C Pouchol

CH Lineweaver

J Clairambault

M Bertolaso

MD Vincent

PCW Davies

RH Chisholm

SV Sharma

T Pradeu

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Plasticity in Cancer Cell Populations: Biology, Mathematics and Philosophy of Cancer

Clairambault, Jean

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HAL Id: hal-03066491https://hal.archives-ouvertes.fr/hal-03066491Submitted on 15 Dec 2020HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.Plasticity in Cancer Cell Populations: Biology,Mathematics and Philosophy of CancerJean ClairambaultTo cite this version:Jean Clairambault. Plasticity in Cancer Cell Populations: Biology, Mathematics and Philosophyof Cancer. George Bebis; Max Alekseyev; Heyrim Cho; Jana Gevertz; Maria Rodriguez Martinez.”Mathematical and Computational Oncology”, Proceedings of the Second International Symposium,ISMCO 2020, San Diego, CA, USA, October 8-10, 2020, G. Bebis, M. Alekseyev, H. Cho, J. Gevertz,M. Rodriguez Martinez (Eds.), Springer LNBI 12508, pp. 3-9, October 2020., 12508, Springer, pp.3-9,2020, LNBI - Lecture Notes in Bioinformatics, ￿10.1007/978-3-030-64511-3_1￿. ￿hal-03066491￿Plasticity in cancer cell populations: biology,mathematics and philosophy of cancer?Jean Clairambault1[0000−0002−8336−9641]Inria & LJLL, Sorbonne University, Paris, Francejean.clairambault@inria.frhttps://who.rocq.inria.fr/Jean.Clairambault/Jean Clairambault en.htmlAbstract. In this presentation that partly subsumes and summarisesin the form of adapted excerpts some recent articles of which I am au-thor or co-author [2], [3], [11], I suggest that cancer is fundamentally adisease of the control of cell differentiation in multicellular organisms,uncontrolled cell proliferation being a mere consequence of blockade, orunbalance, of cell differentiations. Cancer cell populations, that can re-verse the sense of differentiations, are extremely plastic and able to adaptwithout mutations their phenotypes in order to transiently resist druginsults [10], which is likely due to the reactivation of ancient, normallysilenced, genes [5], [7], [12]. Stepping from mathematical models of nongenetic plasticity in cancer cell populations [4], [6] and questions theyraise, I propose an evolutionary biology approach to shed light on thisproblem a) from a theoretical viewpoint by a description of multicellu-lar organisms in terms of multi-level structures, which integrate functionand matter from lower to upper levels, and b) from a practical pointof view by proposing future tracks for cancer therapeutics, as cancer isprimarily a failure of multicellularity in animals and humans. This ap-proach resorts to the emergent field of knowledge known as philosophyof cancer [1], [8], [9].Keywords: Cancer Cells · Plasticity · Mathematical models · Philoso-phy of cancerIntroductionCoherent multicellular organisms are not only cohesive from a spatial, anatomicalpoint of view, but also coherent from the phenotypic and cell-functional point ofview of compatibility, cooperativity (division of tasks) between cells and tissues,making possible the achievement of a stable, functional and reproductive whole.I make here the simple hypothesis of a system of communication ways be-tween trees of differentiation, relying on the control of transcription factors thatdetermine differentiations, and that I call “the cohesion watch”. It may be consid-ered as a part of the immune system, whose armed force is the immune response,? Invited paper2 J. Clairambaultinnate as well as adaptive, humoral and cellular, but is not the whole of the im-mune system, that I view as the conductor of the unity of the organism. Withinthe immune system in this extended vision that is thus more general than theimmune response, this “cohesion watch” is in charge of the control of compatibili-ties and cooperations between the anatomical and the phenotypic/cell-functionalsystems, ultimately leading to an anatomically cohesive and functionally coher-ent multicellular organism.1 Plasticity in cancer cell populations1.1 Non genetic phenotype switchingPhenotype switching, or more generally continuous phenotype-determined cellplasticity, is an essential process originally observed during development, butis also now recognised as an important phenomenon upon injury and disease.One of the best described examples of phenotypic switching in cancer dependson the process of epithelial to mesenchymal transition (EMT) and its reversion(MET) [11]. In the context of anti-cancer therapies, cell plasticity enables tumourcells to change to a cell phenotypic identity that may be dependent or not onthe drug target, without additional secondary genetic mutations. Indeed, thediscovery of oncogenic-driven mutations