Dynamic Analysis and Robust Strategy for the Delayed Paradoxical Cell Population Control Circuit

Synthetic paradoxical control circuits have been used to regulate cell population density. However, paradoxical interactions and inherent time delays in these circuits complicate stable population control due to their effects on system dynamics. This article proposes a strategy to achieve robust population control by analyzing the bistable switching and oscillatory behavior in a delayed paradoxical cell population control circuit. First, five distinct population outcomes are identified, along with stabilization criteria for these states, highlighting the presence of bistability. Specifically, we reveal two bistable switching mechanisms: one driven by the initial cell population density and the other by the time delay for blasticidin-induced cell death. Furthermore, we demonstrate that the time delay can destabilize the effective control state via a Hopf bifurcation, leading to periodic oscillations, which can be mitigated by adjusting the blasticidin concentration. Based on these findings, we propose a robust control strategy by regulating initial cell population density and blasticidin concentration. These insights advance the design of robust population control circuits, with broad implications for synthetic biology and cell therapy.