Abstract
Tissue homeostasis (feedback control) is an important mechanism that regulates the population of different cell types within a tissue. In type-1 diabetes, auto-immune attack and consequent death of pancreatic β cells result in the failure of homeostasis and loss of organ function. Synthetically engineered adult stem cells with homeostatic control based on digital logic have been proposed as a solution for regenerating β cells. Such previously proposed homeostatic control circuits have thus far been unable to reliably control both stem-cell proliferation and stem-cell differentiation. Using analog circuits and feedback systems analysis, we have designed an in silico circuit that performs homeostatic control by utilizing a novel scheme with both symmetric and asymmetric division of stem cells. The use of a variety of feedback systems analysis techniques, which is common in analog circuit design, including root-locus techniques, Bode plots of feedback-loop frequency response, compensation techniques for improving stability, and robustness analysis help us choose design parameters to meet desirable specifications. For example, we show that lead compensation in analog circuits instantiated as an incoherent feed-forward loop in the biological circuit improves stability, whereas simultaneously reducing steady-state tracking error. Our symmetric and asymmetric division scheme also improves phase margin in the feedback loop, and thus improves robustness. This paper could be useful in porting an analog-circuit design framework to synthetic biological applications of the future.