favoured the development of diversetargeted therapies and showed unprecedented clinical response. Unfortunately,responses are in general incomplete and transient, as resistances develop uponcontinuous treatment exposure. Along with well-known genetic alterations, cellplasticity has recently emerged as an unavoidable contributor to therapy evasion.1.2 Transient drug-induced tolerance in cancerThe biological mechanisms that induce cancer cell plasticity upon drug treat-ment remain to be fully established. Nonetheless, they seem to involve a transi-tion whereby tumour cells undergo a slow proliferating drug tolerant state, nailedthe name of drug-tolerant persisters (DTPs), before possibly further developingsecondary mutational drug resistance. Persisters were firstly described in bacteriaupon antibiotic challenges. Similarly, a sub-population of non-small cell lung can-cer (NSCLC) cells has been shown to engage in a reversible phenotypic change inwhich DTPs survive the initial onslaught of anti-cancer therapies [10]. Similarphenomena were observed in glioblastoma and melanoma. Biological observa-tions support the idea that a tiny subpopulation, diverging from predominantcell phenotype prior to targeted therapy, may be subjected to a combination ofLamarckian plasticity and Darwinian selection upon anti-cancer therapies.1.3 Dedifferentiation and transdifferentiationConversion of lineage has been extensively studied in the context of develop-ment. The well-known, metaphoric, Waddington landscape has been proposedCancer plasticity 3to illustrate the fact that a progenitor cell normally rolls down within epige-netic differentiation valleys and can develop, due to phenotypic bifurcations,into the various terminally differentiated tissue types that constitute a coherentmulticellular organism (see also Section 3). In the context of cancer, dedifferen-tiation and transdifferentiation have been observed upon therapeutic challenges,which suggests a possible plasticity in the cancers Waddington landscape, withmetaphorically flattened valleys and lowered epigenetic barriers.2 Mathematics of plasticity with therapeutic control2.1 How to mathematically model plasticity in cancerCell plasticity is the ability of cells to change their phenotypes without geneticmutations in response to environmental cues. In a series of papers starting in2013, a team of mathematicians, to which I belong, at Laboratoire Jacques-Louis Lions, Sorbonne University, Paris, taking plasticity to be a concept of thecontinuum, and initially stimulated by an article published in 2010 [10] thatreported reversible resistance in a cancer cell culture exposed to massive dosesof drugs, gradually and completely reversed when the drug was withdrawn fromthe culture, tackled the question of understanding and predicting this plastic be-haviour of cancer cell populations by mathematical modelling (reviewed in [4]).The behaviour of these plastic cell populations was modelled by partial differen-tial equations (PDEs) in which the structuring variable, i.e., the parameter-likeone that codes for the biological variability of interest, i.e., the heterogeneity ofcell population, was here a continuous variable representing the expression ofa continuous resistance phenotype, from 0 (totally sensitive) to 1 (totally resis-tant). The modelled cell populations are able to change their phenotypes underhigh drug pressure so as to become reversibly resistant to the drug, meaning bythis the fact that, as real cells when the drug was rinsed from the culture, thecell population spontaneously became sensitive again to the same drug [10].2.2 Adaptive dynamics: asymptotic behaviour of cell populationsSuch mathematical models, that resort to the field of adaptive dynamics [4], [6]consist of partial differential equations (PDEs) structured in continuous pheno-types coding for the expression of drug resistance genes; they involve differentfunctions representing targets for different drugs, cytotoxic and cytostatic, withcomplementary effects in limiting tumour growth. These phenotypes evolve con-tinuously under drug exposure, and their fate governs the evolution of the cellpopulation under treatment.This evolutionary point of view, which relies on biological observations andresulting modelling assumptions, naturally extends to questioning the very na-ture of cancer as evolutionary disease, seen not only at the short time scale of ahuman life, but also at the billion year-long time scale of Darwinian evolution,from unicellular organisms to evolved multicellular organs such as animals andman. Such questioning, not so recent, but recently revived [5], [12], [7] in cancerstudies, may have consequences for understanding and treating