Inférence des cinétiques des grand réseaux chimiques multi-échelles

Offre de thèse

Date limite de candidature

10-06-2025

Date de début de contrat

01-10-2025

Directeur de thèse

UNTERBERGER Jérémie

Encadrement

co-encadrement

Type de contrat

Concours pour un contrat doctoral

Candidater à cette offre

école doctorale

IAEM - INFORMATIQUE - AUTOMATIQUE - ELECTRONIQUE - ELECTROTECHNIQUE - MATHEMATIQUES

équipe

PROBAS STATS

contexte

Context. Many chemists have been confronted, since the groundbreaking Miller–Urey experiment in 1952 or even before, with the difficulty of dealing with large chemical reaction networks comprising hundreds of molecule types or more. Such networks arise in particular in a prebiotic context. The Miller–Urey experiment demonstrated the synthesis of a large diversity of organic molecules from inorganic components, and set out a vast research program aiming at understanding physico-chemical conditions and processes having led to the emergence of life on the early Earth, through a sequence of mostly unknown evolution steps. With the multiplication of observations of exoplanets since 2004, the interest has broadened to the discussion of possible “biosignatures” attesting to the presence of life elsewhere in the Universe. Depending on research groups, emphasis has been put either on “RNA-first” or “metabolism-first” scenarios. In both cases, the key element to be demonstrated is an evolution mechanism leading to more complex molecules or molecule networks, which could possibly be extrapolated to extant biological systems. In this respect, autocatalytic processes, characterized by linear instabilities of the underlying equations, are expected to play a prominent role. Challenges. Detection of compounds proceeds through complex GC-MS (gas chromatography/ mass spectroscopy) or LC/MS (liquid chromatography/mass spectroscopy) techniques. The mass spectrum of a compound is in the form of a series of peaks. Databases provide only a tiny fraction of these signatures. For samples with a large diversity, only raw formulas are readily accessible; thus, it is impossible to write down a closed list of chemical compounds. Experiments clearly show several time phases, in which new compounds may appear, and then disappear, which are very difficult to interpret. From the mathematical side, huge progress has been made very recently towards a general characterization of autocatalysis, and beyond that, a semi-quantitative description in terms of “hierarchical models” of the time behavior of generic chemical reaction networks under a scale-separation hypothesis.

spécialité

Mathématiques

laboratoire

IECL - Institut Elie Cartan de Lorraine

Mots clés

statistique bayésienne, réseaux chimiques

Détail de l'offre

Nombre de chimistes ont été confrontés, depuis l'expérience fondatrice de Miller et Urey dans les années 50, ou même avant, à la difficulté de comprendre de grands réseaux de réactions chimiques comprenant des centaines de molécules ou plus. De tels réseaux apparaissent notamment dans un contexte prébiotique. L'expérience de Miller-Urey a démontré la synthèse d'une grande diversité de molécules organiques à partir de composés inorganiques, et suscité un grand programme de recherche consacré à la compréhension des conditions et processus physico-chimiques ayant conduit à l'émergence de la vie sur la Terre archaïque par une suite de pas d'évolution largement inconnus. Avec la multiplication d'observations d'exoplanètes depuis 2004, l'intérêt s'est élargi à la discussion de 'biosignatures' possibles témoignant de la présence de vie ailleurs dans l'univers.

L'objectif de la thèse est de fitter des données expérimentales obtenues en chimie organique par une famille de modèles appelés: modèles hiérarchiques, obtenus récemment par l'un de nous en simplifiant les équations d'action de masse via l'utilisation d'arguments du groupe de renormalisation. Les modèles hiérarchiques sont obtenus à partir des équations du mouvement par un algorithme fini.

Le fitting, formant le coeur de la thèse, consistera en une procédure de maximisation d'espérance (EM) à l'intérieur d'une famille variationnelle bien définie, dans un cadre bayésien.

Keywords

Bayesian statistics, chemical networks

Subject details

Many chemists have been confronted since the groundbreaking experiment by Miller and Urey in the 50es, or even before, with the difficulty of dealing with large chemical networks comprising hundreds of molecules or more. Such networks arise in particular in a prebiotic context. The famous 1952 Miller-Urey experiment demonstrated the synthesis of a large diversity of organic molecules from inorganic components, and set out a large research program aiming at understanding physico-chemical conditions and processes having led to the emergence of life on the early Earth through a sequence of by-and-large unknown evolution steps. With the multiplication of observations of exoplanets since 2004, the interest has broadened to the discussion of possible 'biosignatures' attesting to the presence of life elsewhere in the Universe. Our main project is to fit experimental results by a family of models called hierarchical models recently obtained by one of us by simplifying the original mass action equations through the use of renormalization group arguments. Hierarchical models are constructed from equations of motion by a finite algorithm. The fitting procedure itself, which will be the heart of the PhD thesis, consists in an expectation maximization procedure within a well-identified variational family, in a Bayesian framework.

Profil du candidat

Nous cherchons un mathématicien ou physicien statisticien très motivé, avec une formation en statistique inférentielle et/ou en physique statistique, et un fort intérêt pour les applications et interactions avec des scientifiques de formations très diverses. Une certaine aisance en programmation Python est demandée.

Candidate profile

We are looking for a highly motivated mathematician or theoretical physicist
with a background in statistical inference and/or statistical physics, and strong interest
in applications and interactions with scientists from very different backgrounds. Some
proficiency in algorithmic programming in Python is required.

Référence biblio

• Nghe P., Unterberger J. (2022). Stoechiometric and dynamical autocatalysis for
diluted chemical reaction networks, J. Math. Biol. 85.
• Nandan P., Nghe P., Stuyver T., Unterberger J. A parametrization of kinetics of
organic chemistry reaction mechanisms, work in progress.
• Parikh N., Boyd S. (2014). Proximal algorithms, Foundations and Trends in Optimization
1.
• Robinson W. E., Daines E., van Duppen P., de Jong T., Huck W. T. S. (2022).
Environmental conditions drive self-organization of reaction pathways in a prebiotic
reaction network, Nature Chemistry 14.
• Unterberger J. Optimal multi-time-scale estimates for diluted autocatalytic chemical
networks (preprint).