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18 results on '"Clairambault, Jean"'

1. Mathematical modelling of cancer growth and drug treatments: taking into account cell population heterogeneity and plasticity

Author

Clairambault, Jean, Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Silviu-Iulian Niculescu, Clairambault, Jean, Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), and Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)

Subjects
[SDV] Life Sciences [q-bio], MSC 35B40, 35G92, 49J20, 92C50, [SDV.CAN] Life Sciences [q-bio]/Cancer, [SDV]Life Sciences [q-bio], [SDV.BA]Life Sciences [q-bio]/Animal biology, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [SDV.CAN]Life Sciences [q-bio]/Cancer, [MATH] Mathematics [math], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], [MATH]Mathematics [math]
Abstract

Version v2 après acceptation du document par la conférence de la prépublication hal-03938311; International audience; Mathematical models of cancer growth and evolution of cancer cell characteristics, aka traits or phenotypes, together with optimisation and optimal control methods to contain them, in the framework of adaptive dynamics of cell populations, are presented. They take into account the heterogeneity of cancer cell populations, i.e., their biological variability, and their intrinsic plasticity, i.e., their nongenetic instability that allows them to quickly adapt to changing environments. The presented vision of the cancer disease, which is specific to multicellular organisms, relies on a relatively novel vision, consistent with a billion-year evolutionary perspective. Based on recent contributions from philosophy of cancer, these mathematical models aim at designing theoretical therapeutic strategies to simultaneously contain tumour progression and limit adverse events of drugs to healthy cell populations.

Published
2023

2. A phenotype-structured model for the tumour-immune response

Author

Kaid, Zineb, Clairambault, Jean, Pouchol, Camille, Department of Mathematics [Tlemcen], Université de Tlemcen, Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), and Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)

Subjects
Immune checkpoint inhibitors, Mathematics - Analysis of PDEs, Tumour-Immune interactions, FOS: Biological sciences, Asymptotic analysis, Cell Behavior (q-bio.CB), FOS: Mathematics, Quantitative Biology - Cell Behavior, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Phenotype-structured model, Analysis of PDEs (math.AP)
Abstract

This paper presents a mathematical model for tumour-immune response interactions in the perspective of immunotherapy by immune checkpoint inhibitors (ICIs). The model is of the integrodifferential Lotka-Volterra type, in which heterogeneity of the cell populations is taken into account by structuring variables that are continuous internal traits (aka phenotypes) representing a lumped ''aggressiveness'', i.e., for tumour cells, ability to thrive in a viable state under attack by immune cells or drugs-which we propose to identify as a potential of de-differentiation-, and for immune cells, ability to kill tumour cells. We analyse the asymptotic behaviour of the model in the absence of treatment. By means of two theorems, we characterise the limits of the integro-differential system under an a priori convergence hypothesis. We illustrate our results with numerical simulations, which show that our model exemplifies the three Es of immunoediting: elimination, equilibrium, and escape.

Published
2023

3. Phenotype divergence and cooperation in isogenic multicellularity and in cancer

Author

Alvarez, Frank, Clairambault, Jean, CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT), Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), and Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)

Subjects
[SHS.HISPHILSO]Humanities and Social Sciences/History, Philosophy and Sociology of Sciences, Cooperation, Mathematics - Analysis of PDEs, Differentiation, Multicellularity, Cancer disease, Structured population models, Philosophy of science, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Analysis of PDEs (math.AP)
Abstract

We discuss the mathematical modelling of two of the main mechanisms which pushed forward the emergence of multicellularity: phenotype divergence in cell differentiation, and between-cell cooperation. In line with the atavistic theory of cancer, this disease being specific of multicellular animals, we set special emphasis on how both mechanisms appear to be reversed, however not totally impaired, rather hijacked, in tumour cell populations. Two settings are considered: the completely innovating, tinkering, situation of the emergence of multicellularity in the evolution of species, which we assume to be constrained by external pressure on the cell populations, and the completely planned-in the body plan-situation of the physiological construction of a developing multicellular animal from the zygote, or of bet hedging in tumours, assumed to be of clonal formation, although the body plan is largely-but not completely-lost in its constituting cells. We show how cancer impacts these two settings and we sketch mathematical models for them. We present here our contribution to the question at stake with a background from biology, from mathematics, and from philosophy of science.

