A cell-cell repulsion model on a hyperbolic Keller-Segel equation.

In this work, we discuss a cell-cell repulsion model based on a hyperbolic Keller-Segel equation with two populations, which aims at describing the cell growth and dispersion in the co-culture experiment from the work of Pasquier et al. (Biol Direct 6(1):5, 2011). We introduce the notion of solution integrated along the characteristics, which allows us to prove the existence and uniqueness of solutions and the segregation property for the two species. From a numerical perspective, we also observe that our model admits a competitive exclusion principle which is different from the classical competitive exclusion principle for the corresponding ODE model. More importantly, our model shows the complexity of the short term (6 days) co-cultured cell distribution depending on the initial distribution of each species. Through numerical simulations, we show that the impact of the initial distribution on the proportion of each species in the final population lies in the initial number of cell clusters and that the final proportion of each species is not influenced by the precise distribution of the initial distribution. We also find that a fast dispersion rate gives a short-term advantage while the vital dynamics contributes to a long-term population advantage. When the initial condition for the two species is not segregated, the numerical simulations suggest that asymptotic segregation occurs when the dispersion coefficients are not equal for two populations.