Multimodality and Flexibility of Stochastic Gene Expression

Innocentini, Guilherme C. P.; Forger, Michael; Ramos, Alexandre F.; Radulescu, Ovidiu; Hornos, José Eduardo Martinho

doi:10.1007/s11538-013-9909-3

Cited by 24 publications

(32 citation statements)

References 38 publications

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“…In the literature, different methodologies have been used to describe simple gene regulation models on the basis of a separation of timescales. Qian et al (12) obtain a factorization of the stationary probability density for an autoregulated gene; similarly, Innocentini et al (23) have considered a multistate promoter without feedback. These methodologies require the corresponding protein distributions to be obtained analytically, which becomes generally intractable when posttranscriptional mechanisms based on bimolecular protein interactions are considered or when the full time dependence of the distribution function is desired.…”

Section: Discussionmentioning

confidence: 99%

Phenotypic switching in gene regulatory networks

Thomas

Popović

Grima

2014

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

174

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: Discussionmentioning

confidence: 99%

Phenotypic switching in gene regulatory networks

Thomas

Popović

Grima

2014

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

174

168

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“…All these further indicate that our mechanism is completely new compared with that in [23]. Finally, and most importantly, the transcription coupling of our model has not been contained in the above-mentioned models.…”

Section: Conclusion and Discussionmentioning

confidence: 75%

“…From this point of view, some parts of our work can be seen as a compensation of this result in [22]. In [23] reduce the noise when the occupancy probability of the intermediate state increases at a fixed transcription level. Obviously, their intermediate state should at least be an active state, otherwise, high occupancy of this state will lead to a very low transcription level, which can be more noisy.…”

Section: Conclusion and Discussionmentioning

confidence: 96%

Reinitiation enhances reliable transcriptional responses in eukaryotes

Liu

Yuan

Aihara

et al. 2014

J. R. Soc. Interface.

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Gene transcription is a noisy process carried out by the transcription machinery recruited to the promoter. Noise reduction is a fundamental requirement for reliable transcriptional responses which in turn are crucial for signal transduction. Compared with the relatively simple transcription initiation in prokaryotes, eukaryotic transcription is more complex partially owing to its additional reinitiation mechanism. By theoretical analysis, we showed that reinitiation reduces noise in eukaryotic transcription independent of the transcription level. Besides, a higher reinitiation rate enables a stable scaffold complex an advantage in noise reduction. Finally, we showed that the coupling between scaffold formation and transcription can further reduce transcription noise independent of the transcription level. Furthermore, compared with the reinitiation mechanism, the noise reduction effect of the coupling can be of more significance in the case that the transcription level is low and the intrinsic noise dominates. Our results uncover a mechanistic route which eukaryotes may use to facilitate a more reliable response in the noisy transcription process.

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“…For slow switching, the mRNA distribution is bimodal, with discontinuities at the modal values k 0 /ρ and k 1 /ρ values, where the probability density diverges on one side and is zero on the other side. The bimodality resulting from slow switching is well understood and signalled in many other places in the literature (see for instance [45,46]). We can emphasize that the discontinuity of the solution is a consequence of the hyperbolicity of advection fluxes.…”

Section: The Finite Difference (Fd) Liouville-master Methodsmentioning

confidence: 83%

Time Dependent Stochastic mRNA and Protein Synthesis in Piecewise-Deterministic Models of Gene Networks

2018

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We discuss piecewise-deterministic approximations of gene networks dynamics. These approximations capture in a simple way the stochasticity of gene expression and the propagation of expression noise in networks and circuits. By using partial omega expansions, piecewise deterministic approximations can be formally derived from the more commonly used Markov pure jump processes (chemical master equation). We are interested in time dependent multivariate distributions that describe the stochastic dynamics of the gene networks. This problem is difficult even in the simplified framework of piecewise-deterministic processes. We consider three methods to compute these distributions: the direct Monte-Carlo; the numerical integration of the Liouville-master equation; and the push-forward method. This approach is applied to multivariate fluctuations of gene expression, generated by gene circuits. We find that stochastic fluctuations of the proteome and, much less, those of the transcriptome can discriminate between various circuit topologies.

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Multimodality and Flexibility of Stochastic Gene Expression

Cited by 24 publications

References 38 publications

Phenotypic switching in gene regulatory networks

Phenotypic switching in gene regulatory networks

Reinitiation enhances reliable transcriptional responses in eukaryotes

Time Dependent Stochastic mRNA and Protein Synthesis in Piecewise-Deterministic Models of Gene Networks

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