Published
2023
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4. Perspectives in cancer treatment. Reply to comments on 'Improving cancer treatments via dynamical biophysical models'

Author

Kuznetsov, Maxim, Clairambault, Jean, Volpert, Vitali, Volpert, Vitaly, P. N. Lebedev Physical Institute of the Russian Academy of Sciences [Moscow] (LPI RAS), Russian Academy of Sciences [Moscow] (RAS), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Modélisation multi-échelle des dynamiques cellulaires : application à l'hématopoïese (DRACULA), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-Inria Lyon, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Modélisation mathématique, calcul scientifique (MMCS), and This work is supported by the Ministry of Science and Higher Education of the Russian Federation: agreement no. 075-03-2020-223/3 (FSSF-2020-0018).

Subjects
Optimization, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Mathematical oncology, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematical medicine
Abstract

International audience; We would like to thank the authors of the comments [1]-[5] for their interesting and stimulating ideas, as well as for discussing some issues that remained outside the scope of our review [6]. We agree with these comments and we will return to some of them in the discussion below.

Published
2022

5. Stepping From Modeling Cancer Plasticity to the Philosophy of Cancer

Author

Clairambault, Jean, Sorbonne Université (SU), Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), and Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)

Subjects
Philosophy, [SDV.BDD.EO]Life Sciences [q-bio]/Development Biology/Embryology and Organogenesis, Evolution, [SDV]Life Sciences [q-bio], Multicellularity, [SHS.PHIL]Humanities and Social Sciences/Philosophy, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [SDV.CAN]Life Sciences [q-bio]/Cancer, Therapeutics, ComputingMilieux_MISCELLANEOUS, Cancer
Abstract

Open access; International audience

Published
2020

6. A survey of adaptive cell population dynamics models of emergence of drug resistance in cancer, and open questions about evolution and cancer

Author

Clairambault, Jean, Pouchol, Camille, Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Sorbonne Université (SU), Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS), and Camille Pouchol acknowledges support from theSwedish Foundation of Strategic Research grant AM13-004

Subjects
Drug-induced drug resistance, Darwinian evolution, Cell population dynamics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Structured models, Cancer therapeutics, Optimal control
Abstract

Copyright: ⃝c 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.; International audience; This article is a proceeding survey (deepening a talk given by the first author at the BioMath 2019 International Conference on Mathematical Models and Methods, held in Będlewo, Poland) of mathematical models of cancer and healthy cell population adaptive dynamics exposed to anticancer drugs, to describe how cancer cell populations evolve toward drug resistance. Such mathematical models consist of partial differential equations (PDEs) structured in continuous phenotypes coding for the expression of drug resistance genes; they involve different functions representing targets for different drugs, cytotoxic and cytostatic, with complementary effects in limiting tumour growth. These phenotypes evolve continuously under drug exposure, and their fate governs the evolution of the cell population under treatment. Methods of optimal control are used, taking inevitable emergence of drug resistance into account, to achieve the best strategies to contain the expansion of a tumour. This evolutionary point of view, which relies on biological observations and resulting modelling assumptions, naturally extends to questioning the very nature of cancer as evolutionary disease, seen not only at the short time scale of a human life, but also at the billion year-long time scale of Darwinian evolution, from unicellular organisms to evolved multicellular organs such as animals and man. Such questioning, not so recent, but recently revived, in cancer studies, may have consequences for understanding and treating cancer. Some open and challenging questions may thus be (non exhaustively) listed as:-May cancer be defined as a spatially localised loss of coherence between tissues in the same mul-ticellular organism, 'spatially localised' meaning initially starting from a given organ in the body, but also possibly due to flaws in an individual's epigenetic landscape such as imperfect control of differentiation genes?-If one assumes that "The genes of cellular cooperation that evolved with multicellularity about a billion years ago are the same genes that malfunction in cancer." (Davies and Lineweaver, 2011), how can these genes be systematically investigated, looking for zones of fragility-that depend on individuals-in the 'tinkering' (F. Jacob, 1977) evolution is made of, tracking local defaults of coherence?-What is such coherence made of and to what extent is the immune system responsible for it (the self and differentiation within the self)? Related to this question of self, what parallelism can be established between the development of multicellularity in different species proceeding from the same origin and the development of the immune system in these different species?