cancer4 J. Clairambault2.3 Theoretical therapeutics: multi-targeted optimal controlThese mathematical models, intended to represent the effects of a cancer treat-ment on cell populations, and ultimately on patients, with the aim to overcometheir capacities of resistance induced by the treatment itself, naturally gave laterrise to the proposal of theoretically optimised therapeutic strategies. Methodsof optimal control have been used, taking inevitable emergence of drug resis-tance into account, to achieve the best strategies to contain the expansion of atumour. Such strategies, that have recently been the object of active researchaim at containing or eradicating cancer growth, avoiding the two major pitfallsof treatments in clinical oncology, namely unwanted toxic side effects in healthycell populations and emergence of resistance in cancer populations [4], [6].3 Evolutionary biology and philosophy of cancer3.1 ‘Nothing makes sense in biology except in the light of evolution’This celebrated motto of the zoologist Theodosius Dobzhansky is particularlytrue in developmental biology and in cancer, that is firstly an evolutionary dis-ease, more precisely a disease of evolutionary multicellular organisation becauseit may be considered as a backward step in the course of evolution towardsorganised multicellularity, according to the atavistic theory of cancer ([5], [12],see next Subsection). Cancer thus represents an evolution at the time scale of aliving multicellular organism, anatomically localised in a given organ, possiblyextended to other tissues by remote metastases, towards genetically new unicel-lular species developing, likely with branching by successions of mutations, theirdiversity at the expense of the host organism. I contend that the disappearanceof successive physiological control mechanisms puts cancer cell populations inthe state of a very primitive multicellular organisation, as proposed below.3.2 The atavistic theory of cancerIn 2011, independently, physicists Paul Davies and Charles Lineweaver, and on-cologist Mark Vincent avocated the idea that cancer is a de-repression of a defaultsurvival program common to all cells [12] which was expressed by Davies andLineweaver as the atavistic theory of cancer [5]. Alternatively saying, cancer is adisease of the evolution of multicellular organisms in which a localised collectionof cells organises itself and proliferates for its own benefit (possibly trying toreinvent the wheel of multicellularity and bound to failure). This hypothesis hasbeen assessed from phylostratigraphic analyses of the genomes of different speciesthat allowed to establish links between the genes that are essential to multicel-lularity and those that are altered in cancer, and from more recent studies thatelicit disrupted relationships between genes of multicellularity and genes that aredisrupted in cancer. This emerging field of research of course presupposes thatcancer is an evolutionary disease of multicellular organisms, ‘evolutionary’ heremeaning related to the Darwinian evolution of living species. In this respect,Cancer plasticity 5plasticity is related to loss of control of the differentiations that make a mul-ticellular organism coherent and functional, and any disruption in this controlmay lead to cancer, without necessarily resorting to cancer stem cells. In otherwords, loss of control on differentiation, which is most likely related to defectivecontrol by the immune system, is actually the plasticity of cancer.3.3 Failed control of differentiations: cancer is a failure of cohesionThe task of the hypothesised cohesion watch, part of an extended version of theimmune system, is thus to ensure compatibilities a) between morphogens of thebody plan, able to drive it actually from the zygote to a constituted multicellularbeing in an irreversible way within the 3D space of cells of a given individual(in jawed vertebrates defined by the major hiostocompatibility complex, MHC,and by some likely equivalent forerunners in non-vertebrates); b) between phe-notypic functionalities, ensuring compatibility between differentiation trees thatyield lineages within a given subpopulation during embryogenesis, and ultimatelybetween cooperating subpopulations (division of work) of terminally differenti-ated cells; c) between the body plan space distribution and the time distributionof phenotypes in each epigenetic landscape attached to the body plan.To mentally illustrate this construction, I propose as a further metaphorthe wickerwork basket. Starting from a circle endowed with lots of connectionsbetween its elements, that is supposed to represent the body plan, functionalwillow-like twigs stem from each of these elements, representing