3.1 Introduction

Data and image analysis, statistical, ODEs, PDEs, and agent-based approaches are used either individually or in combination, with a strong focus on PDE analysis and agent-based approaches. Mamba was created in January 2014. It aims at developing models, simulations, numerical and control algorithms to solve questions from life sciences involving dynamics of phenomena encountered in biological systems such as protein intra-cellular spatio-temporal dynamics, cell motion, early embryonic development, multicellular growth, wound healing and liver regeneration, cancer evolution, healthy and tumor growth control by pharmaceuticals, protein polymerization occurring in neurodegenerative disorders, control of dengue epidemics, etc.

Another guideline of our project is to remain close to the most recent questions of experimental biology or medicine. In this context, we develop many close and fruitful collaborations with biologists and physicians.

We focus mainly on the creation, investigation and transfer of new mathematical models, methods of analysis and control, and numerical algorithms, but in selected cases software development as that of CellSys and TiQuant by D. Drasdo and S. Hoehme is performed. More frequently, the team develops “proof of concept” numerical codes in order to test the adequacy of our models to experimental biology.

We have organized the presentation of our research program in three methodological axes (Subsections 3.2, 3.3 and 3.4) and two application axes (Subsections 4.2 and 4.4). Evolving along their own logic in close interaction with the methodological axes, the application axes are considered as application-driven research axes in themselves. The methodological research axes are the following.

Axis 1 is devoted to work in physiologically-based design, analysis and control of population dynamics. It encompasses populations of bacteria, of yeasts, of cancer cells, of neurons, of aggregating proteins, etc. whose dynamics are represented by partial differential equations (PDEs), structured in evolving physiological traits, such as age, size, size-increment, time elapsed since last firing (neurons).

Axis 2 is devoted to reaction equations and motion equations of agents in living systems. It aims at describing biological phenomena such as tumor growth, chemotaxis and wound healing.

Axis 3 tackles questions of model and parameter identification, combining stochastic and deterministic approaches and inverse problem methods in nonlocal and multi-scale models.

3.2 Methodological axis 1: Analysis and control for population dynamics

Population dynamics is a field with varied and wide applications, many of them being in the core of MAMBA interests - cancer, bacterial growth, protein aggregation. Their theoretical study also brings a qualitative understanding on the interplay between individual growth, propagation and reproduction in such populations. In the past decades, many results where obtained in the BANG team on the asymptotic and qualitative behavior of such structured population equations, see e.g.  157, 76, 107, 89. Other Inria teams interested by this domain are Mycenae, Numed and Dracula, with which we are in close contacts. Among the leaders of the domain abroad, we can cite among others our colleagues Graeme Wake (New Zealand), Glenn Webb (USA), Jacek Banasiak (South Africa), Odo Diekmann (Netherlands), with whom we are also in regular contact. Most remarkably and recently, connections have also been made with probabilists working on Piecewise Deterministic Markov Processes (F. Malrieu at the university of Rennes, Jean Bertoin at the ETH in Zurich, Vincent Bansaye at Ecole Polytechnique, Julien Berestycki at Cambridge, Amaury Lambert at College de France, M. Hoffmann at Paris Dauphine, Alex Watson in UCL, London and J. Bertoin in Zurich), leading to a better understanding of the links between both types of results – see also the Methodological axis 3.

We divide this research axis, which relies on the study of structured population equations, according to four different applications, bringing their own mathematical questions, e.g., stability, control, or blow-up.

Time asymptotics for nucleation, growth and division equations

Following the many results obtained in the BANG team on the asymptotic and qualitative behavior of structured population equation, we put our effort on the investigation of limit cases, where the trend to a steady state or to a steady exponential growth described by the first eigenvector fails to happen. In  83, the case of equal mitosis (division into two equally-sized offspring) with linear growth rate was studied, and strangely enough, it appeared that the general relative entropy method could also be adapted to such a non-dissipative case. Many discussions and common workshops with probabilists, especially through the ANR project PIECE coordinated by F. Malrieu, have led both communities to work closer.

We also enriched the models by taking into account a nucleation term, modeling the spontaneous formation of large polymers out of monomers  163. We investigated the interplay between four processes: nucleation, polymerization, depolymerization and fragmentation.

New perspectives are now to consider not only one species but several interacting ones, which may exhibit complex interplays which may lead to damped oscillations or to infinite growth; these are in collaboration with C. Schmeiser and within the Vienna associated team MaMoCeMa (J. Delacour's Ph.D) and with K. Fellner from Graz (M. Mezache's Ph.D).

Cell population dynamics and its control

One of the important incentives for such model design, source of many theoretical works, is the challenging question of drug-induced drug resistance in cancer cell populations, described in more detail below in the Applicative axis 1, Cancer. The adaptive dynamics setting used consists of phenotype-structured integro-differential [or reaction-diffusion, when phenotype instability is added under the form of a Laplacian] equations describing the dynamic behavior of different cell populations interacting in a Lotka-Volterra-like manner that represents common growth limitation due to scarcity of expansion space and nutrients. The phenotype structure allows us to analyse the evolution in phenotypic traits of the populations under study and its asymptotics for two populations  142, 139, 138, 140. Space may be added as a complementary structure variable provided that something is known of the (Cartesian) geometry of the population  141, which is seldom the case. A recent review of mathematical methods aiming at improving cancer treatments has been published in Physics of Life Reviews  136.

Modelling Mendelian and non-Mendelian inheritances in density-dependent population dynamics

Classical strategies for controlling mosquitoes responsible of vector-borne disease are based on mechanical methods, such as elimination of oviposition sites; and chemical methods, such as insecticide spraying. Long term usage of the latter generates resistance 86, 123, transmitted to progeny according to Mendelian inheritance (in which each parent contributes randomly one of two possible alleles for a trait). New control strategies involve biological methods such as genetic control, which may either reduces mosquito population in a specific area or decreases the mosquito vector competence 65, 133, 175. Among the latter, infection of wild populations by the bacterium Wolbachia appears promising (see also Applicative axis 2 below). Being maternally-transmitted, the latter obeys non-Mendelian inheritance law. Motivated by the effects of the (possibly unwanted) interaction of these two types of treatment, we initiated the study of modelling of Mendelian and non-Mendelian inheritances in density-dependent population dynamics. First results are shown in 151.

Control and macroscopic limits of collective dynamics

The term self-organization is used to describe the emergence of complex organizational patterns from simple interaction rules in collective dynamics systems. Such systems are valuable tools to model various biological systems or opinion dynamics, whether it be the collective movement of animal groups, the organization of cells in an organism or the evolution of opinions in a large crowd. A special case of self-organization is given by consensus, i.e. the situation in which all agents' state variables converge. Another phenomenon is that of clustering, when the group is split into clusters that each converge to a different state. A natural question in this framework is that of control: can the system be guided to a desired predetermined configuration? In the case when self-organization is not achieved naturally by the system, can it be driven to it? On the contrary, in the case where consensus and clustering are situations to be avoided (for example in crowd dynamics), can we design control strategies to keep the system away from clustering?

Another natural question is that of the large population limit. When the number of agents tends to infinity, the previous system of equations becomes unmanageable, a problem well-known as the curse of dimensionality. A common answer to this issue consists of studying the macroscopic limit of the system. It is then crucial to understand whether the limit system retains the properties of the microscopic one.

Models of neural network

Mean field limits have been proposed by biophysicists in order to describe neural networks based on physiological models. The various resulting equations are called integrate-and-fire, time elapsed models, voltage-conductance models. Their specific nonlinearities and the blow-up phenomena make their originality which has led to develop specific mathematical analysis 154, followed by 149, 132, 155, 88. This field also yields a beautiful illustration for the capacity of the team to combine and compare stochastic and PDE modelling (see Methodological axis 3), in 93.

Models of interacting particle systems

The organisation of biological tissues during development is accompanied by the formation of sharp borders between distinct cell populations. The maintenance of this cell segregation is key in adult tissue homeostatis, and its disruption can lead tumor cells to spread and form metastasis. This segregation is challenged during tissue growth and morphogenesis due to the high mobility of many cells that can lead to intermingling. Therefore, understanding the mechanisms involved in the generation and maintain of cell segregation is of tremendous importance in tissue morphogenesis, homeostasis, and in the development of various invasive diseases such as tumors. In this research axis, we aim to provide a mathematical framework which enables to quantitatively link the segregation and border sharpening ability of the tissue to these cell-cell interaction phenomena of interest 75. As agent-based models do not enable precise mathematical analysis of their solutions due to the lack of theoretical results, we turn towards continuous -macroscopic- models and aim to provide a rigorous link between the different models 75.

Models of population dynamics structured in phenotype

The collaboration of Jean Clairambault with Emmanuel Trélat and Camille Pouchol (from September last year assistant professor at MAP5 Paris-Descartes, University of Paris), together now with Nastassia Pouradier Duteil, has been continued and presently leads us to a possible quantitative biological identification of the structuring phenotypes of the model developed in  162, through a beginning collaboration with an Indian systems biologist (Mohit Kumar Jolly, IIS Bangalore). Our motivation in this collaboration is to couple a physiologically based system of 6 ODEs developed by our Indian collaborator with our phenotype-structured cell population dynamics model  96, 98.

In the framework of the HTE project EcoAML 2016-2020, Thanh Nam Nguyen, Jean Clairambault, Delphine Salort and Benoît Perthame, in collaboration with Thierry Jaffredo at IBPS-SU, have designed a phenotype-structured integrodifferential model of interactions between haematopoietic stem cells (healthy or leukaemic) and their supporting stromal cells  146. In this model, without diffusion, to our relative astonishment, our postdoctoral fellow T.N. Nguyen predicts in particular that under special circumstances, a coexistence between healthy and leukaemic stem cell subpopulations is possible. The explanation of such possible theoretical coexistence still remains to be explained.

The idea of cooperation between cell subpopulations in a tumour is also studied using phenoytype-structured models of cell populations by Frank Ernesto Alvarez Borges, PhD student of Stéphane Mischler (Paris-Dauphine University), Mariano Rodríguez Ricard (University of Havana, Cuba) and Jean Clairambault, in collaboration with José Antonio Carrillo (Oxford). A feature of these models, in as much as conflicting continuous phenotypes (e.g., adhesivity vs. motility, or fecundity vs. viability, or fecundity vs. motility  1) are supposed to structure a unique cell population, is that they can also represent the emergence of multicellularity in such a cell population, when two subpopulations of the same population, i.e., endowed with the same genome and represented w.r.t. relevant heterogeneity in the cell population by such conflicting phenotypes, are determined by two different choices of the 2-d phenotype. This has been this year the object of a submitted article associating Frank Ernesto Alvarez Borges, José antonio Carrillo (Oxford) and Jean Clairambault 8, and this collaboration will be continued. In a simplified representation when the two phenotypes are just extreme values of a 1-d continuous phenotype (e.g., 0 for total adhesivity and no motility, 1 for no adhesivity and complete motility) this situation may be related to the previously described case, developed in  146, in which two extreme values of a convex function linked to proliferation are occupied by the two extreme phenotype values (0 and 1), leading to the coexistence of two cell subpopulations.

