RESEARCH CENTRE

Inria Saclay Centre

IN PARTNERSHIP WITH:

CNRS, INRAE

2023
ACTIVITY REPORT

Project-Team

MUSCA

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

Contents

Project-Team MUSCA

1 Team members, visitors, external collaborators

2 Overall objectives

3 Research program

3.1 General scientific positioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Design, analysis and reduction of network-based dynamic models . . . . . . . . . . . . . . .
3.3 Design, analysis and simulation of stochastic and deterministic models for structured
populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Coupling biochemical networks with cell and population dynamics . . . . . . . . . . . . . .

4 Application domains

5 Social and environmental responsibility

5.1 Impact of research results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 Highlights of the year

7 New software, platforms, open data

7.1 New software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.1 pyDynPeak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8 New results

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8.1 Deterministic and stochastic compartmental models . . . . . . . . . . . . . . . . . . . . . . .
8.1.1 Nonlinear compartmental modeling to monitor ovarian follicle population dynamics
9
on the whole lifespan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
8.1.2 A stochastic model for neural progenitor dynamics in the mouse cerebral cortex . .
8.1.3 Modeling compartmentalization in cell signaling networks . . . . . . . . . . . . . . .
9
8.1.4 Modeling the inactivation of chromosome-X . . . . . . . . . . . . . . . . . . . . . . . 10
8.2 Size-structured population dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
8.2.1 A size-structured model of fish oocytes population dynamics . . . . . . . . . . . . . . 10
8.2.2 Mathematical modeling of adipocyte size distributions: identifiability and parameter

estimation from rat data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

8.2.3 A Lifschitz-Slyozov type model for adipocyte size dynamics : limit from Becker-

Döring system and numerical simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 11
8.2.4 Long-time asymptotic of the Lifshitz-Slyozov equation with nucleation . . . . . . . . 12
8.2.5 Some remarks about the well-posedness of Lifshitz-Slyozov equations with nucle-

ation kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
8.3 Coupling biochemical dynamics with cell population dynamics . . . . . . . . . . . . . . . . 12
8.3.1 Modeling the interplay between the gut microbiota and its host : application to the

analysis of diet impact on symbiosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

8.3.2 Deterministic limit of a PDMP model of epithelial tissue interacting with diffusing

chemicals and application to the intestinal crypt

. . . . . . . . . . . . . . . . . . . . . 13
8.3.3 Study of the numerical method for an inverse problem of a simplified intestinal crypt 13
8.4 Computational modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
8.4.1 Four functional profiles for fiber and mucin metabolism in the human gut microbiome 13
8.4.2 Harnessing Fc/FcRn Affinity Data from Patents with Different Machine Learning

Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

8.4.3 Maching Learning Models on Time Series Data to predict the behavior of the Biolu-

minescence Resonance Energy Transfer

. . . . . . . . . . . . . . . . . . . . . . . . . . 14
8.5 Exploration of signaling networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
8.5.1 A single domain intrabody targeting the follicle-stimulating hormone receptor (FSHR)

impacts FSH-induced G protein-dependent signalling . . . . . . . . . . . . . . . . . . 15

8.5.2 Towards the convergent therapeutic potential of G protein-coupled receptors in

autism spectrum disorders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

9 Partnerships and cooperations

15
9.1 International initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
9.1.1 Associate Teams in the framework of an Inria International Lab or in the framework

9.2 International research visitors

of an Inria International Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
9.1.2 Participation in other International Programs . . . . . . . . . . . . . . . . . . . . . . . 16
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
9.2.1 Visits of international scientists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9.2.2 Visits to international teams
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9.4 National initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9.5 Regional initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

9.3 European initiatives

9.3.1 H2020 projects

10 Dissemination

18
10.1 Promoting scientific activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
10.1.1 Scientific events: organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
10.1.2 Scientific events: selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
10.1.3 Journal
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
10.1.4 Invited and contributed talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
10.1.5 Leadership within the scientific community . . . . . . . . . . . . . . . . . . . . . . . . 20
10.1.6 Scientific expertise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
10.1.7 Research administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
10.2 Teaching - Supervision - Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
10.2.1 Teaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
10.2.2 Supervision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
10.2.3 Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
10.3 Popularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
10.3.1 Articles and contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
10.3.2 Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

