2023Activity reportProject-TeamMUSCA

Network behavior

In the case of autonomous systems (with no explicit dependency on time), the main theoretical challenge is the prediction of the long time dynamics, given the algebraic complexity associated with putative stationary states in high dimension. In physiological systems, the intracellular reaction networks are not under a static or constant input stimulation but rather subject to complex and highly dynamic signals such as (neuro-)hormones 21 or metabolites. These systems are thus non-autonomous in nature. Understanding to what extent reaction network motifs are able to encode or decode the dynamic properties of a time-dependent signal is a particularly challenging theoretical question, which has yet been scarcely addressed, either in simplified case-studies 71,11 or in the framework of “pulse-modulated systems” 52.

Network reduction

The high dimension of realistic networks calls for methods enabling to perform model reduction. Our strategy for model reduction combines several tools, that can be applied separately or sequentially to the initial model. Both in stochastic biochemical systems and population dynamics, large species abundance calls in general for the functional law of large number and central limit theorems, for which powerful results are now established in standard settings of finite dimension models 59. However, in more and more biological applications, the very large spectrum of orders of magnitude in reaction rates (or birth and death rates) leads naturally to consider simultaneously large species abundance with timescale separation, which generally results in either algebraic-differential reduced models, or to hybrid reduced models with both deterministic and stochastic dynamics. We will apply the generic methodology provided by the singular perturbation theory of Fenichel-Tikhonov in deterministic systems, and Kurtz's averaging results in stochastic systems, which, in the context of high dimensional reaction networks or population dynamics, are still the matter of active research both in the deterministic 60, 53 and stochastic context 42, 58, 70.

Other reduction approaches of deterministic systems will consist in combining regular perturbation expansion with standard linear model order reduction (MOR) techniques. We will continue our previous work 14, 13 on the derivation of convergence and truncation error bounds for the regular perturbation series expansion (also known as Volterra series expansion) of trajectories of a wide class of weakly nonlinear systems, in the neighborhood of stable hyperbolic equilibria. The challenge will be to obtain biologically interpretable reduced models with appropriate features such as for instance positivity and stability. Finding a general approach for the reduction of strongly nonlinear systems is still an open question, yet it is sometimes possible to propose ad-hoc reduced models in specific cases, using graph-based decomposition of the model 74, combined with the reduction of weakly nonlinear subsystems.

Statistical Inference, Data-fitting

Once again, a key challenge in parameter estimation is due to the high dimension of the state space and/or parameter space. We will develop several strategies to face this challenge. Efficient Maximum likelihood or pseudo-likelihood methods will be developed and put in practice 128, using either existing state-of-the art deterministic derivative-based optimization 75 or global stochastic optimization 50. In any case, we pay particular attention to model predictivity (quantification of the model ability to reproduce experimental data that were not used for the model calibration) and parameter identifiability (statistical assessment of the uncertainty on parameter values). A particularly challenging and stimulating research direction of interest concerning both model reduction and statistical inference is given by identifiability and inference-based model reduction 62. Another strategy for parameter inference in complex, nonlinear models with fully observed state, but scarce and noisy observations, is to couple curve clustering, which allows reducing the system state dimension, with robust network structure and parameter estimation. We are currently investigating this option, by combining curve clustering 56 based on similarity criteria adapted to the problem under consideration, and an original inference method inspired by the Generalized Smoothing (GS) method proposed in 73, which we call Modified Generalized Smoothing (MGS). MGS is performed using a penalized criterion, where the log-likelihood of the measurement error (noisy data) is penalized by a model error for which no statistical model is given. Moreover, the system state is projected onto a functional basis (we mainly use spline basis), and the inference simultaneously estimates the model parameters and the spline coefficients.

Model behavior

The theoretical challenges associated with the analysis of structured population models are numerous, due to the lack of a unified methodological framework. The analysis of the well-posedness 19 and long-time behavior 7, and the design of appropriate numerical schemes 1, 3 often rely on more or less generic techniques 69, 64 that we need to adapt in a case-by-case, model-dependent way: general relative entropy 65, 47, measure solution framework 57, 44, 51, martingale techniques 45, finite-volume numerical schemes 61, just to name a few.

Due to their strong biological anchorage, the formulation of our models often leads to new mathematical objects, which raises open mathematical questions. Specific difficulties generally arise, for instance from the introduction of nonlocal terms at an “unusual place” (namely in the velocities rather than boundary conditions 19), or the formulation of particularly tricky boundary conditions 9. When needed, we call to external collaborators to try to overcome these difficulties.

Model reduction

Even if the use of a structured population formalism leads to models that can be considered as compact, compared to the high-dimensional ODE systems introduced in section 3.2, it can be useful to derive reduced versions of the models, for sake of computational costs, and also and above all, for parameter calibration purposes.

To proceed to such a reduction, we intend to combine several techniques, including moment equations 68, dimensional reduction 6, timescale reduction 4, spatial homogenization 4010, discrete to continuous reduction 9 and stochastic to deterministic limit theorems 15.

Once again, all these techniques need to be applied on a case-by-case basis, and they should be handled carefully to obtain rigorous results (appropriate choice of metric topology, a priori estimates).

Statistical inference, Data-fitting

The calibration of structured population models is challenging, due to both the infinite-dimensional setting and the difficulty to obtain rich enough data in our application domains. Our strategy is rather empirical. We proceed to a sequence of preliminary studies before using the experimental available data. Sensitivity analyses 55, 46, and theoretical studies of the inverse problems associated with the models 5 intend to preclude unidentifiable situations and ill-posed optimization problems. The generation and use of synthetic data (possibly noised simulation outputs) allow us to test the efficiency of optimization algorithms and to delimit an initial guess for the parameters. When reduced or simplified versions of the models are available (or derived specifically for calibration purposes) 2, these steps are implemented on the increasingly complex versions of the model. In situations where PDEs are or can be interpreted as limits of stochastic processes, it is sometimes possible to estimate parameters on the stochastic process trajectories, or to switch from one formalism to the other.

