Stochastic Models of Gene Expression with Delayed Degradation

Miękisz, Jacek; Poleszczuk, Jan; Bodnar, Marek; Foryś, Urszula

doi:10.1007/s11538-010-9622-4

Cited by 47 publications

(50 citation statements)

References 46 publications

(75 reference statements)

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“…3. Recent work has analyzed protein steady-state distributions for models with a constant time delay in protein degradation [24][25][26]. However, the processes of transcription and translation are generally lumped together and it is assumed that proteins are produced in a single step from the DNA in these models.…”

Section: B Model With Delayed Degradationmentioning

confidence: 99%

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

2013

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Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

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Section: B Model With Delayed Degradationmentioning

confidence: 99%

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

2013

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“…Bratsun et al obtained a very good agreement of deterministic and stochastic description. Therefore, in our opinion both types of description need to be corrected, compare [23] for detailed explanation, also in the context of stochastic description.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…In this subsection we describe the reaction channels studied in [19] and the deterministic models of the channels based on the ideas described in [23].…”

Section: Models Descriptionmentioning

confidence: 99%

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Analysis of biochemical reactions models with delays

Bodnar

Foryś

Poleszczuk

2011

Journal of Mathematical Analysis and Applications

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Deterministic descriptions of three biochemical reaction channels formerly considered by Bratsun et al. (2005) [19] are studied. These descriptions are based on the mass action law and for the simple protein production with delayed degradation differ from that proposed by Bratsun et al. An explicit solution to this model is calculated. For the model of reaction with negative feedback and delayed production, global stability of a unique positive steady state is proved. According to the models of these two reaction channels considered in the present paper there cannot appear delayed induced oscillations. For the model of reaction with negative feedback, dimerisation and delayed protein production, local stability for a unique positive steady state is shown for some range of parameters. It is also proved that for some range of parameters the destabilisation due to the increasing delay can occur and delayed induced oscillations may appear.

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“…Transformation of enzyme-substrate complex to enzyme-product complex involves conformational changes accompanied by some time delay which reduces the optimal conversion [3][4][5]. So most of the enzymatic reactions are not instantaneous and natural time delay is also observed in the evolution of cell states [6,7]. The time delay in reaction system has been studied through mathematical modeling by many researchers [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Modeling of a delay induced biochemical system for product optimization

2017

Commun. Optim. Theory

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Abstract. Enzymatic reactions occur through active sites of enzymes, which combine with the substrates to form intermediate complexes and subsequently lead to product. Transformation from one intermediate to another requires time dependent conformational changes of complexes. These changes are thus often accompanied by some time delay during formation of product. Time delay due to conformational changes can be avoided by controlling suitable reaction parameters, which are better identified by mathematical modeling. In this research article, we have proposed a delay differential equation model of enzymatic reaction system and analyzed the dynamics of the system critically from analytical and numerical points of view. It has been observed that time delay affects the stability and performance characteristics of the system. A control induced delay differential equation model is derived to reduce the delay induced instability of the system which contributes product optimization.

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Stochastic Models of Gene Expression with Delayed Degradation

Cited by 47 publications

References 46 publications

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

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

Analysis of biochemical reactions models with delays

Modeling of a delay induced biochemical system for product optimization

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