2023Activity reportProjectTeamMUSCA
RNSR: 202023600V Research center Inria Saclay Centre
 In partnership with:CNRS, INRAE
 Team name: MUltiSCAle population dynamics for physiological systems
 In collaboration with:Physiologie de la reproduction et des comportements (PRC), Mathématiques et Informatique Appliquée du Génome à l'Environnement (MAIAGE)
 Domain:Digital Health, Biology and Earth
 Theme:Modeling and Control for Life Sciences
Keywords
Computer Science and Digital Science
 A3.4. Machine learning and statistics
 A6.1.1. Continuous Modeling (PDE, ODE)
 A6.1.2. Stochastic Modeling
 A6.1.4. Multiscale modeling
 A6.2.1. Numerical analysis of PDE and ODE
 A6.2.3. Probabilistic methods
 A6.3.1. Inverse problems
 A6.3.4. Model reduction
Other Research Topics and Application Domains
 B1.1.2. Molecular and cellular biology
 B1.1.3. Developmental biology
 B1.1.7. Bioinformatics
 B1.1.8. Mathematical biology
 B1.1.10. Systems and synthetic biology
 B2.2. Physiology and diseases
 B2.3. Epidemiology
 B3.6. Ecology
1 Team members, visitors, external collaborators
Research Scientists
 Frédérique Clément [Team leader, INRIA, Senior Researcher, HDR]
 Pascale Crépieux [CNRS, Senior Researcher, HDR]
 Frédéric JeanAlphonse [CNRS, Researcher]
 Béatrice Laroche [INRAE, Senior Researcher, HDR]
 Anne Poupon [CNRS, Senior Researcher, CTO of Mabsilico halftime, HDR]
 Eric Reiter [INRAE, Senior Researcher, HDR]
 Romain Yvinec [INRAE, Senior Researcher, HDR]
Faculty Member
 Magali Ribot [UNIV ORLÉANS, until Aug 2023, On halftime delegation, HDR]
PostDoctoral Fellows
 Léo Darrigade [INRIA, PostDoctoral Fellow]
 Xavier Leray [INRAE, PostDoctoral Fellow, until Jun 2023]
PhD Students
 Louis Fostier [INRAE]
 Marie Haghebaert [INRAE]
 Léo Meyer [UNIV ORLÉANS, until Sep 2023]
Technical Staff
 Guillaume Thomas [INRIA, Engineer, from Oct 2023]
Interns and Apprentices
 Alice Fohr [INRIA, Intern, from Apr 2023 until Aug 2023]
 Pamela Romero [INRIA, Intern, from Mar 2023 until Jun 2023]
Administrative Assistant
 Bahar Carabetta [INRIA]
Visiting Scientist
 Mauricio Sepúlveda [Universidad de Concepción, until Aug 2023]
2 Overall objectives
MUSCA is intrinsically interdisciplinary and brings together applied mathematicians and experimental biologists. We address crucial questions arising from biological processes from a mathematical perspective. Our main research line is grounded on deterministic and stochastic population dynamics, in finite or infinite dimension. We study open methodological issues raised by the modeling, analysis and simulation of multiscale in time and/or space dynamics in the field of physiology, with a special focus on developmental and reproductive biology, and digestive ecophysiology.
3 Research program
3.1 General scientific positioning
The formalism at the heart of our research program is that of structured population dynamics, both in a deterministic and stochastic version. Such a formalism can be used to design multiscale representations (say at the meso and macro levels), possibly embedding twoway (bottomup and topdown) interactions from one level to another. We intend to couple structured population dynamics with dynamics operating on the microscopic level typically large biochemical networks (signaling, metabolism, gene expression), whose outputs can be fed into the higher level models (see section 3.4). To do so, model reduction approaches have to be designed and implemented to properly formulate the “entry points” of the micro dynamics into the meso/macro formalism (e.g. formulation of velocity terms in transport equations, choice of intensities for stochastic processes) and to enable one to traceback as much as possible the variables and parameters from one scale to another. This approach is common to EPC MUSCA's two main applications in reproductive/developmental biology on one side, and microbiota/holobiont biology on the other side, while being applied to different levels of living organisms. Schematically, the meso level corresponds to the cells of a multicellular organism in the former case, and to the individual actors of a microbial community for the latter case.
Our general multiscale framework will be deployed on the study of direct problems as well as inverse problems. In some situations these studies will be accompanied with a postprocessing layer of experimental data, which may be necessary to make the observations compatible with the model state variables, and will be based on dedicated statistical tools. Even if our approach may use classical modeling bricks, it is worth highlighting that the design of de novo models, specifically suited for addressing dedicated physiological questions, is a central part of our activity. Due to their intrinsic multiscale nature (in time and/or space), infinite dimensional formulation (PDE and/or measurevalued stochastic processes) and nonlinear interactions (across scales), such models raise most of the time open questions as far as their mathematical analysis, numerical simulation, and/or parameter calibration. We intend to cope with the resulting methodological issues, possibly in collaboration with external experts when needed to tackle open questions.
3.2 Design, analysis and reduction of networkbased dynamic models
We will deal with models representing dynamic networks, whether in a biochemical or ecological context. The mathematical formulation of these models involve Ordinary Differential Equations (ODE), Piecewise Deterministic Markov Processes (PDMP), or Continuous Time Markov Chains (CTMC). A prototypical example is the (massaction) Chemical Reaction Network (CRN) 54, defined by a set of $d$ species and a directed graph $\mathcal{R}$ on a finite set of stoichiometric vectors $\{y\in {\mathbb{N}}^{d}\}$ (the linear combination of reactant and product species). A subclass of CRN corresponds to a standard interaction network model in ecology, the generalized LotkaVolterra (gLV) model, that lately raised a lot of interest in the analysis of complex microbial communities 77, 49. The model describes the dynamics of interacting (microbial) species through an intrinsic $d$dimensional growth rate vector $\mu $ and a directed weighted interaction graph given by its $d\times d$ matrix $A$. The stochastic versions of these models correspond respectively to a Continuous Time Markov Chain (CTMC) in the discrete statespace ${\mathbb{N}}^{d}$, and a birthdeath jump process. This general class of models is relatively standard in biomathematics 54, 48, yet their theoretical analysis can be challenging due to the need to consider high dimensional models for realistic applications. The curse of dimensionality (state space dimension and number of unknown parameters) makes also very challenging the development of efficient statistical inference strategies.
Most of EPC MUSCA's models based on CRNs deal with (unstructured) population dynamics (complex microbial communities, neutral models in ecology, cell dynamics in developmental processes, macromolecule assemblies), biochemical kinetics and chemical reaction networks (signaling, gene, and metabolic networks), coagulationfragmentation models (in particular BeckerDöring model). Notwithstanding the diversity of our modeling applications, we have to face common methodological issues to study such models, ranging from the theoretical analysis of model behavior to parameter inference.
