The role of incoherent feedforward circuits in regulating precision of event timing

Dey, Supravat; Kannoly, Sherin; Bokes, Pavol; Dennehy, John J.; Singh, Abhyudai

doi:10.1101/2020.05.17.100420

Cited by 3 publications

(4 citation statements)

References 75 publications

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“…τ ←→ kv 0 α e αt − 1 , dτ = kv 0 e αt dt, (33) which after been applied to (30), reduces the system into a master equation of a Poisson process:…”

Section: Discussionmentioning

confidence: 99%

“…In other words, production is balanced by dilution of gene-product concentration in a growing cell. In most models, effects of deterministic dilution by growth are taken to be equivalent to a random process such as either degradation or segregation at division [30]- [33]. It is however unclear whether explicitly accounting for cell-size and growth would result in the same FPT statistics as the models that do not do it.…”

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confidence: 99%

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Threshold-crossing time statistics for gene expression in growing cells

Nieto

Ghusinga

Vargas-García

et al. 2022

Preprint

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Many intracellular events are triggered by attaining critical concentrations of their corresponding regulatory proteins. How cells ensure precision in the timing of the protein accumulation is a fundamental problem, and contrasting predictions of different models can help us understand the mechanisms involved in such processes. Here, we formulate the timing of protein threshold-crossing as a first passage time (FPT) problem focusing on how the mean FPT and its fluctuations depend on the threshold protein concentration. First, we model the protein-crossing dynamics from the perspective of three classical models of gene expression that do not explicitly accounts for cell growth but consider the dilution as equivalent to degradation: (birth-death process, discrete birth with continuous deterministic degradation, and Fokker-Planck approximation). We compare the resulting FPT statistics with a fourth model proposed by us (growing cell) that comprises size-dependent expression in an exponentially growing cell. When proteins accumulate in growing cells, their concentration reaches a steady value. When dilution by cell growth is modeled as degradation, cells can reach concentrations higher than this steady-state level at a finite time. In the growing cell model, on the other hand, the FPT moments diverge for thresholds higher than the steady-state level. This effect can be interpreted as a transition between noisy dynamics when cells are small to an almost deterministic behavior when cells grow enough. We finally study the mean FPT that optimizes the timing precision. The growing cell model predicts a higher optimal FPT and less variability than the classical models.

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“…τ ←→ kv 0 α e αt − 1 , dτ = kv 0 e αt dt, (33) which after been applied to (30), reduces the system into a master equation of a Poisson process:…”

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

Threshold-crossing time statistics for gene expression in growing cells

Nieto

Ghusinga

Vargas-García

et al. 2022

Preprint

Self Cite

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“…In this work, we consider a model of gene expression based on stochastic hybrid system formalism. Protein production is assumed to occur in bursts and is modeled as a stochastic event, whereas dilution due to cell growth is modeled using a deterministic ODE [38], [47], [48]. We provide analytical results on FPT moments and compute the optimal feedback strategy that minimizes noise in FPT around a given fixed mean under different modeling assumptions.…”

Section: Introductionmentioning

confidence: 99%

Regulatory strategies to schedule threshold crossing of protein levels at a prescribed time

Nieto

Ghusinga

Singh

2022

Preprint

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The timing of diverse cellular processes is based on the instant when the concentration of regulatory proteins crosses a critical threshold level. Hence, noise mechanisms inherent to these protein synthesis pathways drive statistical fluctuations in such events' timing. How to express proteins ensuring both the threshold crossing at a prescribed time and minimal timing fluctuations? To find this optimal strategy, we formulate a model where protein molecules are synthesized in random bursts of gene activity. The burst frequency depends on the protein level creating a feedback loop, and cellular growth dilutes protein concentration between consecutive bursts. Counterintuitively, our analysis shows that positive feedback in protein production is best for minimizing variability in threshold crossing times. We analytically predict the optimal feedback strength in terms of the dilution rate. As a corollary to our result, a no-feedback strategy emerges as the optimal strategy in the absence of dilution. We further consider other noise sources, such as randomness in either the initial condition or the threshold level, and find that in many cases, we need either strongly negative or positive feedback for precise scheduling for events.

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“…In a previous study, we used a panel of phage λ holin mutants that varied in their lysis times to show that the cell-to-cell variation or “noise” in lysis timing takes a concave-up shape with respect to lysis time, suggesting an optimal lysis time that minimizes noise (Kannoly et al ., 2020). A theoretical approach further suggests that the noise in lysis timing is minimized when both holin and its antagonist antiholin are expressed at an optimal ratio (Dey et al ., 2020). In a follow up study, we elucidated the biological significance of minimizing the noise in lysis timing and demonstrated that there exists a range of optimal lysis times where phage fitness is maximized in a quasi-continuous culture (Kannoly, Singh and Dennehy, 2020).…”

Section: Introductionmentioning

confidence: 99%

A Single-Cell Approach Reveals Variation in Cellular Phage-Producing Capacities

Kannoly

Oken

Shadan

et al. 2021

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Virus burst size, a component of viral fitness, is the average number of viral particles released from a single infected cell. In this study, we estimated bacteriophage lambda (λ) burst size mean and distribution at different lysis times. To estimate phage λ burst sizes at single-cell level, we employed a lysis-deficient E. coli lysogen, which allowed chemical lysis at desired times after the induction of lytic cycle. Induced cultures of E. coli lysogen were diluted and aliquoted into the wells of 96-well plates. A high dilution rate results in mostly empty wells and minimizes the probability of having multiple cells in wells that do receive cells. Burst size was estimated by titering single-cell lysates obtained after chemical lysis at desired times. Our data shows that the viral burst size initially increases exponentially with the lysis time, and then saturates at longer lysis times. We also demonstrate that cell-to-cell variation or “noise” in lysis timing does not significantly contribute to the burst size noise. The burst size noise remains constant with increasing mean burst size. The most likely explanation for the experimentally observed constant burst size noise is that cell-to-cell differences in burst size originate from differences in cellular capacity to produce phages. The mean burst size measured at different lysis times is positively correlated to cell volume, which may determine the cellular phage production capacity. However, experiments controlling for cell size indicates that there are other factors in addition to cell size that determine this cellular capacity.ARTICLE IMPORTANCEPhages produce offspring by hijacking a cell’s replicative machinery. Previously, it was noted that the variation in the number of phages produced by single infected cells far exceeded cell size variation. It has been hypothesized that this variation is a consequence of variation in the timing of host cell lysis. Here we show that cell-to-cell variation in lysis timing does not significantly contribute to the burst size variation. We suggest that the constant burst size variation across different host lysis times results from cell-to-cell differences in capacity to produce phages. We find that the mean burst size measured at different lysis times is positively correlated to cell volume, which may determine the cellular phage production capacity. However, experiments controlling for cell size indicates that there are other factors in addition to cell size that determine this cellular capacity.

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The role of incoherent feedforward circuits in regulating precision of event timing

Cited by 3 publications

References 75 publications

Threshold-crossing time statistics for gene expression in growing cells

Threshold-crossing time statistics for gene expression in growing cells

Regulatory strategies to schedule threshold crossing of protein levels at a prescribed time

A Single-Cell Approach Reveals Variation in Cellular Phage-Producing Capacities

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