The principle of structuring cell population heterogeneities by a hidden phenotype has also been applied, in collaboration with Camille Pouchol (Université Paris Cité) and Zineb Kaid, PhD student at Tlemcen University, to study the interactions between a tumour cell population and a population of immune cells, NK-lymphocytes and CD8+ T-lymphocytes. The tumour cell population heterogeneity is defined by a continuous malignancy phenotype related to its potential of de-differentiation or transdifferentiation, whereas the heterogeneity within the immune cell population is coded by a continuous anti-tumor aggressiveness phenotype, which is drastically decreased by tumour cells in the process of immunotolerance, resulting in so-called “exhausted T-cells”. This process is fought by so-called Immune Checkpoint Inhibitors, a new class of drugs used in cancer immunotherapy, with some limited, nevertheless remarkable, success in clinical oncology, in particular in the treatment of melanoma. We have studied these tumour-immune interactions in the perspective of representing and later optimising the impact of such immunotherapies, a ongoing work which is reported in a preprint  53.

Collaborations

• Nucleation, growth and fragmentation equations: Klemens Fellner, university of Graz, Austria; Piotr Gwiązda, Polish Academy of Sciences, Poland; Christian Schmeiser, university of Vienna, through the associated team MaMoCeMa.
• Cell population dynamics and its control: Tommaso Lorenzi, former Mamba postdoc, now at the University of St. Andrews, Scotland, maintains a vivid collaboration with the Mamba team. He is in particular an external member of the HTE program MoGlImaging (see also Applicative axis 1). Emmanuel Trélat, Sorbonne Université professor, member of LJLL and of the CAGE Inria team, is the closest Mamba collaborator for optimal control. Benedetto Piccoli, Professor at Rutgers University (Camden, New Jersey), is collaborating on the analysis and control of collective dynamics. Nathalie Ayi, Sorbonne University, is participating in the development of graph-limit methods.
• Mendelian inheritance and resistance in density-dependent population dynamics: Pastor Pérez-Estigarribia, Christian Schaerer, Universidad Nacional de Asunción, Paraguay.
• Neural networks: Delphine Salort, Professor Sorbonne Université, Laboratory for computations and quantification in biology, and Patricia Reynaud, University of Nice, Maria Cáceres, University of Granada.
• Models of interacting particle systems: Pierre Degond, Imperial College London; Julien Barré, APMO, Orléans; Ewelina Zatorska, University College London; Sara Merino from the university of Vienna (through the associated team MaMoCeMa).

3.3 Methodological axis 2: Reaction and motion equations for living systems

The Mamba team had initiated and is a leader on the works developed in this research axis. It is a part of a consortium of several mathematicians in France through the ANR Blanc project Kibord, which involves in particular members from others INRIA team (DRACULA, COMMEDIA). Finally, we mention that from Sept. 2017 on, Mamba benefited from the ERC Advanced Grant ADORA (Asymptotic approach to spatial and dynamical organizations) of Benoît Perthame.

We divide this research axis, which relies on the study of partial differential equations for space and time organisation of biological populations, according to various applications using the same type of mathematical formalisms and methodologies: asymptotic analysis, weak solutions, numerical algorithms.

Aggregation equation

In the mathematical study of collective behavior, an important class of models is given by the aggregation equation. In the presence of a non-smooth interaction potential, solutions of such systems may blow up in finite time. To overcome this difficulty, we have defined weak measure-valued solutions in the sense of duality and its equivalence with gradient flows and entropy solutions in one dimension  129. The extension to higher dimensions has been studied in  91. An interesting consequence of this approach is the possibility to use the traditional finite volume approach to design numerical schemes able to capture the good behavior of such weak measure-valued solutions  122, 130.

Identification of the mechanisms of single cell motion

In this research axis, we aim to study the mechanisms of single cell adhesion-based and adhesion free motion. This work is done in the frame of the recently created associated team MaMoCeMa (see Section 9) with the WPI, Vienna. In a first direction 170 with N. Sfakianakis (Heidelberg University), we extended the live-cell motility Filament Based Lamellipodium Model to incorporate the forces exerted on the lamellipodium of the cells due to cell-cell collision and cadherin induced cell-cell adhesion. We took into account the nature of these forces via physical and biological constraints and modelling assumptions. We investigated the effect these new components had in the migration and morphology of the cells through particular experiments. We exhibit moreover the similarities between our simulated cells and HeLa cancer cells.

In a second work done in collaboration with the group of biologist at IST (led by Michael Sixt Austria), we developed and analyzed a two-dimensional mathematical model for cells migrating without adhesion capabilities 131. Cells are represented by their cortex, which is modelled as an elastic curve, subject to an internal pressure force. Net polymerization or depolymerization in the cortex is modelled via local addition or removal of material, driving a cortical flow. The model takes the form of a fully nonlinear degenerate parabolic system. An existence analysis is carried out by adapting ideas from the theory of gradient flows. Numerical simulations show that these simple rules can account for the behavior observed in experiments, suggesting a possible mechanical mechanism for adhesion-independent motility.

Free boundary problems for tumor growth

Fluid dynamic equations are now commonly used to describe tumor growth with two main classes of models: those which describe tumor growth through the dynamics of the density of tumoral cells subjected to a mechanical stress; those describing the tumor through the dynamics of its geometrical domain thanks to a Hele-Shaw-type free boundary model. The first link between these two classes of models has been rigorously obtained thanks to an incompressible limit in  153 for a simple model. This result has motivated the use of another strategy based on viscosity solutions, leading to similar results, in  134.

Since more realistic systems are used in the analysis of medical images, we have extended these studies to include active motion of cells in  152, viscosity in  158 and proved regularity results in  144. The limiting Hele-Shaw free boundary model has been used to describe mathematically the invasion capacity of a tumour by looking for travelling wave solutions, in  156, see also Methodological axis 3. It is a fundamental but difficult issue to explain rigorously the emergence of instabilities in the direction transversal to the wave propagation. For a simplified model, a complete explanation is obtained in  135.

Coupling of diffusion and growth

The growth of an organism is triggered by signaling molecules called morphogens that diffuse in the organism during its development. Meanwhile, the diffusion of the morphogens is itself affected by the changes in shape and size of the organism. In other words, there is a complete coupling between the diffusion of the morphogens and the evolution of the shapes. We are working on the elaboration of a mathematical framework for diffusion equations on time-evolving manifolds, both theoretically and in collaboration with developmental biologists, for the special case of the diffusion of Gurken during the oogenesis of Drosophila.

Migration of cells in extracellular matrix

A single cell based model has been developed that reproduces a large set of experimental observations of cells migrating in extracellular matrix based on physical mechanisms with mimimal internal cell dynamics. This includes individually migrating cells in micro-channels of different size, and their collective dynamics in case of many cells, as well as the impact of cell division and growth. The model explicitly mimics the extracellular matrix as the cells as deformable objects with explicit filopodia.

Collaborations

• Shanghai Jiao Tong University, joint publications with Min Tang on bacterial models for chemotaxis and free boundary problems for tumor growth.
• Imperial College London, joint works with José Antonio Carrillo on aggregation equation.
• University of Maryland at College Park, UCLA, Univ. of Chicago, Univ. Autónoma de Madrid, Univ. of St. Andrews (Scotland), Politecnico di Torino and Politecnico di Milano,joint works on mathematics of tumor growth models.
• Joint work with Francesco Rossi (Università di Padova, Italy) and Benedetto Piccoli (Rutgers University, Camden, New Jersey, USA) on Developmental PDEs.
• Cooperation with Shugo Yasuda (University of Hyogo, Kobe, Japan) and Vincent Calvez (EPI Dracula) on the subject of bacterial motion.
• Cooperation with Nathalie Ferrand (INSERM), Michèle Sabbah (INSERM) and Guillaume Vidal (Centre de Recherche Paul Pascal, Bordeaux) on cell aggregation by chemotaxis.
• Nicolas Vauchelet, Université Paris 13

3.4 Methodological axis 3: Model and parameter identification combining stochastic and deterministic approaches in nonlocal and multi-scale models

Direct parameter identification is a great challenge particularly in living systems in which part of parameters at a certain level are under control of processes at smaller scales. Mamba developed and addressed model and parameter identification methods and strategies in a number of mathematical and computational model applications including growth and fragmentation processes emerging in bacterial growth and protein misfolding, in liver regeneration 113, TRAIL treatment of HeLa cells 77, growth of multicellular spheroids 128, blood detoxification after drug-induced liver damage 169, 119.

This naturally leads to increasingly combine methods from various fields: image analysis, statistics, probability, numerical analysis, PDEs, ODEs, agent-based modeling methods, involving inverse methods as well as direct model and model parameter identification in biological and biomedical applications. Model types comprise agent-based simulations for which Mamba is among the leading international groups, and Pharmocokinetic (PK) simulations that have recently combined in integrated models (PhD theses Géraldine Cellière, Noémie Boissier). The challenges related with the methodological variability has led to very fruitful collaborations with internationally renowned specialists of these fields, e.g. for bacterial growth and protein misfolding with Marc Hoffmann (Paris Dauphine) and Patricia Reynaud-Bouret (University of Nice) in statistics, with Philippe Moireau (Inria M3DISIM) in inverse problems and data assimilation, and with numerous experimentalists.

Estimation methods for growing and dividing populations

In this domain, all originated in two papers in collaboration with J.P. Zubelli in 2007  159, 111, whose central idea was to used the asymptotic steady distribution of the individuals to estimate the division rate. A series of papers improved and extended these first results while keeping the deterministic viewpoint, lastly  83. The last developments now tackle the still more involved problem of estimating not only the division rate but also the fragmentation kernel (i.e., how the sizes of the offspring are related to the size of the dividing individual)  104. In parallel, in a long-run collaboration with statisticians, we studied the Piecewise Deterministic Markov Process (PDMP) underlying the equation, and estimated the division rate directly on sample observations of the process, thus making a bridge between the PDE and the PDMP approach in  109, a work which inspired also very recently other groups in statistics and probability  78, 125 and was the basis for Adélaïde Olivier's Ph.D thesis  148, 127 and of more recent work  147110 (see also axis 5).

Data assimilation and stochastic modeling for protein aggregation

Estimating reaction rates and size distributions of protein polymers is an important step for understanding the mechanisms of protein misfolding and aggregation (see also axis 5). In  66, we settled a framework problem when the experimental measurements consist in the time-dynamics of a moment of the population.

To model the intrinsic variability among experimental curves in aggregation kinetics - an important and poorly understood phenomenon - Sarah Eugène's Ph.D, co-supervised by P. Robert  116, was devoted to the stochastic modeling and analysis of protein aggregation, compared both with the deterministic approach traditionally developed in Mamba  163 and with experiments.

Parameter identification in multi-level and multi-scale models of liver

Several projects are pursued on multiscale, multilevel modeling of liver regeneration and its consequences with integration of an increasingly amount of data. So far the most promising strategy working was for every additional data set, first testing whether the model would be able to simulate it without any modifications, and to modify the model if necessary by inclusion of further biological mechanisms or information. A key unsolved problem is that biological data seem often not perfectly reproducable, and measurements at different times may differ from each other. This can result from slightly different experimental settings or conditions, or different measurement methods. While for testing of qualitative mechanisms this is usually sufficient, the quantitative difference is sometimes of the order of the effect which makes a quantitative modeling very challenging. For ammonia detoxification during fibrosis, extensive simulations have been performed varying multiple clinically relevant parameters. The basis model needed to integrate multiple data sets and could only be modelled if modifications in tissue microarchitecture, adaptations of intracellular enzyme activities, and possible aging effects were taken into account (ongoing project close to finalization).