11 Scientific production

24
11.1 Major publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
11.2 Publications of the year
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
11.3 Cited publications

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Project-Team MUSCA

Creation of the Project-Team: 2020 July 01

Keywords

Computer sciences and digital sciences

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

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Inria Annual Report 2023

1 Team members, visitors, external collaborators

Research Scientists

• Frédérique Clément [Team leader, INRIA, Senior Researcher, HDR]

• Pascale Crépieux [CNRS, Senior Researcher, HDR]

• Frédéric Jean-Alphonse [CNRS, Researcher]

• Béatrice Laroche [INRAE, Senior Researcher, HDR]

• Anne Poupon [CNRS, Senior Researcher, CTO of Mabsilico half-time, HDR]

• Eric Reiter [INRAE, Senior Researcher, HDR]

• Romain Yvinec [INRAE, Senior Researcher, HDR]

Faculty Member

• Magali Ribot [UNIV ORLÉANS, until Aug 2023, On half-time delegation, HDR]

Post-Doctoral Fellows

• Léo Darrigade [INRIA, Post-Doctoral Fellow]

• Xavier Leray [INRAE, Post-Doctoral 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]

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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 per-
spective. 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 two-way (bottom-up and top-down) 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 multi-cellular 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 post-processing layer of experi-
mental 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 measure-valued 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 network-based 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 (mass-action) Chemical Reaction Network (CRN) [54], defined by a set of d species and a
directed graph R on a finite set of stoichiometric vectors {y ∈ Nd } (the linear combination of reactant and
product species). A subclass of CRN corresponds to a standard interaction network model in ecology,
the generalized Lotka-Volterra (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 µ and a directed weighted interaction graph given
by its d × d matrix A. The stochastic versions of these models correspond respectively to a Continuous
Time Markov Chain (CTMC) in the discrete state-space Nd , and a birth-death 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

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Inria Annual Report 2023

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 (com-
plex microbial communities, neutral models in ecology, cell dynamics in developmental processes,
macromolecule assemblies), biochemical kinetics and chemical reaction networks (signaling, gene, and
metabolic networks), coagulation-fragmentation models (in particular Becker-Döring model). Notwith-
standing 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
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 [12] [8], 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

Project MUSCA

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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.

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 measure-valued stochastic processes (sometimes referred as Individual-Based Models–IBM).
A typical deterministic instance is the McKendrick-Von Foerster model, a paragon of (nonlinear) conser-
vation 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 finite-dimension model as presented
in section 3.2. According to the nature of the structuring variable, diffusion operators may arise and
lead to consider second-order parabolic PDEs. For finite population dynamics, the stochastic version of
these models can be represented using the formalism of Poisson Measure-driven 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 well-posed 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 de-
terministic 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 coun-
terparts. 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
tissue-homeostasis processes, structured microbial populations involved in eco-physiological systems
and molecule assemblies.

As in the case of finite dimension models, the study of these various models involve common meth-

odological 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 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 math-
ematical 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.

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Inria Annual Report 2023

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 equa-
tions [68], dimensional reduction [6], timescale reduction [4], spatial homogenization [40][10], 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.

3.4 Coupling biochemical networks with cell and population dynamics

A major challenge for multiscale systems biology is to rigorously couple intracellular biochemical net-
works 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 contrast-
ing 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 infra-individual 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. infra-individual) 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 differ-
entiation 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 long-lasting developmental and reproductive process characterized

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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 hypothalamo-pituitary 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 “middle-out”, cell dynamics-based viewpoint [2], completed
progressively with morphogenesis processes [17].

On the intracellular level, we are interested in understanding the endocrine dialogue within the
hypothalamo-pituitary-gonadal (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 Protein-Coupled Receptor)
signaling networks [12]. In the HPG axis, we focus on the pituitary hormones FSH (Follicle-Stimulating
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, FSH-R and LH-R, 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 well-being 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.

