14 novembre 2024 à Grenoble, Institut Fourier salle B29, 10h-12h
In ecology, the Fisher-KPP equation is often motivated by the proliferation of a population of randomly moving individuals in an environment with finite ressources. In this talk, I will show that this
equation also appears as the limit of a Stefan problem originating from an active gel model of a proliferating cell monolayer with a free boundary. The advancement of the leading edge still relies on cell
proliferation and protrusive activity at the tissue margin but the effective diffusion coefficient has now a direct mechanical interpretation.
11h : Nicolas ZADEH (Université Libre de Bruxelles): Kinetic description and numerical study of a network of resonate and fire neurons
An important feature of some neurons is their ability to display resonant-like properties. The resonate and fire (RF) model (Izhikevich, 2001) allows for a simple description of such neurons, for a meager computational cost. We will first present a mean-field description of a network of interconnected RF neurons, following the kinetic formalism.
Then a numerical approximation finite differences scheme designed to tackle the equation will be seen, having mass and positivity preservation properties. Some simulations giving validity to the mean-field approach conclude the talk.
10 octobre 2024 à l’UMPA, ENS Lyon
10h : Thao Nguyen (ENS de Lyon, laboratoire LBMC): Multiscale Modeling of Neuroblastoma Organoids: From Gene Regulatory Networks to Spatial Dynamics
In this talk, I will present a multiscale model of neuroblastoma organoids, which are child tumors of the sympathetic nervous system derived from the primitive neural crest cells. At the molecular level, we implemented a simple gene regulatory network (GRN) in the form of a toggle switch between two genes, one driving the stemness and the other characterizing a differentiated phenotype. This GRN has been encoded as a biologically realistic mechanistic model driven by transcriptional burst for gene expression. Cellular decision-making (proliferation, death, differentiation) is driven by protein concentrations produced by the GRN. To check the realism of the 3D structures obtained, we compared the simulation results, both visually and using appropriate statistics, with immunohistochemistry (IHC) images, using quantitative measurements of spatial distributions.
11h : Léo Girardin (ICJ, Lyon 1): Persistence and propagation of structured populations in space-time periodic media
This talk is concerned with asymptotic persistence, extinction and spreading properties for structured population models resulting in non-cooperative Fisher-KPP systems with space-time periodic coefficients. Results are formulated in terms of a family of generalized principal eigenvalues associated with the linearized problem. When the maximal generalized principal eigenvalue is negative, all solutions to the Cauchy problem become locally uniformly positive in long-time, at least one space-time periodic uniformly positive entire solution exists, and solutions with compactly supported initial condition asymptotically spread in space at a speed given by a Freidlin-Gärtner-type formula. When another, possibly smaller, generalized principal eigenvalue is nonnegative, then on the contrary all solutions to the Cauchy problem vanish uniformly and the zero solution is the unique space-time periodic nonnegative entire solution. When the twogeneralized principal eigenvalues differ and zero is in between, the long-time behavior depends on the decay at infinity of the initial condition. The proofs rely upon double-sided controls by solutions of cooperative systems. The control from below is new for such systems and makes it possible to shorten the proofs and extend the generality of the system simultaneously.
Journée 3 à Grenoble le 21 juin 2024 (10h-16h)
10h30 – 11h30: Julien Chevallier (LJK, Grenoble), Estimation de la densité d’un graphe de dépendance en grande dimension
L’objectif est d’estimer la densité de connexion d’un graphe de dépendance entre N agents, dans la limite où N tend vers l’infini, à partir de la seule observation de N processus à temps discret en interaction. Plus précisément, le modèle que nous proposons possède : 1) un graphe d’Erdos-Rényi de paramètre p, 2) conditionnellement à ce graphe latent, les observations forment une chaine de Markov à valeurs dans {0,1}^N. Dans ce cadre, l’objectif est d’estimer le paramètre p.
Je présenterai notre estimateur et sa vitesse de convergence. Si le temps le permet, je présenterai, au choix de l’audience : 1) des arguments heuristiques qui expliquent sa convergence, 2) quelques détails sur des résultats de matrices aléatoires, 3) quelques détails sur le contrôle des corrélations spatio-temporelles du processus. Enfin, je présenterai des illustrations issues de simulations.Travail en collaboration avec Eva Löcherbach et Guilherme Ost.