Collaborations

• Marc Hoffmann, Université Paris-Dauphine, for the statistical approach to growth and division processes, Miguel Escobedo, Bilbao and Magali Tournus, Marseille, for the deterministic approach.
• Philippe Moireau, Inria M3DISIM, for the inverse problem and data assimilation aspects  73, 67

4.1 Introduction

The team has three main application-driven research axes. Applicative axis 1 focuses on cancer, an application on which almost all team members work, with various approaches. A main focus of the team is to study cancer as a Darwinian evolutionary phenomenon in phenotype-structured cell populations. Optimal control methods take into account the two main pitfalls of clinical cancer therapeutics, namely unwanted toxic side effects in healthy cell populations and drug resistance in cancer cell populations. Other studies concern telomere shortening, and multi-scale models. Applicative axis 2 is devoted to growth, evolution and regeneration in populations and tissues. It involves protein aggregation and fragmentation models for neurodegenerative diseases (prion, Alzheimer), organ modeling, mainly of the liver, its damages induced by toxic molecules, and its regeneration after toxic insult. Applicative axis 3 is new and encompasses works related to epidemiology, both for infectious and vector-borne diseases.

4.2 Applicative axis 1: Focus on cancer

The MAMBA team designs and analyses mathematical models of tumor growth and therapy, at the cell population level, using agent-based or partial differential equations, with special interest in methodologies for therapeutic optimization using combined anticancer drug treatments. Rather than, or not only, modeling the effect of drugs on molecular targets, we represent these effects by their functional consequences on the fate of healthy and cancer cell populations: proliferation (velocity of the cell division cycle, decreasing it, e.g., by antagonizing growth factor receptors), apoptosis, cell death or senescence. Our goal in doing this is to circumvent the two main issues of anticancer therapy in the clinic, namely unwanted toxic side effects in populations of healthy cells and emergence of drug-induced drug resistance in cancer cell populations. This point of view leads us to take into account phenomena of transient and reversible resistance, observed in many cancer cell populations, by designing and analyzing models of cell populations structured in continuous phenotypes, relevant for the description of the behavior of cell populations exposed to drugs: either degree of resistance to a given drug, or potential of resistance to drug-induced stress, proliferation potential, and plasticity. Such modeling options naturally lead us to to take into account in a continuous way (i.e., by continuous-valued phenotype or relevant gene expression) the wide phenotypic heterogeneity of cancer cell populations. They also lead us to adopt the point of view of adaptive dynamics according to which characteristic traits of cell populations evolve with tumor environmental pressure (drugs, cytokines or metabolic conditions, mechanical stress and spatial conditions), in particular from drug sensitivity to resistance. This position is original on the international scene of teams dealing with drug resistance in cancer. Recently, we have also extended our approach to the study of Tumour-Immune System interac

Modeling Acute Myeloid Leukemia (AML) and its control by anticancer drugs by PDEs and Delay Differential equations

In collaboration with Catherine Bonnet (Inria DISCO, Saclay) and François Delhommeau (St Antoine hospital in Paris), together with DISCO PhD students José Luis Avila Alonso and Walid Djema, this theme has led to common published proceedings of conferences: IFAC, ACC, CDC, MTNS  69, 70, 71, 82, 102, 68. These works study the stability of the haematopoietic system and its possible restabilization by combinations of anticancer drugs with functional targets on cell populations: proliferation, apoptosis, differentiation.

Adaptive dynamics setting to model and circumvent evolution towards drug resistance in cancer by optimal control

We tackle the problem to represent and inhibit - using optimal control algorithms, in collaboration with Emmanuel Trélat, proposed Inria team CAGE - drug-induced drug resistance in cancer cell populations. This theme, presently at the core of our works on cancer modeling with a evolutionary perspective on tumor heterogeneity, is documented in a series of articles  94, 95, 138, 139, 141. Taking into account the two main pitfalls of cancer therapy, unwanted side effects on healthy cells and evolution towards resistance in cancer cells, it has attracted to our team the interest of several teams of biologists, with whom we have undertaken common collaborative works, funded by laureate answers to national calls (see ITMO Cancer HTE call).

This theme is also at the origin of methodological developments (see Research axis 1). In collaboration with Shensi Shen from Institut Gustave Roussy and Francois Vallette from Université de Nantes, we aim to develop simple non-spatial models to understand the mechanisms of drug resistance acquisition -and loss- in melanoma and glioblastoma. The models are systematically compared with in vitro and in vivo data generated by our collaborators and treated via image processing techniques developed in the team.

Senescence modeling by telomere shortening

In many animals, aging tissues accumulate senescent cells, a process which is beneficial to protect from cancer in the young organism. In collaboration with Teresa Teixeira and Zhou Xu from IBCP, we proposed a mathematical model based on the molecular mechanisms of telomere replication and shortening and fitted it on individual lineages of senescent Saccharomyces cerevisiae cells, in order to decipher the causes of heterogeneity in replicative senescence  84.

Biomechanically mediated growth control of cancer cells other cell types

Model simulations indicate that the response of growing cell populations on mechanical stress follows a simple universal functional relationship and is predictable over different cell lines and growth conditions despite the response curves look largely different. We developed a hybrid model strategy in which cells were represented by coarse-grained individual units calibrated in a high resolution cell model and parameterized each model cell by measurable biophysical and cell-biological parameters. Cell cycle progression in our model is controlled by volumetric strain, the latter being derived from a bio-mechanical relation between applied pressure and cell compressibility. After parameter calibration from experiments with mouse colon carcinoma cells growing against the resistance of an elastic alginate capsule, the model adequately predicts the growth curve in i) soft and rigid capsules, ii) in different experimental conditions where the mechanical stress is generated by osmosis via a high molecular weight dextran solution, and iii) for other cell types with different growth kinetics. Our model simulation results suggest that the growth response of cell population upon externally applied mechanical stress is the same, as it can be quantitatively predicted using the same growth progression function 137. This model has now been extended to compare the efficiency of different culturing methods, monolayer growth, multicellular spheroids growth and growth within elastic capsules. The methodology of culturing is relevant in terms of cell yield and cell homogeneity.

Bio-mechanical models of tissue growth

The degenerate Cahn-Hilliard equation is a standard model to describe living tissues. It takes into account cell populations undergoing short-range attraction and long-range repulsion effects. In this framework, we consider the usual Cahn-Hilliard equation with a singular single-well potential and degenerate mobility. These degeneracy and singularity induce numerous difficulties, in particular for its numerical simulation. To overcome these issues, we propose in [hal-02274417] a relaxation system formed of two second order equations which can be solved with standard packages. This system is endowed with an energy and an entropy structure compatible with the limiting equation. Here, we study the theoretical properties of this system; global existence and convergence of the relaxed system to the degenerate Cahn-Hilliard equation. We also study the long-time asymptotics which interest relies on the numerous possible steady states with given mass.

Free boundary multiphase models of tumor growth

Multiphase mechanical models are now commonly used to describe living tissues including tumour growth. The specific model we study here consists of two equations of mixed parabolic and hyperbolic type which extend the standard compressible porous media equation, including cross-reaction terms. We study the incompressible limit, when the pressure becomes stiff, which generates a free boundary problem. We establish the complementarity relation and also a segregation result. Several major mathematical difficulties arise in the two species case which are addressed in 87. Firstly, the system structure makes comparison principles fail. Secondly, segregation and internal layers limit the regularity available on some quantities to BV. Thirdly, the Aronson-Bénilan estimates cannot be established in our context. We are lead, as it is classical, to add correction terms. This procedure requires technical manipulations based on BV estimates only valid in one space dimension. Another novelty is to establish an $L^1$ version in place of the standard upper bound.

Philosophy of cancer

The quite natural idea that cancer is a disease of the control of coherent multicellularity, expressed when cohesion of tissues and coherence of (unknown, except maybe for the case of a centralised circadian clock) synchronising signals fail to ensure it, by a regression towards unicellularity, stopping in this “reverse evolution path” at a coarse, incoherent multicellularity state  2 continues to be developed and popularised by Jean Clairambault in seminars and workshops, and published in review articles  96, 98 and conference proceedings  97. This view, and the investigation of the immune system in the design of such coherence of all multicellular organisms  3 is naturally inscribed in a philosophy of cancer perspective, and from a mathematical viewpoint, to multicellularity genes - and links between them and unicellularity genes - seen as a hyperstructure  4 above structures consisting of the genes of unicellularity, i.e., those that make a single cell a coherent living system, such hyperstructure being failed in cancer; this view is presently under development with colleagues from universities of the Paris region, together with Nils Baas at NTNU, Trondheim, Norway). This perspective, that makes use of category theory as a structuring point of view to apprehend multicellularity and cancer, is also meant to endow us with an innovative methodology to apply topological data analysis (TDA) to investigate cancer genome data.

Modelling of TMZ induced drug resistance

Temozolomide (TMZ) is a standard chemotherapy treatment in patients with glioblastoma. Resistance to this drug is correlated to the presence of a specific enzyme, which activity in cancer cells creates a drug-induced cell death resistant phenotype. Understanding the transition of cancer cells to a resistant phenotype is still a topic of research where multiple hypothesis have been studied: From an adaptive process to an inherent resistance to treatment. It has been recently shown that if TMZ treatment does not significantly induce cell death in glioblastoma, it still generates a response in terms of the spatial arrangement of cell aggregates. Moreover, the coupling of TMZ with irradiation has been shown to generate a better response in patients compared with using irradiation alone. Therefore, understanding the mechanisms of glioblastoma reaction to TMZ treatment could open new therapeutic avenues. In the frame of the post-doctorate of Gissell Estrada Rodriguez, we developed a 2D mathematical model in 63, suggesting a new possible mechanism for TMZ induced rearrangement of cancer cells (see section new results).

Modelling of the Epithelial-Mesenchymal Transition (EMT)

Understanding cell-fate decisions remains a major research challenge in developmental biology. In particular, the forward and backward epithelial-mesenchymal cellular transitions (EMT-MET) play a crucial role in embryonal development, tissue repair and cancer metastasis. The epithelial cell phenotype (E) is characterized by strong cell-to-cell adhesion, while the mesenchymal phenotype (M) is characterized by a strong cellular motility. Recent research has shown that there even exists a third hybrid phenotype (E/M) with mixed characteristics, that enables collective cell migration. EMT and MET play a crucial role in cancer metastasis, for instance when cancer cells from a primary tumor gain the ability to migrate through the bloodstream or lymph system to distant organs and then recover their adhesion to form secondary tumors. Thus, understanding the dynamics of MET and EMT is crucial for decoding metastasis and for designing effective therapeutics.

Collaborations

• AML modelling: Catherine Bonnet, DISCO Inria team, Saclay, and François Delhommeau, INSERM St Antoine (also collaborator in the INSERM HTE laureate project EcoAML, see below).
• INSERM HTE laureate project MoGlImaging, headed by E. Moyal (Toulouse): François Vallette, CRCNA and INSERM Nantes
• INSERM HTE laureate project EcoAML, headed by François Delhommeau, INSERM St Antoine: François Delhommeau, Thierry Jaffredo (IBPS), Delphine Salort (LCQB-IBPS)

• Adaptive dynamics to model drug resistance and optimal control to circumvent it:

  Alexandre Escargueil, Michèle Sabbah (1 PhD thesis in common), St Antoine Hospital, Paris

  Emmanuel Trélat (1 PhD thesis in common) at Inria team CAGE and Laboratoire Jacques-Louis Lions at Sorbonne Université.

  Frédéric Thomas at CREEC, Montpellier.

  Tommaso Lorenzi (Univ. of St Andrews).

