Incorporating spatial diffusion into models of bursty stochastic transcription.

Area of Science:

• Molecular Biology
• Systems Biology
• Computational Biology

Background:

• Gene expression dynamics are inherently stochastic and spatial at the molecular level.
• Existing models often overlook subcellular spatial resolution, limiting insights into mRNA transport and localization.
• Tools for analyzing spatial stochastic processes in gene expression are still developing.

Purpose of the Study:

• To introduce a novel spatial stochastic model for nuclear messenger RNA (mRNA) with two-state transcriptional dynamics.
• To provide a framework for inferring gene expression dynamics from spatial patterns at subcellular resolution.
• To address the limitations of current models in incorporating spatial information.

Main Methods:

• Developed a spatial stochastic model incorporating two-state (telegraph) transcriptional dynamics for nuclear mRNA.
• Described model observations using a spatial Cox process driven by a stochastically switching partial differential equation.
• Derived analytical solutions for spatial and demographic moments and validated them through simulations.

Main Results:

• The distribution of mRNA counts can be accurately approximated by a Poisson-beta distribution, even with complex spatial dynamics.
• The model allows for efficient parameter inference from static snapshot data.
• Analytical solutions for spatial and demographic moments were derived and validated.

Conclusions:

• The proposed spatial stochastic model advances the understanding of gene expression dynamics at subcellular resolution.
• This work enables more accurate inference of molecular dynamics from spatial data.
• It opens new avenues for studying gene expression using spatial patterns.