7.1.1 pyDynPeak

• Keywords:
  Data processing, Endocrinology
• Scientific Description:
  Analysis of time series taking into account the inherent properties of secretion events (form and pulse half-life, regularity of changes in rhythm)
• Functional Description:
  Detection of LH pulses (luteinizing hormone) and analysis of their rhythm. Visualisation, diagnostic and interactive correction of the detections.
• URL:
  https://­gitlab.­inria.­fr/­musca/­pydynpeak
• Authors:
  Frédérique Clément, Hande Gozukan, Christian Poli
• Contact:
  Frédérique Clément

8.1.1 Nonlinear compartmental modeling to monitor ovarian follicle population dynamics on the whole lifespan

Participants: Guillaume Ballif, Frédérique Clément, Romain Yvinec.

In the framework of Guillaume Ballif's PhD, we have introduced an ODE-based compartmental model of ovarian follicle development all along lifespan 43. The model monitors the changes in the follicle numbers in different maturation stages with aging. Ovarian follicles may either move forward to the next compartment (unidirectional migration) or degenerate and disappear (death). The migration from the first follicle compartment corresponds to the activation of quiescent follicles, which is responsible for the progressive exhaustion of the follicle reserve (ovarian aging) until cessation of reproductive activity. The model consists of a data- driven layer embedded into a more comprehensive, knowledge-driven layer encompassing the earliest events in follicle development. The data-driven layer is designed according to the most densely sampled experimental dataset available on follicle numbers in the mouse. Its salient feature is the nonlinear formulation of the activation rate, whose formulation includes a feedback term from growing follicles. The knowledge-based, coating layer accounts for cutting-edge studies on the initiation of follicle development around birth. Its salient feature is the co-existence of two follicle subpopulations of different embryonic origins. We have then setup a complete estimation strategy, including (i) the study of structural identifiability based on differential elimination, using the Structural identifiability Julia package, (ii) a sensitivity analysis based on the elementary effect method of Morris, (iii) the elaboration of a relevant optimization criterion combining different sources of data (the initial dataset on follicle numbers, together with data in conditions of perturbed activation, and data discriminating the subpopulations) with appropriate error models, and a model selection step. We have finally illustrated the model potential for experimental design (suggestion of targeted new data acquisition) and in silico experiments.

8.1.2 A stochastic model for neural progenitor dynamics in the mouse cerebral cortex

Participants: Frédérique Clément, Jules Olayé.

We have designed and analyzed a stochastic model of embryonic neurogenesis in the mouse cerebral cortex, within the framework of compound Poisson processes, with time-varying, probabilistic fate decisions, and possibly stochastic cell cycle durations 33. The core of the model is the stochastic counterpart of our former deterministic compartmental model based on transport equations 18. The model accounts for the dynamics of different progenitor cell types and neurons. The expectation and variance of the cell number of each type are derived analytically and illustrated through numerical simulations. The effects of stochastic transition rates between cell types, and stochastic duration of the cell division cycle have been investigated sequentially. The model does not only predict the number of neurons, but also their spatial distribution into deeper and upper cortical layers. The model outputs are consistent with experimental data providing the number of neurons and intermediate progenitors according to embryonic age in control and mutant situations.

8.1.3 Modeling compartmentalization in cell signaling networks

Participants: Frédérique Clément, Léo Darrigade, Romain Yvinec.

In the framework of the COMPARTIMENTAGE exploratory action, we have initiated a new thematics on the compartmentalization of cell signaling, with a special focus on the compartimentalization of G Protein-Coupled Receptors

During the CEMRACS 2022 summer school, Romain Yvinec, Erwan Hingant and Juan Carlo supervised a project dedicated to the modeling of compartmentalization within intracellular signaling pathways. Together with Claire Alamichel, Nathan Quiblier, and Saoussen Latrach, they have introduced a new modeling approach for the signaling systems of G protein-coupled receptors, taking into account the compartmentalization of receptors and their effectors, both at the plasma membrane and in dynamic intra-cellular vesicles called endosomes 31. The first building block of the model is about compartment dynamics. It takes into account creation of de novo endosomes, i.e. endocytosis, recycling of endosomes back to the plasma membrane, degradation through transfer into lysosomes, as well as endosome fusion through coagulation dynamics. The second building block corresponds to the biochemical reactions arising in each compartment and to the transfer of molecules between the dynamical compartments. They have proven sufficient conditions to obtain exponentially the ergodicity for the size distribution of intracellular compartments. In parallel, they have designed a finite volume scheme to simulate the model and illustrated two application cases for receptor trafficking and spatially biased second effector signaling.

In the framework of Leo Darrigade's post-doc, we have then designed a piecewise deterministic Markov process of intracellular GPCR trafficking and cAMP production. The stochastic part of the model accounts for the formation, coagulation, fragmentation and recycling of intracellular vesicles carrying the receptors, while the deterministic part of the model represents the chemical reactions mediating the response to the activated receptor. Assuming that the different stochastic jump rates are constant, and that the deterministic flow associated with chemical reactions is exponentially contractive, we have proven that this process converges exponentially to a unique stationary measure. In parallel, we have developped a simplified ODE-based model of receptor signaling and trafficking to analyze experimental time series of cAMP concentration. The goal is to estimate kinetic parameters of receptor trafficking and signaling activity in different compartments. Special care has been devoted to describe rigorously the metadata (e.g. type of ligand, dose, pharmacological perturbations) related to each dataset.

8.1.4 Modeling the inactivation of chromosome-X

Participants: Frédérique Clément, Alice Fohr, Hélène Leman.