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 nonautonomous in nature. Understanding to what extent reaction network motifs are able to encode or decode the dynamic properties of a timedependent signal is a particularly challenging theoretical question, which has yet been scarcely addressed, either in simplified casestudies 71,11 or in the framework of “pulsemodulated 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 algebraicdifferential 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 FenichelTikhonov 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 adhoc reduced models in specific cases, using graphbased decomposition of the model 74, combined with the reduction of weakly nonlinear subsystems.
Statistical Inference, Datafitting
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 pseudolikelihood methods will be developed and put in practice 128, using either existing stateofthe art deterministic derivativebased 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 inferencebased 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 loglikelihood 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.
3.3 Design, analysis and simulation of stochastic and deterministic models for structured populations
The mathematical formulation of structured population models involves Partial Differential Equation (PDE) and measurevalued stochastic processes (sometimes referred as IndividualBased Models–IBM). A typical deterministic instance is the McKendrickVon Foerster model, a paragon of (nonlinear) conservation laws. Such a formalism rules the changes in a population density structured in time and (possibly abstract) space variable(s). The transport velocity represents the time evolution of the structured variable for each “individual” in the population, and might depend on the whole population (or a part of it) in the case of nonlinear interactions (for instance by introducing nonlocal terms through moment integrals or convolutions). The source term models the demographic evolution of the population, controlled by birth or death events. One originality of our multiscale approach is that the formulation of velocities and/or source terms may arise, directly or indirectly, from an underlying finitedimension model as presented in section 3.2. According to the nature of the structuring variable, diffusion operators may arise and lead to consider secondorder parabolic PDEs. For finite population dynamics, the stochastic version of these models can be represented using the formalism of Poisson Measuredriven stochastic differential equations.
From the modeling viewpoint, the first challenge to be faced with this class of models yields in the model formulation itself. Obtaining a wellposed and mathematically tractable formulation, that yet faithfully accounts for the “behavioral law” underlying the multiscale dynamics, is not an obvious task.
On one side, stochastic models are suited for situations where relatively few individuals are involved, and they are often easier to formulate intuitively. On the other side, the theoretical analysis of deterministic models is generally more tractable, and provides one with more immediate insight into the population behavior. Hence, the ideal situation is when one can benefit from both the representation richness allowed by stochastic models and the power of analysis applicable to their deterministic counterparts. Such a situation is actually quite rare, due to the technical difficulties associated with obtaining the deterministic limit (except in some linear or weakly nonlinear cases), hence compromises have to be found. The mathematical framework exposed above is directly amenable to multiscale modeling. As such, it is central to the biomathematical bases of MUSCA and transverse to its biological pillars. We develop and/or analyze models for structured cell population dynamics involved in developmental or tissuehomeostasis processes, structured microbial populations involved in ecophysiological systems and molecule assemblies.
As in the case of finite dimension models, the study of these various models involve common methodological issues.
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 wellposedness 19 and longtime 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 casebycase, modeldependent way: general relative entropy 65, 47, measure solution framework 57, 44, 51, martingale techniques 45, finitevolume 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 highdimensional 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 casebycase basis, and they should be handled carefully to obtain rigorous results (appropriate choice of metric topology, a priori estimates).
Statistical inference, Datafitting
The calibration of structured population models is challenging, due to both the infinitedimensional 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 illposed 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.
3.4 Coupling biochemical networks with cell and population dynamics
A major challenge for multiscale systems biology is to rigorously couple intracellular biochemical networks with physiological models (tissue and organic functions) 72, 41, 76, 63. Meeting this challenge requires reconciling very different mathematical formalisms and integrating heterogeneous biological knowledge in order to represent in a common framework biological processes described on very contrasting spatial and temporal scales. On a generic ground, there are numerous methodological challenges associated with this issue (such as model or graph reduction, theoretical and computational connection between different modeling formalisms, integration of heterogenous data, or exploration of the whole parameter space), which are far from being overcome at the moment.
Our strategy is not to face frontally these bottlenecks, but rather to investigate in parallel the two facets of the question, through (i) the modeling of the topology and dynamics of infraindividual networks or dynamics, accounting for individual variability and local spatialization or compartmentalization at the individual level, as encountered for instance in cell signaling; and (ii) the stochastic and/or deterministic multiscale modeling of populations, establishing rigorous link between the individual and population levels. To bridge the gap, the key point is to understand how intracellular (resp. infraindividual) networks produce outputs which can then be fed up in a multicellular (resp. microbial population) framework, in the formulation of terms entering the multiscale master equations. A typical example of such outputs in individual cell modeling is the translation of different (hormonal or metabolic) signaling cues into biological outcomes (such as proliferation, differentiation, apoptosis, or migration). In turn, the dynamics emerging on the whole cell population level feedback onto the individual cell level by tuning the signal inputs qualitatively and quantitatively.
4 Application domains
The multiscale modeling approach described in section 3 is deployed on biological questions arising from developmental and reproductive biology, as well as digestive ecophysiology.