Published
2019

7. Emergence of cytotoxic resistance in cancer cell populations

Author

Lorenzi, Tommaso, Chisholm, Rebecca H., Lorz, Alexander, Larsen, Annette K, Almeida, Luís, Escargueil, Alexandre, Clairambault, Jean, Centre de Mathématiques et de Leurs Applications (CMLA), École normale supérieure - Cachan (ENS Cachan)-Centre National de la Recherche Scientifique (CNRS), University of New South Wales [Sydney] (UNSW), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Modelling and Analysis for Medical and Biological Applications (MAMBA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Cancerologie Fondamentale et Clinique des Tumeurs Solides, Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de la Santé et de la Recherche Médicale (INSERM), V. Volpert and J. Clairambault, and Clairambault, Jean

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]
Abstract

International audience; We formulate an individual-based model and an integro-differential model of phenotypic evolution, under cytotoxic drugs, in a cancer cell population structured by the expression levels of survival-potential and proliferation-potential. We apply these models to a recently studied experimental system. Our results suggest that mechanisms based on fundamental laws of biology can reversibly push an actively-proliferating, and drug-sensitive, cell population to transition into a weakly-proliferative and drug-tolerant state, which will eventually facilitate the emergence of more potent, proliferating and drug-tolerant cells.

Published
2015

8. Enabling multiscale modeling in systems medicine: From reactions in cells to organ physiology

Author

Wolkenhauer, Olaf, Auffray, Charles, Brass, Olivier, Clairambault, Jean, Deutsch, Andreas, Drasdo, Dirk, Gervasio, Francesco, Preziosi, Luigi, MAINI, Philip, Marciniak-Czochra, Anna, Kossow, Christina, Kuepfer, Lars, Rateitschak, Katja, Ramis-Conde, Ignacio, Ribba, Benjamin, Schuppert, Andreas, Smallwood, Rod, Stamatakos, Georgios, Winter, Felix, Byrne, Helen, Department of Systems Biology and Bioinformatics, University of Rostock, Wallenberg Research Centre at Stellenbosch University, Genexpress - SYSTEMOSCOPE Génomique Fonctionnelle et Biologie Systémique pour la Santé, Institut des Sciences Biologiques du CNRS, Modelling and Analysis for Medical and Biological Applications (MAMBA), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Database group, Computer Science and engeenering Department [San Diego] (DB CSE UCSD), University of California [San Diego] (UC San Diego), University of California-University of California, University College of London [London] (UCL), Department of Mathematics [Torino] (DIMAT), Politecnico di Torino = Polytechnic of Turin (Polito), Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford OX1 3LB, United Kingdom, IAM Heidelberg, Universität Heidelberg [Heidelberg], Institute of Applied Microbiology, RWTH Aachen University, Aachen, Germany, Computational Systems Biology [Leverkusen], Bayer Technology Services [Leverkusen], Numerical Medicine (NUMED), Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Inria Grenoble - Rhône-Alpes, Rheinisch-Westfälische Technische Hochschule Aachen (RWTH), Kroto Research Institute, University of Sheffield [Sheffield], National Technical University of Athens [Athens] (NTUA), Institut für Anorganische und Analytische Chemie, Westfälische Wilhelms-Universität Münster (WWU), Centre for Plant Integrative Biology [Nothingham] (CPIB), University of Nottingham, UK (UON), Stellenbosch University, Department of Computer Science and Engineering [Univ California San Diego] (CSE - UC San Diego), University of California (UC)-University of California (UC), Centre for Mathematical Biology, Mathematical Institute, Universität Heidelberg [Heidelberg] = Heidelberg University, École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Rheinisch-Westfälische Technische Hochschule Aachen University (RWTH), Westfälische Wilhelms-Universität Münster = University of Münster (WWU), Clairambault, Jean, Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), and Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)

Subjects
Multiscale modelling, Systems Biology, [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Popularisation, Systems Medicine
Abstract

International audience; Systems medicine is an interdisciplinary approach that integrates data from basic research and clinical practice to improve our understanding and treatment of diseases. Systems medicine can be seen as a further development of systems biology and bioinformatics towards applica-tions of clinical relevance. The term 'systems' refers to systems approaches, emphasizing a close integration of data generation with mathematical modeling [1-3]. The (mal)functioning of the human body is a complex process, characterized by multiple interactions between systems that act across multiple levels of structural and functional organization -from molecular reactions to cell-cell interac-tions in tissues to the physiology of organs and organ systems. Over the past decade, we have gained detailed insights into the structure and function of molecular, cellu-lar and organ-level systems, with technologies playing an important role in the generation of data at these different scales.