In the framework of the master internship of Alice Fohr (M2 Mathématiques pour les Sciences du Vivant, Université Paris-Saclay), we have initiated a new thematics on mathematical modeling for the understanding of X chromosome inactivation. In mammals, females are endowed with two X chromosomes, which could lead to an over-transcription of X-linked genes compared to males. Early during embryonic development, a compensation mechanism settles, which ends up by silencing either the father-inherited or the mother-inherited X chromosome, in a random manner. We have studied the qualitative behavior of an ODE-based toggle-switch model proposed in 67. Using the theory of bifurcation analysis, we have confirmed the numerical results obtained in 67 on the stationary states, from which one can select different configurations of small-size gene networks ensuring the initiation and maintenance of a single X chromosome inactivation. We have then derived the deterministic model as the large-size limit of a continuous-time Markov process representing the unitary events associated with transcription. Finally, we have started investigating the clonal propagation of the X-chromosome inactivation status along cell lineages in the framework of branching processes.

8.2.1 A size-structured model of fish oocytes population dynamics

Participants: Frédérique Clément, Louis Fostier, Romain Yvinec.

Oogenesis is the process of production and maturation of female gametes (oocytes), which ends up in fish with spawning. This process is critical to the survival of species, and particularly sensitive to environmental alterations (e.g. temperature, pollutants). In the framework of Louis Fostier's PhD, we have developed a model representing the oocyte population dynamics, from the earliest phases to egg laying, and taking into account the key stages of physiological and environmental controls. The model formulation is based both on knowledge available in two model fish species, the zebrafish and medaka, and on mathematical models that we have previously developed for mammalian oogenesis. The evolution of the oocyte population is governed by a size-structured population dynamics model, formalized in the form of a transport partial differential equation, with nonlocal nonlinearities on the velocity term and boundary conditions, capturing the effect of interactions between oocytes on the recruitment of new oocytes and on the growth rate. We have shown the well-posedness of the model in its generic formulation, and we have studied the associated stationary problem. Under certain additional hypotheses, concerning the growth rate term, we have determined the long-time behavior of the model, and in particular the local stability of the stationary solutions, by linearization methods.

8.2.2 Mathematical modeling of adipocyte size distributions: identifiability and parameter estimation from rat data

Participants: Léo Meyer, Magali Ribot, Romain Yvinec, and collaborators.

Fat cells, called adipocytes, are designed to regulate energy homeostasis by storing energy in the form of lipids. The adipocyte size distribution is assumed to play a role in the development of obesity-related diseases. The population of adipocytes is characterized by a bimodal size distribution. We have proposed a model based on a partial differential equations to describe the adipocyte size distribution 35. The model includes a description of the lipid fluxes and cell size fluctuations. From the formulation of a stationary solution we can obtain a fast computation of bimodal distributions. We have investigated the parameter identifiability and estimated parameter values with the CMA-ES algorithm. We have first validated the procedure on synthetic data, then estimated parameter values with experimental data of thirty-two rats. We have discussed the estimated parameter values and their variability within the population, as well as the relation between estimated values and their biological significance. Finally, a sensitivity analysis has been performed to specify the influence of parameters on the cell size distribution and explain the differences between the model and measurements. The proposed framework enables the characterization of adipocyte size distribution with four parameters and can be easily adapted to measurements of cell size distribution in different health conditions.

8.2.3 A Lifschitz-Slyozov type model for adipocyte size dynamics : limit from Becker-Döring system and numerical simulation

Participants: Léo Meyer, Magali Ribot, Romain Yvinec, and collaborators.

Biological data show that the size distribution of adipocytes follows a bimodal distribution. In 39, we have introduced a Lifshitz-Slyozov type model, based on a transport partial differential equation, for the dynamics of the size distribution of adipocytes. We have proven a new convergence result from the related Becker-Döring model, a system composed of several ordinary differential equations, toward mild solutions of the Lifshitz-Slyozov model using distribution tail techniques. This result allowed us to propose a new advective-diffusive model, the second-order diffusive Lifshitz-Slyozov model, which is expected to better fit the experimental data. Numerical simulations of the solutions to the diffusive Lifshitz-Slyozov model have been performed using a well-balanced scheme and the model outputs have been compared to solutions to the transport model. The simulations show that both bimodal and unimodal profiles can be reached asymptotically, depending on several parameters. We put in evidence that the asymptotic profile for the second-order system does not depend on initial conditions, unlike for the transport Lifshitz-Slyozov model.

8.2.4 Long-time asymptotic of the Lifshitz-Slyozov equation with nucleation

Participants: Romain Yvinec, and collaborators.

We have studied the Lifshitz-Slyozov model with inflow boundary conditions of nucleation type 23. We have shown that, for a collection of representative rate functions, the size distributions approach degenerate states concentrated at zero size for sufficiently large times. The proof relies on monotonicity properties of some quantities associated with an entropy functional. Moreover, we have given numerical evidence on the fact that the convergence rate to the goal state is algebraic in time. Besides their mathematical interest, these results can be relevant for the interpretation of experimental data.

8.2.5 Some remarks about the well-posedness of Lifshitz-Slyozov equations with nucleation kinetics

Participants: Romain Yvinec, and collaborators.

The Lifshitz-Slyozov model is a nonlocal transport equation that can describe certain types of phase transitions in terms of the temporal evolution of a mixture of monomers and aggregates. Most applications of this model so far do not require boundary conditions. However, there is a recent interest in situations where a boundary condition might be needed-e.g. in the context of protein polymerization phenomena. Actually, the boundary condition may change dynamically in time, depending on an activation threshold for the monomer concentration. This new setting raises a number of mathematical difficulties for which the existing literature is scarce. In 32, we have constructed examples of solutions for which the boundary condition becomes activated (resp. deactivated) dynamically in time. We also discussed how to approach the well-posedness problem for such situations.

8.3.1 Modeling the interplay between the gut microbiota and its host : application to the analysis of diet impact on symbiosis

Participants: Marie Haghebaert, Béatrice Laroche, Lorenzo Sala, and collaborators.

