Precision of Biomolecular Timekeeping Through Regulated Degradation

The timing of biochemical processes within cells is inextricably linked to the level of key regulatory proteins crossing critical threshold levels. Recent research has primarily focused on the stochastic nature of event timing resulting from the buildup in molecular concentration to a high threshold. This contribution, however, centers on the complementary scenario: the decrease in protein levels over time until they reach a low critical threshold. We aim to understand the timing precision resulting from unique degradation pathways and their inherent stochastic nature, especially under low-copy number conditions. More specifically, we explore how integer-valued protein molecular counts decrease stochastically following Michaelis-Menten kinetics. This approach encompasses both zero-order (where the net degradation rate is independent of protein levels) and first-order (where the rate is proportional to protein levels) decay processes. Our results show that while zero-order decay can be sluggish in terms of mean timing, it provides the highest precision in timing with the lowest noise in threshold-crossing time. Conversely, upon considering randomness in the initial protein levels, first-order decay demonstrates better precision compared to zero-order. Interestingly, in the presence of multiple noise sources, timing stochasticity can be minimized when Michaelis-Menten decay kinetics operate under sub-saturation conditions. This characterization of timing driven by decreasing copy numbers has implications for improving the precision of biological clocks and understanding the timing of cell-cycle events.