The design principles of biochemical timers: circuits that discriminate between transient and sustained stimulation

Many cellular responses for which timing is critical display temporal filtering - the ability to suppress response until stimulated for longer than a given minimal time. Temporal filtering can play a key role in filtering noise, choreographing the timing of events, and mediating the interpretation of dynamically encoded signals. To define the biochemical circuits capable of kinetic filtering, we comprehensively searched the space of three-node networks. We define a metric of \"temporal ultrasensitivity\", a measure of the steepness of activation as a function of stimulus duration. We identified five classes of core network motifs capable of temporal filtering, each with different functional properties such as rejecting high frequency noise, committing to response (bistability), and distinguishing between long stimuli. Combinations of the two most robust motifs, double inhibition (DI) and positive feedback with AND logic (PFAND), underlie several natural timer circuits involved in processes such as cell cycle transitions, T cell activation, and departure from the pluripotent state. The biochemical network motifs described in this study form a basis for understanding the common ways in which cells make dynamic decisions.