The health and well-being of a host are deeply influenced by the interactions with its gut microbiota. Diet, especially the amount of fiber intake, plays a pivotal role in modulating these interactions impacting microbiota composition and functionality. We have introduced a novel mathematical model 37, designed to delve into these interactions, by integrating dynamics of the colonic epithelial crypt, bacterial metabolic functions and sensitivity to inflammation as well as colon flows in a transverse colon section. Unique features of our model include accounting for metabolic shifts in epithelial cells based on butyrate and hydrogen sulfide concentrations, representing the effect of innate immune pattern recognition receptors activation in epithelial cells, capturing bacterial oxygen tolerance based on data analysis, and considering the effect of antimicrobial peptides on the microbiota. Using our model, we show a proof-of-concept that a high-protein, low-fiber diet intensifies dysbiosis and compromises symbiotic resilience. Our simulation results highlight the critical role of adequate butyrate concentrations in maintaining mature epithelial crypts. Through differential simulations focused on varying fiber and protein inputs, our study offers insights into the system's resilience following the onset of dysbiosis. The present model, while having room for enhancement, offers essential understanding of elements such as oxygen levels, the breakdown of fiber and protein, and the basic mechanisms of innate immunity within the colon environment.

8.3.2 Deterministic limit of a PDMP model of epithelial tissue interacting with diffusing chemicals and application to the intestinal crypt

Participants: Léo Darrigade, Béatrice Laroche, Simon Labarthe.

Mathematical models of biological tissues are a promising tool for multiscale data integration, computational experiments and system biology approaches. While some data and insights are rooted at the cell level, macroscopic mechanisms emerge and are observed at the tissue scale, rendering tissue modeling an inherently multiscale process. As a consequence, tissue models can be broadly categorized as either individual-based or continuous population-based. In 34, we have introduced a generic individual-based model of epithelial tissue including the main regulation processes such as cell division, differentiation, migration and death, together with cell-cell mechanical interactions. We have also considered the coupling with diffusing molecules. The model is a measure-valued piecewise-deterministic Markov process, coupled with reaction-diffusion PDEs. The well-posedness of the model is assessed, and the large population deterministic limit is rigorously derived. Finally, numerical experiments are conducted: the model is applied to the context of epithelial tissues in the intestinal crypt and the convergence towards the deterministic model is illustrated numerically.

8.3.3 Study of the numerical method for an inverse problem of a simplified intestinal crypt

Participants: Marie Haghebaert, Béatrice Laroche, Mauricio Sepúldeva.

We have considered the study of an inverse problem for an intestinal crypt model 38. The original model is based on the interaction of epithelial cells with microbiota-derived chemicals diffusing in the crypt from the gut lumen. The five types of cells considered in the original model were reduced in this work to three types of cells for simplifications of the inverse problem. The inverse problem consists in determining the shape of the secretory cells of the deep crypt from observations of the stem cells and progenitor cells at a fixed time. The method used is the calculation of the adjoint state associated with the second-order BGK numerical scheme, which allows calculating the critical points of the Lagrangian associated with the inverse problem, and applying a gradient method in order to minimize the cost function. The algorithm is described, and some numerical examples are given.

8.4.1 Four functional profiles for fiber and mucin metabolism in the human gut microbiome

Participants: Simon Labarthe, Béatrice Laroche, and collaborators.

Deciphering the complex interactions between the gut microbiome and host requires evolved analysis methods focusing on the microbial ecosystem functions. We have integrated a priori knowledge on anaerobic microbiology with statistical learning to design synthetic profiles of fiber degradation from metagenomic analyses 26. We have identified four distinct functional profiles related to diet, dysbiosis, inflammation and disease. We have used non-negative matrix factorization to mine metagenomic datasets, after selecting manually 91 KEGG orthologies and 33 glycoside hydrolases, further aggregated in 101 functional descriptors. The profiles were identified from a training set of 1153 samples and thoroughly validated on a large database of 2571 unseen samples from 5 external metagenomic cohorts. Profiles 1 and  2 are the main contributors to the fiber-degradation-related metagenome. Profile 1 takes over Profile 2 in healthy samples, and the unbalance of these profiles characterizes dysbiotic samples. Profile 3 takes over Profile 2 during Crohn’s disease, inducing functional reorientations towards unusual metabolism such as fucose and H2S degradation or propionate, acetone and butanediol production. Profile 4 gathers under-represented functions, like methanogenesis. Two taxonomic makes up of the profiles were investigated, using either the covariation of 203 prevalent genomes or metagenomic species, both providing consistent results with their functional characteristics. It appeared that Profiles 1 and 2 were respectively mainly composed of bacteria from the phyla Bacteroidetes and Firmicutes, while Profile 3 is representative of Proteobacteria and Profile 4 of Methanogens.

8.4.2 Harnessing Fc/FcRn Affinity Data from Patents with Different Machine Learning Methods

Participants: Anne Poupon, and collaborators.

Monoclonal antibodies are biopharmaceuticals with a very long half-life due to the binding of their Fc portion to the neonatal receptor (FcRn), a pharmacokinetic property that can be further improved through engineering of the Fc portion, as demonstrated by the approval of several new drugs. Many Fc variants with increased binding to FcRn have been found using different methods, such as structure-guided design, random mutagenesis, or a combination of both, and are described in the literature as well as in patents. Our hypothesis is that this material could be subjected to a machine learning approach in order to generate new variants with similar properties. We therefore compiled 1323 Fc variants affecting the affinity for FcRn, which were disclosed in twenty patents. These data were used to train several algorithms, with two different models, in order to predict the affinity for FcRn of new randomly generated Fc variants 24. To determine which algorithm was the most robust, we first assessed the correlation between measured and predicted affinity in a 10-fold cross-validation test. We then generated variants by in silico random mutagenesis and compared the prediction made by the different algorithms. As a final validation, we produced variants, not described in any patent, and compared the predicted affinity with the experimental binding affinities measured by surface plasmon resonance (SPR). The best mean absolute error (MAE) between predicted and experimental values was obtained with a support vector regressor (SVR) using six features and trained on 1251 examples. With this setting, the error on the log(KD) was less than 0.17. The obtained results show that such an approach could be used to find new variants with better half-life properties that are different from those already extensively used in therapeutic antibody development.

