Identification of optimal parameter combinations for the emergence of bistability

Bistability underlies cellular memory and maintains alternative differentiation states. Bistability can emerge only if its parameter range is either physically realizable or can be enlarged to become realizable. We derived a general rule and showed that the bistable range of a reaction parameter is maximized by a pair of other parameters in any gene regulatory network provided they satisfy a general condition. The resulting analytical expressions revealed whether or not such reaction pairs are present in prototypical positive feedback loops. They are absent from the feedback loop enclosed by protein dimers but present in both the toggle-switch and the feedback circuit inhibited by sequestration. Sequestration can generate bistability even at narrow feedback expression range at which cooperative binding fails to do so, provided inhibition is set to an optimal value. These results help to design bistable circuits and cellular reprogramming and reveal whether bistability is possible in gene networks in the range of realistic parameter values.