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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 man-
agement of ovarian aging, the development of sustainable breeding practices, and the monitoring of
micro-pollutant 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 model-assisted 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 start-up (a spin-off of the BIOS group), which continues to
interact with BIOS and MUSCA on antibody-related projects (SELMAT and Contrabody for example).

6 Highlights of the year

• Six month scientific stay of Prof. Mauricio Sepúldeva (Universidad del Concepción) in the frame-

work of the d’Alembert program from Université Paris-Saclay

• Half-time 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 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

Project MUSCA

8 New results

9

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 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.

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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 un-
derstanding 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 Size-structured population dynamics

8.2.1 A size-structured model of fish oocytes population dynamics

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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 estima-

tion 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

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Inria Annual Report 2023

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 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 well-being of a host are deeply influenced by the interactions with its gut microbi-
ota. 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 sym-
biotic 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

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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, compu-
tational 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 coup-
ling 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 popula-
tion 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 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 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

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Inria Annual Report 2023

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%.

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8.5 Exploration of signaling networks

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 collaborat-
ors.

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
Gαs 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 spec-

trum 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 data-
base: oxytocin OTR; vasopressin V1A and V1B ; metabotropic glutamate mGlu5 and mGlu7 ; GABAB2 ;
dopamine D1, D2 and D3 ; serotoninergic 5-HT1B ; β 2-adrenoceptor; cholinergic M3 ; adenosine A2A and
A3 ; angiotensin AT2 ; cannabinoid CB1 ; chemokine CX3 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-HT2Aand 5-HT7 , 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 D2 , 5-HT2A , CB1 , OTR and V1A 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

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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 Lifshitz-Slyozov type) and
moving/free-boundary 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 spe-
cific numerical schemes, and conceive appropriate strategies for inverse problems, in a synergistic
way.

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: Ro-
main Yvinec and Mauricio Sepúlveda (Universidad de Concepción, Chile)

• i-GPCRNet, International Research Network (IRN) on GPCRs, involved musca members: Pas-

cale 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 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: June-August (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 Jean-Alphonse

Visitor: Livio Casarini

Status: Professor

Institution of origin: University of Modena and Reggio Emilia

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Country: Italy

Dates: November 2022-November 2023

17

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

tion

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 (États-Unis)

Dates of the stay: August 14 2023-July 14 2024

Topic of the stay: Multiscale mathematical modeling in reproductive physiology

Funding: INRAE Phase/Digit-BIO/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 (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: Pas-
cale Crépieux.

• ERNEST (European Research Network on Signal transduction) COST Action 18133.

9.4 National initiatives

• ANR OVOPAUSE (2022-2026, 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 Jean-Alphonse, Eric Reiter,
Romain Yvinec.

• ANR MOSDER (2022-2025, PI Frédéric Jean-Alphonse, 420 K€) “Multi-dimensional Organization
of Signaling Dynamics Encoded by gonadotropin Receptors”. Involved MUSCA members: Pas-
cale Crépieux, Frédéric Jean-Alphonse, Eric Reiter, Romain Yvinec.

• ANR PARTHAGE (2022-2026, 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 (2021-2025, 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.

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Inria Annual Report 2023

• ANR PHEROSENSOR (2021-2026, PI Philippe Lucas, 1492K€) “Early detection of pest insects using

pheromone receptor-based olfactory sensors”. Involved MUSCA member: Béatrice Laroche.

• ANR ABLISS (2019-2023, PI Anne Poupon, 441 K€) “Automating building from Literature of Sig-
nalling Systems”. Involved MUSCA members: Anne Poupon, Eric Reiter, Pascale Crépieux, Ro-
main Yvinec.

• LabEx MAbImprove (2011-2025, PI Hervé Watier). Involved MUSCA members : Eric Reiter, Frédéric Jean-

Alphonse, Pascale Crépieux, Anne Poupon, Romain Yvinec.

• INRAE metaprogram DIGIT-BIO, IMAGO project (2022-2024, PIs Frédéric Jean-Alphonse and
Béatrice Laroche, 47 K€), “Imagerie et modélisation des dynamiques spatio-temporelles de la sig-
nalisation et du trafic des récepteurs couplés aux protéines G (RCPG)”. Involved MUSCA members:
all permanent members.