8.4.3 Maching Learning Models on Time Series Data to predict the behavior of the Bioluminescence Resonance Energy Transfer

Participants: Misbah Razzaq, Pamela Romero, Romain Yvinec.

In the framework of the international internship of Pamela Romero, we have used Machine Learning to predict BRET time series in the context of cell signaling. Bioluminescence Resonance Energy Transfer (BRET) is used in to measure dynamic events on the molecular scale, such as protein-protein interactions. We have selected Random Forest Regression models and tested different numerical experiments. The first case was based on a point-to-point prediction: for each time step in the series the next one is predicted, which requires knowing a lot of information, not available in practice. The second case introduced a feedback in the prediction: the result of the previous prediction is used as an input for the current prediction, which requires knowing only the first point of the time series, a much more realistic situation. The third case corresponds to a prediction spanning multiple time steps. The inputs of the different test cases are the BRET time series, and relative information on the cell signaling experiments, such as the nature and dose of the ligand (stimulus), the type of receptor, and possible pharmacological perturbations. In all three experiments, we obtained good results in the testing set with errors close to zero and accuracy between 80% and 98%.

8.5.1 A single domain intrabody targeting the follicle-stimulating hormone receptor (FSHR) impacts FSH-induced G protein-dependent signalling

Participants: Pascale Crépieux, Frédéric Jean-Alphonse, Eric Reiter, and collaborators.

Intracellular variable fragments from heavy-chain antibody from camelids (intra-VHH) have been successfully used as chaperones to solve the 3D structure of active G protein-coupled receptors bound to their transducers. However, their effect on signaling has been poorly explored, although they may provide a better understanding on the relationships between receptor conformation and activity. We have isolated and characterized iPRC1, the first intra-VHH recognizing a member of the large glycoprotein hormone receptors family, the follicle-stimulating hormone receptor (FSHR) 27. This intra-VHH recognizes the third intracellular loop of FSHR and decreases cAMP production in response to FSH, without altering G$\alpha$s recruitment. Hence, iPRC1 behaves as an allosteric modulator and provides a new tool to complete structure/activity studies performed so far on this receptor.

8.5.2 Towards the convergent therapeutic potential of G protein‐coupled receptors in autism spectrum disorders

Participants: Pascale Crépieux, Xavier Leray, and collaborators.

Autism spectrum disorders (ASDs) are diagnosed in 1/100 children worldwide, based on two core symptoms: deficits in social interaction and communication, and stereotyped behaviors. G protein-coupled receptors (GPCRs) are the largest family of cell surface receptors that transduce extracellular signals to convergent intracellular signaling and downstream cellular responses that are commonly dysregulated in ASD. Despite hundreds of GPCRs being expressed in the brain, only 23 are genetically associated with ASD according to the Simons Foundation Autism Research Initiative (SFARI) gene database: oxytocin OTR; vasopressin V${}_{1\mathrm{A}}$ and V${}_{1\mathrm{B}}$ ; metabotropic glutamate mGlu${}_5$ and mGlu${}_7$ ; GABA${}_{\mathrm{B}2}$ ; dopamine D${}_1$, D${}_2$ and D${}_3$ ; serotoninergic 5-HT${}_{1\mathrm{B}}$ ; $\beta$ 2-adrenoceptor; cholinergic M${}_3$ ; adenosine A${}_{2\mathrm{A}}$ and A${}_3$ ; angiotensin AT${}_2$ ; cannabinoid CB${}_1$ ; chemokine CX${}_3$ CR1; orphan GPR37 and GPR85; and olfactory OR1C1, OR2M4, OR2T10 and OR52M1. We have reviewed the therapeutic potential of these 23 GPCRs, as well as 5-HT${}_{2A}$and 5-HT${}_7$ , for ASD 22. For each GPCR, we discuss its genetic association, genetic and pharmacological manipulation in animal models, pharmacopoeia for core symptoms of ASD and rank them based on these factors. Among these GPCRs, we highlight D${}_2$ , 5-HT${}_{2\mathrm{A}}$ , CB${}_1$ , OTR and V${}_{1\mathrm{A}}$ as the more promising targets for ASD. We discuss that the dysregulation of GPCRs and their signaling is a convergent pathological mechanism of ASD. Their therapeutic potential has only begun as multiple GPCRs could mitigate ASD.

9.1.1 Associate Teams in the framework of an Inria International Lab or in the framework of an Inria International Program

9.1.2 Participation in other International Programs

• ECOS SUD-CHILI 2020 : ECOS n° C20E03, “Coarsening dynamics: numerical and theoretical analysis of the Lifshitz-Slyozov equation with nucleation and applications to biology.” PIs: Romain Yvinec and Mauricio Sepúlveda (Universidad de Concepción, Chile)
• i-GPCRNet, International Research Network (IRN) on GPCRs, involved musca members: Pascale Crépieux , Frédéric Jean-Alphonse , Eric Reiter , Romain Yvinec
• Bill & Melinda Gates Foundation, ContraBody (2021-2025, PI Eric Reiter , 1.8 M US$) “Non-hormonal contraception by nanobody produced from within the body”. In partnership with University of Modena E Regio Emilia, Italy, MabSilico, France and InCellArt, France. Involved MUSCA members : Eric Reiter , Pascale Crépieux , Frédéric Jean-Alphonse , Romain Yvinec
• Medical Research Council, MICA (2022-2025, PI Waljit Dhillo, 642k€) “Investigating kisspeptin receptor signalling to improve the treatment of reproductive disease”. Involved MUSCA member: Eric Reiter

9.2.1 Visits of international scientists

9.2.2 Visits to international teams

9.3.1 H2020 projects

• ERC Advanced grant, Homo.Symbiosus (2019-2024, PI Joël Doré, 2.5 M€) “Assessing, preserving and restoring man-microbes symbiosis”. Involved MUSCA member: Béatrice Laroche .
• ERC Starting grant, Therautism (2020-2024, PI Lucie Pellissier, 1.5 M€) “New molecular targets and proof-of-concept therapies for Autism Spectrum Disorders”. Involved MUSCA member: Pascale Crépieux .
• ERNEST (European Research Network on Signal transduction) COST Action 18133.

