Research

Research overview

The SIMBA team has mathematical expertise in:

  1. Stochastic modeling for health
  2. Analysis of biological and medical data
  3. Ecology and evolution

The team’s main application domains are:

  1. Tumor growth and heterogeneity
  2. Telomere length dynamics
  3. Gene networks and single-cell data
  4. Vegetal epidemiology

The team’s main ongoing fundings are:

  1. DyLT (Dynamics of Telomeres Length) project within the PEPR Maths VivES (2024-2029)
  2. AI4scMED (IA multi-échelle pour une médecine de précision en cellules uniques) project within PEPR Santé Numérique (2023-2028)
  3. Predi-CLL (Quantifying and predicting the evolution of clonal heterogeneity in chronic lymphocytic leukemia) project funded by ITMO Cancer, MIC call (2023-2027)
  4. Associate team MAGO (Modelling and analysis for growth-fragmentation processes), Inria funding (2022-2024)
  5. Associate team AStoNiche (Towards a stochastic theory of niche construction), Inria funding (2024-2026)

Stochastic modeling for health

Our methodological expertise gathers:

  • Piecewise deteministic Markov processes (PDMP), branching processes, individual-based models (IBM), stochastic cellular automata
  • Multi-scale models (averaging, parameter scaling, homogeneization…) and links between macroscopic and microscopic models
  • Numerical methods for population dynamics (hybrid algorithms, moment closure)
  • Stochastic control, Markov decision processes
  • Main applications: cancer growth/heterogeneity (collaborations with CHRU Strasbourg, Institut de Cancérologie de Lorraine), chronic obstructive pulmonary disease (COPD, collaboration with CHU Bordeaux), telomere length (collaboration with CHRU Nancy)

Analysis of biological and medical data

Our methodological expertise gathers:

  • Integration and exploitation of heterogeneous, high dimensional, correlated, incomplete data
  • Statistical learning and regression (variable selection, goodness-of-fit tests, parametric and non-parametric estimation)
  • Signal or streaming data analysis (stochastic approximation, change-point detection)
  • Network inference (single-cell data, bursty gene expression, zero-inflated data)
  • Inference for stochastic processes (PDMP, branching processes, Bayesian methods, variational methods)
  • Applications: gene networks (collaborations with CHRU Strasbourg, ENS Lyon, EPHE, ETH Zürich), fetal reference curves (INSERM), risk scores for heart failure (collaboration with CHRU Nancy)

Ecology and evolution

Our methodological expertise gathers:

  • Piecewise deteministic Markov processes (PDMP), branching processes, individual-based models (IBM)
  • Scaling limits of IBM (complex microscopic interactions, concentration limits), long time behavior
  • Population dynamics with extinction and quasi-stationary distributions (speed of convergence, spectral versus stochastic methods, numerical approximation)
  • Applications: vegetal epidemiology (collaborations with INRAe), adaptive dynamics, modeling of allometric relationships (collaboration with Univ. Lille) 

Tumor growth and heterogeneity

We have collaborations on:

  • Dynamics of circulating tumor DNA (ctDNA) and heterogeneity (phylogenetic) reconstruction (collaboration with J.-L. Merlin and A. Harlé from Institut de Cancérologie de Lorraine and E. Pencreach from CHRU Strasbourg).
  • Heterogeneity reconstruction for chronic lymphocytic leukemia (collaboration with CHRU Strasbourg). See our Predi-CLL project funded by ITMO Cancer.
  • Therapeutic management and monitoruing of patients with low-grade gliomas from MRI, anatomopathological and biological data (collaboration with CRAN, CHRU Nancy and the start-up Deep river).

Telomere length dynamics

We have collaborations with A. Benetos and S. Toupance from CHRU Nancy on:

  • Telomere length distribution in human, its relations with the patients’ fragility
  • Telomere signature
  • Diagnostic aid and risk measurement integrating telomere length data
  • Modeling the evolution of telomere length distribution with age and across generations

For more detail, see the web page (under construction) of the DyLT project of PEPR Maths VivES.