• INRAE metaprogram DIGIT-BIO, IMMO project (2021-2023, PIs Violette Thermes and Romain Yvinec,
51.4 K€), “IMagerie et MOdélisation multi-échelles pour la compréhension de la dynamique ovari-
enne chez le poisson”. Involved MUSCA members: Frédérique Clément, Romain Yvinec.

• INRAE metaprogram HOLOFLUX, MOTHERS project (2023-2024, PI Florent Kempf). “Monit-
oring the gut microbiota, resistance against salmonella, animal performance and immune re-
sponse through an adult, pathogen-free microbiota”. Involved MUSCA members: Béatrice Laroche,
Lorenzo Sala.

• ANSES GinFiz project (2021-2024, 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 (2022-2024, PI Romain Yvinec, 120 K€) : “Imagerie et
Modélisation Spatio-Temporelles 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 (2020-2023, PI Eric Reiter, 630
K€) “Méthodes in silico pour la sélection et la maturation d’anticorps : développement, valida-
tion et application à différentes cibles thérapeutiques”. Involved MUSCA members: Eric Reiter,
Pascale Crépieux, Frédéric Jean-Alphonse, Romain Yvinec.

• Appel à projet région Centre Val de Loire, INTACT (2019-2023, PI Pascale Crépieux, 200 K€) “Phar-
macologie réverse à l’aide d’anticorps intracellulaires anti-RFSH actif”. Involved MUSCA members:
Pascale Crépieux, Eric Reiter, Frédéric Jean-Alphonse, 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 03-05, Paris

Frédéric Jean-Alphonse, i-GPCRnet annual meeting, October 25-27, Strasbourg

Magali Ribot, Journées Maths-Bio-Santé, Université, November 27 - December 1, Marne la Vallée

Mauricio Sepúlveda, online Seminars in EDP and Applied Mathematics, Brazil ; INRIA-CHILE 2023
Scientific Days, December 4-7, Santiago, Chile

Project MUSCA

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10.1.2 Scientific events: selection

Member of the conference program committees

Frédérique Clément, ReproSciences 2023, May 03-05, Paris

Magali Ribot, Member of the selection board, RTR Rouen workshop on maths for biology, June
28-30

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 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

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Eric Reiter

Inria Annual Report 2023

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

Seminars

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

Léo Meyer, Modeling and analysis of adipocyte size distribution, Bio-Maths seminar, Institut
Camille Jordan, Université Lyon 1–Claude Bernard; INTERFACE team’s seminar, Laboratoire Jean-
Alexandre Dieudonné, Université côte d’azur; Maths-Bio-Santé 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 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

Project MUSCA

Béatrice Laroche

21

• member of the Steering Committee of the INRAE metagrogram HOLOFLUX

Anne Poupon

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

prove

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 (Math-
ématiques, 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

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Inria Annual Report 2023

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 Septem-
ber 09, supervisors: Magali Ribot and Romain Yvinec

PhD: Pauline Raynaud, “Intracellular antibodies to explore the relationships between conforma-
tions 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, con-
sequences 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”, star-
ted November 2022, supervisors: Frédérique Clément and Romain Yvinec, associate supervisor:
Violette Thermes

PhD in progress: Juliette Gourdon, “Manipulation of the intracellular traffic and endosomal sig-
naling 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

Project MUSCA

23

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 multidiscip-
linary 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 Ri-
bot

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 Popularization

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

24

Inria Annual Report 2023

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] B. Aymard, F. Clément, F. Coquel and M. Postel. ‘A numerical method for kinetic equations with
discontinuous equations : application to mathematical modeling of cell dynamics’. In: SIAM
Journal on Scientific Computing 35.6 (2013), 27 pages. DOI: 10.1137/120904238. URL: https://h
al.archives-ouvertes.fr/hal-00751454.

[2] B. Aymard, F. Clément, D. Monniaux and M. Postel. ‘Cell-Kinetics Based Calibration of a Multiscale
Model of Structured Cell Populations in Ovarian Follicles’. In: SIAM Journal on Applied Mathematics
76.4 (2016), pp. 1471–1491. DOI: 10.1137/15M1030327. URL: https://hal.archives-ouverte
s.fr/hal-01186381.

