Reminder of the objectives given for the last evaluation

The aim of this project is the development of modern tools for multi-scale modeling in biological phenomena. During the period 2014-2017, the objectives we had fixed were to develop modern tools for multi-scale modeling of biological phenomena, as detailed hereafter:

1. Multi-scale modeling of erythropoiesis, the process of red blood cell production, in order to describe normal, stress, and pathological erythropoiesis, using mathematical and computational models. This led to:
2. Multi-scale modeling of the CD8 T cell immune response, in order to develop a predictive model of the CD8 T cell response, by confronting the model at different stages to in vivo-acquired experimental data;
3. Population dynamics modeling, with the aim to develop general mathematical tools to study them. The main tools we were using were structured equations, in which the cell population is endowed with relevant structures, or traits. We identified limitations in using these formalisms, this is why we started developing multi-scale approaches;
4. Modeling of Chronic Myeloid Leukemia (CML) treatment, using ordinary differential equations models. Our team had already developed a first model of mutant leukemic cells being resistant to chemotherapy. A next step would be to identify the parameters using experimental data;
5. Multi-scale modeling carried out on the basis of hybrid discrete-continuous models, where dissipative particle dynamics (DPD) are used in order to describe individual cells and relatively small cell populations, partial differential equations (PDE) are used to describe concentrations of bio-chemical substances in the extracellular matrix, and ordinary differential equations for intracellular regulatory networks (Figure 1). An emphasis would be made on developing codes that are both flexible and powerful enough to implement variants of the model, perform simulations, produce desired outputs, and provide tools for analysis; to do so:
6. We planned to contribute to a recent project named chronos, whose code (written in C++) represents heterogeneous populations of individual cells evolving in time and interacting physically and biochemically, and the objective is to make the code flexible enough to implement different formalisms within the same model, so that different components of the model can be represented in the most appropriate way;
7. Partial differential equations (PDE) analysis, with a focus on reaction-diffusion equations, transport equations (hyperbolic PDEs) in which the structure can be age, maturity, protein concentration, etc., with particular cases where transport equations are reduced to delay differential equations (DDE).

Comments on these objectives over the evaluation period

We have had strong contributions to objectives 1, 2, 3, 4, and consequently to objective 5, as well as to objective 7, as mentioned in previous sections. These contributions represented the core of the team's research activity over the evaluation period, as stressed by our publications. It is however noticeable that multi-scale modeling of the immune response and of pathological hematopoiesis (leukemia) has come to represent a proportionally more important part of our activity.

Objective 6 has been pursued, the project chronos evolved to a better defined project SiMuScale that is currently being developed and aims at structuring the team's activity and providing a simulation platform that could be adapted to various biological questions necessitating multi-scale modeling.

Objectives for the next four years

The main objectives for the next four years are to continue to improve the 3 previous points: 1) Mathematical and computational modeling for cell population dynamics; 2) Multi-scale modeling of hematopoiesis and leukemia; 3) Multi-scale modeling of the immune response. In addition, we will pursue our effort to develop a simulation platform for multi-scale models (SiMuScale) and we intend to develop the use of mixed effect models and other statistical approaches to deal with the challenges offered by modern biology, in particular the generation of single cell data.

5.1.1 Modeling and characterization of inter-individual variability in CD8 T cell responses in mice

To develop vaccines, it is mandatory yet challenging to account for inter-individual variability during immune responses. Even in laboratory mice, T cell responses of single individuals exhibit a high heterogeneity that may come from genetic backgrounds, intra-specific processes (e.g., antigen-processing and presentation) and immunization protocols. To account for inter-individual variability in CD8 T cell responses in mice, we propose in 6 a dynamical model coupled to a statistical, nonlinear mixed effects model. Average and individual dynamics during a CD8 T cell response are characterized in different immunization contexts (vaccinia virus and tumor). On one hand, we identify biological processes that generate inter-individual variability (activation rate of naive cells, the mortality rate of effector cells, and dynamics of the immunogen). On the other hand, introducing categorical covariates to analyze two different immunization regimens, we highlight the steps of the response impacted by immunogens (priming, differentiation of naive cells, expansion of effector cells and generation of memory cells). The robustness of the model is assessed by confrontation to new experimental data. Our approach allows to investigate immune responses in various immunization contexts, when measurements are scarce or missing, and contributes to a better understanding of inter-individual variability in CD8 T cell immune responses.

5.1.2 Multiscale modeling of germinal center recapitulates the temporal transition from memory B cells to plasma cells differentiation as regulated by antigen affinity-based Tfh cell help

Germinal centers play a key role in the adaptive immune system since they are able to produce memory B cells and plasma cells that produce high affinity antibodies for an effective immune protection. The mechanisms underlying cell-fate decisions are not well understood but asymmetric division of antigen, B-cell receptor affinity, interactions between B-cells and T follicular helper cells (triggering CD40 signaling), and regulatory interactions of transcription factors have all been proposed to play a role. In addition, a temporal switch from memory B-cell to plasma cell differentiation during the germinal center reaction has been shown. To investigate if antigen affinity-based Tfh cell help recapitulates the temporal switch we implemented in 15 a multiscale model that integrates cellular interactions with a core gene regulatory network comprising BCL6, IRF4, and BLIMP1. Using this model, we show that affinity-based CD40 signaling in combination with asymmetric division of B-cells result in switch from memory B-cell to plasma cell generation during the course of the germinal center reaction. We also show that cell fate division is unlikely to be (solely) based on asymmetric division of Ag but that BLIMP1 is a more important factor. Altogether, our model enables to test the influence of molecular modulations of the CD40 signaling pathway on the production of germinal center output cells.