11h30 – 12h30: Patrick Vallet (INRAE, Grenoble)
13h45 – 14h45: Clara Lage (ENS de Lyon): Identifying a piecewise affine signal from its nonlinear observation – application to DNA replication analysis
An important challenge in DNA replication analysis is to recover a so-called timing profile, that contains important information about the replication dynamics, from nonlinear observations. We show that this can be expressed as a nonlinear inverse problem where the unknown timing profile can be assumed to be piecewise affine. As this problem cannot be directly addressed with techniques for linear inverse problems, we propose a novel formalism and computational approach to harness it. In the noiseless case, we establish sufficient identifiability conditions for the timing profile, and prove that it is the solution of a non-convex optimization problem. These problems are specially challenging because of their multiple local minima. We propose the DNA-Inverse optimization method that is capable of finding their global solution in the noiseless case and proved to be effective in numerical experiments for noisy signals. Comparative analysis against state-of-the-art optimization methods highlights the superior computational efficiency of our approach. The method enables the automatic recovery of all configurations of the replication dynamics, crucial for DNA replication analysis, which was not possible with previous methods.
15h – 16h: Vincent Miele (CNRS, LECA Chambéry/Grenoble): ELGRIN, un modèle statistique pour quantifier l’effet des interactions biotiques sur la distribution des espèces le long de gradients environnementaux.
We propose a novel statistical model, called ELGRIN (in reference to Charles Elton and Joseph Grinnell) that can handle the effects of both environmental factors and known interspecific interactions (aka a metanetwork) on species distributions. We rely on Markov random fields to handle dependencies between variables using a graph. More specifically, ELGRIN jointly models the presence and absence of all species in a given area in function of environmental covariates and the topological structure of the known metanetwork. It separates the interspecific interaction effects from those of the environment on species distributions.
Using various simulated and empirical data, we demonstrate the suitability of ELGRIN to address the objectives for various types of interspecific interactions like mutualism, competition and trophic interactions. We then apply the model on vertebrate trophic networks in the European Alps.
16 mai 2024 : ICJ, Lyon
10h : Audrey Denizot (AIstroSight, Inria Lyon) : Towards elucidating astrocyte function in the brain: insights from stochastic spatially-extended models
Astrocytes are cells of the brain that have recently emerged as key regulators of signal transmission, taking part in higher brain functions such as memory and learning. Astrocytes communicate with neighboring cells with changes in intracellular calcium concentration: Ca2+ signals. Most of these signals occur at the nanoscale, hindering their study in live tissue, so that computational approaches are essential to gain insights into their dynamics. To take into account the complex morphology of astrocytes and the stochasticity of reactions occuring in the resulting nanoscopic compartments, we have developed reaction-diffusion particle-based and voxel-based models of astrocyte Ca2+ dynamics. Our simulations revealed mechanisms by which spatial factors such as the clustering of Ca2+ channels, Ca2+ buffering, ER shape and distribution influence the spatio-temporal properties of Ca2+ signals. Astrocytes and their Ca2+ signals are essential to the functioning of the nervous system and are altered in most brain disorders. As research has for long focused on treating neurons, little is known about astrocyte (patho-)physiology and better characterizing astrocyte function might lead to the discovery of new treatments for the diseased brain.
11h: Jimmy Garnier (LAMA, Univ. Savoie Mont-Blanc): Mutualism at the leading edge: Insights into the eco-evolutionary dynamics of host-symbiont communities during range expansion
The evolution of mutualism between host and symbiont communities plays an essential role in maintaining ecosystem function and should therefore have a profound effect on their range expansion dynamics. In particular, the presence of mutualistic symbionts at the leading edge of a host-symbiont community should enhance its propagation in space. I will present a theoretical framework that captures the eco-evolutionary dynamics of host-symbiont communities, and allow us to investigate how the evolution of resource exchange may shape community structure during range expansion.
