Section: New Results

Cancer

Participants : Luís Lopes Neves de Almeida, Rebecca Chisholm, Jean Clairambault, François Delhommeau [Haematology department, St Antoine Hospital, Paris] , Dirk Drasdo, Ján Eliaš, Alexandre Escargueil [Cancer biology and therapeutics lab, St Antoine Hospital, Paris] , Ghassen Haddad [ENIT, Tunis] , Shalla Hanson [Department of mathematics, Duke University, Durham, NC] , Pierre Hirsch [Haematology department, St Antoine Hospital, Paris] , Groups Invade, Lungsysii, Tim Johann, Group Klingmueller [German Cancer Center, Heidelberg] , Michal Kowalczyk [Univ. Santiago de Chile] , Annette Larsen [Cancer biology and therapeutics lab, St Antoine Hospital, Paris] , Tommaso Lorenzi, Alexander Lorz, Benoît Perthame, Andrada Quillas Maran, Fernando Quirós [Univ. Autónoma de Madrid] , Michèle Sabbah [Cancer biology and therapeutics lab, St Antoine Hospital, Paris] , Min Tang [Jiaotong University, Shanghai] , Emmanuel Trélat [LJLL, UPMC] , Paul Van Liedekerke, Nicolas Vauchelet, Irène Vignon-Clementel [REO] , Yi Yin.

Drug resistance

We have continued to develop our phenotypically based models of drug-induced drug resistance in cancer cell populations, representing their Darwinian or Lamarckian evolution under drug pressure by integro-differential equations. In one of them [23] , a 1D space variable has been added to the phenotypic structure variable to account for drug diffusion in tumour spheroids. In another one, focusing on both Darwinian selection and Lamarckian-like (non-genetic) instruction, published in Cancer Research [41] , where deterministic and agent-based modelling are processed in parallel, we have added advection and diffusion terms to the initial integro-differential model and considered a physiologically based 2-dimensional phenotypic structure variable. This model, designed to take account of previously published biological observations on (reversible) drug tolerance persistence in a cultured population of non-small cell lung cancer (NSCLC) cells [90] , reproduces the observations and we propose to assess the model by testing biologically based hypotheses. This work, also presented in various conferences ([34] , [35] , [31] ) is conducted in close collaboration with the INSERM-UPMC team “Cancer biology and therapeutics” (A. Larsen, A. Escargueil, M. Sabbah) at St Antoine Hospital. It has also led our postdoctoral fellows Rebecca Chisholm and Tommaso Lorenzi to prolong their work on the Cancer Research paper by publishing two more articles [21] , [48] , one of which is a joint work with Alexander Lorz. This work is currently continued from the point of view of optimal control in Camille Pouchol's PhD thesis.

Evolution and cancer, therapy optimisation

Guided by our goal to understand and overcome drug resistance in cancer cell populations[41] , we are considering cancer as an evolutionary phenomenon at two time scales: a large time scale (billions of years) of evolution of the genomes, from unicellular organisms to organised multicellularity (viewing cancer as more an archeoplasm than a neoplasm, an evolution backwards, following Davies and Lineweaver, Phys Biol 2011, and others  [78] , [66] , [92] , [79] ) with shortcomings due to malfunctions in the processes of control of cell differentiation, and a short time scale (duration of a human life) of evolution in the “epigenetic landscape” of a given genome (as advocated by Sui Huang and Angela Pisco, e.g. recently in Nature, Br J Cancer and elsewhere  [76] , [77] , [85] , [86] , [94] ). It leads us to propose theoretical frameworks for innovative cancer therapeutics from this evolutionary biology viewpoint, taking into account the major clinical issue of drug resistance in cancer cell populations, as presented in [31] and exposed to a medical audience at the symposium “Réseau Cancer des Points Cardinaux” (http://www.frog-oncogeriatrie.com/fichiers/evnmt_41.pdf ).