10.1.1 Scientific events: organization

10.1.2 Scientific events: selection

10.1.3 Journal

10.1.4 Invited and contributed talks

Frédérique Clément

• Introduction to the development of ovarian follicles, Kickoff ai4scmed, PEPR 22-PESN-0002, September 26, Paris

Léo Darrigade

• Compartimentation cellulaire et signalisation des GPCRs at Journée Institut Denis Poisson - PRC, July 13, Orléans
• Modeling of the compartmentalized GPCR signaling, 3rd International I-GPCR NET meeting, October 25-27, Strasbourg
• Modeling intracellular compartmentalized GPCR signaling, poster communication, Journées Math Bio Santé, November 29- December 01, Marne La Vallée

Louis Fostier

• Un modèle de dynamique de population cellulaire pour l'ovogenèse des poissons, Journées Math Bio Santé, November 29- December 01, Marne La Vallée
• Fish oogenesis modeling: Oocyte population dynamics, poster communication, ReproSciences 2023, May 03-05, Paris
• Nested neural SINDy approach, together with Clément Flint and Reyhaneh Hashemi, closure of the CEMRACS 2023 Hackathon, August 24, Marseille

Eric Reiter

• Development of nanobodies to allosterically modulate the follicle stimulating hormone receptor, Bill & Melinda Gates Foundation, Nonhomonal Contraceptive Discovery Program Meeting, April 26, Cornell University, Ithaca, USA
• Des fragments d’anticorps pour contrôler la reproduction sans injecter d’hormone, Colloque Biotechnocentre, October 19, Nouans-le-Fuzelier, France

Mauricio Sepúlveda

• Inverse problem for an intestinal crypt model, CFR23 Control and Related Fields conference, March 27-29, Sevilla, Spain
• Inverse problem for an intestinal crypt model, PDEMAS Days, March 27-29, Granada, Spain
• Inverse problem for an intestinal crypt model, Mathematics Days of the South Zone, April 17-19, Santiago, Chile
• Inverse problem for an intestinal crypt model, World Conference on Physics and Mathematics, May 22-23, Berlin, Germany
• Inverse problems for some biological models, 5th workshop on Mathematics, Computer Science and Complex systems, July 14-15, Essaouira, Marroco

10.1.5 Leadership within the scientific community

Frédérique Clément

• expert of ITMO BCDE
• member of the steering committee of RT REPRO
• member of the scientific board of PIXANIM (Phénotypage par Imagerie in/eX vivo de l'ANImal à la Molécule)
• scientific member of the FC3R COR

Pascale Crépieux

• member (and board member) of CNRS section 24 , “Physiologie, physiopathologie, biologie du cancer”

Frédéric Jean-Alphonse

• coordinator of Key Question 1 (How can target activity be modulated through antibody binding?), LabEx MAbImprove
• member of the Early career scientist comittee (ECS) at the IRN iGPCRnet

Béatrice Laroche

• member of the Steering Committee of the INRAE metagrogram HOLOFLUX

Anne Poupon

• coordinator of “Central Development Instrument 1 (Interdisciplinary Innovation)”, LabEx MAbImprove

Magali Ribot

• co-head of the SMAI group SMAI-MABIOME dedicated to maths for biology and medicine
• member of SMAI scientific committee
• member of the GDR MATHSAV scientific committee

Romain Yvinec

• co-head of WP “Biomathematics, Bioinformatics and Biophysics for Reproduction”, GDR 3606 REPRO
• member of the Directory committee of the i-GPCRnet International Research Network (IRN)

10.1.6 Scientific expertise

• Frédérique Clément , reviewer for the Swiss National Fundation for Science
• Pascale Crépieux , reviewer for BPI-France, ANSES, Medical Research Council UK
• Romain Yvinec , member of the CE 45: Interfaces: mathematics, digital sciences–biology, health, ANR AAPG 2023
• Magali Ribot , member of the selection boards for the recruitment of a professor (Université de Tours), and associate professors (Université de Marseille et Université Paris Cité) ; member of the admission board for the recruitment of Chargés de Recherche, CNRS, section 41

10.1.7 Research administration

• Frédérique Clément is invited member of the scientific council of Graduate School Life Sciences and Health of University Paris-Saclay, and member of Bureau du comité des équipes-projets du Centre Inria de Saclay
• Béatrice Laroche is director of MaIAGE
• Léo Meyer was a PhD students' representative in the council of Doctoral School MIPTIS (Mathématiques, Informatique, Physique Théorique et Ingénierie des Systèmes)
• Eric Reiter is deputy director of UMR PRC
• Magali Ribot is deputy director of Institut Denis Poisson, UMR, Universités d’Orléans–Tours, and member of CIRM administrative committee
• Romain Yvinec is co-head of the Bios team in UMR PRC

10.2.1 Teaching

• Pascale Crépieux , M2 Biology of Reproduction, Université de Tours (4h)
• Pascale Crépieux , M2 Infectiology, Immunity, Vaccinology and Biopharmaceuticals, Université de Tours (4h)
• Pascale Crépieux , M2 Physiopathology, Université de Tours (4h)
• Louis Fostier , L1 Computer Science, Université de Tours, Algebra and Analysis (54h)
• Léo Meyer , L3 Mathematics, Université d'Orléans, Numerical tools (32h)
• Eric Reiter , M2 Infectiology, Immunity, Vaccinology and Biopharmaceuticals, Université de Tours (4h)
• Eric Reiter , M2 Physiopathology, Université de Tours (2h)
• Magali Ribot , L3 Numerical analysis, Université d’Orléans (52h)
• Magali Ribot , M2 Modeling for the agrégation de mathématiques, Université de Tours (38h)
• Magali Ribot , M1 Scientific computing and modeling, Université d’Orléans (30h)
• Magali Ribot , M2 Lessons to prepare the agrégation interne de mathématiques, Université d’Orléans (20h)