• Telomere shortening: Teresa Teixeira and Zhou Xu (IBCP, Paris).
• Biomechanical control of cancer cells: Pierre Nassoy, Bioimaging and Optofluidics Group, LP2N – UMR 5298. IOGS, CNRS & University of Bordeaux; TreeFrog Pharmaceutics, 30 Avenue Gustave Eiffel Bâtiment A, 33600 Pessac
• EMT: Camille Pouchol (Université de Paris), Mohit Kumar Jolly (Indian Institute of Science, Bengalore)

4.3 Applicative axis 2: Growth, evolution and regeneration in populations and tissues

The applications in this category span very different subjects from amyloid diseases, wound healing, liver regeneration and toxicity, up to bacterial growth and development of organisms. As the applications, the methods span a wide range. Those concerning identification of models and parameters with regard to data have partially been outlined in axis 3. Focus in this axis is on the model contribution to the biologically and/or medically relevant insights and aspects.

Liver-related modelling is partially performed within the INRIA team MIMESIS (Strasbourg) with the focus on real-time, patient-specific biomechanical liver models to guide surgery and surgeons. Internationally, spatial temporal liver related models are developed in Fraunhofer MEVIS (Bremen), by T. Ricken (TU Dortmund), and P. Segers group (Leuven).

Different from these, Mamba has a strong focus on spatial-temporal modeling on the histological scale, integration of molecular processes in each individual cell, and single-cell (agent) based models  112. Works by Schliess  169, 119 have been highlighted in editorials.

Mathematical modeling of protein aggregation is a relatively recent domain, only a few other groups have emerged yet; among them we can cite the Inria team Dracula, with whom we are in close contact, and e.g., the work by Jean-Michel Coron (Sorbonne Université) and Monique Chyba (Hawaii, USA) in control, and Suzanne Sindi (USA) for the modeling of the yeast prion. We have interactions with all these groups and organized a workshop in June 2017, gathering both the biophysics and applied mathematics communities.

Amyloid disease

Application to protein aggregation in amyloid diseases is a long-standing interest of Mamba, dating back to 2010  90, and developed through the collaboration with n rHuman Rezaei's team at Inra. More recently, with Wei-Feng Xue in Canterbury, we investigated the intrinsic variability among identical experiments of nucleation  105, 117, Sarah Eugène's Ph.D subject (co-supervised by Philippe Robert)  116.

In collaboration with Tom Banks first  74, 73 and then Philippe Moireau, we developed quantitative comparisons between model and data. Through data assimilation and statistical methods  66, we proposed new models and mechanisms.

Wound healing: adipose tissues

After injury, if regeneration can be observed in hydra, planaria and some vertebrates, regeneration is rare in mammals and particularly in humans. In this research axis, we investigated the mechanisms by which biological tissues recover after injury. We explored this question on adipose tissue, using the mathematical framework recently developed in 161. Our assumption is that simple mechanical cues between the Extra-Cellular Matrix (ECM) and differentiated cells can explain adipose tissue morphogenesis and that regeneration requires after injury the same mechanisms. We validated this hypothesis by means of a two-dimensional Individual Based Model (IBM) of interacting adipocytes and ECM fiber elements 160. The model successfully generated regeneration or scar formation as functions of few key parameters, and seemed to indicate that the fate of injury outcome could be mainly due to ECM rigidity.

Following these encouraging results, the team is currently taking a step further in the model validation and confrontation to experimental data. The first direction concerns the development of a 3D framework to validate the mechanisms observed in 2D, in the frame of the PhD of P. Chassonnery, co-directed by D. Peurichard and L. Casteilla (RESTORE, Toulouse).

Influence of cell mechanics in embryonic bile duct lument formation: insight from quantitative modeling

In vitro construction of hepatic tissue for regenerative therapy consists in recapitulating mechanisms of embryonic development. However, implementing those mechanisms in a spatially and temporally coordinated way remains difficult. Specifically, the construction of bile ducts and in particular the controlled formation of luminal structures formed by cholangiocytes is a challenge. The team works on a high resolution individual-based computational model which can help in unravelling the mechanisms of initial bile duct lumen formation. Guided by the quantification of morphological features and expression of genes in developing bile ducts from embryonic mouse liver, hypotheses for the mechanisms of biliary lumen formation were generated and tested with the model. Our simulations with a hybrid simulation technology as developed in ref.   137 suggest that successful bile duct lumen formation primarily requires the simultaneous contribution of several mechanisms discussed in the literature.

Mathematical modelling of axolotl regeneration

Tissue response after injury/amputation induces one or two alternatives: scar formation versus regeneration (complete recovery of tissue shape and functions). In most mammals, regeneration is considered largely impaired for the benefit of a fibrotic scar after injury automatically associated with dysfunctions, but complete regeneration has been largely described and investigated in animal models such as zebra fish, salamander, or axolotl. Despite several processes regulating regeneration have been identified at different scales -from diffusing molecules and cellular gene expression patterns up to tissue mechanics-, how these mechanisms individually or collectively play a role in the regulation of regenerative processes remains poorly understood. In order to give insights into the mechanisms of tissue regeneration, Valeria Caliaro started an Inria PhD project in october 2019, in collaboration with Osvaldo Chara, internationally recognized group leader of SysBio in Argentina. This project focuses on the role of cell proliferation in space and time along the two first phases of regeneration after injury: (i) initiation of a regeneration response, (ii) tissue patterning during regenerate growth. The first part of the project aims at building an agent-based model featuring few key mechanisms regulating cell proliferation after injury. By introducing heuristic rules which rely on Prof O. Chara expertise, we propose a 2D-ABM using methodologies borrowed from socio-dynamics and collective behavior studies (based on many interacting agent systems). While the focus is made on proliferation-based mechanisms, other mechanisms responsible for collective behavior such as volume exclusion, diffusion or aggregation are taken into account. The resulting model will provide a synthetic tissue model which will serve to investigate regeneration in cellular systems, focusing on cell proliferation properties. The second part of the PhD will be devoted to the derivation of continuous models from the agent-based formalism. This will provide a large scale ‘synthetic tissue’ model to explore the role of large scale effects in general tissue models.

Quantitative cell-based model predicts mechanical stress response of growing tumor spheroids

Model simulations indicate that the response of growing cell populations on mechanical stress follows the same functional relationship and is predictable over different cell lines and growth conditions despite experimental response curves look largely different. We developed a hybrid model strategy in which cells are represented by coarse-grained individual units calibrated with a high resolution cell model and parameterized by measurable biophysical and cell-biological parameters. Cell cycle progression in our model is controlled by volumetric strain, the latter being derived from a bio-mechanical relation between applied pressure and cell compressibility. After parameter calibration from experiments with mouse colon carcinoma cells growing against the resistance of an elastic alginate capsule, the model adequately predicts the growth curve in i) soft and rigid capsules, ii) in different experimental conditions where the mechanical stress is generated by osmosis via a high molecular weight dextran solution, and iii) for other cell types with different growth kinetics from the growth kinetics in absence of external stress. Our model simulation results suggest a generic, even quantitatively same, growth response of cell populations upon externally applied mechanical stress, as it can be quantitatively predicted using the same growth progression function (5.

Bacterial population growth

We exploited all the methods developed to estimate the division rate of a population (see axis 3) to address a seminal question of biology: is it a size-sensing or a timing mechanism which triggers bacterial growth? In  165, we showed that a sizer model is robust and fits the data well. Several studies from other groups came at the same time, showing a renewed interest on a question dated back to Jacques Monod's PhD thesis (1941). Of special interest is the “adder” model, for which we are currently developing new estimation methods  110.

A quantitative high resolution computational mechanics cell model for growing and regenerating tissues

Mathematical models are increasingly designed to guide experiments in biology, biotechnology, as well as to assist in medical decision making. They are in particular important to understand emergent collective cell behavior. For this purpose, the models, despite still abstractions of reality, need to be quantitative in all aspects relevant for the question of interest. Considered was as showcase example the regeneration of liver after drug-induced depletion of hepatocytes, in which the surviving and dividing hepatocytes must squeeze in between the blood vessels of a network to refill the emerged lesions. Here, the cells’ response to mechanical stress might significantly impact the regeneration process. We present a 3D high-resolution cell-based model integrating information from measurements in order to obtain a refined and quantitative understanding of the impact of cell-biomechanical effects on the closure of drug-induced lesions in liver. Our model represents each cell individually and is constructed by a discrete, physically scalable network of viscoelastic elements, capable of mimicking realistic cell deformation and supplying information at subcellular scales. The cells have the capability to migrate, grow, and divide, and the nature and parameters of their mechanical elements can be inferred from comparisons with optical stretcher experiments. Due to triangulation of the cell surface, interactions of cells with arbitrarily shaped (triangulated) structures such as blood vessels can be captured naturally. Comparing our simulations with those of so-called center-based models, in which cells have a largely rigid shape and forces are exerted between cell centers, we find that the migration forces a cell needs to exert on its environment to close a tissue lesion, is much smaller than predicted by center-based models. To stress generality of the approach, the liver simulations were complemented by monolayer and multicellular spheroid growth simulations. In summary, our model can give quantitative insight in many tissue organization processes, permits hypothesis testing in silico, and guide experiments in situations in which cell mechanics is considered important 137.

Liver regeneration and disease: towards a full virtual liver model at histological scale

In our work towards a full virtual liver model at histological level, a number of steps were performed. The models under points (1)-(4) focus on either a single or a few liver lobules. A liver lobule is the smallest repetitive functional and anatomical building block of liver, while (5) addresses a much larger organisational building block of the liver, a liver lobe that consists of thousands to hundreds of thousands of lobules depending on the species. A second strand (6), (7) addresses image analysis, which in most cases forms the entrance to modeling as it provides the data necessary to generate model hypotheses and to parameterize a model.

(1) Cell types: In a former work by Hoehme et. al. ( 126) a model of liver regeneration after drug-induced damage was established considering hepatocytes and blood vessels. This model has now been expanded to include all relevant cell types, including hepatocytes, blood vessels, hepatic stellate cells, Kupffer cells, invading macrophages and other immune cells. Thereby it is now possible to study perturbations in the temporal scenario of damage and regeneration after signaling events or cells types are knocked down individually or collectively. This model is currently compared to respective perturbation experiments. In addition, alternative mechanisms at the level of molecularly intermediated cell-cell communication discussed in the vast medical and biological literature have been implemented and are systematically assessed for their biological consequence at the tissue level. This permits an in-silico testing of alternative hypotheses contributing to a more efficient identification of informative future experiments.

(2) Liver disease: Degenerative liver diseases such as liver fibrosis and cirrhosis develop out of a disturbed balance of degenerative and regenerative processes. The model under (1) has thereby been extended by the formation of extracellular matrix, mimicked as fiber networks, to capture the disease process leading to liver fibrosis. In that process characteristic streets form that modify the mechanics, perfusion behavior and detoxification capacity of the liver. The model is now used to simulate disease pathways emerging from different administration schemes of drugs that are knowning to long-term lead to hepatocellular cancer.

(3) Consequence of liver fibrosis: Whole-slide scans from fibrotic liver in a mouse model has been analysed at different time points after emergence of the disease with regard to the degree of excess matrix to mimic the possible consequences of fibrotic inclusions on perfusion and function of liver within a multiscale model that considers ammonia detoxification in each individual hepatocyte as well as blood flow and transport processes in the liver lobule. This model has now be confronted on multimodal data in healthy liver, liver after a toxic dose of a drug, and fibrosis. The requirement to explain simultaneously all data sets in the same model imposes significant challenges for which solutions are currently explored.

