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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.

No MeSH data available.


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Estimation of mean burst size from sequence size function ϕ(τ).For the transcriptional scheme shown in (a), the variations of ϕ″(τ) and ϕ(τ) as a function of time τ (scaled by 103) are shown in (b) and (c) respectively. The three lines correspond to three different values of β, 50 (dashed line), 100 (dotted line) and 200 (dashed-dotted line), while keeping km = 500: Exact burst size for these three cases are 11, 6 and 3.5, respectively. Estimated mean burst size has been indicated by filled symbols and the inflexion points in the sequence size function are shown by empty symbols. Other parameters: α1 = 1,α2 = 0.5,α3 = 0.25,α4 = 0.75,β1 = 0.1,β2 = 0.2,β3 = 0.5.
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pcbi.1004292.g004: Estimation of mean burst size from sequence size function ϕ(τ).For the transcriptional scheme shown in (a), the variations of ϕ″(τ) and ϕ(τ) as a function of time τ (scaled by 103) are shown in (b) and (c) respectively. The three lines correspond to three different values of β, 50 (dashed line), 100 (dotted line) and 200 (dashed-dotted line), while keeping km = 500: Exact burst size for these three cases are 11, 6 and 3.5, respectively. Estimated mean burst size has been indicated by filled symbols and the inflexion points in the sequence size function are shown by empty symbols. Other parameters: α1 = 1,α2 = 0.5,α3 = 0.25,α4 = 0.75,β1 = 0.1,β2 = 0.2,β3 = 0.5.

Mentions: The form, , is exact for the two-state random telegraph model. Using the expressions obtained for the first four steady-state moments, we can derive an analytic condition that determines whether the underlying mechanism can be represented by (see Supplementary S2 Text). However, if the arrival process is complex and involves multiple rate-limiting steps, then will not be an accurate representation of the underlying kinetic process. In such cases, we need to use gL(s) of higher order. The next step in this iterative process is to take . This form of gL(s) is valid if there are only two rate-limiting steps in the promoter transition from OFF to ON state. For kinetic schemes that involve more than two steps, it will serve as an approximate reduced representation. Interestingly, it turns out that even if is not a correct representation of the underlying kinetic process, this reduced representation works very well as far as estimating burst size is concerned. In Fig 4, we have illustrated the effectiveness of this approach for a complex kinetic scheme for the promoter transition from OFF to ON state. The figure also illustrates the effectiveness of the approach outlined in the previous subsection for determining the mean burst size using the sequence-size function ϕ(τ).


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

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

Estimation of mean burst size from sequence size function ϕ(τ).For the transcriptional scheme shown in (a), the variations of ϕ″(τ) and ϕ(τ) as a function of time τ (scaled by 103) are shown in (b) and (c) respectively. The three lines correspond to three different values of β, 50 (dashed line), 100 (dotted line) and 200 (dashed-dotted line), while keeping km = 500: Exact burst size for these three cases are 11, 6 and 3.5, respectively. Estimated mean burst size has been indicated by filled symbols and the inflexion points in the sequence size function are shown by empty symbols. Other parameters: α1 = 1,α2 = 0.5,α3 = 0.25,α4 = 0.75,β1 = 0.1,β2 = 0.2,β3 = 0.5.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi.1004292.g004: Estimation of mean burst size from sequence size function ϕ(τ).For the transcriptional scheme shown in (a), the variations of ϕ″(τ) and ϕ(τ) as a function of time τ (scaled by 103) are shown in (b) and (c) respectively. The three lines correspond to three different values of β, 50 (dashed line), 100 (dotted line) and 200 (dashed-dotted line), while keeping km = 500: Exact burst size for these three cases are 11, 6 and 3.5, respectively. Estimated mean burst size has been indicated by filled symbols and the inflexion points in the sequence size function are shown by empty symbols. Other parameters: α1 = 1,α2 = 0.5,α3 = 0.25,α4 = 0.75,β1 = 0.1,β2 = 0.2,β3 = 0.5.
Mentions: The form, , is exact for the two-state random telegraph model. Using the expressions obtained for the first four steady-state moments, we can derive an analytic condition that determines whether the underlying mechanism can be represented by (see Supplementary S2 Text). However, if the arrival process is complex and involves multiple rate-limiting steps, then will not be an accurate representation of the underlying kinetic process. In such cases, we need to use gL(s) of higher order. The next step in this iterative process is to take . This form of gL(s) is valid if there are only two rate-limiting steps in the promoter transition from OFF to ON state. For kinetic schemes that involve more than two steps, it will serve as an approximate reduced representation. Interestingly, it turns out that even if is not a correct representation of the underlying kinetic process, this reduced representation works very well as far as estimating burst size is concerned. In Fig 4, we have illustrated the effectiveness of this approach for a complex kinetic scheme for the promoter transition from OFF to ON state. The figure also illustrates the effectiveness of the approach outlined in the previous subsection for determining the mean burst size using the sequence-size function ϕ(τ).

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