outputs (1) a simplified effective graph containing the dominant reaction pathways, obtained through recursive coarse-graining; and (2) analytical formulas for the dynamics in terms of kinetic rates, called hierarchical formulas. These formulas are approximate but interpretable, accurate when scale separation is effective, and provide a reliable multiscale description of the dynamics. Their domains of validity define kinetic phases, each typically associated with a distinct pattern of chemical composition. We show on a simple example that this approach enables fast and reliable inference of kinetic rates from concentration time series. Hierarchical formulas have been implemented as a Python package and are illustrated on a simplified model of the formose reaction.
ER -