scholarly journals Urn models for stochastic gene expression yield intuitive insights into the probability distributions of single-cell mRNA and protein counts

2020 ◽  
Vol 17 (6) ◽  
pp. 066001
Author(s):  
Krishna Choudhary ◽  
Atul Narang
Keyword(s):  
Gene Expression ◽  
Single Cell ◽  
Probability Distributions ◽  
Stochastic Gene Expression ◽  
Urn Models

scholarly journals Urn models for regulated gene expression yield physically intuitive solutions for probability distributions of single-cell counts

2020 ◽  
Author(s):  
Krishna Choudhary ◽  
Atul Narang
Keyword(s):  
Gene Expression ◽  
Gene Regulation ◽  
Single Cell ◽  
Hypergeometric Functions ◽  
Probability Distributions ◽  
Time Intervals ◽  
Probability Mass ◽  
Regulated Gene Expression ◽  
Short Time ◽  
Mass Functions

AbstractFitting the probability mass functions from analytical solutions of stochastic models of gene expression to the count distributions of mRNA and protein molecules in single cells can yield valuable insights into mechanisms of gene regulation. Solutions of chemical master equations are available for various kinetic schemes but, even for the models of regulation with a basic ON-OFF switch, they take complex forms with generating functions given as hypergeometric functions. Gene expression studies that have used these to fit the data have interpreted the parameters as burst size and frequency. However, this is consistent with the hypergeometric functions only if a gene stays active for short time intervals separated by relatively long intervals of inactivity. Physical insights into the probability mass functions are essential to ensure proper interpretations but are lacking for models of gene regulation. We fill this gap by developing urn models for regulated gene expression, which are of immense value to interpret probability distributions. Our model consists of a master urn, which represents the cytosol. We sample RNA polymerases and ribosomes from it and assign them to recipient urns of two or more colors, which represent time intervals with a homogeneous propensity for gene expression. Colors of the recipient urns represent sub-systems of the promoter states, and the assignments to urns of a specific color represent gene expression. We use elementary principles of discrete probability theory to derive the solutions for a range of kinetic models, including the Peccoud-Ycart model, the Shahrezaei-Swain model, and models with an arbitrary number of promoter states. For activated genes, we show that transcriptional lapses, which are events of gene inactivation for short time intervals separated by long active intervals, quantify the transcriptional dynamics better than bursts. Our approach reveals the physics underlying the solutions, which has important implications for single-cell data analysis.

scholarly journals Drugs modulating stochastic gene expression affect the erythroid differentiation process

2018 ◽  
Author(s):  
Anissa Guillemin ◽  
Ronan Duchesne ◽  
Fabien Crauste ◽  
Sandrine Gonin-Giraud ◽  
Olivier Gandrillon
Keyword(s):  
Gene Expression ◽  
Single Cell ◽  
Erythroid Differentiation ◽  
Causative Role ◽  
Stochastic Gene Expression ◽  
Differentiation Process ◽  
Modeling Tools ◽  
Erythroid Progenitor ◽  
Differentiated Cells

AbstractBackgroundTo understand how a metazoan cell makes the decision to differentiate, we assessed the role of stochastic gene expression (SGE) during the erythroid differentiation process. Our hypothesis is that stochastic gene expression has a role in single-cell decision-making. In agreement with this hypothesis, we and others recently showed that SGE significantly increased during differentiation. However, evidence for the causative role of SGE is still lacking. Such demonstration would require being able to experimentally manipulate SGE levels and analyze the resulting impact of these variations on cell differentiation.ResultWe identified three drugs that modulate SGE in primary erythroid progenitor cells. Artemisinin and Indomethacin simultaneously decreased SGE and reduced the amount of differentiated cells. Inversely, α-methylene-γ-butyrolactone-3 (MB-3) simultaneously increased the level of SGE and the amount of differentiated cells. We then used a dynamical modelling approach which confirmed that differentiation rates were indeed affected by the drug treatment.ConclusionUsing single-cell analysis and modeling tools, we provide experimental evidence that in a physiologically relevant cellular system, control of SGE can directly modify differentiation, supporting a causal link between the two.

scholarly journals Selection at the pathway level drives the evolution of gene-specific transcriptional noise

