Exact Distributions for Stochastic Gene Expression Models with Bursting and Feedback

Kumar, Niraj; Platini, Thierry; Kulkarni, Rahul

doi:10.1103/physrevlett.113.268105

Cited by 155 publications

(178 citation statements)

References 26 publications

(80 reference statements)

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“…Moreover, as case studies, we consider two regulatory motifs of transcription in E. coli [74]: 1) a promoter containing a single binding site where a repressor molecule can bind and hinder transcription, and 2) a promoter consisting of a single binding site where an activator molecule can bind and increase the rate of transcription. These regulatory architectures have been extensively explored in different studies, using the implicit assumption that TFs are in abundance [38, 64, 75–79]. …”

Section: Resultsmentioning

confidence: 99%

Effect of transcription factor resource sharing on gene expression noise

et al. 2017

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Gene expression is intrinsically a stochastic (noisy) process with important implications for cellular functions. Deciphering the underlying mechanisms of gene expression noise remains one of the key challenges of regulatory biology. Theoretical models of transcription often incorporate the kinetics of how transcription factors (TFs) interact with a single promoter to impact gene expression noise. However, inside single cells multiple identical gene copies as well as additional binding sites can compete for a limiting pool of TFs. Here we develop a simple kinetic model of transcription, which explicitly incorporates this interplay between TF copy number and its binding sites. We show that TF sharing enhances noise in mRNA distribution across an isogenic population of cells. Moreover, when a single gene copy shares it’s TFs with multiple competitor sites, the mRNA variance as a function of the mean remains unaltered by their presence. Hence, all the data for variance as a function of mean expression collapse onto a single master curve independent of the strength and number of competitor sites. However, this result does not hold true when the competition stems from multiple copies of the same gene. Therefore, although previous studies showed that the mean expression follows a universal master curve, our findings suggest that different scenarios of competition bear distinct signatures at the level of variance. Intriguingly, the introduction of competitor sites can transform a unimodal mRNA distribution into a multimodal distribution. These results demonstrate the impact of limited availability of TF resource on the regulation of noise in gene expression.

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Section: Resultsmentioning

confidence: 99%

Effect of transcription factor resource sharing on gene expression noise

et al. 2017

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“…Due to its simplicity, this idealized problem has been the subject of numerous theoretical studies. 11,[44][45][46][47][48][49] The state of the circuit is defined by two dynamical variables: an operator state variable s = {0, 1} describing whether the gene is active s = 1 (ON) or inactive s = 0 (OFF) and the number of proteins n = {0, 1, 2, . .…”

Section: A Schematic Discussion Of Trajectory Statistics In Gene Netmentioning

confidence: 99%

Dichotomous noise models of gene switches

Potoyan

Wolynes

2015

The Journal of Chemical Physics

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Molecular noise in gene regulatory networks has two intrinsic components, one part being due to fluctuations caused by the birth and death of protein or mRNA molecules which are often present in small numbers and the other part arising from gene state switching, a single molecule event. Stochastic dynamics of gene regulatory circuits appears to be largely responsible for bifurcations into a set of multi-attractor states that encode different cell phenotypes. The interplay of dichotomous single molecule gene noise with the nonlinear architecture of genetic networks generates rich and complex phenomena. In this paper, we elaborate on an approximate framework that leads to simple hybrid multi-scale schemes well suited for the quantitative exploration of the steady state properties of large-scale cellular genetic circuits. Through a path sum based analysis of trajectory statistics, we elucidate the connection of these hybrid schemes to the underlying master equation and provide a rigorous justification for using dichotomous noise based models to study genetic networks. Numerical simulations of circuit models reveal that the contribution of the genetic noise of single molecule origin to the total noise is significant for a wide range of kinetic regimes. C 2015 AIP Publishing LLC. [http://dx

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“…An exact analytical solution of this model is generally not possible for any arbitrary n. However, as shown below, closed-form solutions of the statistical moments can be obtained for n = 1 (non-cooperative feedback) [30]. These solutions are later used to benchmark different moment closure methods.…”

Section: Model Formulationmentioning

confidence: 97%

Approximate statistical dynamics of a genetic feedback circuit

Soltani

Vargas

Kumar

et al. 2015

2015 American Control Conference (ACC)

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Auto-regulation, a process wherein a protein negatively regulates its own production, is a common motif in gene expression networks. Negative feedback in gene expression plays a critical role in buffering intracellular fluctuations in protein concentrations around optimal value. Due to the nonlinearities present in these feedbacks, moment dynamics are typically not closed, in the sense that the time derivative of the lower-order statistical moments of the protein copy number depends on high-order moments. Moment equations are closed by expressing higher-order moments as nonlinear functions of lower-order moments, a technique commonly referred to as moment closure. Here, we compare the performance of different moment closure techniques. Our results show that the commonly used closure method, which assumes a priori that the protein population counts are normally distributed, performs poorly. In contrast, conditional derivative-matching, a novel closure scheme proposed here provides a good approximation to the exact moments across different parameter regimes. In summary our study provides a new moment closure method for studying stochastic dynamics of genetic negative feedback circuits, and can be extended to probe noise in more complex gene networks.

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Exact Distributions for Stochastic Gene Expression Models with Bursting and Feedback

Cited by 155 publications

References 26 publications

Effect of transcription factor resource sharing on gene expression noise

Effect of transcription factor resource sharing on gene expression noise

Dichotomous noise models of gene switches

Approximate statistical dynamics of a genetic feedback circuit

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