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Analytical distributions for stochastic gene expression.

Vahid Shahrezaei1, Peter S Swain

  • 1Centre for Non-linear Dynamics, Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, QC, Canada, H3G 1Y6.

Proceedings of the National Academy of Sciences of the United States of America
|November 8, 2008
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Summary
This summary is machine-generated.

This study presents a new mathematical approximation for modeling gene expression. It enables calculation of protein number distributions, improving quantitative comparisons with experimental data in systems biology.

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Area of Science:

  • Systems Biology
  • Biophysics
  • Computational Biology

Background:

  • Gene expression exhibits significant stochasticity, posing challenges for accurate modeling of genetic networks.
  • Existing models often struggle to capture the full distribution of protein numbers due to inherent randomness.

Purpose of the Study:

  • To develop an approximation for calculating protein number distributions in gene expression.
  • To provide a method for predicting protein level dynamics and steady-state distributions.
  • To enable more quantitative comparisons between theoretical models and experimental data.

Main Methods:

  • Developed a mathematical approximation assuming slower protein decay relative to mRNA.
  • Utilized high-throughput data from budding yeast to validate the assumption.
  • Applied a two-stage gene expression model (transcription and translation as first-order reactions).
  • Derived protein distributions over time and analyzed steady-state distributions considering promoter fluctuations.

Main Results:

  • The approximation allows calculation of mean, variance, and full protein number distributions.
  • Protein synthesis is shown to occur in geometrically distributed bursts.
  • Protein distributions are generally asymmetric and cannot be fully characterized by mean and variance alone.
  • The method allows elimination of mRNA from master equation descriptions.

Conclusions:

  • The developed approximation provides a more accurate and quantitative approach to modeling stochastic gene expression.
  • The findings offer insights into the dynamics of protein synthesis and distribution, especially under promoter fluctuations.
  • This technique facilitates improved integration of computational models with experimental biological data.