A mathematical model of cell population dynamics with autophagy response to starvation

- The role of autophagy in cell population dynamics is studied based on a mathematical model.
- The boundedness of solutions, existence and stability of equilibrium states are studied.
- Numerical studies for yeast response to starvation with autophagy are performed.
- Autophagy is valuable in attenuating cell population fluctuations in random perturbations.

In this paper, we study the role of autophagy in yeast cell population dynamics in response to starvation by a mathematical model based on the logistic growth model. We analytically study the boundedness of solutions, and the existence and stability of equilibrium states under general biologically acceptable assumptions. Finally, we perform numerical studies for Saccharomyces cerevisiae response to starvation with autophagy. The results show that autophagy is valuable in maintaining cell population in starvation, and attenuating population fluctuations in response to perturbations in environmental nutrients. Furthermore, we show that proper level autophagy promotes cell survival through the inhibition of cell death by autophagy as well as the secretion of nutrients from autophagic cells, however excessive autophagy can decrease cell population due to autophagic cell death.