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Dimensionality reduction via path integration for computing mRNA distributions.

Jaroslav Albert1

  • 1Ronin Institute, Montclair, New Jersey, USA.

Journal of Mathematical Biology
|November 3, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a novel method for rapidly calculating mRNA distributions by integrating gene promoter states. The approach efficiently computes separate distributions for distinct mRNA species, outperforming traditional Master Equation methods.

Keywords:
Gene regulatory networksMaster equationPath integralProbability distributionsPromoterSingle-cell RNA data

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Area of Science:

  • Systems Biology
  • Computational Biology
  • Molecular Biology

Background:

  • Gene expression exhibits inherent stochasticity, resulting in variable mRNA copy numbers within cell populations.
  • These variations are primarily driven by the diverse states of gene promoters, each influencing transcription rates.
  • The increasing availability of single-cell mRNA data necessitates faster computational methods for analyzing these distributions.

Purpose of the Study:

  • To develop a computational method for calculating separate mRNA distributions for different mRNA species (partially or fully processed).
  • To provide a more efficient alternative to the Master Equation for computing mRNA distributions.

Main Methods:

  • The proposed method integrates over all possible gene promoter state realizations.
  • This integration is formulated as a set of linear ordinary differential equations.
  • The dimension of these equations depends on the number of promoter states and the desired mRNA copy number cutoff.

Main Results:

  • The new method offers computational advantages over the Master Equation, requiring fewer coupled differential equations.
  • Unlike the Master Equation, this approach does not necessitate a priori selection of probability cutoffs.
  • Results were validated by comparison with Gillespie simulations for ten randomly selected parameter sets.

Conclusions:

  • The developed method provides an efficient and accurate way to compute mRNA distributions for individual mRNA species.
  • This approach enhances the analysis of gene expression noise in single cells.
  • The method's superiority over the Master Equation lies in its computational efficiency and flexibility in handling probability distributions.