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Transcriptional Bursting in Gene Expression: Analytical Results for General Stochastic Models.

Kumar N, Singh A, Kulkarni RV - PLoS Comput. Biol. (2015)

Bottom Line: To address this issue, we invoke a mapping between general stochastic models of gene expression and systems studied in queueing theory to derive exact analytical expressions for the moments associated with mRNA/protein steady-state distributions.These results are then used to derive noise signatures, i.e. explicit conditions based entirely on experimentally measurable quantities, that determine if the burst distributions deviate from the geometric distribution or if burst arrival deviates from a Poisson process.The proposed approaches can lead to new insights into transcriptional bursting based on measurements of steady-state mRNA/protein distributions.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, University of Massachusetts Boston, Boston, Massachusetts, United States of America.

ABSTRACT
Gene expression in individual cells is highly variable and sporadic, often resulting in the synthesis of mRNAs and proteins in bursts. Such bursting has important consequences for cell-fate decisions in diverse processes ranging from HIV-1 viral infections to stem-cell differentiation. It is generally assumed that bursts are geometrically distributed and that they arrive according to a Poisson process. On the other hand, recent single-cell experiments provide evidence for complex burst arrival processes, highlighting the need for analysis of more general stochastic models. To address this issue, we invoke a mapping between general stochastic models of gene expression and systems studied in queueing theory to derive exact analytical expressions for the moments associated with mRNA/protein steady-state distributions. These results are then used to derive noise signatures, i.e. explicit conditions based entirely on experimentally measurable quantities, that determine if the burst distributions deviate from the geometric distribution or if burst arrival deviates from a Poisson process. For non-Poisson arrivals, we develop approaches for accurate estimation of burst parameters. The proposed approaches can lead to new insights into transcriptional bursting based on measurements of steady-state mRNA/protein distributions.

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Related in: MedlinePlus

Effects of extrinsic noise on burst estimation.For the transcriptional scheme shown in the inset, the relative error Δσ(⟨mb⟩) = (⟨mb⟩0−⟨mb⟩σ)/⟨mb⟩0 is plotted. Parameters as α1 = 1, α2 = 0.5, β = 50, ⟨km⟩ = 500 and μm = 1.
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pcbi.1004292.g005: Effects of extrinsic noise on burst estimation.For the transcriptional scheme shown in the inset, the relative error Δσ(⟨mb⟩) = (⟨mb⟩0−⟨mb⟩σ)/⟨mb⟩0 is plotted. Parameters as α1 = 1, α2 = 0.5, β = 50, ⟨km⟩ = 500 and μm = 1.

Mentions: To explore the effects of such fluctuations, we consider the model shown in Fig 5. In this kinetic scheme, the activation of gene from OFF to ON state involves two sequential steps, with rates α1 and α2. To include extrinsic fluctuations in the model, we consider that the rate of transcription km is a Log-normally distributed random variable with mean ⟨km⟩ and standard deviation σkm. For a given value of σkm, we determine the mean burst size following the procedure outlined above: i.e. by taking and then using the simulation values for the first four steady-state moments of mRNAs to estimate the unknown parameters (b1,b2,km,β), and hence the burst size. By varying σkm we study how the estimated burst size ⟨mb⟩σ deviates from the one without extrinsic noise, ⟨mb⟩0. As can be seen in Fig 5, for smaller values of σkm, the estimated burst size ⟨mb⟩σ is reasonably close to ⟨mb⟩0, however, as expected, ⟨mb⟩σ shows monotonic deviations from ⟨mb⟩0 for larger values of σkm.


Transcriptional Bursting in Gene Expression: Analytical Results for General Stochastic Models.

Kumar N, Singh A, Kulkarni RV - PLoS Comput. Biol. (2015)

Effects of extrinsic noise on burst estimation.For the transcriptional scheme shown in the inset, the relative error Δσ(⟨mb⟩) = (⟨mb⟩0−⟨mb⟩σ)/⟨mb⟩0 is plotted. Parameters as α1 = 1, α2 = 0.5, β = 50, ⟨km⟩ = 500 and μm = 1.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4608583&req=5

pcbi.1004292.g005: Effects of extrinsic noise on burst estimation.For the transcriptional scheme shown in the inset, the relative error Δσ(⟨mb⟩) = (⟨mb⟩0−⟨mb⟩σ)/⟨mb⟩0 is plotted. Parameters as α1 = 1, α2 = 0.5, β = 50, ⟨km⟩ = 500 and μm = 1.
Mentions: To explore the effects of such fluctuations, we consider the model shown in Fig 5. In this kinetic scheme, the activation of gene from OFF to ON state involves two sequential steps, with rates α1 and α2. To include extrinsic fluctuations in the model, we consider that the rate of transcription km is a Log-normally distributed random variable with mean ⟨km⟩ and standard deviation σkm. For a given value of σkm, we determine the mean burst size following the procedure outlined above: i.e. by taking and then using the simulation values for the first four steady-state moments of mRNAs to estimate the unknown parameters (b1,b2,km,β), and hence the burst size. By varying σkm we study how the estimated burst size ⟨mb⟩σ deviates from the one without extrinsic noise, ⟨mb⟩0. As can be seen in Fig 5, for smaller values of σkm, the estimated burst size ⟨mb⟩σ is reasonably close to ⟨mb⟩0, however, as expected, ⟨mb⟩σ shows monotonic deviations from ⟨mb⟩0 for larger values of σkm.

Bottom Line: To address this issue, we invoke a mapping between general stochastic models of gene expression and systems studied in queueing theory to derive exact analytical expressions for the moments associated with mRNA/protein steady-state distributions.These results are then used to derive noise signatures, i.e. explicit conditions based entirely on experimentally measurable quantities, that determine if the burst distributions deviate from the geometric distribution or if burst arrival deviates from a Poisson process.The proposed approaches can lead to new insights into transcriptional bursting based on measurements of steady-state mRNA/protein distributions.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, University of Massachusetts Boston, Boston, Massachusetts, United States of America.

ABSTRACT
Gene expression in individual cells is highly variable and sporadic, often resulting in the synthesis of mRNAs and proteins in bursts. Such bursting has important consequences for cell-fate decisions in diverse processes ranging from HIV-1 viral infections to stem-cell differentiation. It is generally assumed that bursts are geometrically distributed and that they arrive according to a Poisson process. On the other hand, recent single-cell experiments provide evidence for complex burst arrival processes, highlighting the need for analysis of more general stochastic models. To address this issue, we invoke a mapping between general stochastic models of gene expression and systems studied in queueing theory to derive exact analytical expressions for the moments associated with mRNA/protein steady-state distributions. These results are then used to derive noise signatures, i.e. explicit conditions based entirely on experimentally measurable quantities, that determine if the burst distributions deviate from the geometric distribution or if burst arrival deviates from a Poisson process. For non-Poisson arrivals, we develop approaches for accurate estimation of burst parameters. The proposed approaches can lead to new insights into transcriptional bursting based on measurements of steady-state mRNA/protein distributions.

No MeSH data available.


Related in: MedlinePlus