(4) Bile flux: Bile flux has been for decades believed to be controlled by convection at the level of liver lobules as well as at the level of the entire organ. By a methodology based on correlative imaging for quantitative intravital flux analysis no directed advection was detectable in bile canaliculi at the resolution limit. Instead, after active transport across hepatocyte membranes bile salts within the liver lobules are transported in the canaliculi by a diffusion-dominated process. Only in the interlobular ducts i.e., at super-lobular level, diffusion is augmented by advection. In silico simulations of bile transport in real 3D bile network microarchitectures can quantitatively explain the data assuming diffusive transport as sole mechanism.

(5) Liver regeneration after partial hepatectomy (partial organ removal): Partial hepatectomy is an adequate therapy in case of diseases or events that destructed only part of the liver. A typical case is a primary tumor or a metastasis affecting only a single liver lobe. Within an biophysical agent-based model capturing many aspects of the cell mechanics we studied regrowth of liver after partial organ removal in mouse calibrated with multivariate experimental data. Our model predicts characteristic proliferation pattern that change from small animals (as mouse) to large animals (as pig).

(6) Bile duct ligation: Bile duct ligation (BDL) is an experimental procedure that mimics obstructive cholestatic disease. One of the early consequences of BDL in rodents is the appearance of so-called bile infarcts that correspond to Charcot-Gombault necrosis in human cholestasis. The mechanisms causing bile infarcts and their pathophysiological relevance are unclear. Therefore, intravital two photon–based imaging of BDL mice was performed with fluorescent bile salts (BS) and non-BS organic anion analogues. Key findings were followed up by matrix-assisted laser desorption ionization imaging, clinical chemistry, immunostaining, and gene expression analyses. Our group performed analysis of intravital imaging. The key finding is that bile microinfarcts occur in the acute phase after BDL in a limited number of dispersed hepatocytes followed by larger infarcts involving neighboring hepatocytes, and they allow leakage of bile from the BS-overloaded biliary tract into blood, thereby protecting the liver from BS toxicity; in the chronic phase after BDL, reduced sinusoidal BS uptake is a dominant protective factor, and the kidney contributes to the elimination of BS until cholemic nephropathy sets in 120.

(7) Periportalisation during liver fibrosis formation: Within a liver lobule, the function of hepatocytes is zonated i.e., certain functions are only executed by either hepatocytes close to the center (pericentral region) or hepatocytes in the periphery of the lobule (periportal region). Little is known about how liver fibrosis influences lobular zonation. To address this question, three mouse models of liver fibrosis were used, CCl4 administration repeated for 2, 6 and 12 months to induce pericentral damage, as well as bile duct ligation (21 days) and a particular mdr2-mouse model to study periportal fibrosis. Analyses were performed by RNA-sequencing, immunostaining of zonated proteins and image analysis. Image analysis was performed by our group. The key result was that liver fibrosis leads to strong alterations of lobular zonation, where the pericentral region adopts periportal features. Beside adverse consequences, periportalization supports adaptation to repeated doses of hepatotoxic compounds 121.

Toxicity extrapolation from in vitro to in vivo

In vivo toxicity prediction from in vitro data is a major objective in toxicology as it permits bypassing animal experiments, and as the predictive power of animal experiments for human is limited. Objective was the prediction of paracetamol (acetaminophen)-induced hepatotoxicity from in vitro experiments. For this purpose, numerous iterations between in vitro experiments, in vivo experiments and simulations were performed for mouse. Using a recent thesis (Géraldine Cellière'ns PhD thesis  92) as a start point, two candidate mechanisms could be identified both explaining the in vivo data after calibration of the in silico model with in vitro toxicity data.

Relating imaging on microscopic scales with imaging on macroscopic scales: From Diffusion-Weighted MRI Calibrated With Histological Data: an Example From Lung Cancer

Diffusion-weighted magnetic resonance imaging (DWI) is a key non-invasive imaging technique for cancer diagnosis and tumor treatment assessment, reflecting Brownian movement of water molecules in tissues. Since densely packed cells restrict molecule mobility, tumor tissues produce usually higher signal (less attenuated signal) on isotropic maps compared with normal tissues. However, no general quantitative relation between DWI data and the cell density has been established. In order to link low-resolution clinical cross-sectional data with high resolution histological information, we developed an image processing and analysis chain, which was used to study the correlation between the diffusion coefficient (D value) estimated from DWI and tumor cellularity from serial histological slides of a resected non-small cell lung cancer tumor. Color deconvolution followed by cell nuclei segmentation was performed on digitized histological images to determine local and cell-type specific 2d (two-dimensional) densities. From these, the 3d cell density was inferred by a model-based sampling technique, which is necessary for the calculation of local and global 3d tumor cell count. Next, DWI sequence information was overlaid with high resolution CT data and the resected histology using prominent anatomical hallmarks for co-registration of histology tissue blocks and non-invasive imaging modalities’ data. The integration of cell numbers information and DWI data derived from different tumor areas revealed a clear negative correlation between cell density and D value. Importantly, spatial tumor cell density can be calculated based on DWI data. In summary, our results demonstrate that tumor cell count and heterogeneity can be predicted from DWI data, which may open new opportunities for personalized diagnosis and therapy optimization  176. The work of that paper has been further advanced to adapt the procedures for clinical use (in preparation).

Collaborations

• Protein aggregation in amyloid diseases: Human Rezae's team at Inra Jouy-en-Josas (France) and W-F Xue's team in at university of Kent (Great Britain); Tom Banks at the North Carolina State University (USA) and Philippe Moireau (M3DISIM)
• Bacterial growth and division: Lydia Robert, Sorbonne Université (France)
• Liver research & toxicology: JG. Hengstler group (IfADo, Dortmund, Germany); R. Gebhardt (Univ. Leipzig); U. Klingmueller (DKFZ, Heidelberg); Irène Vignon-Clementel (INRIA, COMMEDIA)
• Growth in capsules and biomechanics: Pierre Nassoy, Institut dOptique Graduate School, Talence, France; Josef Kaes, Peter Debye Institute for Soft Matter Physics, Physics, Univ. Leipzig, Germany.
• Wound healing: (Adipose tissue regeneration) team of L. Casteilla (StromaLab, Toulouse). (Axolotl regeneration) team of O. Chara, SysBio group, Argentina.
• Diffusion of morphogen: Center for Computational and Integrative Biology, Rutgers University (Camden, New Jersey), joint work with Professor Nir Yakoby's Drosophila Laboratory
• Linking micro and macro-image information: Oliver Sedlaczek, Univ. and DKFZ Heidelberg, Kai Breuhahn, Univ. Heidelberg.

4.4 Applicative axis 3: Modelling and control in mathematical epidemiology

This axis is new and encompasses different works related to epidemiology, both for infectious and vector-borne diseases. The team was working since several years on the modeling, analysis and control of the propagation of vector-borne diseases such as dengue fever. Ordinary or partial differential equations of reaction-diffusion are used, and various (optimal or not) control strategies. In parallel and with the acknowledged opportunity of the onset and spreading of the Covid-19 pandemic, we expanded our interest to issues related to infectious diseases, using similar evolution systems.

Biological control of arboviroses

Sterile Insect Technique (SIT) 114 is a biological control method relying on massive releases of sterile male insects into the wild. The latter compete with wild males to mate with the females, and induce no offspring to the latter, thus reducing the next generation's population. This can result in a progressive reduction, or even disparition, of the target population.

A related technique is based on the infection by Wolbachia124. This symbiotic bacterium is maternally transmitted from infected females to their offspring, but induces cytoplasmic incompatibility172, 85: mating between infected males and uninfected females gives no offspring. Releases of Wolbachia infected males alone is thus comparable to classical SIT.

On the other hand, releasing both infected males and females in sufficient quantity may result in infection of the wild population. This gives rise to an interesting new control principle, as Wolbachia has been shown to severely reduce the insect vectorial ability to transmit dengue, zika or chikungunya, indirectly by lifespan and fertility reduction, and directly by reducing the ability of the viruses to proliferate within the organism 145.

We proposed new insights on the practical and theoretical issues raised by the implementation of the previous methods. Concerning the SIT, we obtained control synthesis results through impulsive periodic release of controlled amplitude 80, and through optimal control approach 81. Concerning Wolbachia technique, we investigated general control principles 79 capable of spreading the infection.

We also considered the effects of hindrances to these strategies 150.

Moreover, while continuing our work on the problem of controling the mosquito population by itself, we have extended our studies to systems that consider the dynamics or the arboviroses in both the human and mosquito populations. This should allow us to confirm the pertinence of our previous and future works concerning the control of the mosquito population, but also motivate new criteria that take directly into account the dynamicsz of the epidemics in the human population.

Mathematical epidemiology of infectious diseases

The current outbreak of Covid-19 resulted in the appearance of many novel experiences at individual and collective, biological and social, national and international levels, making this pandemic a full epistemological experience as well. Motivated by the great number of questions raised by this global event, some members of the team devoted part of their time to exploring more or less closely related scientific issues. One should notice however that this evolution constitutes indeed the continuation of a movement already initiated previously, and only accelerated by the current events.

The issues raised by the effective implementation of the social distancing measures largely implemented on the Earth’s surface during the whole year 2020, have been the focus of intense reflection. We contributed to this debate by studying optimal control policies aiming at reducing the total number of infected people during the whole epidemic outbreak, the so-called epidemic final size. In another research line, we established the equation fulfilled by the epidemic final size for a fully general SEIR model in a heterogenous population characterized by some trait in a discrete or continuous subset, and studied the uniqueness of its solution. This allowed to extend the use and meaningfulness of the classical concept of next-generation operator introduced by O. Diekmann et al.  in 1990 101. Last, in cooperation with the Inria team NeCS (Inria Grenoble-Rhône-Alpes), we studied in a control theory perspective the effects of the testing policies in the dynamics and in the control of the epidemic.

Collaborations

• Biological control of arboviroses: Nicolas Vauchelet (Université Paris 13); Yannick Privat (Université de Strasbourg); Carlota Rebelo (Univ. Lisboa), D. Villela, C. Struchiner (Fiocruz, Brazil); Jorge Zubelli (IMPA, Brazil); Alain Rapaport (INRA-Montpellier), Y. Dumont (CIRAD-Montpellier); Ch. Schaerer, P. Pérez-Estigarribia (UNA, Paraguay), O. Vasilieva (Universidad del Valle, Cali, Colombia), D. Cardona-Salgado (Universidad Autónoma de Occidente, Cali, Colombia); Hervé Bossin (ILM, Papeete); René Gato and Misladys Rodriguez (Inst. Pedro Kouri, La Havane)
• Mathematical epidemiology of infectious diseases: Nicolas Vauchelet (Université Paris 13); Michel Duprez (Inria Nancy - Grand Est); Yannick Privat (Université de Strasbourg); Carlos Canudas de Wit (Inria Grenoble - Rhône-Alpes and CNRS); Alain Kibangou (Université Grenoble-Alpes).

5.1 Footprint of research activities

All members of the team decided to carefully review his or her trip policy (especially by air), in order to reduce carbon footprint.

6.1 Awards

Luis Almeida, Marie Doumic and Benoit Perthame organized (together with Vincent Calvez and Patricia Reynaud-Bouret) the one trimester program at IHP on Mathematical modeling of organization in living matter. from January to April 2022.