5.1.3 Modeling the relationship between antibody-dependent enhancement and disease severity in secondary dengue infection

Sequential infections with different dengue serotypes (DENV-1, 4) significantly increase the risk of a severe disease outcome (fever, shock and hemorrhagic disorders). Two hypotheses have been proposed to explain the severity of dengue disease: (1) antibody-dependent enhancement (ADE); (2) original T cell antigenic sin. In 9, we explored the first hypothesis through mathematical modeling. The proposed model reproduces the dynamic of susceptible and infected target cells, and dengue virus in scenarios of infection-neutralizing and-enhancing antibodies competition induced by two distinct serotypes of dengue virus. The enhancement and neutralization functions are derived from basic concepts of chemical reactions and used to mimic binding to the virus by two distinct populations of antibodies. The analytic study of the model showed the existence of two equilibriums, a disease-free equilibrium and an endemic one. We performed the asymptotic stability analysis for these two equilibriums. The local asymptotic stability of the endemic-equilibrium corresponds to the occurrence of dengue hemorrhagic fever (DHF) or dengue shock syndrome (DSS). We defined the time t DHF at which DHF/DSS occurs as the time when the infected cells (or the virus) population reaches a maximum. This corresponds to the time at which maximum enhancing activity for dengue infection appears. The critical time t DHF was calculated from the model to be few days after the occurrence of the infection, which corresponds to what is observed in the literature. Finally, using as output the basic reproduction number $R_0$ we were able to rank the contribution of each parameter of the model. In particular, we have highlighted the evidence of the role of enhancing antibodies in cross-reaction and the occurrence of DHF/DSS.

5.2.1 Practical identifiability in the frame of nonlinear mixed effects models: the example of the in vitro erythropoiesis

Background Nonlinear mixed effects models provide a way to mathematically describe experimental data involving a lot of inter-individual heterogeneity. In order to assess their practical identifiability and estimate confidence intervals for their parameters, most mixed effects modelling programs use the Fisher Information Matrix. However, in complex nonlinear models, this approach can mask practical unidentifiabilities. We rather propose in 10 a multistart approach, and use it to simplify our model by reducing the number of its parameters, in order to make it identifiable. Our model describes several cell populations involved in vitro differentiation of chicken erythroid progenitors grown in the same environment. Inter-individual variability observed in cell population counts is explained by variations of the differentiation and proliferation rates between replicates of the experiment. Alternatively, we test a model with varying initial condition. We conclude by relating experimental variability to precise and identifiable variations between the replicates of the experiment of some model parameters.

5.2.2 Entropy as a measure of variability and stemness in single-cell transcriptomics

We propose in 11 a simple typology that should help non-specialists readers to better grasp the relevance of the term "entropy" for the analysis of single cell transcriptomics data, and differentiate its various occurrences.

5.2.3 Reduction of a stochastic model of gene expression: Lagrangian dynamics gives access to basins of attraction as cell types and metastabilty

Differentiation is the process whereby a cell acquires a specific phenotype, by differential gene expression as a function of time. This is thought to result from the dynamical functioning of an underlying Gene Regulatory Network (GRN). The precise path from the stochastic GRN behavior to the resulting cell state is still an open question. In 18 we propose to reduce a stochastic model of gene expression, where a cell is represented by a vector in a continuous space of gene expression, to a discrete coarse-grained model on a limited number of cell types. We develop analytical results and numerical tools to perform this reduction for a specific model characterizing the evolution of a cell by a system of piecewise deterministic Markov processes (PDMP). Solving a spectral problem, we find the explicit variational form of the rate function associated to a Large deviations principle, for any number of genes. The resulting Lagrangian dynamics allows us to define a deterministic limit of which the basins of attraction can be identified to cellular types. In this context the quasipotential, describing the transitions between these basins in the weak noise limit, can be defined as the unique solution of an Hamilton-Jacobi equation under a particular constraint. We develop a numerical method for approximating the coarse-grained model parameters, and show its accuracy for a symmetric toggle-switch network. We deduce from the reduced model an approximation of the stationary distribution of the PDMP system, which appears as a Beta mixture. Altogether those results establish a rigorous frame for connecting GRN behavior to the resulting cellular behavior, including the calculation of the probability of jumps between cell types (see also 26).

5.2.4 Reverse engineering of a mechanistic model of gene expression using metastability and temporal dynamics

Differentiation can be modeled at the single cell level as a stochastic process resulting from the dynamical functioning of an underlying Gene Regulatory Network (GRN), driving stem or progenitor cells to one or many differentiated cell types. Metastability seems inherent to differentiation process as a consequence of the limited number of cell types. Moreover, mRNA is known to be generally produced by bursts, which can give rise to highly variable non-Gaussian behavior, making the estimation of a GRN from transcriptional profiles challenging. In the article 19, we present CARDAMOM (Cell type Analysis from scRna-seq Data achieved from a Mixture MOdel), a new algorithm for inferring a GRN from timestamped scRNA-seq data, which crucially exploits these notions of metastability and transcriptional bursting. We show that such inference can be seen as the successive resolution of as many regression problem as timepoints, after a preliminary clustering of the whole set of cells with regards to their associated bursts frequency. We demonstrate the ability of CARDAMOM to infer a reliable GRN from in silico expression datasets, with good computational speed. To the best of our knowledge, this is the first description of a method which uses the concept of metastability for performing GRN inference.

