PhD (M/F) on stochastic modelling of treatment emergence in asexuals in the context of pharmacodynamics and pharmacokinetics via multitype stochastic processes

Job Description

Thesis Subject

The evolution of drug resistance in pathogens, such as bacteria and cancer cells, poses a major public health challenge. To design effective strategies for limiting resistance spread, it is crucial to understand the underlying processes during treatment. However, even in simplified laboratory settings, modeling these dynamics is mathematically complex. It requires explicitly accounting for the stochastic demography of both drug-sensitive cells and potential resistant mutants to predict key observables, such as the probability of resistance emergence or the number of resistant lineages on a Petri dish.
Current approaches to modeling resistance evolution fall into two main categories. First, numerical individual-based simulations are widely used but are computationally expensive, particularly when simulating rare emergence events or large populations. Second, general mathematical analyses rely on two simplified frameworks. Stochastic models, inspired by Luria and Delbrück's foundational work, typically consider only two cell types—drug-sensitive and resistant—and assume a fixed drug concentration over time. In contrast, infinite types evolutionary rescue (ER) models typically use Fisher's Geometric Model (FGM), incorporating a diverse range of mutant types and accounting for epistatic interactions. While FGM-based models may improve realism in terms of genetic basis of resistance, they are deterministic and not specifically adapted for asexual pathogens.
Recent work by G. Martin and collaborators has bridged these approaches by integrating the FGM fitness landscape into stochastic models. This has yielded explicit approximations for fixed drug doses in two mutation rate regimes: low mutation rates, where resistance arises in one or a few mutational steps, and high mutation rates, where lineages accumulate many mutations. However, these results are limited by their reliance on extreme mutation regimes and the lack of rigorous diffusion limits derived from the exact demographic process. Additionally, the assumption of a fixed optimum is unrealistic when drug concentrations vary in vivo (e.g., within patients) and even in vitro due to cellular defects accumulating over time. While we derived a deterministic approach for an arbitrarily moving optimum, it does not provide probabilities of extinction vs. evolutionary rescue.
The proposed project aims to address these limitations by extending the framework in three key ways. First, it seeks to rigorously derive diffusion limits for a stochastic K-type linear birth-death model, enabling the calculation of resistance emergence probabilities across the full spectrum of mutation rates. Second, it will incorporate dynamic stress, such as varying drug doses, by modeling fitness landscapes with moving optima. Finally, we will seek to approximate non-exponential cell division times using a two-stage model, moving beyond the traditional assumption of exponential waiting time distributions. These advancements will provide a more realistic and comprehensive understanding of drug resistance evolution, with potential applications in both clinical and experimental settings.
Strong skills in mathematical modelling for biology is a requirement, but basic biological knowledge is expected too, in order to be able to conceptualize and approximate realistic biological systems and analyze lab data. Please note that the student that did a masters thesis on the early stage of the project is applying to this PhD. The selection remains open to other candidates of course.

Your Work Environment

The PhD student will be hosted at the Institut des Sciences de l'Evolution (ISEM UMR 5554) on the Triolet Science campus of the Université de Montpellier, in the Evolution and Demography team. The ISEM is a leading lab in evolutionary sciences on all scales of time (from geological times to experimental evolution over days) and space (from ecosystems to test tubes). The host team is specialized in experimental, field work, molecular evolution and theoretical study of processes at the interface of demographic and evolutionary processes in non-equilibrium populations/species for both conservation (plant and marine organisms) and medical/agronomic applications (microbes, transmissible cancers). The Montpellier site hosts many labs working on ecology and evolution making it a dynamic work environment with visibility worldwide in these fields.
The PhD will be supervised by Guillaume Martin (biologist with expertise on theoretical evolution and demography, fitness landscapes and bacterial experimental evolution) and Pete Czuppon (mathematician with expertise on stochastic processes for biology). Regular visio meetings and visits to Pete's nearby Marseille University should allow smooth co-supervision. G. Martin also runs a wet lab which produces high throughput resistance dynamics on the bacterium E.coli, allowing the interaction of the theoretical development with on-site produced data.

Constraints and risks

none

Compensation and benefits

Compensation

2300 € gross monthly

Annual leave and RTT

44 jours

Remote Working practice and compensation

Pratique et indemnisation du TT

Transport

Prise en charge à 75% du coût et forfait mobilité durable jusqu’à 300€

About the offer

About the CNRS

The CNRS is a major player in fundamental research on a global scale. The CNRS is the only French organization active in all scientific fields. Its unique position as a multi-specialist allows it to bring together different disciplines to address the most important challenges of the contemporary world, in connection with the actors of change.

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