Our main developmental and reproductive thematics are related to gametogenesis, and gonad differentiation and physiology. In females, the gametogenic process of oogenesis (production and maturation of egg cells) is intrinsically coupled with the growth and development of somatic structures called ovarian follicles. Ovarian folliculogenesis is a longlasting developmental and reproductive process characterized by well documented anatomical and functional stages. The proper morphogenesis sequence, as well as the transit times from one stage to another, are finely tuned by signaling cues emanating from the ovaries (especially during early folliculogenesis) and from the hypothalamopituitary axis (especially during late folliculogenesis). The ovarian follicles themselves are involved in either the production or regulation of these signals, so that follicle development is controlled by direct or indirect interactions within the follicle population. We have been having a longstanding interest in the multiscale modeling of follicle development, which we have tackled from a “middleout”, cell dynamicsbased viewpoint 2, completed progressively with morphogenesis processes 17.
On the intracellular level, we are interested in understanding the endocrine dialogue within the hypothalamopituitarygonadal (HPG) axis controling the ovarian function. In multicellular organisms, communication between cells is critical to ensure the proper coordination needed for each physiological function. Cells of glandular organs are able to secrete hormones, which are messengers conveying information through circulatory systems to specific, possibly remote target cells endowed with the proper decoders (hormone receptors). We have settled a systems biology approach combining experimental and computational studies, to study signaling networks, and especially GPCR (G ProteinCoupled Receptor) signaling networks 12. In the HPG axis, we focus on the pituitary hormones FSH (FollicleStimulating Hormone) and LH (Luteinizing Hormone) – also called gonadotropins, which support the double, gametogenic and endocrine functions of the gonads (testes and ovaries). FSH and LH signal onto gonadal cells through GPCRs, FSHR and LHR, anchored in the membrane of their target cells, and trigger intracellular biochemical cascades tuning the cell enzymatic activity, and ultimately controlling gene expression and mRNA translation. Any of these steps can be targeted by pharmacological agents, so that the mechanistic understanding of signaling networks is useful for new drug development.
Our main thematics in digestive ecophysiology are related to the interactions between the host and its microbiota. The gut microbiota, mainly located in the colon, is engaged in a complex dialogue with the large intestinal epithelium of its host, through which important regulatory processes for the host's health and wellbeing take place. Through successive projects, we have developed an integrative model of the gut microbiota at the organ scale, based on the explicit coupling of a population dynamics model of microbial populations involved in fiber degradation with a fluid dynamics model of the luminal content. This modeling framework accounts for the main drivers of the spatial structure of the microbiota, specially focusing on the dietary fiber flow, the epithelial motility, the microbial active swimming and viscosity gradients in the digestive track 16.
Beyond its scientific interest, the ambitious objective of understanding mechanistically the multiscale functioning of physiological systems could also help on the long term to take up societal challenges.
In digestive ecophysiology, microbial communities are fundamental for human and animal wellbeing and ecologic equilibrium. In the gut, robust interactions generate a barrier against pathogens and equilibrated microbiota are crucial for immune balance. Imbalances in the gut microbial populations are associated with chronic inflammation and diseases such as inflammatory bowel disease or obesity. Emergent properties of the interaction network are likely determinant drivers for health and microbiome equilibrium. To use the microbiota as a control lever, we require causal multiscale models to understand how microbial interactions translate into productive, healthy dynamics 20.
In reproductive physiology, there is currently a spectacular revival of experimental investigations (see e.g. 66, 78), which are driven by the major societal challenges associated with maintaining the reproductive capital of individuals, and especially female individuals, whether in a clinical (early ovarian failure of idiopathic or iatrogenic origin in connection with anticancer drugs in young adults and children), breeding (recovery of reproductive longevity and dissemination of genetic progress by the female route), or ecological (conservation of germinal or somatic tissues of endangered species or strains) context. Understanding the intricate (possibly long range and long term) interactions brought to play between the main cell types involved in the gonadal function (germ cells, somatic cells in the gonads, pituitary gland and hypothalamus) also requires a multiscale modeling approach.
5 Social and environmental responsibility
5.1 Impact of research results
Given our positioning in comparative physiology, future outcomes of MUSCA's basic research can be expected in the fields of Medicine, Agronomy (breeding) and Ecophysiology, in a One Health logic. For instance, a deep understanding of female gametogenesis can be instrumental for the clinical management of ovarian aging, the development of sustainable breeding practices, and the monitoring of micropollutant effects on wild species (typically on fish populations). These issues will be especially investigated in the framework of the OVOPAUSE project and they are also implemented as part of our collaboration with INERIS (GinFiz project). In the same spirit, we intend to design methodological and sofware tools for the modelassisted validation of alternatives to hormone use in reproduction control (ovarian stimulation, contraception). This line is driven by the Contrabody project, which has stimulated associated actions such as that dedicated to the automatic assessment of the reproductive status from ovary imaging. In the same spirit, our mechanistic view of the interactions between the host and gut microbiota leads to new approaches of the antibioresistance phenomenon, which is the topic of the PARTHAGE project and has already been the matter of a translational project (COOPERATE). Finally, our systems biology and computational biology approaches dedicated to cell signaling and structural biology clearly target pharmacological design and screening, and, on the long term, have the potential to accelerate and improve drug discovery in the field of reproduction and beyond. Such approaches have proven particularly fruitful with the MabSilico startup (a spinoff of the BIOS group), which continues to interact with BIOS and MUSCA on antibodyrelated projects (SELMAT and Contrabody for example).
6 Highlights of the year
 Six month scientific stay of Prof. Mauricio Sepúldeva (Universidad del Concepción) in the framework of the d'Alembert program from Université ParisSaclay
 Halftime delegation of Prof. Magali Ribot (Université d'Orléans)
 Sabbatic stay of Romain Yvinec in Duke University (from Sept. 2023)
7 New software, platforms, open data
7.1 New software
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 halflife, 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:

