Birth and Death Process Modeling Leads to the Poisson Distribution: A Journey Worth Taking

Rash, Agnes M.; Winkel, Brian

doi:10.1080/10511970802475157

Cited by 5 publications

(3 citation statements)

References 2 publications

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“…Indeed, one observes that the corresponding FFs peak close to these values, in accordance with the observation that stochastic fluctuations are enhanced when the rates of substrate supply are adequately balanced in a stoichiometrically coupled system [34,54,55]. The FF for ceRNA 2 appears to approach one for large values of f 1 , as expected for the pure Poisson birth/death process that characterizes the free regime [56]. On the other hand, for very small but nonzero mean fractional occupancy n 1 (corresponding to small values of f 1 ), m 1 will with high probability only take on the values 0 or 1, as a transcribed molecule will quickly undergo degradation or sequestration in a complex.…”

Section: Mathematical Model Of Cerna Competitionsupporting

confidence: 80%

Probing the Limits to MicroRNA-Mediated Control of Gene Expression

Martirosyan¹,

Figliuzzi²,

Marinari³

et al. 2016

PLoS Comput Biol

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According to the ‘ceRNA hypothesis’, microRNAs (miRNAs) may act as mediators of an effective positive interaction between long coding or non-coding RNA molecules, carrying significant potential implications for a variety of biological processes. Here, inspired by recent work providing a quantitative description of small regulatory elements as information-conveying channels, we characterize the effectiveness of miRNA-mediated regulation in terms of the optimal information flow achievable between modulator (transcription factors) and target nodes (long RNAs). Our findings show that, while a sufficiently large degree of target derepression is needed to activate miRNA-mediated transmission, (a) in case of differential mechanisms of complex processing and/or transcriptional capabilities, regulation by a post-transcriptional miRNA-channel can outperform that achieved through direct transcriptional control; moreover, (b) in the presence of large populations of weakly interacting miRNA molecules the extra noise coming from titration disappears, allowing the miRNA-channel to process information as effectively as the direct channel. These observations establish the limits of miRNA-mediated post-transcriptional cross-talk and suggest that, besides providing a degree of noise buffering, this type of control may be effectively employed in cells both as a failsafe mechanism and as a preferential fine tuner of gene expression, pointing to the specific situations in which each of these functionalities is maximized.

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Section: Mathematical Model Of Cerna Competitionsupporting

confidence: 80%

Probing the Limits to MicroRNA-Mediated Control of Gene Expression

Martirosyan¹,

Figliuzzi²,

Marinari³

et al. 2016

PLoS Comput Biol

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show abstract

“…For such an intensity of the incoming Poisson flow in the system M(t)|M|∞ and the autonomous system the average values of the number of occupied devices are the same and are determined by the equality (7). For the intensity λ(t) of the form (10), the characteristic function (8) takes the form…”

Section: ∂G(u T) ∂Umentioning

confidence: 99%

“…We show that the characteristics of such queuing systems differ significantly, which suggests that the Poisson flow approximation is inappropriate for long-term forecasting [7,8].…”

Section: Introductionmentioning

confidence: 98%

Approximation of the birth process

Nosova

2021

Preprint

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In this article, queuing systems with an unlimited number of devices with an incoming nonstationary Poisson flow and a random flow controlled by a Markov chain are investigated. The inexpediency of approximation of the birth process by Poisson flows in long-term forecasting is shown. Research of a Markov autonomous queuing systemSince the process i (t) is a Markov chain then for its probability distribution P (i, t) = P {i(t) = i}

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Cross coursing in mathematics: physical modelling in differential equations crossing to discrete dynamical systems

Winkel

2012

International Journal of Mathematical Education in Science and

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Birth and Death Process Modeling Leads to the Poisson Distribution: A Journey Worth Taking

Cited by 5 publications

References 2 publications

Probing the Limits to MicroRNA-Mediated Control of Gene Expression

Probing the Limits to MicroRNA-Mediated Control of Gene Expression

Approximation of the birth process

Cross coursing in mathematics: physical modelling in differential equations crossing to discrete dynamical systems

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