5.3.1 Why are periodic erythrocytic diseases so rare in humans?

Many studies have shown that periodic erythrocytic (red blood cell linked) diseases are extremely rare in humans. To explain this observation, we develop in 2 a simple model of erythropoiesis in mammals and investigate its stability in the parameter space. A bifurcation analysis enables us to sketch stability diagrams in the plane of key parameters. Contrary to some other mammal species such as rabbits, mice or dogs, we show that human-specific parameter values prevent periodic oscillations of red blood cells levels. In other words, human erythropoiesis seems to lie in a region of parameter space where oscillations exclusively concerning red blood cells cannot appear. Further mathematical analysis show that periodic oscillations of red blood cells levels are highly unusual and if exist, might only be due to an abnormally high erythrocytes destruction rate or to an abnormal hematopoietic stem cell commitment into the erythrocytic lineage. We also propose numerical results only for an improved version of our approach in order to give a more realistic but more complex approach of our problem.

5.3.2 Periodic solutions for a nonautonomous mathematical model of hematopoietic stem cell dynamics

The main purpose of the paper 1 is to study the existence of periodic solutions for a nonautonomous differential-difference system describing the dynamics of hematopoietic stem cell (HSC) population under some external periodic regulatory factors at the cellular cycle level. The starting model is a nonautonomous system of two age-structured partial differential equations describing the HSC population in quiescent (G0) and proliferating (G1, S, G2 and M) phase. We are interested in the effects of periodically time varying coefficients due for example to circadian rhythms or to the periodic use of certain drugs, on the dynamics of HSC population. The method of characteristics reduces the age-structured model to a nonautonomous differential-difference system. We prove under appropriate conditions on the parameters of the system, using topological degree techniques and fixed-point methods, the existence of periodic solutions of our model.

5.4.1 A reaction-diffusion model of spatial propagation of A beta oligomers in early stage Alzheimer’s disease

The misconformation and aggregation of the protein Amyloid-Beta (A$\beta$) is a key event in the propagation of Alzheimer's Disease (AD). Different types of assemblies are identified, with long fibrils and plaques deposing during the late stages of AD. In the earlier stages, the disease spread is driven by the formation and the spatial propagation of small amorphous assemblies called oligomers. We propose in 4 a model dedicated to studying those early stages, in the vicinity of a few neurons and after a polymer seed has been formed. We build a reaction-diffusion model, with a Becker-Döring-like system that includes fragmentation and size-dependent diffusion. We hereby establish the theoretical framework necessary for the proper use of this model, by proving the existence of solutions using a fixed-point method.

5.4.2 Mathematical modeling of protein self-aggregation and conversion

Following the discovery that prions are self-replicating assemblies of proteins, mathematical models were developed in parallel with experimental methods in order to conceptualize this phenomenon. After four decades of research, much insight has been gained into protein misfolding processes and the neurodegenerative diseases which they cause. However, the complexity of these systems remains undiminished and the classical models of protein aggregation are now showing their limits. In particular, the observed spectrum of objects generated during the propagation of prions is not accounted for in any model, whereas it keeps expanding under the development of experimental tools. In the manuscript 27, our aim is to identify the weaknesses of classical models of prion propagation in light of recent biological evidence. We then suggest modified and improved models, by including different processes, by adding more levels of organization and more diversity to protein aggregates. Three main topics are presented, corresponding to different instances of protein aggregation and different biological systems. The first part takes place in the mammalian nervous system, and investigates the self-aggregation kinetics of PrP, the aptly named prion protein. In the second part, we model the replication of protein aggregates inside dividing yeast cells, by proposing a novel multi-scale approach. In the third part, we explore the spatial propagation of small protein oligomers in the early stages of Alzheimer’s Disease. These three axes are linked by the central role of structural diversity in the global protein aggregation system.

5.8.1 Vaccination in a two-group epidemic model

Epidemic progression depends on the structure of the population. We study in 5 a two-group epidemic model with the difference between the groups determined by the rate of disease transmission. The basic reproduction number, the maximal and the total number of infected individuals are characterized by the proportion between the groups. We consider different vaccination strategies and determine the outcome of the vaccination campaign depending on the distribution of vaccinated individuals between the groups.

5.8.2 Epidemic progression and vaccination in a heterogeneous population. Application to the Covid-19 epidemic

The paper 20 is devoted to a compartmental epidemiological model of infection progression in a heterogeneous population which consists of two groups with high disease transmission (HT) and low disease transmission (LT) potentials. Final size and duration of epidemic, the total and current maximal number of infected individuals are estimated depending on the structure of the population. It is shown that with the same basic reproduction number $R_0$ in the beginning of epidemic, its further progression depends on the ratio between the two groups. Therefore, fitting the data in the beginning of epidemic and the determination of $R_0$ are not sufficient to predict its long time behaviour. Available data on the Covid-19 epidemic allows the estimation of the proportion of the HT and LT groups. Estimated structure of the population is used for the investigation of the influence of vaccination on further epidemic development. The result of vaccination strongly depends on the proportion of vaccinated individuals between the two groups. Vaccination of the HT group acts to stop the epidemic and essentially decreases the total number of infected individuals at the end of epidemic and the current maximal number of infected individuals while vaccination of the LT group only acts to protect vaccinated individuals from further infection.