Authors:
Frédérique Clément, Hande Gozukan, Christian Poli

Contact:
Frédérique Clément
8 New results
8.1 Deterministic and stochastic compartmental models
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 ODEbased 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, knowledgedriven layer encompassing the earliest events in follicle development. The datadriven 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 knowledgebased, coating layer accounts for cuttingedge studies on the initiation of follicle development around birth. Its salient feature is the coexistence 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 timevarying, 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 ProteinCoupled 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 proteincoupled receptors, taking into account the compartmentalization of receptors and their effectors, both at the plasma membrane and in dynamic intracellular 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 postdoc, 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 ODEbased 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 chromosomeX
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 ParisSaclay), 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 overtranscription of Xlinked genes compared to males. Early during embryonic development, a compensation mechanism settles, which ends up by silencing either the fatherinherited or the motherinherited X chromosome, in a random manner. We have studied the qualitative behavior of an ODEbased toggleswitch 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 smallsize gene networks ensuring the initiation and maintenance of a single X chromosome inactivation. We have then derived the deterministic model as the largesize limit of a continuoustime Markov process representing the unitary events associated with transcription. Finally, we have started investigating the clonal propagation of the Xchromosome inactivation status along cell lineages in the framework of branching processes.
8.2 Sizestructured population dynamics
8.2.1 A sizestructured 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 sizestructured 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 wellposedness 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 longtime 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 obesityrelated 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 CMAES algorithm. We have first validated the procedure on synthetic data, then estimated parameter values with experimental data of thirtytwo 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 LifschitzSlyozov type model for adipocyte size dynamics : limit from BeckerDöring 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 LifshitzSlyozov 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 BeckerDöring model, a system composed of several ordinary differential equations, toward mild solutions of the LifshitzSlyozov model using distribution tail techniques. This result allowed us to propose a new advectivediffusive model, the secondorder diffusive LifshitzSlyozov model, which is expected to better fit the experimental data. Numerical simulations of the solutions to the diffusive LifshitzSlyozov model have been performed using a wellbalanced 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 secondorder system does not depend on initial conditions, unlike for the transport LifshitzSlyozov model.
8.2.4 Longtime asymptotic of the LifshitzSlyozov equation with nucleation
Participants: Romain Yvinec, and collaborators.
We have studied the LifshitzSlyozov 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 wellposedness of LifshitzSlyozov equations with nucleation kinetics
Participants: Romain Yvinec, and collaborators.
The LifshitzSlyozov 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 needede.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 wellposedness problem for such situations.
8.3 Coupling biochemical dynamics with cell population dynamics
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 wellbeing 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 proofofconcept that a highprotein, lowfiber 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 individualbased or continuous populationbased. In 34, we have introduced a generic individualbased model of epithelial tissue including the main regulation processes such as cell division, differentiation, migration and death, together with cellcell mechanical interactions. We have also considered the coupling with diffusing molecules. The model is a measurevalued piecewisedeterministic Markov process, coupled with reactiondiffusion PDEs. The wellposedness 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 microbiotaderived 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 secondorder 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 Computational modeling
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 nonnegative 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 fiberdegradationrelated 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 underrepresented 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 halflife 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 structureguided 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 10fold crossvalidation 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 halflife 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 proteinprotein interactions. We have selected Random Forest Regression models and tested different numerical experiments. The first case was based on a pointtopoint 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 Exploration of signaling networks
8.5.1 A single domain intrabody targeting the folliclestimulating hormone receptor (FSHR) impacts FSHinduced G proteindependent signalling
Participants: Pascale Crépieux, Frédéric JeanAlphonse, Eric Reiter, and collaborators.
Intracellular variable fragments from heavychain antibody from camelids (intraVHH) have been successfully used as chaperones to solve the 3D structure of active G proteincoupled 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 intraVHH recognizing a member of the large glycoprotein hormone receptors family, the folliclestimulating hormone receptor (FSHR) 27. This intraVHH recognizes the third intracellular loop of FSHR and decreases cAMP production in response to FSH, without altering G$\alpha $s recruitment. Hence, iPRC1 behaves as an allosteric modulator and provides a new tool to complete structure/activity studies performed so far on this receptor.
8.5.2 Towards the convergent therapeutic potential of G protein‐coupled receptors in autism spectrum disorders
Participants: Pascale Crépieux, Xavier Leray, and collaborators.
Autism spectrum disorders (ASDs) are diagnosed in 1/100 children worldwide, based on two core symptoms: deficits in social interaction and communication, and stereotyped behaviors. G proteincoupled receptors (GPCRs) are the largest family of cell surface receptors that transduce extracellular signals to convergent intracellular signaling and downstream cellular responses that are commonly dysregulated in ASD. Despite hundreds of GPCRs being expressed in the brain, only 23 are genetically associated with ASD according to the Simons Foundation Autism Research Initiative (SFARI) gene database: oxytocin OTR; vasopressin V${}_{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 5HT${}_{1\mathrm{B}}$ ; $\beta $ 2adrenoceptor; 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 5HT${}_{2A}$and 5HT${}_{7}$ , 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${}_{2}$ , 5HT${}_{2\mathrm{A}}$ , 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 Partnerships and cooperations
9.1 International initiatives
9.1.1 Associate Teams in the framework of an Inria International Lab or in the framework of an Inria International Program
ANACONDA

Title:
Theoretical and numerical ANAlysis of CONservation laws for multicellular DynAmics