Published
2014

9. Preface to Session 70 ' Mathematical models and methods to investigate heterogeneity in cell and cell population biology ': Presentation of Session 70 in ICNAAM 2015, Rhodes

Author

Barbarroux, Loic, Clairambault, Jean, Cogan, Nick, Elias, Jan, Hanson, Shalla, Kimmel, Marek, Lorenzi, Tommaso, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Multi-scale modelling of cell dynamics : application to hematopoiesis (DRACULA), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Modelling and Analysis for Medical and Biological Applications (MAMBA), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Tallahassee], Florida State University [Tallahassee] (FSU), Department of Mathematics [Durham], Duke University [Durham], Department of Statistics [Houston], Rice University [Houston], Organiser Session 70: Jean Clairambault, Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université de Lyon-Université de Lyon-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan [Villeurbanne] (ICJ), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL)

Subjects
Agent-based models, Persisters, Treatment optimisation, Genotype/phenotype evolution, Cell population dynamics, Single cell/cell population models, Physiologically structured models, Ordinary/partial/delay differential equations, Spatio-temporal dynamics, Reaction-diffusion equations, Biofilms, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Probabilistic models, Immune response, Drug tolerance, Cell fate decision, Cancer
Abstract

International audience; This session investigates hot topics related to mathematical representations of cell and cell population dynamics in biology and medicine, in particular, but not only, with applications to cancer. Methods in mathematical modelling and analysis, and in statistical inference using single-cell and cell population data, should contribute to focus this session on heterogeneity in cell populations. Among other methods are proposed: a) Intracellular protein dynamics and gene regulatory networks using ordinary/partial/delay differential equations (ODEs, PDEs, DDEs); b) Representation of cell population dynamics using agent-based models (ABMs) and/or PDEs; c) Hybrid models and multiscale models to integrate single-cell dynamics into cell population behaviour; d) Structured cell population dynamics and asymptotic evolution w.r.t. relevant traits; e) Heterogeneity in cancer cell populations: origin, evolution, phylogeny and methods of reconstruction; f) Drug resistance as an evolutionary phenotype: predicting and overcoming it in therapeutics; g) Theoretical therapeutic optimisation of combined drug treatments in cancer cell populations and in populations of other organisms, such as bacteria.

Published
2015

10. Emergence of cytotoxic resistance in cancer cell populations: From individual-level mechanisms to population-level consequences

Author

Lorenzi, Tommaso, Chisholm, Rebecca H., Lorz, Alexander, Larsen, Annette K, Almeida, Luís, Escargueil, Alexandre, Clairambault, Jean, Centre de Mathématiques et de Leurs Applications (CMLA), École normale supérieure - Cachan (ENS Cachan)-Centre National de la Recherche Scientifique (CNRS), University of New South Wales [Sydney] (UNSW), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Modelling and Analysis for Medical and Biological Applications (MAMBA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Cancerologie Fondamentale et Clinique des Tumeurs Solides, Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de la Santé et de la Recherche Médicale (INSERM), and V. Volpert and J. Clairambault

Subjects
lcsh:T58.5-58.64, lcsh:Information technology, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Abstract

International audience; We formulate an individual-based model and an integro-differential model of phenotypic evolution, under cytotoxic drugs, in a cancer cell population structured by the expression levels of survival-potential and proliferation-potential. We apply these models to a recently studied experimental system. Our results suggest that mechanisms based on fundamental laws of biology can reversibly push an actively-proliferating, and drug-sensitive, cell population to transition into a weakly-proliferative and drug-tolerant state, which will eventually facilitate the emergence of more potent, proliferating and drug-tolerant cells.