5.8.3 Traveling waves of a differential-difference diffusive Kermack-McKendrick epidemic model with age-structured protection phase

We consider in 3 a general class of diffusive Kermack-McKendrick SIR epidemic models with an age-structured protection phase with limited duration, for example due to vaccination or drugs with temporary immunity. A saturated incidence rate is also considered which is more realistic than the bilinear rate. The characteristics method reduces the model to a coupled system of a reaction-diffusion equation and a continuous difference equation with a time-delay and a nonlocal spatial term caused by individuals moving during their protection phase. We study the existence and non-existence of non-trivial traveling wave solutions. We get almost complete information on the threshold and the minimal wave speed that describes the transition between the existence and non-existence of non-trivial traveling waves that indicate whether the epidemic can spread or not. We discuss how model parameters, such as protection rates, affect the minimal wave speed. The difficulty of our model is to combine a reaction-diffusion system with a continuous difference equation. We deal with our problem mainly by using Schauder's fixed point theorem. More precisely, we reduce the problem of the existence of non-trivial traveling wave solutions to the existence of an admissible pair of upper and lower solutions.

5.9.1 Nonlocal reaction-diffusion models of heterogeneous wealth distribution

Dynamics of human populations can be affected by various socio-economic factors through their influence on the natality and mortality rates, and on the migration intensity and directions. In 7 we study an economic–demographic model which takes into account the dependence of the wealth production rate on the available resources. In the case of nonlocal consumption of resources, the homogeneous-in-space wealth–population distribution is replaced by a periodic-in-space distribution for which the total wealth increases. For the global consumption of resources, if the wealth redistribution is small enough, then the homogeneous distribution is replaced by a heterogeneous one with a single wealth accumulation center. Thus, economic and demographic characteristics of nonlocal and global economies can be quite different in comparison with the local economy.

5.9.2 Existence and dynamics of strains in a nonlocal reaction-diffusion model of viral evolution

In 8, we develop a mathematical framework for predicting and quantifying virus diversity evolution during infection of a host organism. It is specified as a virus density distribution with respect to genotype and time governed by a reaction-diffusion integro-differential equation taking virus mutations, replication, and elimination by immune cells and medical treatment into account. Conditions for the existence of virus strains that correspond to localized density distributions in the space of genotypes are determined. It is shown that common viral evolutionary traits like diversification and extinction are driven by nonlocal interactions via immune responses, target-cell competition, and therapy. This provides us with a mechanistic explanation for clinically relevant properties like immune escape and drug resistance selection, and allows us to link virus genotypes to phenotypes.

5.9.3 Pattern formation in a three-species cyclic competition model

In nature, different species compete among themselves for common resources and favorable habitat. Therefore, it becomes really important to determine the key factors in maintaining the biodiversity. Also, some competing species follow cyclic competition in real world where the competitive dominance is characterized by a cyclic ordering. In 14, we study the formation of a wide variety of spatiotemporal patterns including stationary, periodic, quasi-periodic and chaotic population distributions for a diffusive Lotka-Volterra type three-species cyclic competition model with two different types of cyclic ordering. For both types of cyclic ordering, the temporal dynamics of the corresponding non-spatial system show the extinction of two species through global bifurcations such as homoclinic and heteroclinic bifurcations. For the spatial system, we show that the existence of Turing patterns is possible for a particular cyclic ordering, while it is not the case for the other cyclic ordering through both the analytical and numerical methods. Further, we illustrate an interesting scenario of short-range invasion as opposed to the usual invasion phenomenon over the entire habitat. Also, our study reveals that both the stationary and dynamic population distributions can coexist in different parts of a habitat. Finally, we extend the spatial system by incorporating nonlocal intra-specific competition terms for all the three competing species. Our study shows that the introduction of nonlocality in intra-specific competitions stabilizes the system dynamics by transforming a dynamic population distribution to stationary. Surprisingly, this nonlocality-induced stationary pattern formation leads to the extinction of one species and hence, gives rise to the loss of biodiversity for intermediate ranges of nonlocality. However, the biodiversity can be restored for sufficiently large extent of nonlocality.

5.9.4 Method of monotone solutions for reaction-diffusion equations

Existence of solutions of reaction-diffusion systems of equations in unbounded domains is studied by the Leray-Schauder (LS) method based on the topological degree for elliptic operators in unbounded domains and on a priori estimates of solutions in weighted spaces, 21. We identify some reaction-diffusion systems for which there exist two subclasses of solutions separated in the function space, monotone and nonmonotone solutions. A priori estimates and existence of solutions are obtained for monotone solutions allowing to prove their existence by the LS method. Various applications of this method are given.