Duration:
2021 > 2023

Coordinator:
Mauricio Sepúlveda

Partners:
Universidad de Concepción, Chile

Inria contact:
Romain Yvinec

Summary:
ANACONDA focuses on the analysis of mathematical models dedicated to multicellular dynamics. It is based on the formalism of structured population dynamics, which is formulated as PDE (partial differential equation) conservation laws. We intend to study two main classes of structured populations PDE models, phase separation models (of LifshitzSlyozov type) and moving/freeboundary problems, to investigate respectively biological issues of cellular growth (mainly of adipocytes), and morphogenesis processes (tissue homeostasis of intestinal crypts, development of ovarian follicles). In both cases, thanks to the complementary expertise gathered in the consortium, we aim to perform the theoretical and numerical analysis of the models, design specific numerical schemes, and conceive appropriate strategies for inverse problems, in a synergistic way.
9.1.2 Participation in other International Programs
 ECOS SUDCHILI 2020 : ECOS n° C20E03, “Coarsening dynamics: numerical and theoretical analysis of the LifshitzSlyozov equation with nucleation and applications to biology.” PIs: Romain Yvinec and Mauricio Sepúlveda (Universidad de Concepción, Chile)
 iGPCRNet, International Research Network (IRN) on GPCRs, involved musca members: Pascale Crépieux , Frédéric JeanAlphonse , Eric Reiter , Romain Yvinec
 Bill & Melinda Gates Foundation, ContraBody (20212025, PI Eric Reiter , 1.8 M US$) “Nonhormonal 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 JeanAlphonse , Romain Yvinec
 Medical Research Council, MICA (20222025, PI Waljit Dhillo, 642k€) “Investigating kisspeptin receptor signalling to improve the treatment of reproductive disease”. Involved MUSCA member: Eric Reiter
9.2 International research visitors
9.2.1 Visits of international scientists
International visits to the team

Visitor:
Mohammed Akli Ayoub

Status:
Associate Professor

Institution of origin:
Khalifa University

Country:
United Arabian Emirates

Dates:
JuneAugust (3 months)

Context of the visit:
Collaboration on the direct action of steroid hormones on gonadotropin receptors’ activities

Mobility program/type of mobility:
Le Studium Loire Valley Institute for Advanced Studies, Visiting researcher program. Host MUSCA member: Frédéric JeanAlphonse

Visitor:
Livio Casarini

Status:
Professor

Institution of origin:
University of Modena and Reggio Emilia

Country:
Italy

Dates:
November 2022November 2023

Context of the visit:
Collaboration on antibody fragments targeting ovarian GPCRs to control reproduction

Mobility program/type of mobility:
Le Studium Loire Valley Institute for Advanced Studies, Visiting researcher program. Host MUSCA member: Eric Reiter
9.2.2 Visits to international teams
Sabbatical programme

Musca member:
Romain Yvinec

Visited institution:
Duke University (ÉtatsUnis)

Dates of the stay:
August 14 2023July 14 2024

Topic of the stay:
Multiscale mathematical modeling in reproductive physiology

Funding:
INRAE Phase/DigitBIO/DRI + INRIA Sabbatical program
Research stays abroad
Magali Ribot : one week stay in Roma in December Collaboration with Roberto Natalini and Maya Briani about numerical schemes for PDE set on a network, using some relaxation techniques
9.3 European initiatives
9.3.1 H2020 projects
 ERC Advanced grant, Homo.Symbiosus (20192024, PI Joël Doré, 2.5 M€) “Assessing, preserving and restoring manmicrobes symbiosis”. Involved MUSCA member: Béatrice Laroche .
 ERC Starting grant, Therautism (20202024, PI Lucie Pellissier, 1.5 M€) “New molecular targets and proofofconcept therapies for Autism Spectrum Disorders”. Involved MUSCA member: Pascale Crépieux .
 ERNEST (European Research Network on Signal transduction) COST Action 18133.
9.4 National initiatives
 ANR OVOPAUSE (20222026, PI Romain Yvinec , 447 K€) “Dynamics and control of female germ cell populations: understanding aging through population dynamics models”. Involved MUSCA Members: Frédérique Clément , Pascale Crépieux , Louis Fostier , Frédéric JeanAlphonse , Eric Reiter , Romain Yvinec .
 ANR MOSDER (20222025, PI Frédéric JeanAlphonse , 420 K€) “Multidimensional Organization of Signaling Dynamics Encoded by gonadotropin Receptors”. Involved MUSCA members: Pascale Crépieux , Frédéric JeanAlphonse , Eric Reiter , Romain Yvinec .
 ANR PARTHAGE (20222026, PI Lulla Opatowski, 620 k€) “Prédire la transmission de la résistance au sein et entre les hôtes en combinant modélisation mathématique, génomique et épidémiologie”. Involved MUSCA member: Béatrice Laroche .
 ANR YDOBONAN (20212025, PI Vincent Aucagne, 497 K€) “Mirror Image Nanobodies: pushing forward the potential of enantiomeric proteins for therapeutic and pharmacological applications”. Involved MUSCA member: Eric Reiter .
 ANR PHEROSENSOR (20212026, PI Philippe Lucas, 1492K€) “Early detection of pest insects using pheromone receptorbased olfactory sensors”. Involved MUSCA member: Béatrice Laroche .
 ANR ABLISS (20192023, PI Anne Poupon , 441 K€) “Automating building from Literature of Signalling Systems”. Involved MUSCA members: Anne Poupon , Eric Reiter , Pascale Crépieux , Romain Yvinec .
 LabEx MAbImprove (20112025, PI Hervé Watier). Involved MUSCA members : Eric Reiter , Frédéric JeanAlphonse , Pascale Crépieux , Anne Poupon , Romain Yvinec .
 INRAE metaprogram DIGITBIO, IMAGO project (20222024, PIs Frédéric JeanAlphonse and Béatrice Laroche , 47 K€), “Imagerie et modélisation des dynamiques spatiotemporelles de la signalisation et du trafic des récepteurs couplés aux protéines G (RCPG)”. Involved MUSCA members: all permanent members.
 INRAE metaprogram DIGITBIO, IMMO project (20212023, PIs Violette Thermes and Romain Yvinec , 51.4 K€), “IMagerie et MOdélisation multiéchelles pour la compréhension de la dynamique ovarienne chez le poisson”. Involved MUSCA members: Frédérique Clément , Romain Yvinec .
 INRAE metaprogram HOLOFLUX, MOTHERS project (20232024, PI Florent Kempf). “Monitoring the gut microbiota, resistance against salmonella, animal performance and immune response through an adult, pathogenfree microbiota”. Involved MUSCA members: Béatrice Laroche , Lorenzo Sala .
 ANSES GinFiz project (20212024, PI Rémy Beaudouin), “Gonadal aromatase inhibition and other toxicity pathways leading to Fecundity Inhibition in Zebrafish: from initiating events to population impacts”. Involved MUSCA members: Frédérique Clément , Romain Yvinec .
 Action Exploratoire Inria Compartimentage (20222024, PI Romain Yvinec , 120 K€) : “Imagerie et Modélisation SpatioTemporelles de la Compartimentation des Voies de Signalisation”. Involved MUSCA Members: all permanent members.
9.5 Regional initiatives
 Ambition recherche développement Centre Val de Loire SELMAT (20202023, PI Eric Reiter , 630 K€) “Méthodes in silico pour la sélection et la maturation d’anticorps : développement, validation et application à différentes cibles thérapeutiques”. Involved MUSCA members: Eric Reiter , Pascale Crépieux , Frédéric JeanAlphonse , Romain Yvinec .
 Appel à projet région Centre Val de Loire, INTACT (20192023, PI Pascale Crépieux , 200 K€) “Pharmacologie réverse à l'aide d'anticorps intracellulaires antiRFSH actif”. Involved MUSCA members: Pascale Crépieux , Eric Reiter , Frédéric JeanAlphonse , Anne Poupon , Romain Yvinec . Industrial partner: McSAF, Tours.
10 Dissemination
10.1 Promoting scientific activities
10.1.1 Scientific events: organization
Member of the organizing committees

