Timing of events, which is essential for many cellular processes, depends on regulatory proteins reaching a critical threshold that in general is dynamically fluctuating due to molecular interactions. Increasing evidence shows considerable cell-to-cell variation in the timing of key intracellular events among isogenic cells, but how expression noise and threshold fluctuations impact both threshold crossing and timing precision remain elusive. Here we first formulate stochastic temporal timing of events as a problem of the first passage time (FPT) to a fluctuating threshold and then transform this problem into a higher-dimensional FPT problem with some fixed threshold. Using a stochastic model of gene regulation, we show that (1) in contrast to the case of fixed threshold, threshold fluctuations can both accelerate response (i.e., shorten the time of threshold crossing) and raise timing precision (i.e., reduce timing variability), (2) there is an optimal mean burst size such that the timing precision is best, and (3) fast threshold fluctuations can perform better in accelerating response and reducing variability than slow threshold fluctuations. These results not only interpret recent experimental observations but also have broad implications for diverse cellular processes and in drug therapy.July22, 2018 1/33 . CC-BY 4.0 International license It is made available under a was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.The copyright holder for this preprint (which . http://dx.doi.org/10.1101/375915 doi: bioRxiv preprint first posted online Jul. 24, 2018;
Author summaryIncreasing evidence shows substantial cell-to-cell variation in the timing of key intracellular events among isogenic cells, which has potential consequences on cellular functions and phenotypes. In general, this variation originates from the stochasticity of two different kinds: gene expression noise that is inherent due to low copy numbers and threshold fluctuations that are generated due to molecular interactions. However, it is unclear how these stochastic origins impact precision in the event timing and the time that regulatory proteins reach threshold levels (called arrival time). In order to reveal this impact, we perform analytical and numerical calculations for the first passage time distributions in a representative stochastic model of gene regulation where an event is triggered when the protein level crosses a dynamically fluctuating threshold. Counterintuitively, we find that fluctuating thresholds not only shorten arrival time but also raise timing precision in contrast to fixed thresholds, and fast threshold fluctuations can both shorten arrival time and reduce timing variability than slow threshold fluctuations. These findings can well explain recent experimental observations such as fractional killing of a cell population, cell apoptosis induced by dynamics of p53 in response to chemotherapy, and dynamic persistence of bacteria.