  We consider a cell population structured by a positive real number,
describing the number of P-glycoproteins carried by the cell. We are interested
in the effect of those proteins on the growth of the population: those proteins
are indeed involve in the resistance of cancer cells to chemotherapy drugs. To
describe this dynamics, we introduce a kinetic model. We then introduce a
rigorous hydrodynamic limit, showing that if the exchanges are frequent, then
the dynamics of the model can be described by a system of two coupled
differential equations. Finally, we also show that the kinetic model converges
to a unique limit in large times. The main idea of this analysis is to use
Wasserstein distance estimates to describe the effect of the kinetic operator,
combined to more classical estimates on the macroscopic quantities.