6.2 Research stays

From October to December 2022, Jules Guilberteau went to the Cancer Systems Biology Laboratory, at the Indian Institute of Science of Bangalore (India), in order to concretize a collaboration with Mohit Kumar Jolly and Paras Jain. The research stay was entirely funded by the Raman-Charpak fellowship, an Indo-French bilateral Fellowship programme, which was awarded to Jules to develop further the collaboration between the team of Indian systems biologists and our team of French mathematicians. The main purpose was to develop PDE models for the Epithelial-Mesenchymal Transition (EMT), a cell differentiation phenomenon which plays a crucial role in cancer development. The previous ODE models developped by M. Kumar Jolly and his team focused on a single cell undergoing EMT, while PDE aim to model the behaviour of a cell colony. Our models include an advection term, based on previous ODE models, a selection term and an integral term representing respectively cell division and epimutations. The use of PDEs for EMT is in its early stages, and allow to consider several phenomena which occur at the same time and involve the whole colony, via non-local terms. We have been able to model some typical behaviours, such as hysteresis, at the scale of a cell colony, and to reproduce (at least qualitatively) some experimental observations that remained out of reach with the previous models.

6.3 Institutional life

In the year 2022, the activity of our team, MAMBA, was impacted by the serious dysfunctions and heavy atmosphere in the institute.

• The failure of the deployment of a new financial and human resource information system (Eksae) impacted and still impacts negatively all administrative colleagues with whom researchers interact. It forces them to duplicate their works, when not making them unable to perform even simple tasks. It also directly impacts researchers, who cannot oversee their budget in any reliable way, and occasionally have to delay simple purchases as a consequence of a reprioritization of overburdened administrative forces.
• The continuously diminishing emphasis on research in the presentation of Inria and the growing fuzziness around the status of researchers and the role and position of the institute attack the meaning of work and our collective values. We are extremely concerned over the neglect by our management of research for itself, showing preference for short term, short lived activities, judged by their “impact”, whatever this may mean.
• The extremely degraded relationship between the Inria Commission d’Évaluation and the current Inria direction is unbearable. It causes a general distrust in the direction’s intentions and in the outcome of future hiring and promoting process. We deeply deplore the current situation. We thank and congratulate the Commission d’Évaluation for its tireless and continued efforts in ensuring fair and bias-free evaluation of the hiring and promotion committees, and for its outstanding information to the researchers.

7.1 New software

8.1 Direct and inverse Problems in Structured-population equations

The many results obtained during the last years have oriented us towards new research directions in the wide field of structured population equations: nonlinear renewal equations applied to neurosciences; the study of the direct and inverse problem in the newly-proposed "adder model"  173; oscillatory behaviors of such equations; the study of models for heterogeneous aggregation, i.e. where the aggregates are formed out of several monomeric species.

8.2 Stochastic Models of Biological Systems

8.3 Stochastic Chemical Networks

Participants: Lucie Laurence, Philippe Robert.

A chemical network is defined with three components

• A set of chemical species $𝒮$;
• A set of complexes, i.e. subsets of elements of chemical species with possible repeated entries;
• A graph connecting complexes.

As an example, if $A$, $B$, $C$, $D$ are chemical species, $p_u$, $u\in \{a,b,c,d\}$, are integers and the relation

corresponds to an edge of the graph for the transformation of the complex $p_{a}A+p_{b}B$ ($p_a$ copies of $A$ and $p_b$ copies of $B$) into the complex $p_{c}C+p_{d}D$. The associated dynamical system is a mass action kinetic, i.e. the rate at which such reaction occurs is given by

if $x_A$, $x_B$ is the number of copies of $A$ and $B$.

Historically, Horn, Jackson and Feinberg developed in the 70's, in a deterministic framework associated to a polynomial differential system, several results based on the geometry of the graph. We can mention the famous deficiency zero theorem, that give sufficient conditions on the structure of the graph of the reaction network to have a stable equilibrium point. Most of the stochastic stability results are essentially based on these results.

The goal of this study is to find alternative ways to show results of stability and convergence in distribution. The general approach is to use some scaling arguments on the Markov process associated to the Chemical Reaction Network studied. Scaling in time and/or in space gets us some converging results, avoiding the usual search for a Lyapunov function. We also used averaging results in specific border cases.

This year we have analyzed topologies of chemical reaction networks: triangular networks: a CRN with three complexes and two chemical species for which we have a complete analyzis of the stability properties as well as some scaling behavior. Secondly, we have studied circular networks with complexes of size two from the point of view of stability. We are currently investigating an unusual averaging principle in this setting. Finally, we are studying $k$-unary networks for which complexes are composed only of copies of one chemical species, despite its simple topolgy the scaling properties of these networks are not trivial at all.

8.4 Allocation of Resources in Prokaryotic Cells

Participants: Vincent Fromion, Philippe Robert, Jana Zaherddine.

The information flow from DNA genes to proteins is a fundamental process that is common to all living organisms. We analyze it in the context of a bacterial cell. The production of proteins is the most important process that takes place inside a bacterium consuming around 90% of its resources.

Bacterium adapts very quickly to changes in the environment. It succeeds in making a balance between supply allocating the resources available in the environment for its growth. All of this is achieved via regulatory mechanisms in the bacterium.

Basically the bacterium has two different regimes. The exponential phase during which resources are abundant, enabling the doubling of the cell on a fast pace. The Stationary phase during which resources are scarce, a regulatory mechanisms known by the "sequestration by the 6S RNA" comes into play. The 6S RNA is a macromolecule which is a regulator of transcription by preventing the polymerase from binding to the gene promoter.

Basically the bacterium has two different regimes. The exponential phase during which resources are abundant, enabling the doubling of the cell on a fast pace. The Stationary phase during which resources are scarce, a regulatory mechanisms known by the "sequestration by the 6S RNA" comes into play. The 6S RNA is a macromolecule which is a regulator of transcription by preventing the polymerase from binding to the gene promoter.

Our main objective is to estimate the efficiency of the 6S RNA regulatory mechanisms via the analysis of the time evolution of the concentration of free, sequestered and in transcription polymerases according to the growth rate. Due the disorganized medium, stochastic models are used for such analysis.

In 49, we have worked on a model for which we have the same constant number $N$ of polymerases. We have studied an important global regulation mechanism of transcription of biological cells using specific macro-molecules, 6S RNAs. The functional property of 6S RNAs is of blocking the transcription of RNAs when the environment of the cell is not favorable. We investigate the efficiency of this mechanism with a scaling analysis of a stochastic model. The evolution equations of our model are driven by the law of mass action and the total number of polymerases is used as a scaling parameter. Two regimes are analyzed: exponential phase when the environment of the cell is favorable to its growth, and the stationary phase when resources are scarce. In both regimes, by defining properly occupation measures of the model, we prove an averaging principle for the associated multi-dimensional Markov process on a convenient timescale, as well as convergence results for “fast” variables of the system. An analytical expression of the asymptotic fraction of sequestrated polymerases in stationary phase is in particular obtained. The consequences of these results are discussed.

We are currently investigating the regulation of translation for which there is also a kind of sequestration mechanism, although it is not as direct as for transcription. Another difficulty of this case is that, in addition to the various states of ribosomes (translating, free, in initiation or sequestered), the production of amino-acids has to be taken into account.

8.5 Analysis and control of populations of mosquitoes

8.6 Modelling and control in epidemiology

8.7 Focus on cancer

8.8 Macroscopic limit and asymptotic behavior of collective dynamics

9.1 Bilateral grants with industry

Participants: Gaëtan Vignoud, Philippe Robert.

10.1 International initiatives

10.2 National initiatives

Mamba (Marie Doumic and Philippe Robert) participates to the GDR "MeDyna" (mechanisms and dynamics of assemblies of peptides and proteins), coordinated by Stéphane Bressanelli from IBPC.

11.1 Promoting scientific activities

11.2 Teaching - Supervision - Juries

12.1 Major publications

• 1 unpublishedL.Luís Almeida, P.-A.Pierre-Alexandre Bliman, G.Grégoire Nadin, B.Benoît Perthame and N.Nicolas Vauchelet. Final size and convergence rate for an epidemic in heterogeneous population.October 2020, working paper or preprint
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• 2 articleM.Marie Doumic, S.Sophie Hecht and D.Diane Peurichard. A purely mechanical model with asymmetric features for early morphogenesis of rod-shaped bacteria micro-colony.Mathematical Biosciences and Engineering176October 2020, http://aimspress.com/article/doi/10.3934/mbe.2020356
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12.2 Publications of the year