[3] B. Aymard, F. Clément and M. Postel. ‘Adaptive mesh refinement strategy for a nonconservat-
ive transport problem’. In: ESAIM: Mathematical Modelling and Numerical Analysis (Aug. 2014),
pp. 1381–1412. DOI: 10.1051/m2an/2014014. URL: https://hal.archives-ouvertes.fr/hal
-00865429.

[4] C. Bonnet, K. Chahour, F. Clément, M. Postel and R. Yvinec. ‘Multiscale population dynamics in
reproductive biology: singular perturbation reduction in deterministic and stochastic models’.
In: ESAIM: Proceedings and Surveys 67 (2020), pp. 72–99. DOI: 10.1051/proc/202067006. URL:
https://hal.inria.fr/hal-03047923.

[5] F. Clément, B. Laroche and F. Robin. ‘Analysis and numerical simulation of an inverse problem for
a structured cell population dynamics model’. In: Mathematical Biosciences and Engineering 16.4
(2019). Le DOI n’est pas actif, voir http://www.aimspress.com/article/10.3934/mbe.20191
50, pp. 3018–3046. DOI: 10.3934/mbe.2019150. URL: https://hal.archives-ouvertes.fr/h
al-02154588.

[6] F. Clément and D. Monniaux. ‘Multiscale modelling of ovarian follicular selection.’ In: Progress in
Biophysics and Molecular Biology 113.3 (Dec. 2013), pp. 398–408. DOI: 10.1016/j.pbiomolbio.2
012.12.005. URL: https://hal.inria.fr/hal-00776209.

[7] F. Clément, F. Robin and R. Yvinec. ‘Analysis and calibration of a linear model for structured cell
populations with unidirectional motion : Application to the morphogenesis of ovarian follicles’. In:
SIAM Journal on Applied Mathematics 79.1 (Feb. 2019), pp. 207–229. DOI: 10.1137/17M1161336.
URL: https://hal.archives-ouvertes.fr/hal-01852560.

[8] F. Clément, F. Robin and R. Yvinec. ‘Stochastic nonlinear model for somatic cell population dynam-
ics during ovarian follicle activation’. In: Journal of Mathematical Biology 82.3 (2021), pp. 1–52. DOI:
10.1007/s00285-021-01561-x. URL: https://hal.inria.fr/hal-02057983.

[9]

J. Deschamps, E. Hingant and R. Yvinec. ‘Quasi steady state approximation of the small clusters in
Becker–Döring equations leads to boundary conditions in the Lifshitz–Slyozov limit’. In: Commu-
nications in Mathematical Sciences 15.5 (2017), pp. 1353–1384. DOI: 10.4310/CMS.2017.v15.n5
.a7. URL: https://hal.archives-ouvertes.fr/hal-01608844.

[10] T. El Bouti, T. Goudon, S. Labarthe, B. Laroche, B. Polizzi, A. Rachah, M. Ribot and R. Tesson.
‘A mixture model for the dynamic of the gut mucus layer’. In: ESAIM: Proceedings 55.décembre
(2016). Ed. by E. Frénod, E. Maitre, A. Rousseau, S. Salmon and M. Szopos, pp. 111–130. DOI:
10.1051/proc/201655111. URL: https://hal.archives-ouvertes.fr/hal-01421708.

[11] P. A. Fletcher, F. Clément, A. Vidal, J. Tabak and R. Bertram. ‘Interpreting frequency responses to
dose-conserved pulsatile input signals in simple cell signaling motifs.’ In: PLoS ONE 9.4 (2014),
e95613. DOI: 10.1371/journal.pone.0095613. URL: https://hal.inria.fr/hal-00981377.

Project MUSCA

25

[12] D. Heitzler, G. Durand, N. Gallay, A. Rizk, S. Ahn, J. Kim, J. D. Violin, L. Dupuy, C. Gauthier, V.
Piketty, P. Crépieux, A. Poupon, F. Clément, F. Fages, R. J. Lefkowitz and E. Reiter. ‘Competing G
protein-coupled receptor kinases balance G protein and β-arrestin signaling.’ In: Molecular Systems
Biology 8 (June 2012), pp. 1–17. DOI: 10.1038/msb.2012.22. URL: https://hal.inria.fr/hal-
00776169.

