Noise in timing and precision of gene activities in a genetic cascade

Almasi‐Hashiani, Amir; Kobiler, Oren; Rokney, Assaf; Oppenheim, Amos B.; Stavans, Joel

doi:10.1038/msb4100113

Cited by 60 publications

(68 citation statements)

References 46 publications

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“…Phage λ has recently emerged as a simple model system for studying event timing at the level of single cells (19,20). After infecting Escherichia coli, λ expresses a protein, holin, which accumulates in the inner membrane.…”

Section: Discussionmentioning

confidence: 99%

“…Triggering of these events in single cells is influenced by fluctuations in protein levels that arise naturally due to noise in gene expression (15)(16)(17)(18). Increasing evidence shows considerable cell-to-cell variation in timing of intracellular events among isogenic cells (19)(20)(21), and it is unclear how noisy expression generates this variation. Characterization of control strategies that buffer stochasticity in event timing are critically needed to understand reliable functioning of diverse intracellular pathways that rely on precision in timing.…”

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confidence: 99%

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First-passage time approach to controlling noise in the timing of intracellular events

Ghusinga

Dennehy

Singh

2017

Proc. Natl. Acad. Sci. U.S.A.

107

127

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In the noisy cellular environment, gene products are subject to inherent random fluctuations in copy numbers over time. How cells ensure precision in the timing of key intracellular events despite such stochasticity is an intriguing fundamental problem. We formulate event timing as a first-passage time problem, where an event is triggered when the level of a protein crosses a critical threshold for the first time. Analytical calculations are performed for the first-passage time distribution in stochastic models of gene expression. Derivation of these formulas motivates an interesting question: Is there an optimal feedback strategy to regulate the synthesis of a protein to ensure that an event will occur at a precise time, while minimizing deviations or noise about the mean? Counterintuitively, results show 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. In contrast, a positive feedback mechanism provides the highest precision in timing for an unstable protein. These theoretical results explain recent experimental observations of single-cell lysis times in bacteriophage λ. Here, lysis of an infected bacterial cell is orchestrated by the expression and accumulation of a stable λ protein up to a threshold, and precision in timing is achieved via feedforward rather than feedback control. Our results have broad implications for diverse cellular processes that rely on precise temporal triggering of events.first-passage time | event timing | stochastic gene expression | feedback control | single cell T iming of events in many cellular processes, such as cell-cycle control (1-3), cell differentiation (4, 5), sporulation (6, 7), apoptosis (8, 9), development (10, 11), temporal order of gene expression (12)(13)(14), and so on, depend on regulatory proteins reaching critical threshold levels. Triggering of these events in single cells is influenced by fluctuations in protein levels that arise naturally due to noise in gene expression (15)(16)(17)(18). Increasing evidence shows considerable cell-to-cell variation in timing of intracellular events among isogenic cells (19-21), and it is unclear how noisy expression generates this variation. Characterization of control strategies that buffer stochasticity in event timing are critically needed to understand reliable functioning of diverse intracellular pathways that rely on precision in timing.Mathematically, noise in the timing of events can be investigated via the first-passage time (FPT) framework, where an event is triggered when a stochastic process (single-cell protein level) crosses a critical threshold for the first time. There is already a rich tradition of using such FPT approaches to study timing of events in biological and physical sciences (22-26). Following this tradition, exact analytical expression for the FPT distribution is computed in experimentally valida...

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Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

First-passage time approach to controlling noise in the timing of intracellular events

Ghusinga

Dennehy

Singh

2017

Proc. Natl. Acad. Sci. U.S.A.

107

127

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“…in I [ {LT, T pR 0 }, and kT pR 0 l is taken to be 15 min [29,30]. As T pR 0 variation only accounts for a small fraction of LT variability [34,35] As we ignore T pR 0 variation in these calculations, the reported values for CV 2 FPT are an upper bound. Assuming constitutive transcription from the wild-type pR' and a lysis threshold X of 1500 holin molecules [36], we obtain the following estimates for the translational burst size and the transcription rate from (3.5) and (4.…”

Section: Connecting Lysis Time To First-passage Timementioning

confidence: 99%

“…Interestingly, mutations in the holin amino acid sequence can significantly change the LT mean and variance [34]. As randomness in the onset of the late promoter expression cannot account for these variations [34,35], stochastic holin expression and accumulation may be key in determining LT differences. Ultimately, the expression and accumulation of holin in the inner membrane depend on several factors: the rate of transcription of late mRNA, the rate of holin protein translation by host ribosomes, the rate of holin insertion into the plasma membrane and the threshold holin concentration required for membrane hole formation.…”

Section: Introductionmentioning

confidence: 99%

Stochastic holin expression can account for lysis time variation in the bacteriophageλ

Singh

Dennehy

2014

J. R. Soc. Interface.

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The inherent stochastic nature of biochemical processes can drive differences in gene expression between otherwise identical cells. While cell-to-cell variability in gene expression has received much attention, randomness in timing of events has been less studied. We investigate event timing at the single-cell level in a simple system, the lytic pathway of the bacterial virus phage l. In individual cells, lysis occurs on average at 65 min, with an s.d. of 3.5 min. Interestingly, mutations in the lysis protein, holin, alter both the lysis time (LT) mean and variance. In our analysis, LT is formulated as the first-passage time (FPT) for cellular holin levels to cross a critical threshold. Exact analytical formulae for the FPT moments are derived for stochastic gene expression models. These formulae reveal how holin transcription and translation efficiencies independently modulate the LT mean and variation. Analytical expressions for the LT moments are used to evaluate previously published single-cell LT data for l phages with mutations in the holin sequence or its promoter. Our results show that stochastic holin expression is sufficient to account for the intercellular LT differences in both wild-type phages, and phage variants where holin transcription and the threshold for lysis have been experimentally altered. Finally, our analysis reveals regulatory motifs that enhance the robustness of lysis timing to cellular noise.

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“…On the one hand, 2 some important cellular processes depend on precision in the timing of key intracellular 3 events, e.g., cell fate decision presumably requires a precise control of gene expression 4 timing [2][3][4][5][6][7][8][9][10][11][12][13][14][15], and the controls of cell cycle and circadian clocks require timing precision 5 that can be crucial for the correct physiology [16][17][18][19][20][21][22][23][24]. Most of these processes are based 6 on gene expression, e.g., an activated gene may be required to reach in a precise time threshold level of p53 to execute apoptosis and this threshold increases with time [26].…”

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confidence: 99%

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

Qiu

Zhang

2018

Preprint

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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.

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Noise in timing and precision of gene activities in a genetic cascade

Cited by 60 publications

References 46 publications

First-passage time approach to controlling noise in the timing of intracellular events

First-passage time approach to controlling noise in the timing of intracellular events

Stochastic holin expression can account for lysis time variation in the bacteriophageλ

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

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