Journée 2 à Marseille le 8 avril 2024
10h30-11h30: Chloé GUICHARNAUD : Tirée ou poussée? Étude de populations en expansion via l’utilisation conjointe de modèles individus-centrés et d’expériences en laboratoire
11h30-12h30: Nathanaël BOUTILLON : Une équation de Fisher-KPP avec une dimension spatiale et une dimension phénotypique : persistance et propagation
15h30-16h30: Marie Jose CHAAYA : A continuous approach of modeling tumorigenesis and axons regulation for the pancreatic cancer
14 mars 2024 : Institut Fourier salle B29, Grenoble
10h : Adeline Leclercq Samson (LJK, UGA) : Some statistical models to quantify the effect of climate change on whales in Greenland
Human activities have a profound impact on marine ecology in Greenland. In this presentation, I will focus on a study of the impact of these activities on narwhals. I will present different stochastic models to analyze the data from this study: point process with memory, stochastic Langevin diffusions. These diffusion processes can be multidimensional, hypoelliptic (with a degenerate noise) and partially observed. I will discuss the question of parameter estimation when only discrete observations are available.
11h : Sylvain Moinard (LECA, UGA) : Indicateurs de biodiversité robustes pour le métabarcoding et outils mathématiques associés
Du fait de l’activité humaine, la biodiversité connaît un bouleversement rapide à l’échelle mondiale. Les mesures de conservation nécessitent de pouvoir évaluer l’état de la biodiversité sur un site donné. L’étude de l’ADN environnemental par métabarcoding permet de remplacer l’observation directe des espèces, laborieuse, et fournit une source d’information prometteuse pour améliorer la gestion des écosystèmes. Cependant, l’estimation des abondances relatives des espèces est encore mal établie pour ce type de données.
Je présenterai d’abord un projet de correction des biais d’abondance induits par le métabarcoding. Ces travaux sont appuyés par une modélisation de la PCR (Polyerase Chain Reaction), cruciale dans ce protocole. Le choix des paramètres optimaux dudit modèle n’est pas établi de manière analytique mais repose sur une optimisation numérique.
Je présenterai donc dans un second temps un nouvel algorithme d’inférence de paramètres pour modèles aléatoires appelé Fixed Landscape Inference MethOd (flimo). Celui-ci est applicable à divers modèles utilisés en écologie. Il fonctionne dans le même cadre que les algorithmes d’Approximate Bayesian Computation (ABC) en procédant par simulations du modèle sans considérer sa vraisemblance. Sur les exemples étudiés, les résultats de flimo sont obtenus beaucoup plus vite que pour les algorithmes utilisés en comparaison, avec une précision similaire.
15 Février 2024: ICJ La Doua, Université de Lyon, salle Fokko du Cloux
10h : Charlotte Camus (ICJ, Lyon) : Modeling the mechanisms of antibody mixtures in viral infections: the cases of sequential homologous and heterologous dengue infections
Les anticorps jouent un rôle essentiel dans la réponse immunitaire aux infections virales, à la vaccination ou à la thérapie par anticorps. Néanmoins, ils peuvent avoir un effet protecteur ou nocif au cours de la réponse immunitaire. En outre, la compétition ou la coopération entre les anticorps, lorsqu’ils sont mélangés, peut renforcer ou réduire cet effet protecteur ou nocif. En utilisant les lois des réactions chimiques pour modéliser la liaison des anticorps aux antigènes et leurs actions pour neutraliser ou renforcer l’infection, nous proposons une nouvelle approche pour modéliser l’activité du complexe antigène-anticorps. L’expression qui en résulte couvre non seulement la liaison purement compétitive ou purement indépendante entre les anticorps, mais aussi la liaison synergique qui, selon le type d’anticorps, peut favoriser soit la neutralisation, soit le renforcement de l’activité virale. Nous intégrons ensuite cette expression dans un modèle intra-hôte (système EDO), impliquant à la fois des cellules cibles saines et infectées, la réplication du virus et la production de deux types d’anticorps au cours d’infections successives. Nous étudions l’existence d’équilibres (sans maladie et endémique) et leurs stabilités asymptotiques locale et globale.
11h: Romain Azaïs (LBMC, Lyon) : Estimation in spinal Galton-Watson trees
We consider a Galton-Watson tree whose birth distribution depends on the hidden type of nodes: normal or special. Every special node gives birth to one special child and a number of normal children whose descendance will be normal. Even in such a very structured two-type population, our ability to distinguish the two types and estimate their birth distribution is constrained by a trade-off between the growth-rate of the population and the similarity of the two birth distributions. Indeed, if the growth-rate is too large, large deviations events are likely to be observed in the sampling of the normal individuals preventing us to distinguish them from special ones. The talk will be illustrated by numerical simulations and asymptotic goodness-of-fit tests for surviving subcritical Galton-Watson trees. Joint work with Benoît Henry.
