Measurement of bistability in a multidimensional parameter space

Bistability plays an important role to generate two stable states for alternative cell fates, or to promote cellular diversity and cell cycle oscillations. Positive feedback loops are necessary for the existence of bistability and ultrasensitive reactions in the loops broaden the parameter range of bistability. The broader parameter range a system's bistability covers, the more robust the two states are. It is challenging to determine the bistable range of a parameter because noise and transient processes induce transitions between the two states. We found that a threshold of transition rates coincides with the bistability boundaries determined by the open-loop approach. With this threshold, we estimated the boundaries for various synthetic single-gene positive feedback loops in yeast in a two dimensional parameter space: the inducer concentration and promoter dynamic range. While the bistable range of inducer concentration was influenced by many factors, the promoter dynamic range was more informative. The narrowest promoter dynamic range at which bistability can emerge revealed whether the full potential of an ultrasensitive reaction, such as dimerization, is exploited in the feedback loop. The convenient control of basal expression to adjust the promoter dynamic range permits a practical and reliable comparison of robustness of related positive feedback loops.