Understanding Cell Dynamics in Cancer from Control and Mathematical Biology Standpoints: Particular Insights into the Modeling and Analysis Aspects in Hematopoietic Systems and Leukemia

WALID DJEMA
Soutenance de thèse de doctorat le 21 Novembre 2017, 13h30 à CentraleSupelec (Gif-sur-Yvette) Salle du conseil du L2S - B4.40

Medical research is looking for new combined targeted therapies against cancer. Our research project -which involves intensive collaboration with hematologists from Saint-Antoine Hospital in Paris- is imbued within a similar spirit and fits the expectations of a better understanding of the behavior of blood cell dynamics. In fact, hematopoiesis provides a paradigm for studying all the mammalian stem cells, as well as all the mechanisms involved in the cell cycle. We address multiple issues related to the modeling and analysis of the cell cycle, with particular insights into the hematopoietic systems. Stability features of the models are highlighted, since trajectories of the systems reflect the most prominent healthy or unhealthy behaviors of the biological process under study. We indeed perform stability analyses of systems describing healthy and unhealthy situations, with a particular interest in the case of acute myeloblastic leukemia (AML). Thus, we pursue the objectives of understanding the interactions between the various parameters and functions involved in the mechanisms of interest. For that purpose, an advanced stability analysis of the cell fate evolution in treated or untreated leukemia is performed in several modeling frameworks, and our study suggests new anti-leukemic combined chemotherapy. Throughout the thesis, we cover many biological evidences that are currently undergoing intensive biological research, such as: cell plasticity, mutations accumulation, cohabitation between ordinary and mutated cells, control and eradication of cancer cells, cancer dormancy, etc.

Among the contributions of Part I of the thesis, we can mention the extension of both modeling and analysis aspects in order to take into account a proliferating phase in which most of the cells may divide, or die, while few of them may be arrested during their cycle for unlimited time. We also introduce for the first time cell-plasticity features to the class of systems that we are focusing on.

Next, in Part II, stability analyses of some differential-difference cell population models are performed through several time-domain techniques, including tools of Comparative and Positive Systems approaches. Then, a new age-structured model describing the coexistence between cancer and ordinary stem cells is introduced. This model is transformed into a nonlinear time-delay system that describes the dynamics of healthy cells, coupled to a nonlinear differential-difference system governing the dynamics of unhealthy cells. The main features of the coupled system are highlighted and an advanced stability analysis of several coexisting steady states is performed through a Lyapunov-like approach for descriptor-type systems. We pursue an analysis that provides a theoretical treatment framework following different medical orientations, among which: i) the case where therapy aims to eradicate cancer cells while preserving healthy ones, and ii) a less demanding, more realistic, scenario that consists in maintaining healthy and unhealthy cells in a controlled stable dormancy steady-state. Mainly, sufficient conditions for the regional exponential stability, estimate of the decay rate of the solutions, and subsets of the basins of attraction of the steady states of interest are provided. Biological interpretations and therapeutic strategies in light of emerging AML-drugs are discussed according to our findings.

Finally, in Part III, an original formulation of what can be interpreted as a stabilization issue of population cell dynamics through artificial intelligence planning tools is provided. In that framework, an optimal solution is discovered via planning and scheduling algorithms. For unhealthy hematopoiesis, we address the treatment issue through multiple drug infusions. In that case, we determine the best therapeutic strategy that restores normal blood count as in an ordinary hematopoietic system.

Mots-clés :  Analyse de stabilité, PDEs et Systèmes à retards, Théorie de Lyapunov, Modélisation des systèmes biologiques, Analyse des systèmes biologiques, Cancer, Dynamique des populations cellulaires, Hématopoïèse, Leucémie.

Composition du jury proposé
Mme Catherine BONNET     CentraleSupélec     CoDirecteur de thèse
M. Jean CLAIRAUMBAULT     Inria Paris, Sorbonne Paris 6     CoDirecteur de thèse
M. Frédéric MAZENC     Inria Saclay, CNRS, CentraleSupélec     CoDirecteur de thèse
Mme Françoise LAMNABHI-LAGARRIGUE     CNRS, L2S, CentraleSupélec     Examinateur
M. Raphaël  ITZYKSON     Hôpital Saint-Louis Paris     Examinateur
M. Alexander MEDVEDEV     Uppsala University, Sweden     Examinateur
M. Mostafa ADIMY     Inria Grenoble-Rhone Alpes     Rapporteur
M. Pierdomenico  PEPE     University of L'Aquila, Italy     Rapporteur