18 Janvier 2024: ENS de Lyon, UMPA salle 435
10h : Bastien Boussau (LBBE, Lyon) : Genome scale genotype-phenotype associations along phylogenies
Identifying the footprints of selection in coding sequences can inform about the importance and function of individual sites. Analyses of the ratio of nonsynonymous to synonymous substitutions (dN/dS) have been widely used to pinpoint changes in the intensity of selection, but cannot distinguish them from changes in the direction of selection, that is, changes in the fitness of specific amino acids at a given position. We have evaluated several methods that detect changes in directional selection associated to discrete phenotypic changes on a phylogeny, and have found that our method Pelican offers a good trade-off between power and speed, enabling whole genome analyses for hundreds of species (Duchemin et al., MBE 2023, https://doi.org/10.1093/molbev/msac247). In this presentation we present Pelican, show how its performance compares to other state-of-the-art methods, including in the presence of confounding factors such as GC-biased gene conversion and CpG hypermutability, present an extension to handle continuous phenotypes, and demonstrate its use on several phenotypes on a data set of 116 whole genomes from mammals. Overall, we demonstrate that Pelican can analyze large amounts of data to look for genotype-phenotype associations, at the level of individual sites or individual genes, for both discrete and continuous phenotypes. Looking forward, we expect that the use of such phylogenetic approaches on large genomic data sets will be instrumental to annotating gene function across the tree of life.
11h : Josué Tchouanti-Fotso (UMPA, Lyon) : Detection of neural synchronization and implications for neuroscience experimental design
Abstract : Two neurons are said to be synchronized when their spike trains coincide more than when they are independent. It is commonly accepted that this phenomenon plays a very important role in the neural activity. The construction of statistical tests for its detection has been the subject of much interest in the literature and in particular with the work of Albert et al. (2015, 2016) on asymptotic tests of Bootstrap and permutation. This presentation is in the same vein, and will focus on the construction of a criterion ensuring the detection of synchonization in the case of a non-asymptotic test. This criterion is constructed in such a way as to ensure control of the first and second kind errors. We also apply this criterion to some classical models of interacting neurons, typically the well known jittering Poisson and Hawkes models, and deduce informations about the choice of some experimental parameters. Joint work with: Éva Löcherbach, Patricia Reynaud-Bouret and Étienne Tanré.
Journée à Lyon le 18 décembre 2023 à l’ENS de Lyon.
Charles Medous (Université Grenoble Alpes) : Construction d’épines pour des populations stochastiques d’individus en interactions.
Abstract : La biologie des systèmes tente d’expliquer les observations expérimentales par l’identification de mécanismes sous-jacents pertinents et l’utilisation de modèles mathématiques. De la morphogénèse décrite par les équations de réaction diffusion de Turing, aux « Genome-wide association studies », le rôle de la modélisation mathématique dans les avancées biologiques n’est plus à prouver. Dans son livre « What is Life », Erwin Schrödinger met en avant les limites de la modélisation déterministe dans l’explication des fluctuations et des sauts dans la dynamique des systèmes biologiques. En résulte l’émergence de modèles stochastiques, prenant en compte l’aléatoire des mécanismes et en particulier les processus de branchement pouvant décrire les comportements individuels dans une population. Depuis quelques décennies, de nombreuses méthodes probabilistes ont été développées pour étudier de tels processus: martingales, super-processus, calcul stochastique, épine …
Nous nous focaliserons dans cet exposé, sur les méthodes d’épine, leur construction rigoureuse dans le cas de processus de Galton-Watson ainsi que leurs diverses utilisations dans des modèles simples. Nous présenterons dans un deuxième temps les processus de branchement avec interactions, les constructions d’épines associées et leur utilisation pour obtenir des estimateurs non biaisés de statistiques d’intérêt sur des individus échantillonnés dans la population.
Raluca Eftimie (Université Franche-Comté) : Computational approaches to investigate the impact of heterogeneous immune responses in cancer evolution.
Abstract : TBA
Bartholomé Vieille (Inrae, Avignon) : Une approximation markovienne d’un processus de Hawkes pour la modélisation de propagation épidémique.
