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A Markovian arrival stream approach to stochastic gene expression in cells
Brian Fralix1, Mark Holmes2, Andreas Löpker3
1School of Mathematical and Statistical Sciences, Clemson University, Clemson, USA. bfralix@clemson.edu.
Journal of Mathematical Biology
|April 22, 2023
Summary
This study generalizes stochastic gene expression models by incorporating both mRNA and protein production. The new framework uses Markovian Arrival Processes for transcription, offering a more flexible approach to modeling gene activity.
Area of Science:
- Computational Biology
- Mathematical Biology
- Biophysics
Background:
- Stochastic gene expression is fundamental to cellular function.
- Existing models often simplify the complex processes of transcription and translation.
- Recent work has focused on refining these models for greater accuracy.
Purpose of the Study:
- To analyze a generalized stochastic gene expression model.
- To incorporate both mRNA and protein production dynamics.
- To relax assumptions on the transcription process.
Main Methods:
- Utilized techniques from point process theory.
- Applied methods from matrix-analytic theory.
- Modeled gene activity and mRNA creation using arbitrary Markovian Arrival Processes.
- Modeled protein production from mRNA using a Poisson process.
Main Results:
- Developed a flexible framework for stochastic gene expression.
- Demonstrated the ability of Markovian Arrival Processes to approximate various point processes.
- Enabled a broader range of assumptions for modeling transcription.
Conclusions:
- The generalized model provides a more comprehensive understanding of gene expression.
- The use of Markovian Arrival Processes enhances the applicability of the model.
- This approach offers significant advancements in the theoretical analysis of gene regulation.
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