Gene networks and single-cell data

We work on:

  • Modeling gene expression at a single-cell level (PDMP models, quantifying epigenetic landscapes)
  • Transcriptional bursting in gene regulatory networks
  • Prediction of gene knockdown downstream effects and identification of therapeutic targets for chronic lymphocytic leukemia (collaboration with L. Vallat from CHRU Strasbourg)

Vegetal epidemiology

We collaborate with M. Grosdidier and B. Marçais from INRAe Champenoux on:

  • Chalara: an ash disease which arrived in France through Grand Est and is spreading throughout France
  • Goal: model the spread of chalara and quantify the potential underlying environmental effects (humidity, temperature…)
  • Seasonal model, based on reaction-diffusion equations, with Bayesian inference

Predi-CLL: Quantifying and predicting the evolution of clonal heterogeneity in chronic lymphocytic leukemia

Project funded by ITMO Cancer, MIC call (2023-2027)

Partners

  • Inria SIMBA team (N. Champagnat, C. Fritsch, U. Herbach, P. Vallois, V. Vidhi, D. Villemonais)
  • Department of Molecular Genetics of Cancers of the University Hospitals of Strasbourg (L. Boutkhil, V. Rimelen, C. Schleiss, I. Schultz, L. Vallat)

Scientific background

The development of targeted therapies has allowed considerable progress in the treatment of many cancers, but their efficacy is dependent on intra-tumor heterogeneity. In lymphomas and leukemias, the identification of gene alterations by high-throughput sequencing allows the characterization of this heterogeneity. In these hemopathies, the initial leukemic clone has a unique immune repertoire corresponding to a specific VDJ gene sequence encoding the antigen receptor. The occurrence of additional mutations in VDJ genes may be responsible for the emergence of subclones with increased antigen receptor reactivity further complicating the clonal heterogeneity of these hemopathies. However, this second level of clonal heterogeneity and its evolution remain poorly characterized and is not considered in the management of these cancers.

Project description

We propose to develop a mathematical model for the evolution of the two levels of clonal heterogeneity in leukemia, allowing to characterize their evolution from longitudinal bulk sequencing data of VDJ and cancer genes mutations, collected throughout the entire project, using a Bayesian approach. We will test the predictive performance of clonal evolution from the inferred model. We will also collect data from ex-vivo 3D culture models allowing to select proliferating clones in a controlled environment (with or without treatment), for which we will collect single-cell sequences. We will test the adequation between these data and the actual evolution of clones in-vivo and use them to improve the predictive performance of the inferred model.

Expected results

We expect that the mathematical model developed will be able to reconstruct and predict the evolution of clonal heterogeneity. We also expect to make the proof of concept that the proliferative characteristics of clones measured from 3D culture models allow to design predictive models for the evolution of clonal heterogeneity depending on the therapy.

Associate team MAGO (Modelling and Analysis for GrOwth-fragmentation processes)

Inria funding

Partners

  • Inria team SIMBA (C. Fritsch, D. Villemonais)
  • University College London (A. Watson, F.-X. Briol)
  • Warwick University (E. Horton)

Abstract

Growth-fragmentation (GF) refers to a collection of mathematical models in which objects – classically, biological cells – slowly gather mass over time, and fragment suddenly into multiple, smaller offspring. These models may be used to represent a range of biological and chemical processes, in which an individual reproduces by fission into two or more new individuals, such as the the evolution of plasmids in bacteria populations and protein polymerisation. As such, in recent years, there has been a growing interest in probabilistic models, in the form of GF processes, in order to gain a better understanding of these real-world processes. However, the complexity of the real-world models and thus of the GF processes makes them

highly intractable, requiring the development of sophisticated probabilistic and statistical techniques to analyse these models. In particular, it is crucial to understand the behaviour of GF models in order to develop algorithms to simulate real-world processes, estimate quantities such as the growth rate of the system and the steady state behaviour, and for the purpose of parameter inference, to allow scientists to gain a better understanding of the behaviour of these complex systems. In this proposal, we aim to develop a suite of GF processes that capture the many complexities and nuances of a range of fundamental biological and chemical processes. We will then analyse the macroscopic and microscopic behaviour of these stochastic systems, developing new simulation techniques, methods for parameter inference and goodness of fit tests, for use with real data.

Associate team AStoNiche (Towards a stochastic theory of niche construction)

Inria funding

Partners

  • Inria team SIMBA (N. Champagnat, C. Fritsch, E. Strickler, D. Villemonais, N. Zalduendo-Vidal)
  • Universidad de Valparaiso (R. Rebolledo Berroeta, N. Rivera)
  • Pontificia Universidad Catolica de Chile & Santa Fe Institute (P. Marquet)
  • Universidad de O’Higgins (C. Quininao)
  • Universidad de Santiago de Chile (L. Videla)

Objectives

We aim to provide a general stochastic formulation of the niche construction process. In particular, we want to take into account the feedbacks of species on their environment, and the evolutionary aspects that follow. This requires to deal with different time-scales (ecological, niche construction, evolutionary…) and to keep track of non-extinct traits that may be positively selected after niche construction. We plan to use mean-field stochastic individual-based model and branching processes and consider appropriate parameter scalings.

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