5.9.5 Solvability of some integro-differential equations with anomalous diffusion and transport

The article 22 deals with the existence of solutions of an integro-differential equation in the case of anomalous diffusion with the negative Laplace operator in a fractional power in the presence of the transport term. The proof of existence of solutions is based on a fixed-point technique. Solvability conditions for elliptic operators without the Fredholm property in unbounded domains are used. We discuss how the introduction of the transport term impacts the regularity of solutions.

5.9.6 Analysis and numerical simulations of a reaction-diffusion model with fixed active bodies

We propose in 23 an interaction model for two substances (molecules) of concentrations $f$ and $g$. The substance $f$ is assumed to be involved in the growth process of $g$, and in contrast, the substance $g$ inhibits the production of $f$. Our model is based on a reaction-diffusion system for the interaction of two considered substances (molecules). We analyze its well-posedness and perform a numerical scheme to simulate the behavior of the solutions. As an application, we investigate the role of A$\beta$-oligomers in the early stage of Alzheimer's disease propagation, more precisely for the impact of A$\beta$-oligomers in neuron impairment as studied in [M. Andrade-Restrepo et al., Modeling the spatial propagation of A$\beta$ oligomers in Alzheimer's disease, in CEMRACS 2018 - Numerical and Mathematical Modeling for Biological and Medical Applications: Deterministic, Probabilistic and Statistical Descriptions, Marseille, France, 2018, pp. 1-10].

5.9.7 Turing instability in an economic–demographic dynamical system may lead to pattern formation on a geographical scale

Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the emergence of densely populated areas at their present locations is widely believed to be linked to more favourable environmental and climatic conditions. In 24, we challenge this point of view. We first identify a few areas at different parts of the world where the environmental conditions (quantified by the temperature, precipitation and elevation) show a relatively small variation in space on the scale of thousands of kilometres. We then examine the population distribution across those areas to show that, in spite of the approximate homogeneity of the environment, it exhibits a significant variation revealing a nearly periodic spatial pattern. Based on this apparent disagreement, we hypothesize that there may exist an inherent mechanism that may lead to pattern formation even in a uniform environment. We consider a mathematical model of the coupled demographic-economic dynamics and show that its spatially uniform, locally stable steady state can give rise to a periodic spatial pattern due to the Turing instability, the spatial scale of the emerging pattern being consistent with observations. Using numerical simulations, we show that, interestingly, the emergence of the Turing patterns may eventually lead to the system collapse.

5.9.8 Global attractor in alpha-norm for some partial functional differential equations of neutral and retarded type

The aim of the work 25 is to study the existence of a global attractor for some partial neutral functional differential equations; the convergence of all the solutions to the attractor is given in terms of the alpha-norm which is more important than the classical norm. Firstly, we show some interesting properties on the semigroup solution like the asymptotic smoothness. Secondly, when the semigroup is compact dissipative, then we show the existence of the global attractor. For illustration, an application is provided for some model arising in physical systems.

5.9.9 Longtime behavior of a second order finite element scheme simulating the kinematic effects in liquid crystal dynamics

We consider in 12 an unconditional fully discrete finite element scheme for a nematic liquid crystal flow with different kinematic transport properties. We prove that the scheme converges towards a unique critical point of the elastic energy subject to the finite element subspace, when the number of time steps go to infinity while the time step and mesh size are fixed. A Lojasiewicz type inequality, which is the key for getting the time asymptotic convergence of the whole sequence furnished by the numerical scheme, is also derived.

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

6.1.2 STIC/MATH/CLIMAT AmSud project

6.1.3 Participation in other International Programs

6.2.1 Visits of international scientists

6.3.1 FP7 & H2020 projects

6.4.1 ANR

6.4.2 Other projects

• Thomas Lepoutre is a member of the ERC MESOPROBIO (head Vincent Calvez) dedicated to "Mesoscopic models for propagation in biology", 2015-2021.

INGERENCE

• Title:
  INferring GEne REgulatory NEtworks from single CEll Data to improve vaccine design
• Date/Duration:
  2018-2021.
• Participants:
  Olivier Gandrillon and Fabien Crauste

Mecan'os

• Title:
  Si tu ne peux pas l'avoir, (re)construis le !
• Partner Institution(s):
  • Institut Camille Jordan, France
  • CUNY, New-York, USA
  • university Abou Bekr Belkaid of Tlemcen, Algeria
• Date/Duration:
  September 2021-August 2023
• Additionnal info/keywords:
  La croissance rapide de la population gériatrique, qui est souvent atteinte de perte dégénérative de l’os, associée à une forte augmentation du nombre de personnes subissant une chirurgie de reconstruction osseuse (accident de voiture ou cancer des os), va permettre au marché des prothèses osseuses d’atteindre la somme de 4 milliards de dollars en 2025. À l’heure actuelle, ce marché est dominé par des matériaux synthétiques qui, malheureusement, présentent un fort risque de mauvaise intégration squelettique. Le remplacement de ces prothèses induit de nouvelles interventions chirurgicales et donc une augmentation des dépenses de santé. Nous pensons donc qu’il est grand temps de s’intéresser aux prochaines générations d’implants. Pour cette raison, notre équipe de bio-ingénieurs (USA) et mathématiciens (France et Algérie) est en train de développer un procédé de construction des prothèses de nouvelle génération adaptables à chaque personne. Partant du principe que la nature ne peut pas être égalée dans son inventivité, nous sommes convaincus que la solution viendra de la création d’implants biocompatibles par un contrôle numérique de l’expression des gènes des cellules osseuses venant des patients eux-mêmes. Étant donné que notre collaboration s’est déjà avérée fructueuse avec des donneurs de cellules âgés de 20 ans, nous souhaitons travailler en élargissant drastiquement la tranche d’âge. À cette fin, notre volonté est de renforcer notre collaboration et nos interactions pour apporter une solution rapide, efficace et adaptée aux personnes qui nécessite une chirurgie de reconstruction osseuse.

