Timing in single cells: fundamental limits and mechanisms for noise suppression

Precise timing can be advantageous in many biological processes, whether to coordinate events in the cell cycle, determine the duration of cell states, or create reliable rhythms. However, it can be hard to achieve because chemical reactions often produce exponentially distributed waiting times for individual events even when the rates are perfectly constant. Here we develop mathematical theories to dissect classes of timing mechanisms in single cells -- derive fundamental limits and optimal strategies, and how simpler and realistic circuits would approach the optimal. For some broad but naturally occurring distributions, the noise is limited by the inverse quartic root of the average number of states, and even that requires intricate mechanisms. We discuss how known synthetic and natural genetic timers appear to employ these mechanisms to create precise rhythms or accurate multigenerational cell fate decisions.