Extrinsic Noise and Heavy-Tailed Laws in Gene Expression

Ham, Lucy; Brackston, Rowan D.; Stumpf, Michael

doi:10.1103/physrevlett.124.108101

Cited by 55 publications

(56 citation statements)

References 57 publications

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“…Our argument relies on moment generating functions, which for a random variable X with distribution f , is defined as M f (t) := E(e tx ) for t ∈ R. We here take heavy-tailed to mean that the moment generating function is undefined for positive t. As in Ref. 11, the effects of extrinsic variability on the multistate systems is captured via a compound distribution; see Eq. 9 there.…”

Section: Effects Of Extrinsic Noisementioning

confidence: 99%

“…The model does not account for more complex control mechanisms, nor more complex gene regulatory networks involva) Electronic mail: lucy.ham@unimelb.edu.au b) Electronic mail: d.schnoerr@imperial.ac.uk c) Electronic mail: r.brackston13@imperial.ac.uk d) Electronic mail: mstumpf@unimelb.edu.au ing feedback. Recent work has shown that, while the Telegraph model is able to capture some degree of the variability in gene expression levels, it fails to explain the large variability and over-dispersion in the tails seen in many experimental datasets 11 . Furthermore, it has become evident that gene promoters can be in multiple states and may involve interactions between a number of regulatory factors, leading to a different mRNA synthesis rate for each state; such states may be associated with the presence of multiple copies of a gene in a genome, or with the key steps involved in chromatin remodelling [12][13][14][15] , DNA looping 16 or supercoiling 17 .…”

Section: Introductionmentioning

confidence: 99%

“…Despite its deficiencies, the Telegraph model remains a useful framework around which more complicated models can be constructed and, as we will show here, provides a foundation from which to develop further analytical results. A number of extensions and modifications of the Telegraph model have emerged, the simplest of which is perhaps the extension to allow for a second basal rate of transcription-the "leaky" Telegraph model 11,18,19 . A further extension incorporating the additional effects of extrinsic noise is given in Refs.…”

Section: Introductionmentioning

confidence: 99%

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Exactly solvable models of stochastic gene expression

Ham

Schnoerr

Brackston

et al. 2020

Preprint

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Stochastic models are key to understanding the intricate dynamics of gene expression. But the simplest models which only account for e.g. active and inactive states of a gene fail to capture common observations in both prokaryotic and eukaryotic organisms. Here we consider multistate models of gene expression which generalise the canonical Telegraph process, and are capable of capturing the joint effects of e.g. transcription factors, heterochromatin state and DNA accessibility (or, in prokaryotes, Sigma-factor activity) on transcript abundance. We propose two approaches for solving classes of these generalised systems. The first approach offers a fresh perspective on a general class of multistate models, and allows us to “decompose” more complicated systems into simpler processes, each of which can be solved analytically. This enables us to obtain a solution of any model from this class. We further show that these models cannot have a heavy-tailed distribution in the absence of extrinsic noise. Next, we develop an approximation method based on a power series expansion of the stationary distribution for an even broader class of multistate models of gene transcription. The combination of analytical and computational solutions for these realistic gene expression models also holds the potential to design synthetic systems, and control the behaviour of naturally evolved gene expression systems, e.g. in guiding cell-fate decisions.

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Section: Effects Of Extrinsic Noisementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exactly solvable models of stochastic gene expression

Ham

Schnoerr

Brackston

et al. 2020

Preprint

Self Cite

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“…This is of particular relevance for current data analysis where mRNA labelling techniques give access to mRNA abundance distributions in populations of cells. In order to extract mechanistic information of the transcriptional process from these distributions, it is paramount to link the details of the distribution to the properties of the different biomolecular mechanisms [3,26]. While in this paper we analysed the error in the transcription rate estimation due to neglecting cell cycle variability and replication, future work will address how taking into account such details may also affect the inference of other biochemical parameters such as gene activation and deactivation rates, or the mean burst size.…”

Section: Discussionmentioning

confidence: 99%

“…While in this paper we analysed the error in the transcription rate estimation due to neglecting cell cycle variability and replication, future work will address how taking into account such details may also affect the inference of other biochemical parameters such as gene activation and deactivation rates, or the mean burst size. The necessity of such study becomes apparent from the mRNA distributions obtained, which can be approximated accurately by negative binomials in scenarios with constitutive gene expression, challenging the common practice to use negative binomial distributions as a signature of bursty transcription [1,26,27].…”

Section: Discussionmentioning

confidence: 99%

Effects of cell cycle variability on lineage and population measurements of mRNA abundance

Pérez-Carrasco

Beentjes

Grima

2020

Preprint

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Many models of gene expression do not explicitly incorporate a cell cycle description. Here we derive a theory describing how mRNA fluctuations for constitutive and bursty gene expression are influenced by the stochasticity in the duration of the cell cycle and DNA replication. By means of the analytical expressions for the moments, we show that the error introduced in the predicted mean number of mRNAs, when noise in the cell cycle duration is omitted, is a monotonic decreasing function of η which is proportional to the ratio of the mean cell cycle duration and the mRNA lifetime; contrastingly, the error in the variance of the mRNA distribution peaks for intermediate values of η consistent with genome-wide measurements in many organisms. Using eukaryotic cell data, we estimate the errors in the mean and variance to be at most 3% and 25%. Furthermore we derive an accurate negative binomial mixture approximation to the mRNA distribution and show that under certain conditions, bimodality can result from the doubling of the transcription rate when DNA duplicates. Finally, we show that for real genomic data, disregarding cell cycle stochasticity can introduce errors in the inference of transcription rates larger than 10%, supporting the relevance of the analysis presented.

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Inference on autoregulation in gene expression with variance-to-mean ratio

Wang

2023

J. Math. Biol.

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Some genes can promote or repress their own expressions, which is called autoregulation. Although gene regulation is a central topic in biology, autoregulation is much less studied. In general, it is extremely difficult to determine the existence of autoregulation with direct biochemical approaches. Nevertheless, some papers have observed that certain types of autoregulations are linked to noise levels in gene expression. We generalize these results by two propositions on discrete-state continuous-time Markov chains. These two propositions form a simple but robust method to infer the existence of autoregulation from gene expression data. This method only needs to compare the mean and variance of the gene expression level. Compared to other methods for inferring autoregulation, our method only requires non-interventional one-time data, and does not need to estimate parameters. Besides, our method has few restrictions on the model. We apply this method to four groups of experimental data and find some genes that might have autoregulation. Some inferred autoregulations have been verified by experiments or other theoretical works.

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Extrinsic Noise and Heavy-Tailed Laws in Gene Expression

Cited by 55 publications

References 57 publications

Exactly solvable models of stochastic gene expression

Exactly solvable models of stochastic gene expression

Effects of cell cycle variability on lineage and population measurements of mRNA abundance

Inference on autoregulation in gene expression with variance-to-mean ratio

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