micrOS-macrOS

• Title:
  modélisation multi-échelle de l'os
• Partner Institution(s):
  • Institut Camille Jordan, France
  • CUNY, New-York, USA
  • university Abou Bekr Belkaid of Tlemcen, Algeria
• Date/Duration:
  September 2021-August 2023
• Additionnal info/keywords:
  Notre projet a pour objectif d’apporter un nouvel éclairage sur le rôle des micro-ARN dans la construction d’implants osseux de nouvelle génération. L’originalité de notre approche est de prédire quantitativement les résultats expérimentations afin de (1) réduire le nombre d’essais précliniques et (2) établir un cadre unique de personnalisation de régénération de tissu osseux humain.

• Thomas Lepoutre and Olivier Gandrillon have been granted and IXXI project on relaxation experiments for gene expression.

7.1.1 Scientific events: organisation

7.1.2 Journal

7.1.3 Invited talks

• Mostafa Adimy: International online workshop on Mathematical Modelling in Biomedicine, Moscow, Russia, 25-29 octobre 2021  
• Mostafa Adimy: 1st International E-Conference on Differential Equations and Applications (IE-CDEA 2021), Fez, Maroc, 24-25 septembre 2021
• Mostafa Adimy: VI Latin American Congress of Mathematicians (CLAM2021), Montevideo, Uruguay, 13-17 septembre 2021
• Samuel Bernard: EWM-EMS Summer School on Multi-scale Modeling for Pattern Formation in Biological Systems (Web), 19 July - 23 July 2021

7.2.1 Supervision

• PhD in progress: Kyriaki Dariva , “Modélisation mathématique des interactions avec le système immunitaire en leucémie myéloide chronique”. Université Lyon 1, since September 2018, supervisor: Thomas Lepoutre
• PhD in progress: Alexey Koshkin, “Inferring gene regulatory networks from single cell data”, ENS de Lyon, until December 2021, supervisors: Olivier Gandrillon and Fabien Crauste
• PhD in progress: Paul Lemarre, “Modélisation des souches de prions”. Université Lyon 1, until May 2021, supervisors: Laurent Pujo-Menjouet et Suzanne Sindi (University of California, Merced)
• PhD in progress: Léonard Dekens, “Adaptation d'une population avec une reproduction sexuée à un environnement hétérogène : modélisation mathématique et analyse asymptotique dans un régime de petite variance”, Université Lyon 1, since September 2019, supervisor: Vincent Calvez.
• PhD in progress: Mete Demircigil, “Etude du mouvement collectif chez Dictyostelium Discoideum et autres espèces. Modélisation, Analyse et Simulation”, ENS-Lyon, since September 2019, supervisor: Vincent Calvez.
• PhD in progress: Ghada Abi Younes, “Modélisation mathématique des maladies inflammatoires”, Université Lyon, since November 2019, supervisor: Vitaly Volpert.
• PhD in progress: Elias Ventre, “Paysage et trajectoire - des réseaux de régulation génique aux trajectoires cellulaires", ENS, since October 2019, supervisors: Olivier Gandrillons, Thibault Espinasse and Thomas Lepoutre.
• PhD in progress: Cheikh Gueye, “Problèmes inverses pour l'estimation de paramètre de modèles mathématiques”, Université Lyon, since October 2019, supervisors: Laurent Pujo-Menjouet and Léon Tine.
• PhD in progress: Matteo Bouvier (CIFRE with the Vidium company), supervisor: Olivier Gandrillon.
• PhD in progress: Margaux Prieux, supervisors: Olivier Gandrillon and Jacqueline Marvel.
• PhD supervision: Aquilina Al Khouri, since April 2020, contract interrupted in October 2021, supervisors: Samuel Bernard and Jonathan Rouzaud-Cornabas.
• Post-doc: Madge Martin, supervisors: Olivier Gandrillon and Fabien Crauste.

7.2.2 Juries

• Alexey Koshkin, “Inferring gene regulatory networks from single cell data” (Olivier Gandrillon supervisor)
• Paul Lemarre, “Modélisation des souches de prions” (Laurent Pujo-Menjouet supervisor and Mostafa Adimy examiner).
• Olivier Gandrillon: PhD defense of Souad Zreika, La différenciation érythrocytaire : caractérisation moléculaire de l'engagement cellulaire, University of Lyon, examiner.
• Mostafa Adimy: PhD defense of Youssef Hbid, Modélisation et analyse prédictive des risques et des conséquences post accident vasculaire cérébral, Sorbonne université, reviewer.
• Mostafa Adimy: PhD defense of Karim Amin, Qualitative Analysis of Delay Differential Equations Modelling Tropical Diseases, Politehnica University of Bucharest, reviewer.