10.2.2 Supervision

• PhD: Camille Gauthier, “Manipulation of the activity and physiology of LH receptor through a small fragment of antibody”, defended on December 7, supervisors: Pascale Crépieux and Eric Reiter
• PhD: Marie Haghebaert, “Tools and methods for modeling the dynamics of complex microbial ecosystems from temporal experimental observations: application to the dynamics of the intestinal microbiota”, defended on December 20, supervisor: Béatrice Laroche
• PhD: Léo Meyer, “Modeling and analysis of models for adipocyte growth”, defended on September 09, supervisors: Magali Ribot and Romain Yvinec
• PhD: Pauline Raynaud, “Intracellular antibodies to explore the relationships between conformations and activity of hormone receptors, and their application in reverse pharmacology”, defended on December 12, supervisors: Pascale Crépieux and Gilles Bruneau
• PhD: Anielka Zehnaker, “Selective modulation of FSH receptor signaling pathways in vivo, consequences on ovarian and testicular functions ”, defended on December 12, supervisor: Eric Reiter
• PhD in progress: Marlène Davilma, “Role of miRNAs in the control of oocyte reserve in fish”, started October 2023, supervisors: Frédérique Clément and Violette Thermes
• PhD in progress: Louis Fostier, “Multiscale mathematical modeling of oogenesis in fish”, started November 2022, supervisors: Frédérique Clément and Romain Yvinec , associate supervisor: Violette Thermes
• PhD in progress: Juliette Gourdon, “Manipulation of the intracellular traffic and endosomal signaling of gonadotropin receptors, LH/CGR and FSHR, by nanobodies: deciphering the molecular mechanisms and the consequences on reproduction”, started October 2021, supervisors: Eric Reiter and Frédéric Jean-Alphonse
• PhD in progress: Paguiel Hossie, “Fixation and competition within the gut microbiota”, started October 2022, supervisors : Cécile Carrère and Magali Ribot
• PhD in progress: Marion Meutelet, “Study of convection-reaction-diffusion PDEs with membrane transmission conditions” started October 2023, supervisors : Boris Andreainov and Magali Ribot
• PhD in progress: Eleonora Pastremoli, “Towards a digital twin of the gut microbiota: a multidisciplinary approach for an in-depth understanding of composition, function and interaction with the host”, started October 2023, supervisors : Béatrice Laroche and Lorenzo Sala
• PhD follow-up committee of Simone Nati Poltri (INRIA - Université de Bordeaux), member Magali Ribot
• PhD follow-up committee of Tu-Ky Ly (ED ABIES), members Frédérique Clément and Romain Yvinec
• Master internship: Lucille Berthet, M1 Biologie de la Reproduction, Université de Tours, supervisor: Pascale Crépieux
• Master internship: Zoé Chamard, M2 Infectiology, Immunity, Vaccinology and Biopharmaceuticals, Université de Tours, supervisor: Eric Reiter
• Master internship: Alice Fohr, M2 Mathématiques pour les Sciences du Vivant, Université Paris-Saclay, supervisors: Frédérique Clément and Hélène Leman
• Master internship: Chloé Weckel, M2 Mathématiques, Données et apprentissage, Université Paris Cité, supervisor: Romain Yvinec
• International internship: Pamela Romero Jofré, Master in Computer Science, Master of Science in Engineerig, Pontificia Universidad Católica de Chile, supervisors: M. Razzaq and Romain Yvinec
• CEMRACS 2023 Hackathon, July 24-August 25, collective project on “Estimation of interactions in microbial communities via a neural network-based generalized smoothing algorithm”, supervisors: Béatrice Laroche and Lorenzo Sala

10.2.3 Juries

Béatrice Laroche

• PhD jury of Clotilde Djuikem, Université Côte d'Azur, January 5

Frédérique Clément

• PhD Jury of Manon Lesage (referee), Université de Rennes 1, January 26
• HDR Jury of Xavier Druart, Université de Tours, December 05

Magali Ribot

• PhD Jury of Sébastien Tran Tien (referee), Université Claude Bernard - Lyon 1 , July 3
• PhD Jury of Pedro Jaramillo, INRIA - Université de Bordeaux, December 8
• PhD Jury of Marie Haghebaert, INRAE - Université Paris Saclay, December 20
• HDR Jury of Annabelle Collin, INRIA - Université de Bordeaux, December 7
• HDR Jury of Vincent Perrollaz, Université de Tours, December 18

10.3.1 Articles and contents

Explorations au coeur du système reproducteur, L'Edition de l'Université Paris-Saclay #20 Hiver 2022/2023

Des chercheurs italiens en immersion dans l’unité PRC, e-Confluence, Journal interne du Centre INRAE Val-de-Loire, n°12, Juillet 2023

Pharmacologie réverse à l'aide d'anticorps intracellulaires anti-RFSH actif, Echosciences

10.3.2 Education

Magali Ribot was a member of the national olympiades jury of mathematics for high school students in Première

