Retroactivity Affects the Adaptive Robustness of Transcriptional Regulatory Networks

Adaptation refers to the system's ability to respond transiently to an input signal and subsequently recover to the initial states. Adaptive robustness, the ability of a network to achieve adaptation, is subject to the loading effects arising from modular interconnections, known as retroactivity. Studying the effects of retroactivity on adaptive robustness facilitates the employment of retroactivity to improve circuit performance in synthetic biology. In this paper, we developed a framework for quantifying adaptive robustness via statistical model checking and used this framework to investigate the effects of retroactivity on adaptive robustness. We found that increasing retroactivity tends to raise adaptive robustness in networks where the output protein does not perform regulatory functions, such as incoherent feedforward loops.