International journals

• 1 articleM.Mostafa Adimy, P.Pablo Amster and J.Julián Epstein. Periodic solutions for a nonautonomous mathematical model of hematopoietic stem cell dynamics.Nonlinear Analysis: Theory, Methods and Applications211October 2021, 112397
  HALDOIback to text
• 2 articleM.Mostafa Adimy, L.Louis Babin and L.Laurent Pujo-Menjouet. Why Are Periodic Erythrocytic Diseases so Rare in Humans?Bulletin of Mathematical Biology841November 2021, 1-19
  HALDOIback to text
• 3 articleM.Mostafa Adimy, A.Abdennasser Chekroun and T.Toshikazu Kuniya. Traveling waves of a differential-difference diffusive Kermack-McKendrick epidemic model with age-structured protection phase.Journal of Mathematical Analysis and Applications5051December 2021, 125464
  HALDOIback to text
• 4 articleM.Martin Andrade-Restrepo, I.Ionel Sorin Ciuperca, P.Paul Lemarre, L.Laurent Pujo-Menjouet and L.Leon Tine. A reaction-diffusion model of spatial propagation of Aβ oligomers in early stage Alzheimer’s disease.Journal of Mathematical Biology825April 2021, 1-25
  HALDOIback to text
• 5 articleS.Sebastian Aniţa, M.Malay Banerjee, S.Samiran Ghosh and V.Vitaly Volpert. Vaccination in a two-group epidemic model.Applied Mathematics Letters119March 2021, 1-7
  HALDOIback to text
• 6 articleC.Chloe Audebert, D.Daphné Laubreton, C.Christophe Arpin, O.Olivier Gandrillon, J.Jacqueline Marvel and F.Fabien Crauste. Modeling and characterization of inter-individual variability in CD8 T cell responses in mice.In Silico Biology141-2May 2021, 13-39
  HALDOIback to text
• 7 articleM.Malay Banerjee, S. V.Sergei V Petrovskii and V.Vitaly Volpert. Nonlocal Reaction–Diffusion Models of Heterogeneous Wealth Distribution.Mathematics 94February 2021, 1-18
  HALDOIback to text
• 8 articleN.Nikolai Bessonov, G.Gennady Bocharov, A.Andreas Meyerhans, V.Vladimir Popov and V.Vitaly Volpert. Existence and Dynamics of Strains in a Nonlocal Reaction-Diffusion Model of Viral Evolution.SIAM Journal on Applied Mathematics81January 2021, 107-128
  HALDOIback to text
• 9 articleF. D.Felipe De A Camargo, M.Mostafa Adimy, L.Lourdes Esteva, C.Clémence Métayer and C. P.Cláudia P Ferreira. Modeling the Relationship Between Antibody-Dependent Enhancement and Disease Severity in Secondary Dengue Infection.Bulletin of Mathematical Biology838August 2021, 1-28
  HALDOIback to text
• 10 articleR.Ronan Duchesne, A.Anissa Guillemin, O.Olivier Gandrillon and F.Fabien Crauste. Practical identifiability in the frame of nonlinear mixed effects models: the example of the in vitro erythropoiesis.BMC BioinformaticsOctober 2021, 1-21
  HALDOIback to text
• 11 articleO.Olivier Gandrillon, M.Mathilde Gaillard, T.Thibault Espinasse, N. B.Nicolas B Garnier, C.Charles Dussiau, O.Olivier Kosmider and P.Pierre Sujobert. Entropy as a measure of variability and stemness in single-cell transcriptomics.Current Opinion in Systems Biology27September 2021, 1-14
  HALDOIback to text
• 12 articleM. S.Mouhamadou Samsidy Goudiaby, A.Ababacar Diagne and L.Léon Matar Tine. Longtime behavior of a second order finite element scheme simulating the kinematic effects in liquid crystal dynamics.Communications on Pure & Applied Analysis20102021, 1-16
  HALDOIback to text
• 13 articleM.Maxim Kuznetsov, J.Jean Clairambault and V.Vitaly Volpert. Improving cancer treatments via dynamical biophysical models.Physics of Life ReviewsOctober 2021, 1-84
  HALback to text
• 14 articleK.Kalyan Manna, V.Vitaly Volpert and M.Malay Banerjee. Pattern Formation in a Three-Species Cyclic Competition Model.Bulletin of Mathematical Biology83March 2021, 1-37
  HALDOIback to text
• 15 articleE.Elena Merino Tejero, D.Danial Lashgari, R.Rodrigo García-Valiente, X.Xuefeng Gao, F.Fabien Crauste, P.Philippe Robert, M.Michael Meyer-Hermann, M. R.María Rodríguez Martínez, S. M.S. Marieke van Ham, J.Jeroen Guikema, H.Huub Hoefsloot and A.Antoine Van Kampen. Multiscale Modeling of Germinal Center Recapitulates the Temporal Transition From Memory B Cells to Plasma Cells Differentiation as Regulated by Antigen Affinity-Based Tfh Cell Help.Frontiers in Immunology11February 2021
  HALDOIback to text
• 16 articleA.Anastasia Mozokhina, A.Anass Bouchnita and V.Vitaly Volpert. Blood Clotting Decreases Pulmonary Circulation during the Coronavirus Disease.Mathematics 919September 2021, 1-18
  HALDOIback to text
• 17 articleN.Nicolas Ratto, A.Anass Bouchnita, P.P Chelle, M.Martine Marion, M. A.Mikhail A. Panteleev, D.D Nechipurenko, B.Brigitte Tardy-Poncet and V.Vitaly Volpert. Patient-Specific Modelling of Blood Coagulation.Bulletin of Mathematical Biology83March 2021, 1-31
  HALDOIback to text
• 18 articleE.Elias Ventre, T.Thibault Espinasse, C.-E.Charles-Edouard Bréhier, V.Vincent Calvez, T.Thomas Lepoutre and O.Olivier Gandrillon. Reduction of a stochastic model of gene expression: Lagrangian dynamics gives access to basins of attraction as cell types and metastabilty.Journal of Mathematical Biology8359November 2021
  HALDOIback to text
• 19 articleE.Elias Ventre. Reverse engineering of a mechanistic model of gene expression using metastability and temporal dynamics.In Silico Biology143-4January 2022, 89-113
  HALDOIback to text
• 20 articleV.Vitaly Volpert, M.Malay Banerjee and S.Swarnali Sharma. Epidemic progression and vaccination in a heterogeneous population. Application to the Covid-19 epidemic.Ecological Complexity472021, 1-28
  HALDOIback to text
• 21 articleV.Vitaly Volpert and V.Vitali Vougalter. Method of Monotone Solutions for Reaction-Diffusion Equations.Journal of Mathematical Sciences253February 2021, 660 - 675
  HALDOIback to text
• 22 articleV.Vitali Vougalter and V.Vitaly Volpert. Solvability of some integro-differential equations with anomalous diffusion and transport.Analysis and Mathematical Physics11June 2021, 1-26
  HALDOIback to text
• 23 articleC.Chang Yang and L.Léon Matar Tine. Analysis and Numerical Simulations of a Reaction-Diffusion Model with Fixed Active Bodies.SIAM Journal on Applied Mathematics814January 2021, 1339-1360
  HALDOIback to text
• 24 articleA.Anna Zincenko, S.Sergei Petrovskii, V.Vitaly Volpert and M.Malay Banerjee. Turing instability in an economic–demographic dynamical system may lead to pattern formation on a geographical scale.Journal of the Royal Society Interface18April 2021, 1-17
  HALDOIback to text

