The effect of a linear feedback mechanism in a homeostasis model

Feedback loops are essential for regulating cell proliferation and maintaining the delicate balance between cell division and cell death. Thanks to the exact solution of a few simple models of cell growth it is by now clear that stochastic fluctuations play a central role in this process and that cell growth (and in particular the robustness and stability of homeostasis) can be properly addressed only as a stochastic process. Using epidermal homeostasis as a prototypical example, we show that it is possible to discriminate among different feedback strategies which turn out to be characterized by different, experimentally testable, behaviours. In particular, we focus on the so-called Dynamical Heterogeneity model, an epidermal homeostasis model that takes into account two well known cellular features: the plasticity of the cells and their adaptability to face environmental stimuli. We show that specific choices of the parameter on which the feedback is applied may decrease the fluctuations of the homeostatic population level and improve the recovery of the system after an external perturbation.