12.3 Cited publications

• 60 articleP.Pedro Aceves-Sanchez, B.Benjamin Aymard, D.Diane Peurichard, P.Pol Kennel, A.Anne Lorsignol, F.Franck Plouraboue, L.Louis Casteilla and P.Pierre Degond. A new model for the emergence of blood capillary networks.Networks & Heterogeneous Media1612021, 91 - 138
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• 61 articleP.Pedro Aceves-Sanchez, P.Pierre Degond, E. E.Eric E Keaveny, A.Angelika Manhart, S.Sara Merino-Aceituno and D.Diane Peurichard. Large-Scale Dynamics of Self-propelled Particles Moving Through Obstacles: Model Derivation and Pattern Formation.Bulletin of Mathematical Biology8210October 2020, 129
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• 62 incollectionL.Luis Almeida, R. H.Rebecca H Chisholm, J.Jean Clairambault, T.Tommaso Lorenzi, A.Alexander Lorz, C.Camille Pouchol and E.Emmanuel Trélat. Why Is Evolution Important in Cancer and What Mathematics Should Be Used to Treat Cancer? Focus on Drug Resistance.Trends in Biomathematics: Modeling, Optimization and Computational Problems: Selected works from the BIOMAT Consortium Lectures, Moscow 2017Springer International PublishingAugust 2018, 107-120
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• 63 articleL.Luis Almeida, G.Gissell Estrada-Rodriguez, L.Lisa Oliver, D.Diane Peurichard, A.Alexandre Poulain and F.Francois Vallette. Treatment-induced shrinking of tumour aggregates: A nonlinear volume-filling chemotactic approach.Journal of mathematical biology8332021, 29
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• 64 unpublishedL.Luis Almeida, A.Alexis Leculier and N.Nicolas Vauchelet. Analysis of the ''Rolling carpet'' strategy to eradicate an invasive species.June 2021, working paper or preprint
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• 65 articleL.Luke Alphey. Genetic control of mosquitoes.Annual review of entomology592014
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• 66 articleA.Aurora Armiento, M.Marie Doumic, P.Philippe Moireau and H.Human Rezaei. Estimation from Moments Measurements for Amyloid Depolymerisation.Journal of Theoretical BiologyMarch 2016
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• 67 phdthesisA.Aurora Armiento. Inverse problems and data assimilation methods applied to protein polymerisation.Université Paris 7 - DiderotJanuary 2017
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• 68 incollectionJ. L.José Luis Avila Alonso, C.Catherine Bonnet, J.Jean Clairambault, H.Hitay Ozbay, S.-I.Silviu-Iulian Niculescu, F.Faten Merhi, A.Annabelle Ballesta, R.Ruoping Tang and J.-P.Jean-Pierre Marie. Analysis of a New Model of Cell Population Dynamics in Acute Myeloid Leukemia.Delay Systems : From Theory to Numerics and Applications1Advances in Delays and DynamicsSpringerJanuary 2014, 315-328
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• 69 inproceedingsJ. L.Jose Luis Avila Alonso, C.Catherine Bonnet, E.Emilia Fridman, F.Frederic Mazenc and J.Jean Clairambault. Stability analysis of PDE's modelling cell dynamics in Acute Myeloid Leukemia.53rd IEEE Conference on Decision and ControlLos Angeles, United StatesDecember 2014
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• 70 inproceedingsJ. L.José Luis Avila Alonso, C.Catherine Bonnet, H.Hitay Ozbay, J.Jean Clairambault and S.-I.Silviu-Iulian Niculescu. A coupled model for healthy and cancer cells dynamics in Acute Myeloid Leukemia.The 19th World Congress of the International Federation of Automatic ControlCape Town, Souh AfricaAugust 2014
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• 71 inproceedingsJ. L.José Luis Avila Alonso, C.Catherine Bonnet, H.Hitay Ozbay, J.Jean Clairambault and S.-I.Silviu-Iulian Niculescu. A discrete-maturity Interconnected Model of Healthy and Cancer Cell Dynamics in Acute Myeloid Leukemia.Mathematical Theory of Networks and SystemsGroningen, NetherlandsJuly 2014
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• 72 articleN.Nathalie Ayi and N.Nastassia Pouradier Duteil. Mean-field and graph limits for collective dynamics models with time-varying weights.Journal of Differential EquationsOctober 2021
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• 73 articleH. T.H. T. Banks, M.Marie Doumic, C.Carola Kruse, S.Stephanie Prigent and H.H Rezaei. Information Content in Data Sets for a Nucleated-Polymerization Model.Journal of Biological Dynamics91June 2015, 26
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• 74 articleH. T.H. T. Banks, M.Marie Doumic-Jauffret and C.Carola Kruse. A numerical scheme for the early steps of nucleation-aggregation Models.Journal of Mathematical Biology741-2January 2017, 259-287
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• 75 articleJ.Julien Barre, P.Pierre Degond, D.Diane Peurichard and E.Ewelina Zatorska. Modelling pattern formation through differential repulsion.Networks and Heterogeneous Media1532020, 307-352
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• 76 articleF.F. Bekkal Brikci, J.J. Clairambault and B.B. Perthame. Analysis of a molecular structured population model with possible polynomial growth for the cell division cycle.Math. Comput. Modelling477-82008, 699--713
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• 77 articleF.François Bertaux, S.Szymon Stoma, D.Dirk Drasdo and G.Gregory Batt. Modeling Dynamics of Cell-to-Cell Variability in TRAIL-Induced Apoptosis Explains Fractional Killing and Predicts Reversible Resistance.PLoS Computational Biology10102014, 14
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• 78 articleJ.J. Bertoin and A. R.A. R. Watson. Probabilistic aspects of critical growth-fragmentation equations.Advances in Applied Probability9 2015
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• 79 articleP.-A.Pierre-Alexandre Bliman. A feedback control perspective on biological control of dengue vectors by Wolbachia infection.European Journal of Control592021, 188--206
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• 80 articleP.-A.Pierre-Alexandre Bliman, D.Daiver Cardona-Salgado, Y.Yves Dumont and O.Olga Vasilieva. Implementation of control strategies for sterile insect techniques.Mathematical biosciences3142019, 43--60
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• 81 articleP.-A.Pierre-Alexandre Bliman, D.Daiver Cardona-Salgado, Y.Yves Dumont and O.Olga Vasilieva. Optimal control approach for implementation of sterile insect techniques.arXiv preprint arXiv:1911.000342019
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• 82 inproceedingsC.Catherine Bonnet, J. L.Jose Luis Avila Alonso, H.Hitay Ozbay, J.Jean Clairambault, S.-I.Silviu-Iulian Niculescu and P.Pierre Hirsch. A Discrete-Maturity Interconnected Model of Healthy and Cancer Cell Dynamics in Acute Myeloid Leukemia.The 10th AIMS Conference on Dynamical Systems,Differential Equations and ApplicationsMadrid, SpainJuly 2014
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• 83 articleT.Thibault Bourgeron, M.Marie Doumic and M.Miguel Escobedo. Estimating the division rate of the growth-fragmentation equation with a self-similar kernel.Inverse Problems302Jan 2014, 025007URL: http://dx.doi.org/10.1088/0266-5611/30/2/025007
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• 84 articleT.Thibault Bourgeron, Z.Zhou Xu, M.Marie Doumic and M. T.Maria Teresa Teixeira. The asymmetry of telomere replication contributes to replicative senescence heterogeneity.Scientific Reports5October 2015, 15326
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• 85 incollectionK.Kostas Bourtzis. Wolbachia-Based Technologies for Insect Pest Population Control.Advances in Experimental Medicine and Biology627Springer, New York, NY02 2008
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• 86 articleA.AW Brown. Insecticide resistance in mosquitoes: a pragmatic review..Journal of the American Mosquito Control Association221986, 123--140
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• 87 articleF.Federica Bubba, B.Benoît Perthame, C.Camille Pouchol and M.Markus Schmidtchen. Hele--shaw limit for a system of two reaction-(cross-) diffusion equations for living tissues.Archive for Rational Mechanics and Analysis23622020, 735--766
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• 88 articleM. J.Maria J. Caceres and B.Benoît Perthame. Beyond blow-up in excitatory integrate and fire neuronal networks: refractory period and spontaneous activity.Journal of Theoretical Biology3502014, 81-89
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• 89 articleV.V. Calvez, M.M. Doumic and P.P. Gabriel. Self-similarity in a general aggregation--fragmentation problem. Application to fitness analysis.Journal de Mathématiques Pures et Appliquées9812012, 1 - 27URL: http://www.sciencedirect.com/science/article/pii/S002178241200013X
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• 90 articleV.V. Calvez, N.N. Lenuzza, M.M. Doumic, J.-P.J.-P. Deslys, F.F. Mouthon and B.B. Perthame. Prion dynamic with size dependency - strain phenomena.J. of Biol. Dyn.412010, 28--42
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• 91 articleJ. A.José Antonio Carrillo, F.Francois James, F.Frédéric Lagoutière and N.Nicolas Vauchelet. The Filippov characteristic flow for the aggregation equation with mildly singular potentials.Journal of Differential Equations260133 pages2016, 304-338
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• 92 phdthesisG.Géraldine Cellière. Multi-scale modeling of hepatic drug toxicity and its consequences on ammonia detoxification.Université Paris 6 - Pierre et Marie CurieJuly 2017
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• 93 articleJ.Julien Chevallier, M. J.Maria J. Caceres, M.Marie Doumic and P.Patricia Reynaud-Bouret. Microscopic approach of a time elapsed neural model.Mathematical Models and Methods in Applied SciencesDecember 2015, 2669
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• 94 articleR. H.Rebecca H Chisholm, T.Tommaso Lorenzi and J.Jean Clairambault. Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation.BBA - General Subjects1860June 2016, 2627 - 2645
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• 95 articleR. H.Rebecca H. Chisholm, T.Tommaso Lorenzi, A.Alexander Lorz, A. K.Annette K. Larsen, L. N.Luís Neves de Almeida, A.Alexandre Escargueil and J.Jean Clairambault. Emergence of Drug Tolerance in Cancer Cell Populations: An Evolutionary Outcome of Selection, Nongenetic Instability, and Stress-Induced Adaptation.Cancer Research756March 2015, 930-939
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• 96 articleJ.Jean Clairambault. An evolutionary perspective on cancer, with applications to anticancer drug resistance modelling and perspectives in therapeutic control.Journal of Mathematical Study2019, 1 - 21
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• 97 inproceedingsJ.J Clairambault. Plasticity in Cancer Cell Populations: Biology, Mathematics and Philosophy of Cancer.Mathematical and Computational Oncology. ISMCO 20201258Lecture Notes on Computer ScienceInvited conference paperInternational Symposium on Mathematical and Computational OncologyChamSpringer12 2020, 3-9
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• 98 articleJ.Jean Clairambault and C.Camille Pouchol. A survey of adaptive cell population dynamics models of emergence of drug resistance in cancer, and open questions about evolution and cancer.BIOMATH81Copyright: 2019 Clairambault et al. This article is distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.May 2019, 23
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• 99 articleJ.Jean Clairambault. Stepping From Modeling Cancer Plasticity to the Philosophy of Cancer.Frontiers in Genetics2020, 11:579738
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• 100 phdthesisJ.Julia Delacour. Mathematical Modelling of p62-Ubiquitin aggregates involved in cellular autophagy.Sorbonne Université ; Universität WienDecember 2020
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• 101 articleO.Odo Diekmann, J. A.Johan Andre Peter Heesterbeek and J. A.Johan AJ Metz. On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations.Journal of mathematical biology2841990, 365--382
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• 102 inproceedingsW.Walid Djema, F.Frederic Mazenc, C.Catherine Bonnet, J.Jean Clairambault, P.P Hirsch and F.François Delhommeau. Stability of a Delay System Coupled to a Differential-Difference System Describing the Coexistence of Ordinary and Mutated Hematopoietic Stem Cells.Conference on Decision and Control Las Vegas, United StatesDecember 2016
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• 103 unpublishedM.Marie Doumic, M.Miguel Escobedo and M.Magali Tournus. An inverse problem: recovering the fragmentation kernel from the short-time behaviour of the fragmentation equation.December 2021, working paper or preprint
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• 104 articleM.Marie Doumic, M.Miguel Escobedo and M.Magali Tournus. Estimating the division rate and kernel in the fragmentation equation.Annales de l'Institut Henri Poincaré (C) Non Linear Analysishttps://arxiv.org/abs/1804.089452018
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• 105 articleM.Marie Doumic, S.Sarah Eugene and P.Philippe Robert. Asymptotics of Stochastic Protein Assembly Models.SIAM Journal on Applied Mathematics766November 2016, 20
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• 106 articleM.Marie Doumic, K.Klemens Fellner, M.Mathieu Mezache and H.Human Rezaei. A bi-monomeric, nonlinear Becker--Döring-type system to capture oscillatory aggregation kinetics in prion dynamics.Journal of theoretical biology4802019, 241--261
