Section: New Results

Focus on cancer

Modelling Acute Myeloid Leukaemia (AML) and its control by anticancer drugs by PDEs and Delay Differential equations

This theme has continued to be developed in collaboration with Catherine Bonnet, Inria DISCO (Saclay)  [93], [94]. Without control by drugs, but with representation of mutualistic interactions between tumor cells and their surrounding support stroll cells, it has also, in collaboration with Delphine Salort and Thierry Jaffredo (LCQB-IBPS) given rise to a recent work by Thanh Nam Nguyen, hired as HTE and ERC postdoctoral fellow at LCQB, submitted as full article [24].

Adaptive dynamics setting to model and circumvent evolution towards drug resistance in cancer by optimal control

The research topic “Evolution and cancer”, designed in the framework of adaptive dynamics to represent and overcome acquired drug resistance in cancer, initiated in  [128], [127] and later continued in  [91], [92], [126], has been recently summarised in  [60] and has been the object of the PhD thesis work of Camille Pouchol, see above “Cell population dynamics and its control” . It is now oriented, thanks to work underway by Cécile Carrère, Jean Clairambault, Tommaso Lorenzi and Grégoire Nadin, in particular towards the mathematical representation of bet hedging in cancer, namely a supposed optimal strategy consisting for cancer cell populations under life-threatening cell stress in diversifying their phenotypes according to several resistance mechanisms, such as overexpression of ABC transporters (P-glycoprotein and many others), of DNA repair enzymes or of intracellular detoxication processes. According to different deadly insults the cancer cell population is exposed to, some phenotypes may be selected, any such successful subpopulation being able to store the cell population genome (or subclones of it if the cell population is already genetically heterogeneous) and make it amenable to survival and renewed replication.

Philosophy of cancer biology

This new research topic in Mamba, dedicated to explore possibly underinvestigated, from the mathematical modelling point of view, parts of the field of cancer growth, evolution and therapy, has been the object of a presentation by Jean Clairambault at the recent workshop “Philosophy of cancer biology'

https://www.philinbiomed.org/event/philosophy-of-cancer-biology-workshop/.

This workshop gathered most members worldwide of this small, but very active in publishing, community of philosophers of science whose field of research is “philosophy of cancer”, as they call it themselves. This topic offers a clear point of convergence between mathematics, biology and social and human sciences.