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This study introduces queueing theory as a novel method for analyzing stochastic gene expression models. This approach offers new analytical solutions for complex models previously unsolvable.

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Area of Science:

  • * Mathematical Biology
  • * Computational Biology
  • * Molecular Systems Biology

Background:

  • * Stochastic models are crucial for understanding gene expression variability.
  • * The chemical master equation is the standard framework, often solved with analytical methods.
  • * Gene expression stochasticity impacts cellular function and decision-making.

Purpose of the Study:

  • * To introduce and review queueing theory as an alternative approach for stochastic gene expression modeling.
  • * To demonstrate the application of infinite-server queues to single-cell stochastic biology.
  • * To provide analytical solutions for complex gene expression models.

Main Methods:

  • * Review of queueing theory principles applied to biological systems.
  • * Interpretation of six types of infinite-server queues in the context of single-cell gene expression.
  • * Derivation of analytical expressions for stationary and nonstationary distributions and moments.
  • * Calculation of bounds on the Fano factor for gene expression noise.

Main Results:

  • * Queueing theory provides a novel framework for analyzing stochastic gene expression.
  • * Analytical expressions for mRNA and protein numbers (distributions and moments) were derived.
  • * Bounds on the Fano factor were established, offering insights into noise characteristics.
  • * The approach is applicable to complex models that are intractable with standard methods.

Conclusions:

  • * Queueing theory offers a powerful and underutilized tool for stochastic gene expression analysis.
  • * This methodology can potentially solve complex models that have been analytically challenging.
  • * The framework facilitates a deeper understanding of molecular noise in single cells.