2017 ◽  
Author(s):  
Gustavo Valadares Barroso ◽  
Natasa Puzovic ◽  
Julien Y Dutheil
Keyword(s):  
Gene Expression ◽  
Single Cell ◽  
Gene Networks ◽  
Phenotypic Variability ◽  
Published Data ◽  
Evolutionary Constraint ◽  
Stochastic Gene Expression ◽  
Transcriptional Noise ◽  
Evolutionary Forces ◽  
A Genome

ABSTRACTBiochemical reactions within individual cells result from the interactions of molecules, typically in small numbers. Consequently, the inherent stochasticity of binding and diffusion processes generate noise along the cascade that leads to the synthesis of a protein from its encoding gene. As a result, isogenic cell populations display phenotypic variability even in homogeneous environments. The extent and consequences of this stochastic gene expression have only recently been assessed on a genome-wide scale, in particular owing to the advent of single cell transcriptomics. However, the evolutionary forces shaping this stochasticity have yet to be unraveled. We take advantage of two recently published data sets of the single-cell transcriptome of the domestic mouse Mus musculus in order to characterize the effect of natural selection on gene-specific transcriptional stochasticity. We show that noise levels in the mRNA distributions (a.k.a. transcriptional noise) significantly correlate with three-dimensional nuclear domain organization, evolutionary constraint on the encoded protein and gene age. The position of the encoded protein in biological pathways, however, is the main factor that explains observed levels of transcriptional noise, in agreement with models of noise propagation within gene networks. Because transcriptional noise is under widespread selection, we argue that it constitutes an important component of the phenotype and that variance of expression is a potential target of adaptation. Stochastic gene expression should therefore be considered together with mean expression level in functional and evolutionary studies of gene expression.

Stochastic Gene Expression in a Single Cell

Science ◽  
2002 ◽  
Vol 297 (5584) ◽  
pp. 1183-1186 ◽  
Author(s):  
M. B. Elowitz
Keyword(s):  
Gene Expression ◽  
Single Cell ◽  
Stochastic Gene Expression

scholarly journals Author response: A new protocol for single-cell RNA-seq reveals stochastic gene expression during lag phase in budding yeast

2020 ◽  
Author(s):  
Abbas Jariani ◽  
Lieselotte Vermeersch ◽  
Bram Cerulus ◽  
Gemma Perez-Samper ◽  
Karin Voordeckers ◽  
...  
Keyword(s):  
Gene Expression ◽  
Single Cell ◽  
Budding Yeast ◽  
Author Response ◽  
Lag Phase ◽  
Stochastic Gene Expression ◽  
Rna Seq

scholarly journals Bayesian estimation for stochastic gene expression using multifidelity models

2018 ◽  
Author(s):  
Huy D. Vo ◽  
Zachary Fox ◽  
Ania Baetica ◽  
Brian Munsky
Keyword(s):  
Gene Expression ◽  
Gene Regulation ◽  
Single Cell ◽  
Simulated Data ◽  
Second Phase ◽  
Stochastic Gene Expression ◽  
Finite State ◽  
Efficient Data ◽  
Computationally Intensive ◽  
Discrete Stochastic Models

AbstractThe finite state projection (FSP) approach to solving the chemical master equation has enabled successful inference of discrete stochastic models to predict single-cell gene regulation dynamics. Unfortunately, the FSP approach is highly computationally intensive for all but the simplest models, an issue that is highly problematic when parameter inference and uncertainty quantification takes enormous numbers of parameter evaluations. To address this issue, we propose two new computational methods for the Bayesian inference of stochastic gene expression parameters given single-cell experiments. We formulate and verify an Adaptive Delayed Acceptance Metropolis-Hastings (ADAMH) algorithm to utilize with reduced Krylov-basis projections of the FSP. We then introduce an extension of the ADAMH into a Hybrid scheme that consists of an initial phase to construct a reduced model and a faster second phase to sample from the approximate posterior distribution determined by the constructed model. We test and compare both algorithms to an adaptive Metropolis algorithm with full FSP-based likelihood evaluations on three example models and simulated data to show that the new ADAMH variants achieve substantial speedup in comparison to the full FSP approach. By reducing the computational costs of parameter estimation, we expect the ADAMH approach to enable efficient data-driven estimation for more complex gene regulation models.

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