Stability analysis of a multiscale model of cell cycle dynamics coupled with quiescent and proliferating cell populations

In this paper, we perform a mathematical analysis of our proposed nonlinear, multiscale mathematical model of physiologically structured quiescent and proliferating cell populations at the macroscale and cell-cycle proteins at the microscale. Cell cycle dynamics (microscale) are driven by growth factors derived from the total cell population of quiescent and proliferating cells. Cell-cycle protein concentrations, on the other hand, determine the rates of transition between the two subpopulations. Our model demonstrates the underlying impact of cell cycle dynamics on the evolution of cell population in a tissue. We study the model's well-posedness, derive steady-state solutions, and find sufficient conditions for the stability of steady-state solutions using semigroup and spectral theory. Finally, we performed numerical simulations to see how the parameters affect the model's nonlinear dynamics.

Automated summary

In this paper, a mathematical analysis is performed on a proposed nonlinear, multiscale mathematical model that describes the dynamics of cell populations and cell-cycle proteins. The model shows the impact of cell cycle dynamics on the evolution of cell population in a tissue. The well-posedness of the model is studied, steady-state solutions are derived, and conditions for the stability of steady-state solutions are found. Numerical simulations are performed to understand the effects of parameters on the model's nonlinear dynamics.