Abstract : In recent years, numerous studies grounded on Hawkes processes have been carried out in many fields including finance, biology and social network. Hawkes processes form a class of self-exciting simple point processes. In this communication, I will introduce a markovian approximation of a specific hidden multivariate Hawkes process considered in a spatial setting and used to model the spatio-temporal spread of an epidemic. The spatial domain is composed of multiple disjoint regions. The baseline intensity is time-dependent, and the jump size is constant and equal to 1. Furthermore, the exciting function is a general one. The closed-form expression of the multivariate characteristic function of such a markovian process will be presented. This allows us to obtain a closed-form formula for the temporal structure of the first moments. I will also discuss other points such as parameter estimation of the state-space epidemic model by Sequential Monte-Carlo.
Pierre Roux (Centrale Lyon) : Modélisation des cellules de grille par une équation de Fokker-Planck non-linéaire et non-locale.
Abstract : Depuis leur découverte en 2005 par Moser, Moser et leurs collègues, les cellules de grilles – des neurones spécifique du cortex entorhinal qui jouent un rôle crucial dans la navigation spatiale des mammifères – ont été l’objet de nombreuses études. Un point clef de leur fonctionnement est qu’elles constituent des modules dont l’activité électrique se stabilise en un motif hexagonal (qui constitue une sorte de grille). Dans cet exposé, je présenterai un modèle aux dérivées partielles de type Fokker-Planck non-linéaire, développé par Carrillo, Clini, Holden et Solem, visant à comprendre l’apparition du motif hexagonal et à étudier sa robustesse au bruit. À travers un mélange de résultats théoriques (existence locale et globale, convergence en entropie relative, bifurcations entraînées par le bruit) et d’explorations numériques, José Antonio Carrillo, Susanne Solem et moi-même avons œuvré à améliorer la compréhension du modèle et du phénomène sous-jacent.
16 Novembre 2023: Institut Fourier, salle B29, Grenoble
Eugenio Cinquemani (Inria): Power spectral analysis for the optimal design of gene reporter systems
An established technique for the monitoring of gene expression dynamics is the use of fluorescent reporter proteins. Synthesized in response to promoter activation of the gene of interest, fluorescent proteins provide a visible readout of gene expression that can be quantified over time both at an ensemble population and at a single-cell level. Fluorescent reporter system response to promoter activation can be described as standard transcription-translation reaction networks, taking the form of stochastic models for single cells and deterministic models for population averages. The kinetic rate constants of these systems constitute design parameters for the experimenter that shape the response to promoter activation.
In this talk, reporter systems are analyzed from a signal processing viewpoint. The power spectral transfer function for stochastic (single-cell) response models is developed and compared with the frequency response of corresponding deterministic (population) models. Both response models are shown to be equivalent to a linear filter, with a noise component for single-cell response coming from intrinsic noise of the gene expression process. These results are next used to explore the design of the kinetic rate constants. Assuming additive measurement noise on the observed fluorescent levels, design guidelines are established to optimize information content of the reporter output in spite of measurement noise and, for single-cell monitoring, of intrinsic noise. A final discussion of the results points out fundamental differences between gene expression monitoring in populations and in single cells.
Loïc Chalmandrier (UGA, LIPhy): Calibrating process-based biodiversity models with functional traits
Process-based models are seldom used to identify the mechanisms that structure species-rich biological communities. One reason is that species demography and interactions are often too difficult to estimate in situ or experimentally. Here, I will show how to use functional trait data and biodiversity data instead to infer species demography and interactions. I will present case studies demonstrating the value of this approach to model abiotic filtering and competition in plant communities and present the future directions of my research on that topic.
12 Octobre 2023: ICJ La Doua, Université de Lyon, salle Fokko du Cloux
Thomas Koffel (Lyon 1, LBBE) : Connecting local and regional scales with stochastic metacommunity models: Competition, ecological drift, and dispersal.