Published
2015

11. Perspective on 'New and Less New Opportunities For Mathematical Biology as Applied To Biological and Clinical Medicine'

Author

Clairambault, Jean, Modelling and Analysis for Medical and Biological Applications (MAMBA), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)

Subjects
medicine, biology, perspective, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], popularisation, Applications of mathematiccs
Abstract

International audience; Another conception that makes applications of mathematics quite different from applications of mathematics to sole biology resides in the interventionist nature of medicine ...

Published
2014

12. Deterministic mathematical modelling for cancer chronotherapeutics: cell population dynamics and treatment optimisation

Author

Clairambault, Jean, Nonlinear Analysis for Biology and Geophysical flows (BANG), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Abstract

Chronotherapeutics has been designed and used for more than twenty years as an effective treatment against cancer by a few teams around the world, among whom one of the first is Francis Lévi's at Paul-Brousse hospital (Villejuif, France), in application of circadian clock physiology to determine best infusion times within the 24-hour span for anticancer drug delivery. Mathematical models have been called in the last ten years to give a rational basis to such optimised treatments, for use in the laboratory and ultimately in the clinic. While actual clinical applications of the theoretical optimisation principles found have remained elusive so far to improve chronotherapeutic treatments in use, mathematical models provide proofs of concepts and tracks to be explored experimentally, to progress from theory to bedside. Starting from a simple ordinary differential equation model that allowed setting and numerically solving a drug delivery optimisation problem with toxicity constraints, this modelling enterprise has been extended to represent the division cycle in proliferating cell populations with different molecular targets, to allow for the representation of anticancer drug combinations that are used in clinical oncology. The main point to be made precise in such a therapeutic optimisation problem is to establish, here in the frame of circadian chronobiology, physiologically based differences between healthy and cancer cell populations in their responses to drugs. To this aim, clear biological evidence at the molecular level is still lacking, so that, starting from indirect observations at the experimental and clinical levels and from theoretical considerations on the model, speculations have been made, that will be exposed in this review of cancer chronotherapeutics models with the corresponding optimisation problems and their numerical solutions, to represent these differences between the two cell populations, with regard to circadian clock control.

Published
2013

13. Modelling the spatial organization of cell proliferation in the developing central nervous system

Author

Clairambault, Jean, Flores, Vladimir, Perthame, Benoît, Rapacioli, Melina, Rofman, Edmundo, Verdes, Rafael, Nonlinear Analysis for Biology and Geophysical flows (BANG), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Department of Biostructural Sciences, Universidad Favaloro, Favaloro Foundation-Favaloro Foundation, Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Instituto Argentino de Matemática (IAM), Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET), Instituto de Matemática Beppo Levi, and Universidad Nacional de Rosario [Santa Fe]

Subjects
cell proliferation, ACM: J.: Computer Applications/J.3: LIFE AND MEDICAL SCIENCES, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], developmental neurobiology, structured partial differential equations, optical tectum, [SDV.BDD]Life Sciences [q-bio]/Development Biology, spatial organization
Abstract

How far is neuroepithelial cell proliferation in the developing central nervous system a deterministic process? Or, to put it in a more precise way, how accurately can it be described by a deterministic mathematical model? To provide tracks to answer this question, a deterministic system of transport and diffusion partial differential equations, both physiologically and spatially structured, is introduced as a model to describe the spatially organized process of cell proliferation during the development of the central nervous system. As an initial step towards dealing with the three-dimensional case, a unidimensional version of the model is presented. Numerical analysis and numerical tests are performed. In this work we also achieve a first experimental validation of the proposed model, by using cell proliferation data recorded from histological sections obtained during the development of the optic tectum in the chick embryo.

Published
2010

14. An age-and-cyclin-structured cell population model with proliferation and quiescence for healthy and tumoral tissues

Author

Bekkal Brikci, Fadia, Clairambault, Jean, Ribba, Benjamin, Perthame, Benoît, Nonlinear Analysis for Biology and Geophysical flows (BANG), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Numerical Medicine (NUMED), Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Département de Mathématiques et Applications - ENS Paris (DMA), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), INRIA, Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Inria Grenoble - Rhône-Alpes, Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), and École normale supérieure - Paris (ENS Paris)

Subjects
Cancer, Population dynamics, Cyclins, Partial Differential Equations, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Tumour growth, Cell cycle
Abstract