the great phys-iological functions of the organism. If no weaving is made between these twigs,the whole set will consist of just flexible differentiation functionalities of a familyof cell types, floating freely in the surrounding space, unrelated to each other.No cohesion, no division of labour can result from such unwoven twigs and trees.The task of the cohesion watch is to ensure such weaving during development,along the twigs from stem cells until tips that are terminally differentiated cells.This naturally includes the solidity of the willow twigs (breaches along the verti-cal axis resulting in blocked differentiations), but the main part of the cohesionwatch is to ensure compatibility between neighbouring twigs.3.4 Speculations on the possible future of cancer therapeuticsRather than fighting uncontrolled proliferation, could we repair altered controlon differentiations? Cell-killing strategies, be they relying on chemotherapiesor on modern immune cell-enhancing drugs, miss the basic targets, that aredifferentiation sites, and better work would undoubtedly be done by enforcingconnections ensured by the cohesion watch, rather than by killing cheater cells.Or else, trying to illustrate this goal with a sociological metaphor: rather thankilling cheater cells by cannonade (i.e., by chemotherapies) or by enforcing theaggressiveness of the police (i.e., by immune checkpoint inhibitors), would it notbe better to imagine how to enforce natural cohesion between cells? To be ableto do this, a better understanding of the mechanisms of control of differentiationat the level of local transcription factors and at the level of chromatin is needed.6 J. ClairambaultConclusionFar from considerations on evolution of a cell population at the time scale of ahuman life - my starting point [4], [6] - , that undoubtedly present a high interestin therapeutics, I have presented in this study an evolutionary point of view oncancer in a billion-year perspective that, from questions on plasticity in cancer,drove me to develop ideas and speculations that resort to what is now known asphilosophy of cancer [1], [8], [9], thus beginning to tread a long and winding pathtowards a fundamental understanding of multicellularity and of its alterationsin cancer, that should lead to correct impaired control of differentiation, ratherthan, or at least together with, control of proliferation.References1. Bertolaso, M.: ‘Philosophy of cancer. A dynamic and relational view’. Springer,Heidelberg, New York (2016)2. Chisholm, R.H., Lorenzi, T. &Clairambault, J.: Cell population heterogeneity andevolution towards drug resistance in cancer: Biological and mathematical assess-ment, theoretical treatment optimisation. Biochim Biophys Acta, 1860 2627-2645https://doi.org/10.1016/j.bbagen.2016.06.009 (2016)3. Clairambault, J.: Stepping from modelling cancer plasticity to philosophy of cancer.Frontiers in Genetics, accepted https://doi.org/10.3389/fgene.2020.579738 (2020)4. Clairambault, J. & Pouchol, C.: A survey of adaptive cell popula-tion dynamics models of emergence of drug resistance in cancer, andopen questions about evolution and cancer. Biomath 8:1905147, 23 pages,https://doi.org/10.11145/j.biomath.2019.05.147 (2019)5. Davies, P.C.W. & Lineweaver, C.H.: Cancer tumors as Metazoa 1.0:tapping genes of ancient ancestors. Phys. Biol. 8(1):015001, 7 pages,https://doi.org/10.1088/1478-3975/8/1/015001 (2011)6. Pouchol, C., Clairambault, J., Lorz, A. & Trélat, E., Asymptotic analysisand optimal control of an integro-differential system modelling healthy andcancer cells exposed to chemotherapy. J. Math. Pures Appl. 116, 268-308https://doi.org/10.1016/j.matpur.2017.10.007 (2018)7. Lineweaver, C.H., Davies, P.C.W. &Vincent, M.: Targeting cancers weaknesses (notits strengths): Therapeutic strategies suggested by the atavistic model. BioEssays36:827835 https://doi.org/10.1002/bies.201400070 (2014)8. Pradeu, T.: ‘The limits of the Self’. Oxford University Press (2012)9. Pradeu, T.: ‘Philosophy of immunology’. Cambridge University Press (2019)10. Sharma, S.V., et al.: A Chromatin-Mediated Reversible Drug-Tolerant State in Cancer Cell Subpopulations. Cell 141, 69-80https://doi.org/10.1016/j.cell.2010.02.027 (2010)11. Shen, S. & Clairambault, J.: Cell plasticity in cancer cell populations (review)[version 1; peer review: 2 approved]. F1000Research 2020, 9 (F1000 Faculty Rev)635 , 16 pages, https://doi.org/10.12688/f1000research.24803.1 (2020)12. Vincent, M.D.: Cancer: a de-repression of a default survival program common toall cells?: a life-history perspective on the nature of cancer. Bioessays 34(1), 72-82https://doi.org/10.1002/bies.201100049 (2011)

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