[13] T. Hélie and B. Laroche. ‘Computable convergence bounds of series expansions for infinite dimen-
sional linear-analytic systems and application’. In: Automatica 50.9 (2014), pp. 2334–2340. DOI:
10.1016/j.automatica.2014.07.011. URL: https://hal.archives-ouvertes.fr/hal-01
123435.

[14] T. Hélie and B. Laroche. ‘Computation of Convergence Bounds for Volterra Series of Linear-Analytic
Single-Input Systems’. In: IEEE Transactions on Automatic Control 56.9 (Sept. 2011), pp. 2062–2072.
DOI: 10.1109/TAC.2010.2091435. URL: https://hal-supelec.archives-ouvertes.fr/ha
l-00655910.

[15] E. Hingant and R. Yvinec. ‘The Becker-Doring Process: Pathwise Convergence and Phase Transition
Phenomena’. In: Journal of Statistical Physics 177.5 (2018), pp. 506–527. DOI: 10.1007/s10955-01
9-02377-2. URL: https://hal.archives-ouvertes.fr/hal-01852561.

[16] S. Labarthe, B. Polizzi, T. Phan, T. Goudon, M. Ribot and B. Laroche. ‘A mathematical model to
investigate the key drivers of the biogeography of the colon microbiota.’ In: Journal of Theoretical
Biology 462.7 (2019), pp. 552–581. DOI: 10.1016/j.jtbi.2018.12.009. URL: https://hal.arc
hives-ouvertes.fr/hal-01761191.

[17] D. Monniaux, P. Michel, M. Postel and F. Clément. ‘Multiscale modeling of ovarian follicular devel-
opment: From follicular morphogenesis to selection for ovulation’. In: Biology of the Cell 108.6 (June
2016), pp. 1–12. DOI: 10.1111/boc.201500087. URL: https://hal.inria.fr/hal-01294630.

[18] M. Postel, A. Karam, G. Pézeron, S. Schneider-Maunoury and F. Clément. ‘A multiscale math-
ematical model of cell dynamics during neurogenesis in the mouse cerebral cortex’. In: BMC
Bioinformatics 20.1 (Dec. 2019). DOI: 10.1186/s12859-019-3018-8. URL: https://hal.inria
.fr/hal-01783141.

[19] P. Shang. ‘Cauchy problem for multiscale conservation laws: Application to structured cell pop-
ulations’. In: Journal of Mathematical Analysis and Applications 401.2 (2013), pp. 896–920. DOI:
10.1016/j.jmaa.2013.01.001. URL: https://hal.inria.fr/hal-00841184.

[20] S. Widder, R. J. Allen, T. Pfeiffer, T. P. Curtis, C. Wiuf, W. T. Sloan, O. X. Cordero, S. P. Brown, B.
Momeni, W. Shou, H. Kettle, H. J. Flint, A. F. Haas, B. Laroche, J.-U. Kreft, P. B. Rainey, S. Freilich,
S. Schuster, K. Milferstedt, J. R. van der Meer, T. Groszkopf, J. Huisman, A. Free, C. Picioreanu,
C. Quince, I. Klapper, S. Labarthe, B. F. Smets, H. Wang, J. Hamelin, J. Harmand, J.-P. Steyer, E.
Trably, I. N. Institute Fellows and O. S. Soyer. ‘Challenges in microbial ecology: building predictive
understanding of community function and dynamics.’ In: ISME Journal 10 (2016). Marco Cosentino
Lagomarsino (LCQB) is a member of Isaac Newton Institute Fellows consortium., pp. 1–12. DOI:
10.1038/ismej.2016.45. URL: https://hal.archives-ouvertes.fr/hal-01512087.

[21] R. Yvinec, P. Crépieux, E. Reiter, A. Poupon and F. Clément. ‘Advances in computational modeling
approaches of pituitary gonadotropin signaling’. In: Expert Opinion on Drug Discovery 13.9 (2018),
pp. 799–813. DOI: 10.1080/17460441.2018.1501025. URL: https://hal.archives-ouverte
s.fr/hal-01913612.

