[9] Maxime Estavoyer, Thomas Lepoutre and Marie Manceau : Mathematical modeling of dermal competence and cellular aggregation effects on feather follicle emergence speed, preprint, 2024

Abstract : During avian morphogenesis, feather follicles generally emerge row by row, in a medio-lateral sequential pattern through a two-stage developmental process. Initially, dermal densification occurs to render the tissue competent. Subsequently, a complex interplay of signaling between dermal cells and proteins leads to the formation of dermal cell aggregates, which initiate feather buds. This study employs a reaction-diffusion-chemotaxis mathematical model to analyze the speeds of these stages and their interactions, to determine the overall emergence speed of feather follicles. Our model enables us to calculate the speed of the competence wave and, through a weakly nonlinear analysis, approximates the emergence speed of follicles within a competence zone. Numerical simulations suggest that when the emergence speed of follicles surpasses the speed of the competence wave, the bud emergence becomes synchronized to the competence wave's speed. Conversely, the formation of follicles does not affect the competence wave. This theoretical and numerical work provides a precise approximation of bud emergence speed in initially naive tissue, highlighting the complex dynamics of feather follicle morphogenesis and the significance of understanding the interplay between dermal competence and cellular aggregation in this process.

[8] Maxime Estavoyer : A reaction telegraph model reveals synergy between motility strategies in Myxococcus xanthus predation, preprint, 2024

Abstract :
The predatory bacterium Myxococcus xanthus can invade prey bacteria using two distinct motility apparatuses. It is commonly acknowledged that adventurous motility is used for isolated bacteria, while social motility corresponds to bacterial clusters. Inspired by recent biological findings, we propose a simple model of predatory invasion focusing on the co-occurrence of these two mechanisms and their possible synergistic effects. At microscopic scale, cell motion is persistent; therefore, we opt for a transport-reaction model, extending previous reaction-diffusion models. Another specificity is the structuration of the bacterial population into clusters with varying speeds and persistence times. In the linear regime, we find a transition from normal speed to anomalous speed, consistent with reaction-diffusion theory but with specificities due to the hyperbolic nature of the model. For the nonlinear regime, we numerically observe and study the existence of transitions between pulled and pushed fronts. Finally, we reproduced biological experiments with mutants lacking each of the motility apparatuses based on relevant modifications of the model. Moreover, we propose a rational basis for the reported synergistic effects. Our work paves the way for a better understanding of the complex waves of bacterial population advance, which are precursors to biofilm formation.

[7] M. Estavoyer, M. Banerjee, N. Torres, J. Blohm, L. Pujo-Menjouet : Spatial pattern analysis of an Aβ-monomer model with inflammation processes for Alzheimer’s disease, preprint, 2024

Abstract :
We study the emergence of spatial patterns for a system of reaction-diffusion equations, modeling the progression of Alzheimer's disease through the interaction of Aβ-monomers, oligomers, microglial cells, and interleukins with neurons. In our work, these spatial patterns stand for inert amyloid plaques, which are extracellular deposits of Aβ-proteins and a characteristic feature of this neurodegenerative disease. Using linear analysis and numerical simulations, we show the existence of spatially heterogeneous solutions and exhibit a wide variety of possible spatially-dependent solutions: time-oscillating, low-amplitude, and high-amplitude patterns. Moreover, we carry out an extensive analysis of high-amplitude patterns in the one- and two-dimensional domains. In particular, we study the stability of branches of heterogeneous steady states through bifurcation diagrams and their selection. From these numerical simulations, we develop some conjectures concerning the influence of inflammation and microglial cells in the formation of amyloid plaques. These findings offer insights into potential anti-inflammatory treatments that might be used to mitigate the progression of Alzheimer's disease and the emergence of inert amyloid plaques.

[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.

[3] J. Restier-Verlet et al. : Accelerated Aging Effects Observed In Vitro after an Exposure to Gamma-Rays Delivered at Very Low and Continuous Dose-Rate Equivalent to 1–5 Weeks in International Space Station, Cells 2024

Abstract :
Radiation impacting astronauts in their spacecraft come from a “bath” of high-energy rays (0.1–0.5 mGy per mission day) that reaches deep tissues like the heart and bones and a “stochastic rain” of low-energy particles from the shielding and impacting surface tissues like skin and lenses. However, these two components cannot be reproduced on Earth together. The MarsSimulator facility (Toulouse University, France) emits, thanks to a bag containing thorium salts, a continuous exposure of 120 mSv/y, corresponding to that prevailing in the International Space Station (ISS). By using immunofluorescence, we assessed DNA double-strand breaks (DSB) induced by 1–5 weeks exposure in ISS of human tissues evoked above, identified at risk for space exploration. All the tissues tested elicited DSBs that accumulated proportionally to the dose at a tissue-dependent rate (about 40 DSB/Gy for skin, 3 times more for lens). For the lens, bones, and radiosensitive skin cells tested, perinuclear localization of phosphorylated forms of ataxia telangiectasia mutated protein (pATM) was observed during the 1st to 3rd week of exposure. Since pATM crowns were shown to reflect accelerated aging, these findings suggest that a low dose rate of 120 mSv/y may accelerate the senescence process of the tested tissues. A mathematical model of pATM crown formation and disappearance has been proposed. Further investigations are needed to document these results in order to better evaluate the risks related to space exploration.

[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.

[4] 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, 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.

Maxime Estavoyer, Propagation and emergence of patterns in biology , under the supervision of Thomas Lepoutre, 2024