[6] M. Estavoyer, M. Dufeu, G. Ranson, S. Lefort, T. Voeltzel, V. Maguer-Satta, O. Gandrillon, T. Lepoutre : Modeling relaxation experiments with a mechanistic model of gene expression , Accepted for publication in BMC Bioinformatics, 2024

Abstract :
Background: In the present work, we aimed at modeling a relaxation experiment which consists in selecting a subfraction of a cell population and observing the speed at which the entire initial distribution for a given marker is reconstituted.

Methods: For this we first proposed a modification of a previously published mechanistic two-state model of gene expression to which we added a state-dependent proliferation term. This results in a system of two partial differential equations. Under the assumption of a linear proliferation rate, we could derive the asymptotic profile of the solutions of this model.

Results: In order to confront our model with experimental data, we generated a relaxation experiment of the CD34 antigen on the surface of TF1-BA cells, starting either from the highest or the lowest CD34 expression levels. We observed in both cases that after approximately 25 days the distribution of CD34 returns to its initial stationary state. Numerical simulations, based on parameter values estimated from the dataset, have shown that the model solutions closely align with the experimental data from the relaxation experiments.

Discussion: Altogether our results strongly support the notion that cells should be seen and modeled as probabilistic dynamical systems.

[5] Maxime Estavoyer and Thomas Lepoutre : Travelling waves for a fast reaction limit of a discrete coagulation-fragmentation model with diffusion and proliferation, Journal of Mathematical Biology, 2024

Abstract : We study traveling wave solutions for a reaction-diffusion model, introduced in the article [5], describing the spread of the social bacterium Myxococcus xanthus. This model describes the spatial dynamics of two different cluster sizes: isolated bacteria and paired bacteria. Two isolated bacteria can coagulate to form a cluster of two bacteria and conversely a pair of bacteria can fragment into two isolated bacteria. Coagulation and fragmentation are assumed to occur at a certain rate denoted k. In this article we study theoretically the limit of fast coagulation fragmentation corresponding mathematically to the limit when the value of the parameter k tends to +∞. For this regime, we demonstrate the existence and uniqueness of a transition between pulled and pushed fronts for a certain critical ratio θ* between the diffusion coefficient of isolated bacteria and the diffusion coefficient of paired bacteria. When the ratio is below θ*, the critical front speed is constant and corresponds to the linear speed. Conversely, when the ratio is above than the critical threshold, the critical spreading speed becomes strictly greater than the linear speed.

[4] M. Estavoyer, M. Barnajee, N. Torres, V. Volpert, L. Pujo-Menjouet : Influence of dating applications on the chances for singles to form couples and vice versa: a mathematical approach, Preprint, 2024

Abstract : Are dating applications efficient for singles to find the good one and build a long-term relationship? To answer this question, we investigate the spatial distribution dynamics of singles and couples. We find that, almost everywhere in developed countries, it follows the same specific Turing-like pattern that can be described by a mathematical model consisting of non-local reaction-diffusion equations. After analysing this phenomenon we adapt our theoretical system to study the impact of dating applications on these dynamics. Our conclusions show that, depending on a small number of parameters, they may, on the one hand, reduce the proportion of singles, but, on the other hand, may unexpectedly lead to the exact opposite situation. Indeed, suppose the selectivity of singles is low enough. In that case, the wide use of dating applications tends to decrease their proportion in the community and when it is too high, they will increase, involving a decrease of couples.

[2] B. Jumentier, C-C. Barrot, M. Estavoyer, J. Tost, B. Heude, O. François, J. Lepeule : High-Dimensional Mediation Analysis: A New Method Applied to Maternal Smoking, Placental DNA Methylation, and Birth Outcomes, Environmental health perspectives, 2023

Abstract :
Background: High-dimensional mediation analysis is an extension of unidimensional mediation analysis that includes multiple mediators, and increasingly it is being used to evaluate the indirect omics-layer effects of environmental exposures on health outcomes. Analyses involving high-dimensional mediators raise several statistical issues. Although many methods have recently been developed, no consensus has been reached about the optimal combination of approaches to high-dimensional mediation analyses.

Objectives: We developed and validated a method for high-dimensional mediation analysis (HDMAX2) and applied it to evaluate the causal role of placental DNA methylation in the pathway between exposure to maternal smoking (MS) during pregnancy and gestational age (GA) and birth weight of the baby at birth.

