Why are cellular switches Boolean? General conditions for multistable genetic circuits

The logic of cellular decision-making is largely controlled by regulatory circuits defining molecular switches. Such switching elements allow to turn a graded input signal into an all-or-nothing output. Traditional studies have focused on this bistable picture of regulation, but higher-order scenarios involving tristable and tetrastable states are possible too. Are these multiswitches allowed in simple gene regulatory networks? Are they likely to be observed? If not, why not? In this paper we present the examination of this question by means of a simple but powerful geometric approach. We examine the relation between multistability, the degree of multimerization of the regulators and the role of autoloops within a deterministic setting, finding that N-stable circuits are possible, although their likelihood to occur rapidly decays with the order of the switch. Our work indicates that, despite two-component circuits are able to implement multistability, they are optimal for Boolean switches. The evolutionary implications are outlined.