Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul

doi:10.1103/physreve.87.042720

Cited by 42 publications

(58 citation statements)

References 32 publications

(50 reference statements)

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“…σ was chosen to be 0.01 to generate cell cycle phase distributions that resembled experimental data. The copy numbers of each factor type ( n i ) for each cell were assumed to follow a Poisson distribution (Shahrezaei & Swain, ; Pendar et al , ), with mean abundance following a lognormal distribution of μ = 1,000 and σ = 0.6 (Ghaemmaghami et al , ; Furusawa et al , ; Eriksson & Fenyö, ).

n_{i} \sim P o i s s o n false(λ_{i} false)

{normalλ}_{i} \sim l o g n o r m a l (μ, σ)

…”

Section: Methodsmentioning

confidence: 99%

Evidence that the human cell cycle is a series of uncoupled, memoryless phases

Chao

Fakhreddin

Shimerov

et al. 2019

Molecular Systems Biology

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The cell cycle is canonically described as a series of four consecutive phases: G1, S, G2, and M. In single cells, the duration of each phase varies, but the quantitative laws that govern phase durations are not well understood. Using time‐lapse microscopy, we found that each phase duration follows an Erlang distribution and is statistically independent from other phases. We challenged this observation by perturbing phase durations through oncogene activation, inhibition of DNA synthesis, reduced temperature, and DNA damage. Despite large changes in durations in cell populations, phase durations remained uncoupled in individual cells. These results suggested that the independence of phase durations may arise from a large number of molecular factors that each exerts a minor influence on the rate of cell cycle progression. We tested this model by experimentally forcing phase coupling through inhibition of cyclin‐dependent kinase 2 ( CDK 2) or overexpression of cyclin D. Our work provides an explanation for the historical observation that phase durations are both inherited and independent and suggests how cell cycle progression may be altered in disease states.

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n_{i} \sim P o i s s o n false(λ_{i} false)

{normalλ}_{i} \sim l o g n o r m a l (μ, σ)

…”

Section: Methodsmentioning

confidence: 99%

Evidence that the human cell cycle is a series of uncoupled, memoryless phases

Chao

Fakhreddin

Shimerov

et al. 2019

Molecular Systems Biology

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show abstract

“…(10), along with the joint probability generating function Q III (z 1 , z 2 ), is outlined in Appendix C, based on the work by Shahrezaei and Swain [27] but without making the approximation that the mRNA lifetime is negligible compared with that of the protein (also see Bokes et al [28] and Pendar et al [29] for alternative derivations). The mean and variance of the final product n 2 are equal to…”

Section: Gene Expression Models and Their Mathematical Formulationmentioning

confidence: 99%

“…Lastly, we would like to make a remark that the time dependent expressions for the generating functions for these extended models were also provided in refs. [29] and [35].…”

Section: Remarks On Several Extensions Of the Basic Modelsmentioning

confidence: 99%

Distribution of population-averaged observables in stochastic gene expression

Bhattacharyya

Kalay

2014

Phys. Rev. E

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Observation of phenotypic diversity in a population of genetically identical cells is often linked to the stochastic nature of chemical reactions involved in gene regulatory networks. We investigate the distribution of population averaged gene expression levels as a function of population, or sample, size for several stochastic gene expression models to find out to what extent population averaged quantities reflect the underlying mechanism of gene expression. We consider three basic gene regulation networks corresponding to transcription with and without gene state switching and translation. Using analytical expressions for the probability generating function of observables and Large Deviation Theory, we calculate the distribution and first two moments of the population averaged mRNA and protein levels as a function of model parameters, population size and number of measurements contained in a data set. We validate our results using stochastic simulations also report exact results on the asymptotic properties of population averages which show qualitative differences among different models.

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“…Systems operating at a complex-balanced equilibrium are a notable exception in that they admit tractable product-form distributions [21][22][23][24]. Steady-state distributions have also been characterised in terms of generating functions in a growing collection of simple models that are not complex-balanced [25][26][27][28][29][30]. Such representations typically involve the use of special mathematical functions [31].…”

Section: Introductionmentioning

confidence: 99%

Buffering gene expression noise by microRNA based feedforward regulation

Bokes

Hojcka

Singh

2018

Preprint

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Cells use various regulatory motifs, including feedforward loops, to control the intrinsic noise that arises in gene expression at low copy numbers. Here we study one such system, which is broadly inspired by the interaction between an mRNA molecule and an antagonistic mi-croRNA molecule encoded by the same gene. The two reaction species are synchronously produced, individually degraded, and the second species (microRNA) exerts an antagonistic pressure on the first species (mRNA). Using linear-noise approximation, we show that the noise in the first species, which we quantify by the Fano factor, is sub-Poissonian, and exhibits a nonmonotonic response both to the species lifetime ratio and to the strength of the antagonistic interaction. Additionally, we use the Chemical Reaction Network Theory to prove that the first species distribution is Poissonian if the first species is much more stable than the second. Finally, we identify a special parametric regime, supporting a broad range of behaviour, in which the distribution can be analytically described in terms of the confluent hypergeometric limit function. We verify our analysis against large-scale kinetic Monte Carlo simulations. Our results indicate that, subject to specific physiological constraints, optimal parameter values can be found within the mRNA-microRNA motif that can benefit the cell by lowering the gene-expression noise.

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Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes

Cited by 42 publications

References 32 publications

Evidence that the human cell cycle is a series of uncoupled, memoryless phases

Evidence that the human cell cycle is a series of uncoupled, memoryless phases

Distribution of population-averaged observables in stochastic gene expression

Buffering gene expression noise by microRNA based feedforward regulation

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