We present a nonlinear model of the dynamics of a cell population divided in a proliferative and a quiescent compartments. The proliferative phase represents the complete cell division cycle ($G_{1}-S-G_{2}-M$) of a population committed to divide at its end. The model is structured by the time spent by a cell in the proliferative phase, and by the amount of \emph{cyclin~D/(CDK4 or 6)} complexes. Cells can transit from one compartment to the other, following transition rules which differ according to the tissue state: healthy or tumoral. The asymptotic behaviour of solutions of the nonlinear model is analysed in both cases, exhibiting tissue homeostasis or tumour exponential growth. The model is simulated by numerical solutions which confirm its theoretical predictions.

Published
2006

15. A survey of adaptive cell population dynamics models of emergence of drug resistance in cancer, and open questions about evolution and cancer

Author

Jean Clairambault, Camille Pouchol, Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Sorbonne Université (SU), Department of Mathematics [Sweden] (KTH), Stockholm University, Camille Pouchol acknowledges support from the Swedish Foundation of Strategic Research grant AM13-004, and Clairambault, Jean

Subjects
Drug-induced drug resistance, Population, Structured models, [SDV.CAN]Life Sciences [q-bio]/Cancer, Disease, Biochemistry, Genetics and Molecular Biology (miscellaneous), 03 medical and health sciences, 0302 clinical medicine, [SDV.CAN] Life Sciences [q-bio]/Cancer, Darwinian evolution, medicine, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Epigenetics, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], education, lcsh:QH301-705.5, Organism, 030304 developmental biology, 0303 health sciences, education.field_of_study, Applied Mathematics, lcsh:Mathematics, Cell population dynamics, Cancer, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], medicine.disease, lcsh:QA1-939, Agricultural and Biological Sciences (miscellaneous), Phenotype, Optimal control, Multicellular organism, lcsh:Biology (General), Evolutionary biology, 030220 oncology & carcinogenesis, Darwinism, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Cancer therapeutics
Abstract

This article is a proceeding survey (deepening a talk given by the first author at the BioMath 2019 International Conference on Mathematical Models and Methods, held in Będlewo, Poland) of mathematical models of cancer and healthy cell population adaptive dynamics exposed to anticancer drugs, to describe how cancer cell populations evolve toward drug resistance. Such mathematical models consist of partial differential equations (PDEs) structured in continuous phenotypes coding for the expression of drug resistance genes; they involve different functions representing targets for different drugs, cytotoxic and cytostatic, with complementary effects in limiting tumour growth. These phenotypes evolve continuously under drug exposure, and their fate governs the evolution of the cell population under treatment. Methods of optimal control are used, taking inevitable emergence of drug resistance into account, to achieve the best strategies to contain the expansion of a tumour. This evolutionary point of view, which relies on biological observations and resulting modelling assumptions, naturally extends to questioning the very nature of cancer as evolutionary disease, seen not only at the short time scale of a human life, but also at the billion year-long time scale of Darwinian evolution, from unicellular organisms to evolved multicellular organs such as animals and man. Such questioning, not so recent, but recently revived, in cancer studies, may have consequences for understanding and treating cancer. Some open and challenging questions may thus be (non exhaustively) listed as:-May cancer be defined as a spatially localised loss of coherence between tissues in the same mul-ticellular organism, 'spatially localised' meaning initially starting from a given organ in the body, but also possibly due to flaws in an individual's rms of evolution towards drug resistance governed by the phenotypes which determine landscape such as imperfect epigenetic control of differentiation genes?-If one assumes that "The genes of cellular cooperation that evolved with multicellularity about a billion years ago are the same genes that malfunction in cancer." (Davies and Lineweaver, 2011), how can these genes be systematically investigated, looking for zones of fragility-that depend on individuals-in the 'tinkering' (F. Jacob, 1977) evolution is made of, tracking local defaults of coherence?-What is such coherence made of and to what extent is the immune system responsible for it (the self and differentiation within the self)? Related to this question of self, what parallelism can be established between the development of multicellularity in different species proceeding from the same origin and the development of the immune system in these different species?

