Titres et abstracts(Dans l'ordre alphabétique des orateurs)
Diala Abu Awad Sequenced genomes are now one of the main types of data being sought out to understand the evolutionary history of species. This data is used to infer past demography, divergence between species and selection. And all of this is done under the assumption of an unchanging genomic landscape. But mutation and recombination rates can and do evolve. Genome re-arrangements may also be under selection. Interestingly, there seem to be patterns of genomic changes that seem to correlate with some life-history traits. Are these changes merely a consequence of ecological change, or could they also play a role in causing them? I ask this question in the context of the evolution of self-fertilisation, specifically to understand how the genome as a dynamic trait could influence species persistence.
Gabriel Amselem Growing from a few cells to a population (and back) At the population level, the growth of bacterial populations appears to be deterministic, with a number of cells growing exponentially with time. Yet, at the single-cell level, bacterial division is a stochastic process. A quantitative understanding of the impact of cellular variability on population growth is crucial to distinguish between e.g. the growth dynamics of an isogenic population without intercellular interactions, and that of a population with the apparition of mutants, or with cooperative behaviors, or stress-induced variability. Here we combine experiments, theory and simulations to probe the influence of stochasticity at the single bacterium level on the growth dynamics of bacterial populations. We use droplet microfluidics to monitor the growth dynamics of hundreds of independent ensembles of bacteria that each start with a small number of individuals, and until they reach ∼ 1000 cells. We show that, in addition to the inherent cell-to-cell stochasticity, the variability in the initial conditions — initial number of cells, generation-dependent division times — is key to predict the distribution of population sizes. We then outline a path for recovering the variability in division times at the single-cell level from macroscopic measurements of the variability in population sizes.
Paul Bastide Bayesian Inference of Gaussian Models on Phylogenies with Applications to Viral Trait Evolution
Sylvain Billiard Are there limits to inference in the simplest of ecological systems? Stochastic models describing population dynamics can be used for inferential purposes. Very often, the stochastic models are much simpler than the biological system under study, which makes "acceptable" the lack of precision of parameter estimations or models comparisons. What about the simplest biological systems such as a small growing population of bacteria, followed individually, with a large quantity of resources? My talk will present some inferences from data in this particular case, and my goal is to discuss about the meanings and limits of the use of stochastic models to study such a simple population.
Eugenio Cinquemani Inference of the statistics of a promoter process from population-snapshot gene expression data In [1], we have developed mathematical tools for the analysis of single-cell gene expression data from population snapshots, and an inference algorithm for the estimation of stationary statistics of promoter activation. The stationarity assumption can be limiting, however, especially for control scenarios, where an exogenous input modulates the time evolution of promoter activation. In [2], we address the inference problem in the nonstationary case of modulated processes. Taking further the results from [1], we devise and demonstrate in simulation [1] E.Cinquemani, “Stochastic reaction networks with input processes: Analysis and application to gene expression inference”, Automatica, 101:150-156, 2019, https://hal.inria.fr/hal-01925923 [2] E.Cinquemani, “Inference of the statistics of a modulated promoter process from population snapshot gene expression data”. Proceedings of the 21th IFAC World Congress, Berlin, Germany, July 12-17, 2020, https://hal.inria.fr/hal-03085422
Quentin Cormier We consider a model of interacting (biological) neurons. Each neuron is described by its membrane potential and is of the type « Integrate-and-Fire »: between two successive spikes the membrane potential (V_t) solves an ODE. The neuron « spikes » at the random rate f(V_t) (this rate only depends on the membrane potential of the neuron). At the spiking time, (V_t) is reset to a resting value. At the same time, the discharge is propagated to the other neurons with a jump in their membrane potential. We are interested in the limit where the number of neurons goes to infinity: a typical neuron in this mean-field asymptotic follows a McKean-Vlasov SDE. We study this SDE (well-posedness and invariant probability measures). We then study the (local) stability of these invariant probability measures as well as the existence of periodic solutions in a neighborhood of an unstable invariant probability measure (Hopf bifurcation).
Pete Czuppon We study the early dynamics of an epidemic outbreak started by a single infected individual. We first review existing results on the probability of establishment of an epidemic, and descriptions of epidemic dynamics with renewal equations. We then combine the probability of establishment with this renewal equation, by conditioning the underlying stochastic process on establishment. This adjustment explains why the initial growth of an epidemic exceeds its asymptotic growth rate. We then illustrate the utility of these theoretical results by applying them to the question of early outbreak detection and control. First, we study the situation where infected individuals are detected with a certain probability. In this situation, we compute the probability distribution of the first detection time of an infected individual in an epidemic cluster. Using this distribution, we find that the SARS-CoV-2 variant of concern B.1.1.7 detected (retrospectively) in September 2020 in England first appeared in England around early to mid-August 2020. Additionally, we compute the distribution of the cluster size at the first detection time. Last, we estimate a minimal testing frequency to detect clusters before they exceed a certain threshold size, and we compute the detection rate of infected individuals during a single mass testing effort. For example, in a COVID-19-parameterized model with an effective reproduction number R=1.3, only 26% of potentially infectious individuals are detectable at the time of testing.