Frédérique Clément , ReproSciences 2023, May 0305, Paris

Frédéric JeanAlphonse , iGPCRnet annual meeting, October 2527, Strasbourg

Magali Ribot , Journées MathsBioSanté, Université, November 27  December 1, Marne la Vallée

Mauricio Sepúlveda , online Seminars in EDP and Applied Mathematics, Brazil ; INRIACHILE 2023 Scientific Days, December 47, Santiago, Chile
10.1.2 Scientific events: selection
Member of the conference program committees

Frédérique Clément , ReproSciences 2023, May 0305, Paris

Magali Ribot , Member of the selection board, RTR Rouen workshop on maths for biology, June 2830
Reviewer

Magali Ribot , Banff International Research Station 2025 Proposal Submission
10.1.3 Journal
Member of the editorial boards

Pascale Crépieux and Eric Reiter , associate editors Front. Endocrinol.

Romain Yvinec , associate editor J. Math. Biol.
Reviewer  reviewing activities

Frédérique Clément , Biol. Reprod., J. Math. Biol.

Pascale Crépieux , Sci. Rep. Front. Endocrinol.

Eric Reiter , Front. Endocrinol., Sci. Rep., Endocrinology, Proc. Natl. Acad. Sci. USA, eLife, Science, Nature Comm.

Magali Ribot , J. Comp. Phys., J. Math. Anal. Appl.

Romain Yvinec , Stoch. Models, Stoch. Process. Appl., Math. Model. Nat. Phenom., J. Math. Biol., ESAIM Proc., J. Stat. Phys.
10.1.4 Invited and contributed talks
Frédérique Clément

Introduction to the development of ovarian follicles, Kickoff ai4scmed, PEPR 22PESN0002, 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 IGPCR NET meeting, October 2527, 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 0305, 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, NouansleFuzelier, France
Mauricio Sepúlveda

Inverse problem for an intestinal crypt model, CFR23 Control and Related Fields conference, March 2729, Sevilla, Spain

Inverse problem for an intestinal crypt model, PDEMAS Days, March 2729, Granada, Spain

Inverse problem for an intestinal crypt model, Mathematics Days of the South Zone, April 1719, Santiago, Chile

Inverse problem for an intestinal crypt model, World Conference on Physics and Mathematics, May 2223, Berlin, Germany

Inverse problems for some biological models, 5th workshop on Mathematics, Computer Science and Complex systems, July 1415, Essaouira, Marroco
Seminars

Magali Ribot , PDE models on networks
BioMaths seminar, Institut Camille Jordan, Université Lyon 1–Claude Bernard

Léo Meyer , Modeling and analysis of adipocyte size distribution, BioMaths seminar, Institut Camille Jordan, Université Lyon 1–Claude Bernard; INTERFACE team's seminar, Laboratoire JeanAlexandre Dieudonné, Université côte d'azur; MathsBioSanté Seminar, Institut de Mathématiques de Toulouse, Université Toulouse III–Paul Sabatier

Mauricio Sepúlveda , Inverse Problem for an intestinal crypt model, Seminar PDE Analysis and Applications, Université de Lorraine ; LAMFA seminar, Université de Picardie Jules Verne
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 JeanAlphonse
 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
 cohead of the SMAI group SMAIMABIOME dedicated to maths for biology and medicine
 member of SMAI scientific committee
 member of the GDR MATHSAV scientific committee
Romain Yvinec
 cohead of WP “Biomathematics, Bioinformatics and Biophysics for Reproduction”, GDR 3606 REPRO
 member of the Directory committee of the iGPCRnet International Research Network (IRN)
10.1.6 Scientific expertise

Frédérique Clément , reviewer for the Swiss National Fundation for Science

Pascale Crépieux , reviewer for BPIFrance, 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 ParisSaclay, and member of Bureau du comité des équipesprojets 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 cohead of the Bios team in UMR PRC
10.2 Teaching  Supervision  Juries
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 JeanAlphonse

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 convectionreactiondiffusion 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 indepth understanding of composition, function and interaction with the host”, started October 2023, supervisors : Béatrice Laroche and Lorenzo Sala

PhD followup committee of Simone Nati Poltri (INRIA  Université de Bordeaux), member Magali Ribot