Published
2019

16. An evolutionary perspective on cancer, with applications to anticancer drug resistance modelling and perspectives in therapeutic control

Author

Jean Clairambault, Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), and Clairambault, Jean

Subjects
0303 health sciences, Integro-differential equations, Resistance (ecology), AMS Subject Classifications: 35B40, 35Q92, 35R09, 45J05, 49J20, 92C50, 92D15, 92D25, 93D20, Computer science, Asymptotic analysis, Perspective (graphical), Cancer, Mathematical oncology, medicine.disease, Anticancer drug, Optimal control, 03 medical and health sciences, Multicellular organism, 0302 clinical medicine, Risk analysis (engineering), 030220 oncology & carcinogenesis, medicine, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Control (linguistics), 030304 developmental biology
Abstract

International audience; The question of a mathematical representation and theoretical overcoming by op-timised therapeutic strategies of drug-induced drug resistance in cancer cell populations is tackled here from the point of view of adaptive dynamics and optimal population growth control, using integro-differential equations. Combined impacts of external continuous-time functions, standing for drug actions, on targets in a plastic (i.e., able to quickly change its phenotype in deadly environmental conditions) cell population model, represent a therapeutical control to be optimised. A justification for the introduction of the adaptive dynamics setting, retaining such plasticity for cancer cell populations, is firstly presented in light of the evolution of multicellular species and disruptions in multicellularity coherence that are characteristics of cancer and of its progression. Finally, open general questions on cancer and evolution in the Darwinian sense are listed, that may open innovative tracks in modelling and treating cancer by circumventing drug resistance. This study sums up results that were presented at the international NUMACH workshop, Mulhouse, France, in July 2018.

Published
2019

17. Physiologically structured cell population dynamic models with applications to combined drug delivery optimisation in oncology

Author

Olivier Fercoq, Jean Clairambault, Modelling and Analysis for Medical and Biological Applications (MAMBA), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Traitement et Communication de l'Information (LTCI), Télécom ParisTech-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Nonlinear Analysis for Biology and Geophysical flows (BANG), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Max-plus algebras and mathematics of decision (MAXPLUS), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Operational Research and Optimization Group, The School of Mathematics, The King's Buildings, Operational Research and Optimization (School of Mathematics), University of Edinburgh-University of Edinburgh, Bachar, Mostafa and Batzel, Jerry and Chaplain, Mark, Sorbonne Université (SU), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), and Clairambault, Jean

Subjects
0301 basic medicine, Oncology, medicine.medical_specialty, Population, Circadian clock, [SDV.CAN]Life Sciences [q-bio]/Cancer, Biology, 03 medical and health sciences, 0302 clinical medicine, 35Q92, 49J20, 92C50, Pharmacokinetics, Drug control, Internal medicine, Drug delivery optimisation, medicine, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], education, MSC 35Q92, 49J20, 92C50, Age-structured models, education.field_of_study, Applied Mathematics, Cell population dynamics, Cell cycle, 030104 developmental biology, Tolerability, Cell division cycle, 030220 oncology & carcinogenesis, Modeling and Simulation, Drug delivery, Cancer cell, [SDV.SP.PHARMA]Life Sciences [q-bio]/Pharmaceutical sciences/Pharmacology, Pharmacological models, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