11.2 Publications of the year

International journals

[22] A. Annamneedi, C. Gora, A. Dudas, X. Leray, V. Bozon, P. Crépieux and L. P. Pellissier. ‘Towards the
convergent therapeutic potential of G protein-coupled receptors in autism spectrum disorders’. In:
British Journal of Pharmacology (2023). DOI: 10.1111/bph.16216. URL: https://hal.science
/hal-04220553.

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Inria Annual Report 2023

J. Calvo, E. Hingant and R. Yvinec. ‘Long-time asymptotic of the Lifshitz-Slyozov equation with
nucleation’. In: Kinetic and Related Models (20th Dec. 2023). DOI: 10.3934/krm.2023041. URL:
https://hal.science/hal-04098262.

[24] C. Dumet, M. Pugnière, C. Henriquet, V. Gouilleux-Gruart, A. Poupon and H. Watier. ‘Harnessing
Fc/FcRn affinity data from patents with different machine learning methods’. In: International
Journal of Molecular Sciences 24.6 (16th Mar. 2023), p. 5724. DOI: 10.3390/ijms24065724. URL:
https://cnrs.hal.science/hal-04308512.

[25] D. Klett, L. Pellissier, D. Lomet, F. Derouin-Tochon, V. Robert, T. M. D. Nguyen, A. Duittoz, E. Reiter,
Y. Locatelli, J. Dupont, H. Dardente, F. Jean-Alphonse and Y. Combarnous. ‘Highly-Sensitive In
Vitro Bioassays for FSH, TSH, PTH, Kp, and OT in Addition to LH in Mouse Leydig Tumor Cell’. In:
International Journal of Molecular Sciences 24.15 (2023), p. 12047. DOI: 10.3390/ijms241512047.
URL: https://hal.science/hal-04206799.

[26] S. Labarthe, S. Plancade, S. Raguideau, F. Plaza Oñate, E. Le Chatelier, M. Leclerc and B. Laroche.
‘Four functional profiles for fibre and mucin metabolism in the human gut microbiome’. In:
Microbiome 11.1 (Dec. 2023), p. 231. DOI: 10.1186/s40168-023-01667-y. URL: https://hal.i
nrae.fr/hal-03918193.

[27] P. Raynaud, V. Jugnarain, O. Vaugrente, A. Vallet, T. Boulo, C. Gauthier, A. Inoue, N. Sibille, C. Gauth-
ier, F. Jean-Alphonse, E. Reiter, P. Crépieux and G. Bruneau. ‘A single domain intrabody targeting
the follicle-stimulating hormone receptor (FSHR) impacts FSH-induced G protein-dependent
signalling’. In: FEBS Letters (7th Aug. 2023). DOI: 10.1101/2023.08.07.552286. URL: https://h
al.science/hal-04269864.

[28] A. Zehnaker, A. Vallet, J. Gourdon, C. Sarti, V. Jugnarain, M. Haj Hassan, L. Mathias, C. Gauthier,
P. Raynaud, T. Boulo, L. Beauclair, Y. Bigot, L. Casarini, P. Crépieux, A. Poupon, B. Piégu, F. Jean-
Alphonse, G. Bruneau and É. Reiter. ‘Combined Multiplexed Phage Display, High-Throughput
Sequencing, and Functional Assays as a Platform for Identifying Modulatory VHHs Targeting the
FSHR’. In: International Journal of Molecular Sciences 24.21 (Nov. 2023), p. 15961. DOI: 10.3390/i
jms242115961. URL: https://hal.science/hal-04274818.

Conferences without proceedings

[29] F. Clément and R. Yvinec. ‘Comparative dynamics of female germ cell populations : insight from
imaging and multiscale modeling’. In: Journées INRAE-INRIA 2023. Nancy, France, 5th July 2023.
URL: https://hal.inrae.fr/hal-04194047.

[30] R. Yvinec. ‘Time scale separation in life-long ovarian follicles population dynamics model’. In:
Séminar EDP/ProbaStat Laboratoire de Mathématiques et Applications (LMA) de Poitiers. Poitiers,
France, 2nd Mar. 2023. URL: https://hal.inrae.fr/hal-04194051.

