Temporal precision of regulated gene expression

Abstract

Important cellular processes such as migration, differentiation, and development often rely on precise timing. Yet, the molecular machinery that regulates timing is inherently noisy. How do cells achieve precise timing with noisy components? We investigate this question using a first-passage-time approach, for an event triggered by a molecule that crosses an abundance threshold and that is regulated by either an accumulating activator or a diminishing repressor. We find that either activation or repression outperforms an unregulated strategy. The optimal regulation corresponds to a nonlinear increase in the amount of the target molecule over time, arises from a tradeoff between minimizing the timing noise of the regulator and that of the target molecule itself, and is robust to additional effects such as bursts and cell division. Our results are in quantitative agreement with the nonlinear increase and low noise of mig-1 gene expression in migrating neuroblast cells during Caenorhabditis elegans development. These findings suggest that dynamic regulation may be a simple and powerful strategy for precise cellular timing.

Dynamic variability in apoptotic threshold as a strategy for combating fractional killing

“…where W is the column vector of the transition rates from all accessible states to the 100 absorbing state and the superscript T represents transpose [34,36,[45][46][47][48].…”

“…Such 29 a kind of threshold has a strong biological background and is ubiquitous in biological 30 regulatory systems. For example, consider a representative activity function of Hill 31 type [33][34][35][36] 32 Activation = Z n Z n + K n (1) first-passage properties of stationary threshold crossing [34][35][36][37][38][39][40], while comparatively very 42 few studies have investigated how a dynamically fluctuating threshold impacts timing 43 precision and arrival time theoretically [41][42][43][44] or experimentally [9,12,26]. 44 In this article, we formulate the timing of intracellular events as a first passage 45 time (FPT) problem, where an event is triggered when a stochastic process (in fact 46 single-cell protein level) crosses a dynamically fluctuating threshold for the first time.…”

“…at time t can be described through the following probabilities of timing events in the 138 corresponding FME describing the time evolution of protein pair X and Y can be 143 described as the following master equation [34,36,[45][46][47][48] …”

“…Some of these processes require the precision in the timing that regulatory 461 proteins reach thresholds, e.g., control of cell cycle, whereas the others depend on the 462 time that regulatory proteins reach a threshold level (i.e., arrival time), e.g., apoptotic 463 cells showed a faster accumulation of p53 than surviving cells and a shorter time to 464 reach half-maximal p53 levels. Previous studies focused on precision in the timing of 465 events in response to a fixed threshold [34][35][36][37][38][39][40]. However, the thresholds that biochemical 466 events cross are in general dynamically fluctuating, as interpreted in the introduction.…”

Control strategies for the timing of intracellular events

“…They claimed that for a stable long-lived protein, the optimal strategy is to express the protein at a constant rate without any feedback regulation, and any form of feedback (positive, negative, or any combination of them) will always amplify noise in event timing, whereas for an unstable protein, a positive feedback 3 mechanism provides the highest precision in timing. Unfortunately, however, these qualitative results are not always correct but depend on the detail of feedback regulation (5,8,(41)(42)(43)(44)(45). In other words, the strategies for control of the variability in the timing of intracellular events are not elucidated.…”