Methods: HDMAX2 combines latent factor regression models for epigenome-wide association studies with maximum begin superscript 2 end superscriptmax2 tests for mediation and considers CpGs and aggregated mediator regions (AMRs). HDMAX2 was carefully evaluated using simulated data and compared to state-of-the-art multidimensional epigenetic mediation methods. Then, HDMAX2 was applied to data from 470 women of the Etude des Déterminants pré et postnatals du développement de la santé de l’Enfant (EDEN) cohort.

Results: HDMAX2 demonstrated increased power in comparison with state-of-the-art multidimensional mediation methods and identified several AMRs not identified in previous mediation analyses of exposure to MS on birth weight and GA. The results provided evidence for a polygenic architecture of the mediation pathway with a posterior estimate of the overall indirect effect of CpGs and AMRs equal to 44.5 grams44.5g lower birth weight representing 32.1% of the total effect [standard deviation open parenthesis standard deviation close parenthesis equals 60.7 grams(SD)=60.7g ]. HDMAX2 also identified AMRs having simultaneous effects both on GA and on birth weight. Among the top hits of both GA and birth weight analyses, regions located in COASY, BLCAP, and ESRP2 also mediated the relationship between GA and birth weight, suggesting reverse causality in the relationship between GA and the methylome.

Discussion: HDMAX2 outperformed existing approaches and revealed an unsuspected complexity of the potential causal relationships between exposure to MS and birth weight at the epigenome-wide level. HDMAX2 is applicable to a wide range of tissues and omic layers.

[1] Maxime Estavoyer and Olivier François : Theoretical Analysis of Principal Components in an Umbrella Model of Intraspecific Evolution, Theoretical Population Biology, 2022

Abstract : Principal component analysis (PCA) is one of the most frequently-used approach to describe population structure from multilocus genotype data. Regarding geographic range expansions of modern humans, interpretations of PCA have, however, been questioned, as there is uncertainty about the wave-like patterns that have been observed in principal components. It has indeed been argued that wave-like patterns are mathematical artifacts that arise generally when PCA is applied to data in which genetic differentiation increases with geographic distance. Here, we present an alternative theory for the observation of wave-like patterns in PCA. We study a coalescent model – the umbrella model – for the diffusion of genetic variants. The model is based on a hierarchy of splits from an ancestral population without any particular geographical structure. In the umbrella model, splits occur almost continuously in time, giving birth to small daughter populations at a regular pace. Our results provide detailed mathematical descriptions of eigenvalues and eigenvectors for the PCA of sampled genomic sequences under the model. Removing variants uniquely represented in the sample, the PCA eigenvectors are defined as cosine functions of increasing periodicity, reproducing wave-like patterns observed in equilibrium isolation-by-distance models. Including rare variants in the analysis, the eigenvectors corresponding to the largest eigenvalues exhibit complex wave shapes. The accuracy of our predictions is further investigated with coalescent simulations. Our analysis supports the hypothesis that highly structured wave-like patterns could arise from genetic drift only, and may not always be artificial outcomes of spatially structured data. Genomic data related to the peopling of the Americas are reanalyzed in the light of our new theory.

[3] V. Calvez, A. El Abdouni, M. Estavoyer, I. Madrid, J. Olivier, M. Tournus : Regime switching on the propagation speed of travelling waves of some size-structured Myxobacteria population models, Accepted for publication in ESAIM: Proceedings and Surveys, 2024

Abstract : The spatial propagation of complex populations can depend on some structuring variables. In particular, recent developments in microscopy have revealed the impact of bacteria heterogeneity on the population motility. Biofilms of Myxococcus xanthus bacteria have been shown to be structured in clusters of various sizes, which remarkably, tend to move faster when they consist of a larger number of bacteria. We propose a minimal reaction-diffusion discrete size-structured model modelling a population of Myxococcus with two possible cluster sizes: isolated and paired bacteria. Numerical experiments show that this model exhibits travelling waves whose propagation speed depends on the increased motility of clusters, and the exchange rates between isolated bacteria and clusters. Notably, we evince the existence of a characteristic threshold level θ* on the ratio between cluster motility and isolated bacteria motility, which separates two distinct regimes of propagation speed. When the ratio is below θ*, the propagation speed of the population is constant. However, when the ratio is above θ*, the propagation speed takes higher values. We also consider a generalised model with continuous-size structure, which also shows the same behaviour. We extend the model to include interactions with a prey population, which show qualitative behaviours in agreement to the biological experiments.