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Stochastic Gene Expression Revisited.

Andrzej Tomski1, Maciej Zakarczemny2

  • 1Institute of Mathematics, University of Silesia in Katowice, 40-007 Katowice, Poland.

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Summary
This summary is machine-generated.

This study models gene expression using Iterated Function Systems (IFS), revealing a unique invariant limit measure for stochastic processes. The findings offer a probabilistic description compared to continuous-time models.

Keywords:
gene expression process simulationiterated function systemlimit measurepre-mRNAstochastic gene expression

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Area of Science:

  • Computational Biology
  • Stochastic Processes
  • Systems Biology

Background:

  • Gene expression is a complex stochastic process.
  • Continuous-time Markov models describe stochastic gene expression.
  • Understanding gene activation dynamics is crucial.

Purpose of the Study:

  • To investigate a novel gene expression model using Iterated Function Systems (IFS).
  • To analyze the probabilistic behavior of gene activation and pre-mRNA production.
  • To compare the IFS model with continuous-time Markov processes.

Main Methods:

  • Utilizing Iterated Function Systems (IFS) for gene expression modeling.
  • Incorporating state-dependent probabilities for iterated map selection.
  • Modeling random jump times to represent gene activation periods.
  • Employing piecewise deterministic Markov process concepts.

Main Results:

  • Demonstrated the existence of a unique invariant limit measure for the proposed IFS model.
  • Provided a full probabilistic description of the gene expression process.
  • Established a comparison between the IFS model and continuous-time models.

Conclusions:

  • The Iterated Function System (IFS) model offers a viable framework for understanding stochastic gene expression.
  • The unique invariant limit measure provides key insights into the long-term behavior of the system.
  • This approach enhances the probabilistic description of gene activation dynamics.