First‐Passage Processes in Cellular Biology

Iyer‐Biswas, Srividya; Zilman, Anton

doi:10.1002/9781119165156.ch5

Cited by 75 publications

(86 citation statements)

References 192 publications

(299 reference statements)

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“…There is already a rich tradition of using such FPT approaches to study timing of events in biological and physical sciences (22)(23)(24)(25)(26). Following this tradition, exact analytical expression for the FPT distribution is computed in experimentally validated and commonly used stochastic models of gene expression.…”

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.

113

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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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.

113

127

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“…This is consistent with the observation that often, the effect of chemotherapy on recurrence rates does not last for a long time after chemotherapy ends. Several clinical trials [23][24][25] have shown that improved recurrence rates for patients receiving chemotherapy revert to rates for the control group (who received no chemotherapy) in a relatively short time after termination of treatment, suggesting the presence of residual 45 dormant tumor foci that survive treatment and regenerate the cancer. These data also suggest that shortduration chemotherapy only targets the tumor foci that cycle during chemotherapy.…”

Section: Introductionmentioning

confidence: 99%

“…The backward Kolmogorov approach is often more appropriate to first-passage time problems [45][46][47][48] and will be used in combination with Eq. (15) to derive an equation for S(t).…”

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confidence: 99%

A Quasi Birth-and-Death Model For Tumor Recurrence

Santana

Ganesan

Bhanot

2019

Preprint

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A major cause of chemoresistance and recurrence in tumors is the presence of dormant tumor foci that survive chemotherapy and can eventually transition to active growth to regenerate the cancer. In this paper, we propose a Quasi Birth-and-Death (QBD) model for the dynamics of tumor growth and recurrence/remission of the cancer. Starting from a discrete-state master equation that describes the timedependent transition probabilities between states with different numbers of dormant and active tumor foci, we develop a framework based on a continuum-limit approach to determine the time-dependent probability that an undetectable residual tumor will become large enough to be detectable. We derive an exact formula for the probability of recurrence at large times and show that it displays a phase transition as a function of the ratio of the death rate µ A of an active tumor focus to its doubling rate λ. We also derive forward and backward Kolmogorov equations for the transition probability density in the continuum limit and, using a first-passage time formalism, we obtain a drift-diffusion equation for the mean recurrence time and solve it analytically to leading order for a large detectable tumor size N . We show that simulations of the discretestate model agree with the analytical results, except for O(1/N ) corrections. Finally, we describe a scheme to fit the model to recurrence-free survival (Kaplan-Meier) curves from clinical cancer data, using ovarian cancer data as an example. Our model has potential applications in predicting how changing chemotherapy schedules may affect disease recurrence rates, especially in cancer types for which no targeted therapy is available.model is formulated in terms of a continuous-time master equation in the discrete state space that represents the numbers of dormant and active tumor foci. In Section 4, it is shown that an expansion of the master equation for a large detectable-tumor size N leads to a simplified approach by mapping the original discretestate model to a stochastic process in a continuous two-dimensional state space. In Section 5, we find the large-time probability of recurrence in closed analytic form and calculate the mean recurrence time (MRT) 70 analytically to leading order in N . In Section 5, we compare these analytical results to simulations and describe a scheme to fit the model to recurrence-free survival (Kaplan-Meier) curves from clinical cancer data, using ovarian cancer data as an example. Finally, in Section (6) we present our concluding remarks. Overview of the discrete-state modelThe precise discrete model for tumor recurrence that will be described in this section was inspired by 75 previous work on the effect of quiescence (i.e., the presence of dormant tumor foci) on treatment success, such as the work of Komarova and Wodarz [8], which inspired the stochastic model described below, or to deterministic versions of their model, proposed in [9], [10], or [11]. However, in contrast to these earlier studies, the focus of our paper is on finding a relatio...

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“…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.…”

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confidence: 99%

“…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.…”

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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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First‐Passage Processes in Cellular Biology

Cited by 75 publications

References 192 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

A Quasi Birth-and-Death Model For Tumor Recurrence

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

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