Estimating the Stochastic Bifurcation Structure of Cellular Networks

Song, Carl; Phenix, Hilary; Abedi, Vida; Scott, Matthew P.; Ingalls, Brian; Kærn, Mads; Perkins, Theodore J.

doi:10.1371/journal.pcbi.1000699

Cited by 36 publications

(49 citation statements)

References 37 publications

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“…Gene regulatory networks expressing more than a single phenotype can be characterized by mixture distributions (18). Intuitively, it might be expected that we can describe the probability distribution ΠðZjG; tÞ, given a certain promoter state G, under the assumption that any reactions affecting promoters vary on a much slower timescale than those that affect only gene products.…”

Section: Resultsmentioning

confidence: 99%

Phenotypic switching in gene regulatory networks

Thomas

Popović

Grima

2014

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

168

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Noise in gene expression can lead to reversible phenotypic switching. Several experimental studies have shown that the abundance distributions of proteins in a population of isogenic cells may display multiple distinct maxima. Each of these maxima may be associated with a subpopulation of a particular phenotype, the quantification of which is important for understanding cellular decision-making. Here, we devise a methodology which allows us to quantify multimodal gene expression distributions and single-cell power spectra in gene regulatory networks. Extending the commonly used linear noise approximation, we rigorously show that, in the limit of slow promoter dynamics, these distributions can be systematically approximated as a mixture of Gaussian components in a wide class of networks. The resulting closed-form approximation provides a practical tool for studying complex nonlinear gene regulatory networks that have thus far been amenable only to stochastic simulation. We demonstrate the applicability of our approach in a number of genetic networks, uncovering previously unidentified dynamical characteristics associated with phenotypic switching. Specifically, we elucidate how the interplay of transcriptional and translational regulation can be exploited to control the multimodality of gene expression distributions in two-promoter networks. We demonstrate how phenotypic switching leads to birhythmical expression in a genetic oscillator, and to hysteresis in phenotypic induction, thus highlighting the ability of regulatory networks to retain memory. (5), and cancer cells (6). It has been argued that such stochastic transitions in gene activity can affect stem cell lineage decisions (7,8). Similarly, they may present advantageous strategies when cells make decisions in changing environments (9). Here, we develop a quantitative methodology which allows us to explore the implications of phenotypic switching, and the phenomena associated with it.It is known that gene regulatory networks involving slow promoter switching may lead to distinct expression levels having significant lifetimes; hence, overall expression levels are characterized by bimodal distributions (10-12) or, more generally, by mixture distributions. However, it remains to be resolved how modeling can generally describe and parameterize these distributions. A positive resolution is crucial for the development of testable quantitative and predictive models, e.g., when investigating the sensitivity of bimodality against variation of model parameters, for estimating rate constants from experimentally measured distributions, in the design of synthetic circuitry with tunable gene expression profiles, but, most importantly, when determining the implications of phenotypic decision-making.A class of theoretical models based on the Chemical Master Equation (CME) predicts bimodal protein distributions in the absence of bistability in the corresponding deterministic model (12, 13), some of which have been verified experimentally (1,4,14). Recent efforts to quant...

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Section: Resultsmentioning

confidence: 99%

Phenotypic switching in gene regulatory networks

Thomas

Popović

Grima

2014

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

168

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“…Yeast cells induce or fail to induce the GAL genes when switched to galactose depending on the media in which they had been cultured beforehand. Authors disagree on whether the cells retain this fate indefinitely [5-7]. …”

Section: Introductionmentioning

confidence: 99%

“…A population with two widely separated expression states that persist despite changes — that are remembered — can indicate the existence of a bistable system [7, 36]. In such a system, cells can switch between states (ON and OFF) only when strongly perturbed.…”

Section: Introductionmentioning

confidence: 99%

“…The induction dynamics of the GAL pathway have been a popular subject for modelers [6, 7, 23, 24, 29, 37-41]. Models of how positive feedback among GAL genes can lead to history-dependent bimodality have tried to establish how each of four transcriptional feedback loops (GAL1, GAL2, GAL3, GAL80) strengthens or attenuates persistent memory [6, 23, 24, 41].…”

Section: Introductionmentioning

confidence: 99%

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The yeast galactose network as a quantitative model for cellular memory

2015

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Recent experiments have revealed surprising behavior in the yeast galactose (GAL) pathway, one of the preeminent systems for studying gene regulation. Under certain circumstances, yeast cells display memory of their prior nutrient environments. We distinguish two kinds of cellular memory discovered by quantitative investigations of the GAL network and present a conceptual framework for interpreting new experiments and current ideas on GAL memory. Reinduction memory occurs when cells respond transcriptionally to one environment, shut down the response during several generations in a second environment, then respond faster and with less cell-to-cell variation when returned to the first environment. Persistent memory describes a long-term, arguably stable response in which cells adopt a bimodal or unimodal distribution of induction levels depending on their preceding environment. Deep knowledge of how the yeast GAL pathway responds to different sugar environments has enabled rapid progress in uncovering the mechanisms behind GAL memory, which include cytoplasmic inheritance of inducer proteins and positive feedback loops among regulatory genes. This network of genes, long used to study gene regulation, is now emerging as a model system for cellular memory.

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“…Hysteresis experiments and its quantitative versions can map bistable ranges without the need to devise new constructs and to know any of the system parameter, provided some conditions are met 14,29,30 . When transient kinetics and noise is prominent, as in our synthetic circuits, the hysteresis profiles cannot delimit the bistability boundaries unequivocally, In this case, the open-loop approach can be used, which requires new genetic constructs and mRNA measurements 14 .…”

Section: Discussionmentioning

confidence: 99%

Measurement of bistability in a multidimensional parameter space

2017

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Integrative BiologyInterdisciplinary approaches for molecular and cellular life sciences Bistability plays an important role in the generation of alternative cell fates. In order to function reliably, bistability has to persist even when the system parameters are varied. The narrowest promoter dynamic range which permits the emergence of bistability is strongly dependent on the degree of cooperativity or dimerization. To estimate the bistable ranges of this parameter we used a threshold value of the rate of transitions between the two states. In this way, we show that dimerization in our synthetic circuits is maximally exploited to generate bistability.

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Estimating the Stochastic Bifurcation Structure of Cellular Networks

Cited by 36 publications

References 37 publications

Phenotypic switching in gene regulatory networks

Phenotypic switching in gene regulatory networks

The yeast galactose network as a quantitative model for cellular memory

Measurement of bistability in a multidimensional parameter space

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