Analysis of feedback schemes in proliferating stem cells

Stem cells have emerged as a pivotal player in biomedical research, offering unprecedented opportunities for regenerative medicine, disease modeling, and drug discovery. These undifferentiated cells possess the unique ability to self-renew and differentiate into various specialized cell types, making them invaluable in tissue repair and regeneration. This note analyzes a stochastic model aiming at unraveling the control machinery providing the proper ratio of stem-versus-differentiated cells, in agreement with a couple of feedback schemes regulating cell proliferation. What emerges from the closed-loop schemes analysis is that in order to have an asymptotically stable, nontrivial accumulation of differentiated cells a negative feedback on cell proliferation is required. Numerical simulations in the stochastic setting validate the approximate theoretical results achieved to relate how random fluctuations propagate with respect to variations of model parameters.