International journals

• 22 articleA.Anil Annamneedi, C.Caroline Gora, A.Ana Dudas, X.Xavier Leray, V.Véronique Bozon, P.Pascale Crépieux and L. P.Lucie P. Pellissier. Towards the convergent therapeutic potential of G protein‐coupled receptors in autism spectrum disorders.British Journal of Pharmacology2023HALDOIback to text
• 23 articleJ.Juan Calvo, E.Erwan Hingant and R.Romain Yvinec. Long-time asymptotic of the Lifshitz-Slyozov equation with nucleation.Kinetic and Related Models December 2023HALDOIback to text
• 24 articleC.Christophe Dumet, M.Martine Pugnière, C.Corinne Henriquet, V.Valérie Gouilleux-Gruart, A.Anne Poupon and H.Hervé Watier. Harnessing Fc/FcRn affinity data from patents with different machine learning methods.International Journal of Molecular Sciences246March 2023, 5724HALDOIback to text
• 25 articleD.Danièle Klett, L.Lucie Pellissier, D.Didier Lomet, F.Flavie Derouin-Tochon, V.Vincent Robert, T. M.Thi Mong Diep Nguyen, A.Anne Duittoz, E.Eric Reiter, Y.Yann Locatelli, J.Joëlle Dupont, H.Hugues Dardente, F.Frédéric Jean-Alphonse and Y.Yves Combarnous. Highly-Sensitive In Vitro Bioassays for FSH, TSH, PTH, Kp, and OT in Addition to LH in Mouse Leydig Tumor Cell.International Journal of Molecular Sciences24152023, 12047HALDOI
• 26 articleS.Simon Labarthe, S.Sandra Plancade, S.Sébastien Raguideau, F.Florian Plaza Oñate, E.Emmanuelle Le Chatelier, M.Marion Leclerc and B.Béatrice Laroche. Four functional profiles for fibre and mucin metabolism in the human gut microbiome.Microbiome111December 2023, 231HALDOIback to text
• 27 articleP.Pauline Raynaud, V.Vinesh Jugnarain, O.Océane Vaugrente, A.Amandine Vallet, T.Thomas Boulo, C.Camille Gauthier, A.Asuka Inoue, N.Nathalie Sibille, C.Christophe Gauthier, F.Frédéric Jean-Alphonse, E.Eric Reiter, P.Pascale Crépieux and G.Gilles Bruneau. A single domain intrabody targeting the follicle-stimulating hormone receptor (FSHR) impacts FSH-induced G protein-dependent signalling.FEBS LettersAugust 2023HALDOIback to text
• 28 articleA.Anielka Zehnaker, A.Amandine Vallet, J.Juliette Gourdon, C.Caterina Sarti, V.Vinesh Jugnarain, M.Maya Haj Hassan, L.Laetitia Mathias, C.Camille Gauthier, P.Pauline Raynaud, T.Thomas Boulo, L.Linda Beauclair, Y.Yves Bigot, L.Livio Casarini, P.Pascale Crépieux, A.Anne Poupon, B.Benoît Piégu, F.Frédéric Jean-Alphonse, G.Gilles Bruneau and É.Éric Reiter. Combined Multiplexed Phage Display, High-Throughput Sequencing, and Functional Assays as a Platform for Identifying Modulatory VHHs Targeting the FSHR.International Journal of Molecular Sciences2421November 2023, 15961HALDOI

Conferences without proceedings

• 29 inproceedingsF.Frédérique Clément and R.Romain Yvinec. Comparative dynamics of female germ cell populations : insight from imaging and multiscale modeling.Journées INRAE-INRIA 2023Nancy, FranceJuly 2023HAL
• 30 inproceedingsR.Romain Yvinec. Time scale separation in life-long ovarian follicles population dynamics model.Séminar EDP/ProbaStat Laboratoire de Mathématiques et Applications (LMA) de PoitiersPoitiers, FranceMarch 2023HAL

Reports & preprints

• 31 miscC.Claire Alamichel, J.Juan Calvo, E.Erwan Hingant, S.Saoussen Latrach, N.Nathan Quiblier and R.Romain Yvinec. Modeling compartmentalization within intracellular signaling pathway.January 2024HALback to text
• 32 miscJ.Juan Calvo, E.Erwan Hingant and R.Romain Yvinec. SOME REMARKS ABOUT THE WELL-POSEDNESS OF LIFSHITZ-SLYOZOV'S EQUATIONS WITH NUCLEATION KINETICS.May 2023HALback to text
• 33 miscF.Frédérique Clément and J.Jules Olayé. A stochastic model for neural progenitor dynamics in the mouse cerebral cortex.December 2023HALback to text
• 34 miscL.Léo Darrigade, S.Simon Labarthe and B.Béatrice Laroche. Deterministic limit of a PDMP model of epithelial tissue interacting with diffusing chemicals and application to the intestinal crypt.December 2023HALback to text
• 35 miscA.-S.Anne-Sophie Giacobbi, L.Leo Meyer, M.Magali Ribot, R.Romain Yvinec, H.Hedi Soula and C.Chloe Audebert. Mathematical modeling of adipocyte size distributions: identifiability and parameter estimation from rat data.September 2023HALback to text
• 36 miscC.Caroline Gora, A.Ana Dudas, L.Lucas Court, A.Anil Annamneedi, G.Gaëlle Lefort, T.-S.Thiago-Seike Picoreti-Nakahara, N.Nicolas Azzopardi, A.Adrien Acquistapace, A.-L.Anne-Lyse Lainé, A.-C.Anne-Charlotte Trouillet, L.Lucile Drobecq, E.Emmanuel Pecnard, B.Benoit Piegu, P.Pascale Crépieux, P.Pablo Chamero and L. P.Lucie P. Pellissier. Effect of the social environment on olfaction and social skills in WT and mouse model of autism: Social isolation normalizes Shank3 knockout phenotype.November 2023HAL
• 37 miscM.Marie Haghebaert, B.Béatrice Laroche, L.Lorenzo Sala, S.Stanislas Mondot and J.Joël Doré. Modelling the interplay between the gut microbiota and its host : application to the analysis of diet impact on symbiosis.November 2023HALback to text
• 38 miscM.Marie Haghebaert, B.Béatrice Laroche and M. A.Mauricio A. Sepulveda Cortes. Study of the numerical method for an inverse problem of a simplified intestinal crypt.December 2023HALback to text
• 39 miscL.Léo Meyer, M.Magali Ribot and R.Romain Yvinec. A Lifschitz-Slyozov type model for adipocyte size dynamics : limit from Becker-Döring system and numerical simulation.March 2023HALback to text