Modelling interactions between tumour cells and supporting adipocytes in breast cancer

International audience; In breast cancer, invasion of the micro-environment implies potential bidirectional communica- tion between cancer cells and the adipose tissue. Biological evidence suggests that adipocytes, in particular, are key-actors in tumorigenesis and invasion: they both enhance proliferation of the cancer cells and favor acquisition of a more invasive phenotype. To understand these effects, mathematical modelling (thanks to tools developed in theoretical ecology) is used to perform asymptotic analysis in number of cells and distribution of phenotypes. These models can be tuned through confrontation with experimental data coming from co-cultures of cancer cells with adipocytes.The first part of this report is devoted to presenting the biological background on breast cancer and its environment. We then present the main aspects of the mathematical modelling, and how it is expected to be validated experimentally. In the third part, we summarize and prove many important results that have been obtained on a single integro-differential equation rep- resenting the evolution of a population of individuals structured with a phenotypic trait. The next part consists of a first glance at possible generalizations of those results to a system of integro-differential equations coupled mutualistically. In a fifth and last part, we introduce how we intend to parametrize the models through explicit computations and numerical simulations.