Interactions between tumour cell populations and their cellular micro-environments

A phenotype-structured model of the interactions between a brest cancer cell population (MCF7 cultured cells, collaboration with M. Sabbah, St Antoine Hospital) and its adipocyte stroma support cell population has been developed (T. Lorenzi, C. Pouchol, J. Clairambault) in the framework of Camille Pouchol's Inria internship ([56] ). It has led to hiring C. Pouchol as a PhD student at UPMC (on a university grant “Interfaces pour le Vivant”) on the same subject with perspectives in optimal therapeutic control, under the supervision of J. Clairambault, M. Sabbah and E. Trélat, see below “Supervision”.

Combining chemo- and immunotherapies

Both from the point of view of interactions with the tumour micro-environment and of innovative anticancer therapies, it is necessary to take into account the immune response in cancer. This recently developed activity, (illustrated by presentations in session 70 in ICNAAM 2016 [32] ) has led to the involvement in 2015 of Shalla Hanson as a PhD student in co-tutela between Duke University, NC and UPMC, see below “Supervision”.

Hele-Shaw model of tumour growth

The mathematical analysis of macroscopic models of tumor growth with one type of cancer cells has been continued. On the one hand, in [47] , the concept of viscosity solutions has been implemented for the case with active motion. On the other hand, the regularity of the free boundary is proved in [51] using methods developed for the standard Hele-Shaw equation and a new formulation.

The p53 protein spatio-temporal dynamics

Our previously developed spatio-temporal models for an intracellular dynamical response of the p53 protein to DNA damage, have been exploited further, and several testable biological hypotheses have been proposed in [33] . Among them, we suggest ideas that link spatio-temporal location of the p53 protein with a specific cell fate of a single cell in [33] , [2] and, based on our new oscillator relying on both positive and negative regulation of p53 by Mdm2 (in tight cooperation with MdmX), we provide molecular insights into an excitability of the p53 network, i.e., we propose a molecular explanation for a full pulsatile response of p53 independently of input (ATM) signalling, challenging thus different fates of ATM downstream targets in the regulation of p53 in response to different stimuli, such as $\gamma$- and UV-radiation.

Our mathematical models, all included in J. Eliaš's PhD thesis [2] (defended on the 1st September 2015), contribute to understanding the variability of p53 in response to single and double strand breaks and reveal some new aspects of the core p53-Mdm2 protein feedback.

Lung and breast cancer

We developed an image analysis software and designed image analysis pipelines which we used to quantify the invasion pattern of non-small cell lung cancer (NSCLC) cells in multicellular spheroid in vitro experiments [24] . Based on the analyses, we demonstrated that the concomitant over-expression of FIR (far upstream element binding protein interacting repressor) and its splice variants drives NSCLC migration and dissemination.

We developed an agent-based, centre-based model of cell migration in cancer invasion based upon experimental observations of cell shape and cell behaviour in multicellular spheroid experiments of breast and lung cancer cells. In these experiments, cells deform from a sphere into an oblong shape upon migration, and adopt a spherical shape again whenever they turn back to such spheroids. This was implemented. Moreover, we developed a 3D model for the extracellular matrix (ECM) in which the matrix is modelled by an irregular network of springs with nodes represented as elastic objects. Migrating cells anchor in the network to move, leading to network deformation. We implemented a number of different biological mechanisms of cell migration and cell-ECM interaction. We find that a relatively simple model is sufficient to explain all phenomena of a single invading cell (Palm et. al., in preparation).

The combination of image analysis and of the abovementioned refined invasion model should allow a quantitative model of multicellular invasion following the same line of research as for SK-MES-1 cells, where we inferred a multicellular spheroid growth model from image data within a pipeline of experiment, imaging, image analysis and modelling [17] . In that paper, we used spatial-temporal image data of cell nucleus distribution, cell proliferation, death, and ECM distribution for two growth conditions (oxygen and glucose) to calibrate a model which was then able to quantitatively correctly predict the growth kinetics of the tumor spheroids for two other growth conditions, one strongly glucose limited, another strongly oxygen-limited.

Finally, we developed an image analysis pipeline to estimate the number of cancer cells in a patient with non-small cell lung cancer (NSCLC) from non-invasive image modalities. The estimate bases upon cell counts from histological serial sections of the tumor which have been related to the D-value inferred from Diffusion Weighted (DW) MRI (Yi et. al., paper in preparation).