A kinetic theory approach for modelling tumour and macrophages heterogeneity and plasticity during cancer progression

The heterogeneity and plasticity of macrophages have become a topic of great interest, due to their role in various diseases ranging from cancer to bacterial infections. While initial experimental studies assumed an extreme polarisation situation, with the (anti-tumour) M1 and (pro-tumour) M2 macrophages representing the two extreme cell phenotypes, more recent studies showed a continuum of macrophages polarisation phenotypes. Here, we focus on tumour-macrophage interactions and develop a mathematical model based on kinetic equations for active particles to describe (i) the dynamics of macrophages with a continuum of diverse functional states, ranging from pro-tumour to anti-tumour states; and (ii) the dynamics of tumour cells with a variety of progression (i.e. mutation) states. With the help of this model we show that the growth of solid tumours is associated with an increased clonal heterogeneity, as well as with an increased macrophages phenotypic heterogeneity (caused by a shift from an initial anti-tumour M1-like phenotype to a mixed M1-M2 phenotype). Moreover, we show that the assumption of exponential tumour/immune cell growth leads to an unbounded macrophages growth, which is biologically unrealistic. In contrast, the assumption of logistic tumour/immune cell growth can lead to tumour dormancy (under the control of immune cells), or to tumour growth towards smaller/larger sizes which depend on various model parameters. Finally, we show that tumour dormancy is associated with an increase in the clonal heterogeneity of tumour cells and in the phenotypic heterogeneity of macrophages.