Scientific book chapters

• 25 inbookM.Mostafa Adimy, K.Khalil Ezzinbi and C.Catherine Marquet. Global Attractor in Alpha-Norm for Some Partial Functional Differential Equations of Neutral and Retarded Type.Studies in Evolution Equations and Related TopicsSTEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & HealthSpringer International PublishingMay 2021, 33-49
  HALDOIback to text

Doctoral dissertations and habilitation theses

• 26 thesisA.Alexey Koshkin. Studying a stochastic gene regulatory network driving the germinal center B cell differentiation.ENS de LYON, LBMC, and INRIA DRACULADecember 2021
  HALback to text
• 27 thesisP.Paul Lemarre. Prions come in all shapes and sizes - Mathematical modeling of protein self-aggregation and conversion.Institut Camille Jordan, Université Claude Bernard Lyon 1, FranceMay 2021
  HALback to text

Reports & preprints

• 28 miscA.Aquilina Al Khoury, S.Samuel Bernard and J.Jonathan Rouzaud-Cornabas. Accuracy of Mixed Precision Computation in Large Coupled Biological Systems.June 2021
  HAL
• 29 miscV.Vincent Calvez, M.Mete Demircigil and R.Roxana Sublet. Mathematical modeling of cell collective motion triggered by self-generated gradients.September 2021
  HAL
• 30 miscV.Vincent Calvez, T.Thomas Lepoutre and D.David Poyato. Ergodicity of the Fisher infinitesimal model with quadratic selection.July 2021
  HAL
• 31 reportK.Kyriaki Dariva and P.Pedro Jaramillo. Reconstruction of trajectories-Challenge AMIES.Univ Lyon, Université Claude-Bernard Lyon 1; Université de bordeauxOctober 2021, 1-15
  HAL
• 32 miscK.Kyriaki Dariva and T.Thomas Lepoutre. Influence of the age structure on the stability in a tumor-immune model for chronic myeloid leukemia.February 2021
  HAL
• 33 misc L.Léonard Dekens. Evolutionary dynamics of complex traits in sexual populations in a heterogeneous environment: how normal? October 2021
  HAL
• 34 miscN. P.Nan Papili Gao, O.Olivier Gandrillon, A.András Páldi, U.Ulysse Herbach and R.Rudiyanto Gunawan. Universality of cell differentiation trajectories revealed by a reconstruction of transcriptional uncertainty landscapes from single-cell transcriptomic data.February 2021
  HALDOI
• 35 reportR.Romain Gauchon, N.Nicolas Ponthus, C.Catherine Pothier, C.Christophe Rigotti, V.Vitaly Volpert, S.Stéphane Derrode, J.-P.Jean-Pierre Bertoglio, A.Alexis Bienvenüe, P.-O.Pierre-Olivier Goffard, A.Anne Eyraud-Loisel, S.Simon Pageaud, J.Jean Iwaz, S.Stéphane Loisel and P.Pascal Roy. Lessons learnt from the use of compartmental models over the COVID-19 induced lockdown in France.Université Lyon 1; Ecole Centrale de Lyon; INSA LyonMarch 2021
  HAL