Paolo Dai Pra Microscopic origin of rhythms: a non mean field example. Self organized collective periodic behavior is widely observed in biological systems. A number of mean field models have been proposed to capture this phenomenon at a mathematical level, showing that it may be induced by a combination of factors including noise, dissipation, loss of Markovianity and/or of time reversibility. For models with short range interaction, very little is known, though numerical simulations seem to indicate that the mean field assumption should not matter. Recently we have investigated a simple classical model, a modification of the 1-d Ising model, in order to understand how self organization at microscopic level may produce large scale rhythms. We report some recent (partial) results.
Adrian Gonzalez Casanova Some mathematical questions inspired by the Lenski experiment. We will discuss several mathematical problems related to or inspired by the famous experiment of evolution in action. This includes questions like, what is the speed of adaptation one expects from the design of the experiment? What is the effect of the design of the experiment on the genealogy of the population? Cell size tends to increase, is it reasonable for the bacteria to become less efficient? The talk will be based in several collaborations and ongoing work.
Ulysse Herbach The well-known issue of reconstructing regulatory networks from gene expression measurements has been somewhat disrupted by the emergence and rapid development of single-cell data. Indeed, the traditional way of seeing a gene regulatory network as a deterministic system affected by small noise is being challenged by the highly stochastic, bursty nature of gene expression revealed at single-cell level. Here we describe a mechanistic approach in which the network inference problem is seen as a calibration procedure for a piecewise-deterministic Markov process that, contrary to ordinary or even stochastic differential equation systems often used in this context, is able to acceptably reproduce real single-cell data. More specifically, the idea is to use the distribution of the process, in transient or steady state, as a usual likelihood to be maximized with respect to network parameters. This approach leads to promising inference algorithms, based on closed-form approximate solutions of the related master equation.
Anna Kraut Targeted cancer therapies, in the form of small molecule drugs or monoclonal antibodies, and immunotherapies like adoptive cell transfer with tumour specific T-cells have become a potent treatment strategy for various cancer types over the last years. Both are based on identifying the tumour cells by a distinct feature such as certain antigens or receptors and are thus less invasive to the surrounding healthy tissue. However, tumour heterogeneity proves to be a major obstacle to successful therapies. It is therefore of great importance to gain a better understanding of tumour cell plasticity as a resistance mechanism in order to improve treatment.
Many questions arise when modelling this tumour heterogeneity. Among others, whether diversity of traits should be pictured as discrete cell types or varying on a continuous spectrum, whether resistance is acquired under therapy or simply a selection of preexisting clones, and whether resistance is permanent or a re-sensitisation may occur. In the talk we will address some of those questions using the example of immunotherapy of melanoma. We consider stochastic individual-based models and simulations of such to study how both phenotypic and genotypic plasticity can lead to resistance through a loss of the targeted antigen. However, many questions are still open when it comes to choosing the right model and will be the base for some discussion.
Estelle Kuhn Dynamical phenomena such as infectious diseases are often investigated by following up subjects longitudinally, thus generating time to event data. The spatial aspect of such data is also of primordial importance, as many infectious diseases are transmitted from one subject to another. In this paper, a spatially correlated frailty model is introduced that accommodates for the correlation between subjects based on the distance between them. Estimates are obtained through a stochastic approximation version of the Expectation Maximization algorithm combined with a Monte-Carlo Markov Chain, for which convergence is proven. The novelty of this model is that spatial correlation is introduced for survival data at the subject level, each subject having its own frailty. This univariate spatially correlated frailty model is used to analyze spatially dependent malaria data, and its results are compared with other standard models. Joint work with Ajmal Oodally and Luc Duchateau
Cornelia Pokalyuk Invasion of cooperative parasites in moderately structured host populations
Christophe Pouzat Working Memory and Metastability in a System of Spiking Neurons with Synaptic Plasticity
Björn Reineking Moving ahead: some current challenges in analysing animal movement Movement is important for solving some of the big problems in life: finding food, shelter, a mate. Technological advances in animal tracking, e.g. small GPS tags, have resulted in detailed information on where animals move. However, making sense of this data presents a number of challenges. Here, we will look at some current challenges, such as quantifying individual variation in movement rules or scaling from individual paths to connectivity at the landscape scale.
Alex Watson Growth-fragmentation and quasi-stationary methods A growth-fragmentation is a stochastic process representing cells with continuously growing mass and sudden fragmentation. Growth-fragmentations are used to model cell division and protein polymerisation in biophysics. A topic of wide interest is whether or not these models settle into an equilibrium, in which the number of cells is growing exponentially and the distribution of cell sizes approaches some fixed asymptotic profile. In this work, we present a new spine-based approach to this question, in which a cell lineage is singled out according to a suitable selection of offspring at each generation, with death of the spine occurring at size-dependent rate. The quasi-stationary behaviour of this spine process translates to the equilibrium behaviour, on average, of the growth-fragmentation. We present some Foster-Lyapunov-type conditions for this to hold. This is joint work with Denis Villemonais (École des Mines de Nancy/Université de Lorraine) |
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