Reports & preprints

[31] C. Alamichel, J. Calvo, E. Hingant, S. Latrach, N. Quiblier and R. Yvinec. Modeling compartmental-
ization within intracellular signaling pathway. 12th Jan. 2024. URL: https://hal.science/hal-
04098543.

[32]

J. Calvo, E. Hingant and R. Yvinec. SOME REMARKS ABOUT THE WELL-POSEDNESS OF LIFSHITZ-
SLYOZOV’S EQUATIONS WITH NUCLEATION KINETICS. 17th May 2023. URL: https://hal.scie
nce/hal-04099684.

[33] F. Clément and J. Olayé. A stochastic model for neural progenitor dynamics in the mouse cerebral

cortex. 18th Dec. 2023. URL: https://inria.hal.science/hal-04351283.

[34] L. Darrigade, S. Labarthe and B. Laroche. Deterministic limit of a PDMP model of epithelial tissue
interacting with diffusing chemicals and application to the intestinal crypt. 11th Dec. 2023. URL:
https://hal.science/hal-04336174.

[35] A.-S. Giacobbi, L. Meyer, M. Ribot, R. Yvinec, H. Soula and C. Audebert. Mathematical modeling of
adipocyte size distributions: identifiability and parameter estimation from rat data. 27th Sept. 2023.
URL: https://hal.science/hal-04141173.

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[36] C. Gora, A. Dudas, L. Court, A. Annamneedi, G. Lefort, T.-S. Picoreti-Nakahara, N. Azzopardi, A.
Acquistapace, A.-L. Lainé, A.-C. Trouillet, L. Drobecq, E. Pecnard, B. Piegu, P. Crépieux, P. Chamero
and L. 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. 28th Nov. 2023. URL:
https://hal.science/hal-04312827.

[37] M. Haghebaert, B. Laroche, L. Sala, S. Mondot and J. Doré. Modelling the interplay between the gut
microbiota and its host : application to the analysis of diet impact on symbiosis. 15th Nov. 2023. URL:
https://hal.inrae.fr/hal-04287119.

[38] M. Haghebaert, B. Laroche and M. A. Sepulveda Cortes. Study of the numerical method for an
inverse problem of a simplified intestinal crypt. 9th Dec. 2023. URL: https://hal.inrae.fr/hal-
04332907.

[39] L. Meyer, M. Ribot and R. Yvinec. A Lifschitz-Slyozov type model for adipocyte size dynamics : limit
from Becker-Döring system and numerical simulation. 6th Mar. 2023. URL: https://hal.science
/hal-04016144.

11.3 Cited publications

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<scratchpad>
- Main topic: Research Centre Inria Saclay Centre's Activity Report for 2023
- Key points: The report highlights the team's research activities, collaborations, and achievements in the fields of digital health, biology, and earth sciences.
- Structure: The document is divided into sections, including Project-Team, Activity Report, Domain, Theme, Contents, Highlights of the Year, New Software, and Partnerships and Cooperations.
- Potential artifacts to ignore: Links, HTML tags, and web-related elements
</scratchpad>

<final_summary>
The Inria Saclay Centre's Activity Report for 2023 showcases the team's research activities in digital health, biology, and earth sciences. The report highlights the team's work on multiscale modeling, particularly in the fields of reproductive biology, digestive ecophysiology, and microbiota-host interactions. The team has made significant progress in developing and applying mathematical models to understand complex biological systems, with a focus on structure and function. The report also highlights collaborations with other research centers and institutions, as well as the team's involvement in various international initiatives and projects.
The Inria Saclay Centre's Activity Report for 2023 showcases the team's research activities in digital health, biology, and earth sciences. The report highlights the team's work on multiscale modeling, particularly in the fields of reproductive biology, digestive ecophysiology, and microbiota-host interactions. The team has made significant progress in developing and applying mathematical models to understand complex biological systems, with a focus on structure and function. The report also highlights collaborations with other research centers and institutions, as well as the team's involvement in various international initiatives and projects.