Dimensionality reduction via path integration for computing mRNA distributions

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.