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• 107 articleM.Marie Doumic and P.Pierre Gabriel. Eigenelements of a General Aggregation-Fragmentation Model.Mathematical Models and Methods in Applied Sciences205May 2010, 757-783URL: https://hal.archives-ouvertes.fr/hal-00408088
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• 108 articleM.Marie Doumic, S.Sophie Hecht and D.Diane Peurichard. A purely mechanical model with asymmetric features for early morphogenesis of rod-shaped bacteria micro-colony.Mathematical Biosciences and Engineering176October 2020, http://aimspress.com/article/doi/10.3934/mbe.2020356
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• 109 unpublishedM.Marie Doumic, M.Marc Hoffmann, N.Nathalie Krell and L.Lydia Robert. Statistical estimation of a growth-fragmentation model observed on a genealogical tree.October 2012, 46 pages, 4 figures
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• 110 articleM.Marie Doumic, A.Adéla\"ide Olivier and L.Lydia Robert. Estimating the division rate from indirect measurements of single cells.Discrete and Continuous Dynamical Systems - Series B2510October 2020, 3931--3961
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• 111 articleM.M. Doumic, B.B. Perthame and J.J.P. Zubelli. Numerical Solution of an Inverse Problem in Size-Structured Population Dynamics.Inverse Problems2542009, 045008
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• 112 incollectionD.Dirk Drasdo, A.A. Buttenschön and P.Paul Van Liedekerke. Agent-Based Lattice Models of Multicellular Systems.Numerical Methods and Advanced Simulation in Biomechanics and Biological ProcessesElsevier2018, 223-238
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• 113 articleD.Dirk Drasdo, S.Stefan Hoehme and J. G.Jan G. Hengstler. How predictive quantitative modeling of tissue organization can inform liver disease pathogenesis.Journal of Hepatology614October 2014, 951--956
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• 114 bookV. A.V. A. Dyck, J.J. Hendrichs and A. S.A. S. Robinson. The Sterile Insect Technique, Principles and Practice in Area-Wide Integrated Pest Management.Springer, Dordrecht2006, 787
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• 115 unpublishedC.Charles Elbar, B.Benôit Perthame and A.Alexandre Poulain. Degenerate Cahn-Hilliard and incompressible limit of a Keller-Segel model.December 2021, working paper or preprint
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• 116 phdthesisS.Sarah Eugene. Stochastic modelling in molecular biology: a probabilistic analysis of protein polymerisation and telomere shortening.UPMC LJLLSeptember 2016
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• 117 articleS.Sarah Eugene, W.-F.Wei-Feng Xue, P.Philippe Robert and M.Marie Doumic-Jauffret. Insights into the variability of nucleated amyloid polymerization by a minimalistic model of stochastic protein assembly.Journal of Chemical Physics14417May 2016, 12
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• 118 articleJ.Jingyi Fu, B.Benoit Perthame and M.Min Tang. Fokker--Plank System for Movement of Micro-organism Population in Confined Environment.Journal of Statistical Physics1841July 2021
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• 119 articleA.Ahmed Ghallab, G.Geraldine Cellière, S.Sebastian Henkel, D.Dominik Driesch, S.Stefan Hoehme, U.Ute Hofmann, S.Sebastian Zellmer, P.Patricio Godoy, A.Agapios Sachinidis, M.Meinolf Blaszkewicz, R.Raymond Reif, R.Rosemarie Marchan, L.Lars Kuepfer, D.Dieter Häussinger, D.Dirk Drasdo, G.G Gebhardt and J. G.Jan G. Hengstler. Model-guided identification of a therapeutic strategy to reduce hyperammonemia in liver diseases.Journal of Hepatology644November 2015, 860--871
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• 120 articleA.Ahmed Ghallab, U.Ute Hofmann, S.Selahaddin Sezgin, N.Nachiket Vartak, R.Reham Hassan, A.Ayham Zaza, P.Patricio Godoy, K. M.Kai Markus Schneider, G.Georgia Guenther, Y. A.Yasser A. Ahmed, A.Aya Abbas, V.Verena Keitel, L.Lars Kuepfer, S.Steven Dooley, F.Frank Lammert, C.Christian Trautwein, M.Michael Spiteller, D.Dirk Drasdo, A.Alan Hofmann, P. L.Peter L.M. Jansen, J.Jan Hengstler and R.Raymond Reif. Bile Microinfarcts in Cholestasis Are Initiated by Rupture of the Apical Hepatocyte Membrane and Cause Shunting of Bile to Sinusoidal Blood.HepatologyAugust 2018
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• 121 articleA.Ahmed Ghallab, M.Maiju Myllys, C.Christian H Holland, A.Ayham Zaza, W.Walaa Murad, R.Reham Hassan, Y.Yasser A Ahmed, T.Tahany Abbas, E.Eman A Abdelrahim, K. M.Kai Markus Schneider and others. Influence of liver fibrosis on lobular zonation.Cells8122019, 1556
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• 122 articleL.Laurent Gosse and N.Nicolas Vauchelet. Hydrodynamic singular regimes in 1+1 kinetic models and spectral numerical methods.Journal of Mathematical Analysis and Applications2016
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• 123 articleJ.Janet Hemingway and H.Hilary Ranson. Insecticide resistance in insect vectors of human disease.Annual review of entomology4512000, 371--391
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• 124 articleM.M. Hertig and S. B.S. B. Wolbach. Studies on rickettsia-like micro-organisms in insects.The Journal of medical research4431924, 329
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• 125 phdthesisV. H.Van Ha Hoang. Adaptive estimation for inverse problems with applications to cell divisions.Université de Lille 1 -- Sciences et TechnologiesNovember 2016
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• 126 articleS.Stefan Hoehme, M.Marc Brulport, A.Alexander Bauer, E.Essam Bedawy, W.Wiebke Schormann, M.Matthias Hermes, V.Verena Puppe, R.Rolf Gebhardt, S.Sebastian Zellmer, M.Michael Schwarz, E.Ernesto Bockamp, T.Tobias Timmel, J. G.Jan G. Hengstler and D.Dirk Drasdo. Prediction and validation of cell alignment along microvessels as order principle to restore tissue architecture in liver regeneration.Proceedings of the National Academy of Sciences10723Including Supporting information2010, 10371--10376
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• 127 articleM.Marc Hoffmann and A.Adélaïde Olivier. Nonparametric estimation of the division rate of an age dependent branching process.Stochastic Processes and their ApplicationsDecember 2015
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• 128 articleN.Nick Jagiella, B.Benedikt Müller, M.Margareta Müller, I. E.Irene E. Vignon-Clementel and D.Dirk Drasdo. Inferring Growth Control Mechanisms in Growing Multi-cellular Spheroids of NSCLC Cells from Spatial-Temporal Image Data.PLoS Computational Biology1222016, e1004412
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• 129 articleF.Francois James and N.Nicolas Vauchelet. Equivalence between duality and gradient flow solutions for one-dimensional aggregation equations.Discrete and Continuous Dynamical Systems - Series A3632016, 1355-1382
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• 130 articleF.Francois James and N.Nicolas Vauchelet. Numerical methods for one-dimensional aggregation equations.SIAM Journal on Numerical Analysis5322015, 895-916
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• 131 articleG.Gaspard Jankowiak, D.Diane Peurichard, A.Anne Reversat, C.Christian Schmeiser and M.Michael Sixt. Modelling adhesion-independent cell migration.Mathematical Models and Methods in Applied Sciences2020
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• 132 articleM.-J.Moon-Jin Kang, B.Benoît Perthame and D.Delphine Salort. Dynamics of time elapsed inhomogeneous neuron network model.Comptes Rendus Mathématique353September 2015, 1111-1115
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• 133 articleJ.Joy Kean, S.Stephanie Rainey, M.Melanie McFarlane, C.Claire Donald, E.Esther Schnettler, A.Alain Kohl and E.Emilie Pondeville. Fighting arbovirus transmission: natural and engineered control of vector competence in Aedes mosquitoes.Insects612015, 236--278
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• 134 articleI. C.Inwon C. Kim, B.Benoît Perthame and P. E.Panagiotis E. Souganidis. Free boundary problems for tumor growth: a viscosity solutions approach.Nonlinear Analysis: Theory, Methods and Applications1382016, 207-228
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• 135 articleM.Michal Kolwalczyk, B.Benoît Perthame and N.Nicolas Vauchelet. Transversal instability for the thermodiffusive reaction-diffusion system.Chinese Annals of Mathematics - Series B36513 pages2015, 871-882
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• 136 articleM.Maxim Kuznetsov, J.Jean Clairambault and V.Vitaly Volpert. Improving cancer treatments via dynamical biophysical models.Physics of Life ReviewsOctober 2021, 1-84
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• 137 unpublishedP. V.Paul Van Liedekerke, J.Johannes Neitsch, T.Tim Johann, E.Enrico Warmt, I.Ismael Gonzàlez-Valverde, S.Stefan Hoehme, S.Steffen Grosser, J.Josef Kaes and D.Dirk Drasdo. A quantitative high resolution computational mechanics cell model for growing and regenerating tissues.December 2018, working paper or preprint
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• 138 articleT.Tommaso Lorenzi, R. H.Rebecca H. Chisholm and J.Jean Clairambault. Tracking the evolution of cancer cell populations through the mathematical lens of phenotype-structured equations.Biology Direct111December 2016, 43
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• 139 articleT.Tommaso Lorenzi, R. H.Rebecca H. Chisholm, L.Laurent Desvillettes and B. D.Barry D. Hughes. Dissecting the dynamics of epigenetic changes in phenotype-structured populations exposed to fluctuating environments.Journal of Theoretical Biology386September 2015, 166-176
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• 140 miscT.Tommaso Lorenzi, R. H.Rebecca H. Chisholm and A.Alexander Lorz. Effects of an advection term in nonlocal Lotka-Volterra equations.December 2015
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• 141 articleA.Alexander Lorz, T.Tommaso Lorenzi, J.Jean Clairambault, A.Alexandre Escargueil and B.Benoît Perthame. Modeling the effects of space structure and combination therapies on phenotypic heterogeneity and drug resistance in solid tumors.Bulletin of Mathematical Biology771January 2015, 1-22
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• 142 articleA.Alexander Lorz, T.Tommaso Lorenzi, M. E.Michael E. Hochberg, J.Jean Clairambault and B.Benoît Perthame. Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies.ESAIM: Mathematical Modelling and Numerical AnalysisMarch 2013, 23
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• 143 articleH.Hugo Martin, M.Marie Doumic, M. T.Maria Teresa Teixeira and Z.Zhou Xu. Telomere shortening causes distinct cell division regimes during replicative senescence in Saccharomyces cerevisiae.Cell & Bioscience111October 2021
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• 144 unpublishedA.Antoine Mellet, B.Benoît Perthame and F.Fernando Quiros. A Hele-Shaw Problem for Tumor Growth.December 2015, working paper or preprint
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• 145 articleL. A.Luciano A. Moreira, I.Itaki Iturbe-Ormaetxe, J. A.Jason A. Jeffery, G.Guangjin Lu, A. T.Alyssa T. Pyke, L. M.Lauren M. Hedges, B. C.Bruno C. Rocha, S.Sonja Hall-Mendelin, A.Andrew Day, M.Markus Riegler, L. E.Leon E. Hugo, K. N.Karyn N. Johnson, B. H.Brian H. Kay, E. A.Elizabeth A. McGraw, A. F.Andrew F. van den Hurk, P. A.Peter A. Ryan and S. L.Scott L. O'Neill. A Wolbachia Symbiont in Aedes aegypti Limits Infection with Dengue, Chikungunya, and Plasmodium.Cell13972009, 1268 - 1278
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• 146 articleT. N.Thanh Nam Nguyen, J.Jean Clairambault, T.Thierry Jaffredo, B.Benôit Perthame and D.Delphine Salort. Adaptive dynamics of hematopoietic stem cells and their supporting stroma: A model and mathematical analysis.Mathematical Biosciences and Engineering1605May 2019, 4818--4845
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• 147 articleA.Adélaïde Olivier. How does variability in cells aging and growth rates influence the malthus parameter?Kinetic and Related Models 102June 2017, 481-512
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• 148 phdthesisA.Adelaïde Olivier. Statistical analysis of growth-fragmentation models.Université Paris Dauphine - Paris IXNovember 2015
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• 149 articleK.Khashayar Pakdaman, B.Benoît Perthame and D.Delphine Salort. Adaptation and Fatigue Model for Neuron Networks and Large Time Asymptotics in a Nonlinear Fragmentation Equation.Journal of Mathematical Neuroscience412014, 14
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• 150 inproceedingsP. E.Pastor E. Pérez Estigarribia, P.-A.Pierre-Alexandre Bliman and C. E.Christian E. Schaerer. Modelling and control of Mendelian and maternal inheritance for biological control of dengue vectors.ECC 2021 - European Control ConferenceRotterdam / Virtual, NetherlandsJune 2021
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• 151 articleP. E.Pastor E Pérez-Estigarribia, P.-A.Pierre-Alexandre Bliman and C. E.Christian E Schaerer. A class of fast--slow models for adaptive resistance evolution.Theoretical Population Biology1352020, 32--48
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