Section: Research Program

Research axis 4: Focus on cancer


Luis Almeida, Thibault Bourgeron, Cécile Carrère, Rebecca Chisholm, Jean Clairambault, Marie Doumic, Dirk Drasdo, Sarah Eugène, Paul Van Liedekerke, Tommaso Lorenzi, Alexander Lorz, Benoît Perthame, Yi Yin

Project-team positioning

The MAMBA team designs and analyses mathematical models of tumour growth and therapy, at the cell population level, using agent-based or partial differential equations, with special interest in methodologies for therapeutic optimisation using combined anticancer drug treatments. Rather than, or not only, modelling 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 antagonising 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 analysing models of cell populations structured in continuous phenotypes, relevant for the description of the behaviour 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 modelling 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 tumour 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.

Scientific achievements

Molecular modelling towards theoretical optimisation of anticancer drug delivery

The protein p53, guardian of the genome and tumour suppressor, has been the object of Ján Eliaš's PhD thesis  [85], defended in September 2015, and of articles in 2014 and 2017  [83], [84], [11]. Based on an original intracellular spatial PDE model of the protein dynamics, it allows for the prediction of biologically observed oscillations of p53 nuclear concentrations in case of (e.g. radiotherapy- or anticancer drug-induced) damage to the DNA. In parallel, in  [75], that for us concluded works initiated by a fruitful collaboration with Francis Lévi (retired from CNRS 2014), we associate pharmacokinetics-pharmacodynamics of anticancer drugs, their action on the cell cycle at the cell population level, and optimisation algorithms to maximise their combined action under the constraint of preserving healthy tissue integrity.

Modelling Acute Myeloid Leukaemia (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  [54], [55], [56], [64], [76], [53]. These works study the stability of the haematopoietic system and its possible restabilisation 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 modelling with a evolutionary perspective on tumour heterogeneity, is documented in a series of articles  [73], [74], [105], [106], [108]. 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)

Senescence modelling 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  [66].

Biomechanically mediated growth control of cancer cells

Mechanical feedback has been identified as a key regulator of tissue growth, by which external signals are transduced into a complex intracellular molecular machinery. Using multi-scale computational modelling of multicellular growth in two largely different experimental settings with the same tumour cell line we were able to show that the cellular growth response on external mechanical stress is surprisingly quantitatively predictable. For this purpose, the mechanical parameters of a center-based agent-based model were calibrated with a deformable agent-based cell model, which displays cell shape and hence can deal with high cell compressions. The cell cycle progression function was calibrated with findings of population growth in an elastic capsule. The emerging model was able to correctly predict the growth response both for modified stresses in a capsule as well as the growth response in a different experimental setting  [128], [127].

Model identification for TRAIL treatment

Repetitive administration of TRAIL (TNF-Related Apoptosis Induced-Ligand) on HeLa cells produces characteristic resistance pattern in time that can be explained by cell-to-cell variability in the protein composition. The TRAIL signal transduction pathway is one of the best-studied apoptosis pathways and hence permits detailed comparisons with data. Within a stochastic model of gene expression coupled to transcription and translation to the pathway members, we were able to quantitatively explain the resistance pattern. An important challenge was in parameter identification at each of the level for numerous proteins, whereby the most sensitive parameter was to correctly capture short-lived proteins in the TRAIL toxicity pathway as those mainly determine the regeneration of protein distribution in the cell population and thereby may generate strong stochastic fluctuations [61], [60].


In close cooperation with M. Herrero (U. Complutense, Madrid) we have explored by extensive computer simulations using an agent-based model the consequences of spatially inhomogeneous x-ray irradiation in cancer treatment. The model predicted that in the case of different competing sub-populations, namely cancer stem cells with unlimited division capacity, and cancer cells with limited division capacity, inhomogeneous radiation focusing higher doses at the tumour center and lower doses at the tumour periphery should outperform homogeneous irradiation  [104]. Cancer stem cells are believed to have a longer cell cycle duration than cancer cells, and are less radiosensitive than cancer cells, which is why they often survive radiation and lead to tumour relapse.


  • 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 (2 articles in common  [74], [108]), Michèle Sabbah (2 PhD theses in common) at Annette Larsen's lab, 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: one funded Inria PRE project in common.

  • Telomere shortening: Teresa Teixeira and Zhou Xu (IBCP, Paris), Philippe Robert (Inria RAP).

  • TRAIL treatment: Gregory Batt, Inria Saclay and Inst. Pasteur (France)