PhD followup committee of TuKy 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 ParisSaclay, 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 24August 25, collective project on “Estimation of interactions in microbial communities via a neural networkbased 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 Popularization
10.3.1 Articles and contents
Explorations au coeur du système reproducteur, L'Edition de l'Université ParisSaclay #20 Hiver 2022/2023
Des chercheurs italiens en immersion dans l’unité PRC, eConfluence, Journal interne du Centre INRAE ValdeLoire, n°12, Juillet 2023
Pharmacologie réverse à l'aide d'anticorps intracellulaires antiRFSH actif, Echosciences
10.3.2 Education
Magali Ribot was a member of the national olympiades jury of mathematics for high school students in Première
11 Scientific production
11.1 Major publications
 1 articleA numerical method for kinetic equations with discontinuous equations : application to mathematical modeling of cell dynamics.SIAM Journal on Scientific Computing3562013, 27 pagesHALDOIback to text
 2 articleCellKinetics Based Calibration of a Multiscale Model of Structured Cell Populations in Ovarian Follicles.SIAM Journal on Applied Mathematics7642016, 14711491HALDOIback to textback to text
 3 articleAdaptive mesh refinement strategy for a nonconservative transport problem.ESAIM: Mathematical Modelling and Numerical AnalysisAugust 2014, 1381  1412HALDOIback to text
 4 articleMultiscale population dynamics in reproductive biology: singular perturbation reduction in deterministic and stochastic models.ESAIM: Proceedings and Surveys672020, 7299HALDOIback to text
 5 articleAnalysis and numerical simulation of an inverse problem for a structured cell population dynamics model.Mathematical Biosciences and Engineering164Le DOI n'est pas actif, voir http://www.aimspress.com/article/10.3934/mbe.20191502019, 30183046HALDOIback to text
 6 articleMultiscale modelling of ovarian follicular selection..Progress in Biophysics and Molecular Biology1133December 2013, 398408HALDOIback to text
 7 articleAnalysis and calibration of a linear model for structured cell populations with unidirectional motion : Application to the morphogenesis of ovarian follicles.SIAM Journal on Applied Mathematics791February 2019, 207229HALDOIback to text
 8 articleStochastic nonlinear model for somatic cell population dynamics during ovarian follicle activation.Journal of Mathematical Biology8232021, 152HALDOIback to text
 9 articleQuasi steady state approximation of the small clusters in BeckerDöring equations leads to boundary conditions in the LifshitzSlyozov limit.Communications in Mathematical Sciences1552017, 13531384HALDOIback to textback to text
 10 articleA mixture model for the dynamic of the gut mucus layer.ESAIM: Proceedings55décembre2016, 111130HALDOIback to text
 11 articleInterpreting frequency responses to doseconserved pulsatile input signals in simple cell signaling motifs..PLoS ONE942014, e95613HALDOIback to text