International audience; Optimising drug delivery in the general circulation targeted towards cancer cell pop- ulations, but inevitably reaching also proliferating healthy cell populations imposes to design optimised drug infusion algorithms in a dynamic way, i.e., controlling the growth of both populations simultaneously by the action of the drugs in use, wanted for cancer cells, and unwanted for toxic side effects on healthy cells. Towards this goal, we design models and methods, with optional representation of circadian clock control on proliferation in both populations, according to three axes [15, 16]: a) representing the oncologist's main weapons, drugs, and their fates in the organism by molecular-based pharmacokinetic-pharmacodynamic equations; b) representing the cell populations under attack by drugs, and their proliferation dynamics, including in the models molecular and functional targets for the drugs at stake, by physiologically structured equations; c) using numerical algorithms, optimising drug delivery under different constraints at the whole organism level, representing impacts of multiple drugs with different targets on cell populations. In the present study, two molecular pharmacological ODE models, one for oxali- platin, and one for 5-Fluorouracil, have been designed, using law of mass action and enzyme kinetics, to describe the fate of these two cytotoxic drugs in the organism. An age-structured PDE cell population model has been designed with drug control. targets to represent the effects of oxaliplatin and 5-Fluorouracil on the cell cycle in proliferating cell populations. The models for proliferating cell population dynam- ics involve possible physiological fixed (i.e., out of reach of therapeutic influence) circadian clock control, and varying drug control to be optimised, connected with pharmacological models. Concentrations of drugs, represented by outputs of ODEs, are assumed to be homogeneous in the cell populations under attack by cytotoxic drugs. The possi- bility to describe the effects of other drugs, cytostatic (including in this category anti-angiogenic drugs, considered as acting on the G1 phase, choking its entries and slowing it down), is also presented, but not put in pharmacokinetic equations and actual simulations in this study, that is focused on the combination of 5-FU and oxaliplatin, a classic therapeutic association in the treatment of colorectal cancer. We then set conditions to numerically solve drug delivery optimisation problems (maximisation of cancer cell kill under the constraint of preserving healthy cells over a tolerability threshold) by considering a trade-off between therapeutic and toxic effects. The observed effects on proliferation are growth exponents, i.e., first eigenvalues of the linear PDE systems, in the two populations, healthy and cancer. The solutions to an optimisation problem taking into account circadian clock control are presented as best delivery time schedules for the two drugs used in combined treatments, to be implemented in programmable delivery pumps in the clinic.

Published
2016

18. Phenotype heterogeneity in cancer cell populations

Author

Tommaso Lorenzi, Jean Clairambault, Alexandre E. Escargueil, Alexander Lorz, Luis Almeida, Rebecca H. Chisholm, Emmanuel Trélat, Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Modelling and Analysis for Medical and Biological Applications (MAMBA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Pierre et Marie Curie - Paris 6 (UPMC), Centre National de la Recherche Scientifique (CNRS), Centre de Recherche Saint-Antoine (UMRS893), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de la Santé et de la Recherche Médicale (INSERM), Jean Clairambault, and Clairambault, Jean

Subjects
Drug, Evolution, media_common.quotation_subject, Population, Cell, Drug resistance, Biology, Pharmacology, Physiologically structured models, 03 medical and health sciences, 0302 clinical medicine, medicine, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Epigenetics, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], education, 030304 developmental biology, media_common, Cancer, 0303 health sciences, education.field_of_study, Cell population dynamics, medicine.disease, Phenotype, Partial differential equations, 3. Good health, medicine.anatomical_structure, 030220 oncology & carcinogenesis, Cancer cell, Cancer research
Abstract

International audience; Phenotype heterogeneity in cancer cell populations, be it of genetic, epigenetic or stochastic origin, has beenidentified as a main source of resistance to drug treatments and a major source of therapeutic failures in cancers. The molecularmechanisms of drug resistance are partly understood at the single cell level (e.g., overexpression of ABC transporters or ofdetoxication enzymes), but poorly predictable in tumours, where they are hypothesised to rely on heterogeneity at the cellpopulation scale, which is thus the right level to describe cancer growth and optimise its control by therapeutic strategies inthe clinic. We review a few results from the biological literature on the subject, and from mathematical models that have beenpublished to predict and control evolution towards drug resistance in cancer cell populations.We propose, based on the latter, optimisation strategies of combined treatments to limit emergence of drug resistance tocytotoxic drugs in cancer cell populations, in the monoclonal situation, which limited as it is still retains consistent featuresof cell population heterogeneity. The polyclonal situation, that may be understood as “bet hedging” of the tumour, thusprotecting itself from different sources of drug insults, may lie beyond such strategies and will need further developments. Inthe monoclonal situation, we have designed an optimised therapeutic strategy relying on a scheduled combination of cytotoxicand cytostatic treatments that can be adapted to different situations of cancer treatments.Finally, we review arguments for biological theoretical frameworks proposed at different time and development scales, theso-called atavistic model (diachronic view relying on Darwinian genotype selection in the coursof billions of years) and theWaddington-like epigenetic landscape endowed with evolutionary quasi-potential (synchronic view relying on Lamarckianphenotype instruction of a given genome by reversible mechanisms), to represent evolution towards heterogeneity, possiblypolyclonal, in cancer cell populations and propose innovative directions for therapeutic strategies based on such frameworks.

Published
2015

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