Résumé : Metacommunity ecology extends the metapopulation concept to provide a theoretical framework for understanding multi-species interactions in spatially subdivided landscapes. Despite the interest in metacommunity ecology, the theory is currently loosely organized into disjunct paradigms such as species sorting, patch dynamics, mass effects, and neutral theory. Reconciling these diverse models in a unified framework requires inclusion of three fundamental ecological processes: selection (niche-based processes), ecological drift (stochasticity), and dispersal. I will present a competitive Lotka Volterra metacommunity model that includes all of these processes. First, we look at open systems, where immigrants come from a mainland source population. Then we look at true metacommunities, where immigrants come from other patches in the landscape. Using efficient numerical techniques to calculate equilibria and invasion criteria, we determine how the regional outcome of competition depends on local interactions, dispersal, and local population size.
Julien Clavel (Lyon 1, LEHNA) : Modelling phenotypic traits evolution in deep-times: a phylogenetic approach.
Résumé :The use of statistical approaches for modeling the evolution of species traits on phylogenetic trees, also known as phylogenetic comparative methods, have exploded since Felsenstein’s seminal paper in 1985. Developed at the beginning as a statistical fix for comparative analyses, these approaches are now routinely used to address fundamental questions in macroevolution and macroecology from extant and fossil data. However, their use has been often limited to simplistic models assuming that traits or species are evolving independently of each other’s and from their environment. Here, I present a suite of models that we recently developed to infer the effect of inter-specific interactions and past environmental changes on the evolution of phenotypic traits as well as for understanding the evolution of multidimensional traits – in particular high dimensional multivariate datasets such as 3D geometric morphometrics. These methods show that phylogenies of extant taxa provide valuable information about past and present biodiversity and offer a unified analytical framework for the study of extant and fossil taxa. Future developments of these models and statistical tools will further allow a better integration of data types and research fields for a better understanding of the processes driving the evolution of taxonomic and phenotypic diversity.
14 Septembre 2023: ENS de Lyon, UMPA salle 435
Céline Bonnet (Inria, UMPA): A piecewise deterministic and Markovian approach to study the role of quiescence dynamics in blood cancers.
Résumé : We will see an approach to study the impact of a small microscopic population of cancer cells on a macroscopic population of healthy cells, with an example inspired by pathological hematopoiesis. Hematopoiesis is the biological phenomenon of blood cells production by differentiation of cells called hematopoietic stem cells (HSCs). Cancer HSCs produce a large number of cancer blood cells but randomly stop to produce them (during such a period, the cancer HSC is called quiescent). We will study the impact of such a quiescent state on the production of cancer blood cells and on healthy cells through regulation. We will describe the evolution over time of the number of healthy and cancer cells using a multi-type Markov process. A single cancer HSC is considered while other populations are in large numbers. We show the convergence in law of this process towards a piecewise deterministic Markov process (PDMP). We then study the long time behavior of this limit process. We show the existence and uniqueness of an invariant probability measure using the works of Benaim and co-authors. We finally identify this measure using the solution of a stationary system of partial differential equations describing the impact of cancer HSC quiescent phases and regulation on the cell density of the hematopoietic system studied.
Guillaume Mestdagh (Inria, RDP) : Contrôle optimal pour le recalage d’organe en chirurgie augmentée.
Résumé : La réalité augmentée est utilisée en chirurgie minimalement invasive pour permettre au personnel médical de suivre en temps réel les mouvements du foie du patient. Pour mettre à jour la déformation d’un organe virtuel, une méthode de recalage élastique aligne un modèle biomécanique pré-opératoire du foie avec une surface partielle observée pendant l’opération. Tandis qu’une grande partie des méthodes de recalage élastique consistent à introduire des forces fictives dans le modèle direct, notre approche vise à reconstruire la vraie densité de forces surfaciques qui a créé la déformation observée. Nous exprimons le problème de recalage dans le formalisme du contrôle optimal, en utilisant comme variable d’optimisation la distribution de forces qui s’applique à la surface de l’organe. En permettant de définir à l’avance un ensemble de forces admissibles, cette approche favorise les champs de déplacement ayant un sens physique. Nous commençons par étudier l’existence de solutions pour le problème continu et nous calculons des conditions d’optimalité de premier ordre. Puis nous présentons la méthode d’adjoint que nous avons implémentée afin de traiter le problème numériquement. Finalement, nous validons notre méthode au moyen de cas-test liés à l’application en chirurgie augmentée. Lors de ces essais, nous mesurons l’erreur de recalage, et nous cherchons également, dans un cas particulier, à donner un sens à la distribution de forces obtenue.