12
articleCompeting G proteincoupled receptor kinases balance G protein and
$$ arrestin signaling..Molecular Systems Biology8June 2012, 117HALDOIback to textback to text  13 articleComputable convergence bounds of series expansions for infinite dimensional linearanalytic systems and application.Automatica5092014, 23342340HALDOIback to text
 14 articleComputation of Convergence Bounds for Volterra Series of LinearAnalytic SingleInput Systems.IEEE Transactions on Automatic Control569September 2011, 20622072HALDOIback to text
 15 articleThe BeckerDoring Process: Pathwise Convergence and Phase Transition Phenomena.Journal of Statistical Physics17752018, 506527HALDOIback to text
 16 articleA mathematical model to investigate the key drivers of the biogeography of the colon microbiota..Journal of Theoretical Biology46272019, 552581HALDOIback to text
 17 articleMultiscale modeling of ovarian follicular development: From follicular morphogenesis to selection for ovulation.Biology of the Cell1086June 2016, 112HALDOIback to text
 18 articleA multiscale mathematical model of cell dynamics during neurogenesis in the mouse cerebral cortex.BMC Bioinformatics201December 2019HALDOIback to text
 19 articleCauchy problem for multiscale conservation laws: Application to structured cell populations.Journal of Mathematical Analysis and Applications40122013, 896  920HALDOIback to textback to text
 20 articleChallenges in microbial ecology: building predictive understanding of community function and dynamics..ISME Journal10Marco Cosentino Lagomarsino (LCQB) is a member of Isaac Newton Institute Fellows consortium.2016, 112HALDOIback to text
 21 articleAdvances in computational modeling approaches of pituitary gonadotropin signaling.Expert Opinion on Drug Discovery1392018, 799813HALDOIback to text
11.2 Publications of the year
International journals
 22 articleTowards the convergent therapeutic potential of G protein‐coupled receptors in autism spectrum disorders.British Journal of Pharmacology2023HALDOIback to text
 23 articleLongtime asymptotic of the LifshitzSlyozov equation with nucleation.Kinetic and Related Models December 2023HALDOIback to text
 24 articleHarnessing Fc/FcRn affinity data from patents with different machine learning methods.International Journal of Molecular Sciences246March 2023, 5724HALDOIback to text
 25 articleHighlySensitive 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 articleFour functional profiles for fibre and mucin metabolism in the human gut microbiome.Microbiome111December 2023, 231HALDOIback to text
 27 articleA single domain intrabody targeting the folliclestimulating hormone receptor (FSHR) impacts FSHinduced G proteindependent signalling.FEBS LettersAugust 2023HALDOIback to text
 28 articleCombined Multiplexed Phage Display, HighThroughput 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 inproceedingsComparative dynamics of female germ cell populations : insight from imaging and multiscale modeling.Journées INRAEINRIA 2023Nancy, FranceJuly 2023HAL
 30 inproceedingsTime scale separation in lifelong ovarian follicles population dynamics model.Séminar EDP/ProbaStat Laboratoire de Mathématiques et Applications (LMA) de PoitiersPoitiers, FranceMarch 2023HAL
Reports & preprints
 31 miscModeling compartmentalization within intracellular signaling pathway.January 2024HALback to text
 32 miscSOME REMARKS ABOUT THE WELLPOSEDNESS OF LIFSHITZSLYOZOV'S EQUATIONS WITH NUCLEATION KINETICS.May 2023HALback to text
 33 miscA stochastic model for neural progenitor dynamics in the mouse cerebral cortex.December 2023HALback to text
 34 miscDeterministic limit of a PDMP model of epithelial tissue interacting with diffusing chemicals and application to the intestinal crypt.December 2023HALback to text
 35 miscMathematical modeling of adipocyte size distributions: identifiability and parameter estimation from rat data.September 2023HALback to text
 36 miscEffect 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 miscModelling the interplay between the gut microbiota and its host : application to the analysis of diet impact on symbiosis.November 2023HALback to text
 38 miscStudy of the numerical method for an inverse problem of a simplified intestinal crypt.December 2023HALback to text
 39 miscA LifschitzSlyozov type model for adipocyte size dynamics : limit from BeckerDöring system and numerical simulation.March 2023HALback to text
11.3 Cited publications
 40 articleHomogenization and twoscale convergence.SIAM J. Math. Anal.2361992, 14821518back to text
 41 articleIntegrating intracellular dynamics using CompuCell3D and Bionetsolver: Applications to multiscale modelling of cancer cell growth and invasion.PLoS One732012back to text
 42 articleAsymptotic analysis of multiscale approximations to reaction networks.Ann. Appl. Probab.1642006, 19251961back to text
 43 unpublishedNonlinear compartmental modeling to monitor ovarian follicle population dynamics on the whole lifespan.2022, hal03739205back to text
 44 articleMeasure solutions for some models in population dynamics.Acta Appl. Math.12312013, 141156back to text
 45 articleIndividualbased probabilistic models of adaptive evolution and various scaling approximations.Progr. Probab.592005, 75113back to text
 46 articlePolynomial chaos expansion for sensitivity analysis.Reliab. Eng. Syst. Safe9472009, 11611172back to text
 47 articleRelative entropy method for measurevalued solutions in natural sciences.Topol. Methods Nonlinear Anal.5212018, 311335back to text
 48 bookMathematical Models of Chemical Reactions: Theory and Applications of Deterministic and Stochastic Models.Princeton University Press; 1st edition1989back to text
 49 articleSignatures of ecological processes in microbial community time series.Microbiome612018, 120back to text
 50 articleRobust and efficient parameter estimation in dynamic models of biological systems.BMC Syst. Biol.912015, 74back to text
 51 articleMeasure solutions to the conservative renewal equation.arXiv:1704.005822017back to text
 52 articleFrequency methods in the theory of pulsemodulated control systems.Autom. Remote Control672006, 17521767back to text
 53 articleModel reduction in chemical dynamics: slow invariant manifolds, singular perturbations, thermodynamic estimates, and analysis of reaction graph.Curr. Opin. Chem. Eng.212018, 4859back to text
 54 bookMathematical Modeling in Systems Biology. An Introduction.The MIT Press; 1st edition2013back to textback to text
 55 incollectionA review on global sensitivity analysis methods.Uncertainty management in simulationoptimization of complex systemsSpringer2015, 101122back to text
 56 articleFunctional data clustering: a survey.Adv. Data Ana. Classif.832014, 231255back to text
 57 articleMeasuretransmission metric and stability of structured population models.Nonlinear Anal. Real World Appl.252015, 930back to text
 58 articleCentral limit theorems and diffusion approximations for multiscale Markov chain models.Ann. Appl. Probab.2422014, 721759back to text
 59 articleStrong approximation theorems for density dependent Markov chains.Stochastic Process. Appl.61978, 223240back to text
 60 articleA multitimescale analysis of chemical reaction networks: I. Deterministic systems.J. Math. Biol.6032009, 387–450back to text
 61 bookFinite Volume Methods for Hyperbolic Problems.Cambridge ; New YorkCambridge University Pressaug 2002back to text
 62 articleDriving the model to its limit: Profile likelihood based model reduction.PLoS One1192016, 118back to text
 63 articleMultiscale modeling of GMP differentiation based on singlecell genealogies: Multiscale modeling of GMP differentiation.FEBS J.279182012, 34883500back to text
 64 bookStochastic Models for Structured Populations.ChamSpringer International Publishing2015back to text
 65 articleGeneral relative entropy inequality: an illustration on growth models.J. Math. Pures Appl.8492005, 12351260back to text
 66 articleA way for in vitro/ex vivo egg production in mammals.J. Reprod. Dev.6542019, 281287back to text
 67 articleA symmetric toggle switch explains the onset of random X inactivation in different mammals.Nature Struct. Mol. Biol.2652019, 350360back to textback to text
 68 articleA general mathematical framework for the analysis of spatiotemporal point processes.Theor. Ecol.712014, 101113back to text
 69 bookTransport equations in biology.Frontiers in MathematicsBaselBirkhäuser Basel2007back to text
 70 articleLarge deviations of Markov chains with multiple timescales.Stoch. Process. Appl.2018back to text
 71 articleMathematical modeling of gonadotropinreleasing hormone signaling.Mol. Cell. Endocrinol.4492017, 42  55back to text
 72 articleMultiscale modeling of the early CD8 Tcell immune response in lymph nodes: An integrative study.Computation242014, 159181back to text
 73 articleParameter estimation for differential equations: a generalized smoothing approach.J. Roy. Statist. Soc. Ser. B6952007, 741796back to text
 74 articleA model reduction method for biochemical reaction networks.BMC Syst. Biol.812014, 52back to text
 75 articleData2Dynamics: A modeling environment tailored to parameter estimation in dynamical systems.Bioinformatics31212015, 35583560back to text
 76 articleMorpheus: A userfriendly modeling environment for multiscale and multicellular systems biology.Bioinformatics3092014, 13311332back to text
 77 articleEcological modeling from timeseries inference: insight into dynamics and stability of intestinal microbiota.PLoS Comput. Biol.9122013, e1003388back to text
 78 articleA microfluidic culture model of the human reproductive tract and 28day menstrual cycle.Nat. Commun.82017, 14584back to text