Supervisor: J. Unterberger
Host Institution: Institut Élie Cartan de Lorraine (IECL), Université de Lorraine, Nancy, France
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Scientific Context Large chemical reaction networks (CRNs), involving hundreds of interacting species, arise naturally in prebiotic chemistry, systems chemistry, and astrochemistry. Since the 1952 Miller–Urey experiment demonstrated the abiotic synthesis of complex organic molecules, understanding the dynamical organization of such networks has remained a major scientific challenge.
These systems are characterized by: high dimensionality; strong separation of kinetic scales; poorly known reaction parameters; and sensitivity to stochastic effects.
While the general mathematical theory of CRNs is well established [1], scalable and interpretable methods for large multiscale systems are still lacking.
Project Overview This project builds on a novel multiscale reduction method, currently developed for linear CRNs [2], based on an explicit separation of time scales, and producing:
• coarse-grained, renormalized formulas based on hierarchical graphs;
• a fast and accurate strategy for statistical inference of effective kinetic parameters.
The method yields a low-complexity, interpretable algorithm (implemented in Python) capable of accurately predicting dominant dynamical regimes.
The PhD project aims to extend this framework:
1. to nonlinear reaction networks, using linearization around stationary states, multiscale perturbation methods and tropical geometry techniques;
2. to stochastic dynamics, incorporating noise-induced transitions and multistationarity into the hierarchical description.
References. [1] M. Feinberg, Foundations of Chemical Reaction Network Theory. Applied Math. Sciences, Springer (2019). [2] P. Nghe, J. Unterberger. Stoechiometric and dynamical autocatalysis for diluted chemical reaction networks, J. Math. Biol. (2022). J. Unterberger, General multi-scale estimates for Lyapunov data of Perron-Frobenius matrices. The case of diluted autocatalytic chemical reaction networks, arXiv:2511.11073. J. Unterberger, U. Herbach, R. Cellier. Hierarchical models for large chemical reaction networks (preprint).
Expected Outcomes
• A multiscale mathematical framework for large nonlinear CRNs
• A stochastic extension describing noise-driven dynamics
• A user-friendly computational tool for chemists
• Applications to experimentally relevant reaction systems
The resulting software will help identify dominant pathways, predict time evolution under varying conditions, and infer effective kinetic parameters from experimental data.
Candidate Profile We seek a highly motivated candidate with a strong background in mathematics or theoretical physics, interest in dynamical systems or statistical physics, and solid Python programming skills.
Research Environment The project will be carried out at IECL, in tight collaboration with mathematicians, statisticians, theoretical physicists, and experimental chemists in Nancy and nearby Paris area (ESPCI, Ecole Supérieure de Physique et Chimie Industrielle; Saclay, BioCIS Lab for biomolecules), who are partners of the supervisor in a wider research project on the origin of life. The candidate will also benefit from interactions in Nancy with the probability and statistics team at IECL, and the computational biology and chemistry team at the LPCT lab.
Contact jeremie.unterberger@univ-lorraine.fr, website: [
jeremieunterberger.wixsite.com]
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