Analytical approximations for spatial stochastic gene expression in single cells and tissues.

Area of Science:

• Computational biology
• Biophysics
• Systems biology

Background:

• Gene expression involves stochastic and diffusive processes, especially in spatial settings.
• Spatial stochastic simulations are computationally intensive, limiting understanding of intrinsic noise effects.
• Deterministic models often overlook the significance of noise in spatial gene expression.

Purpose of the Study:

• To derive approximate steady-state mean concentration expressions from the reaction-diffusion master equation (RDME).
• To investigate the influence of spatial dimensionality, rate constants, and diffusion coefficients on gene expression.
• To highlight the role of intrinsic noise in spatial gene expression.

Main Methods:

• Derivation of analytical expressions for steady-state mean concentrations from the RDME.
• Development of closed-form solutions for systems with one effective species.
• Validation through comparison with stochastic simulations (RDME and Brownian dynamics).

Main Results:

• Derived expressions for mean concentrations explicitly depend on spatial dimensionality, rate constants, and diffusion coefficients.
• For single effective species, a simple closed-form solution was obtained.
• Demonstrated that mean concentrations can depend on diffusion coefficients even in homogeneous systems, contradicting deterministic predictions.

Conclusions:

• Intrinsic noise significantly impacts spatial gene expression, affecting mean concentrations in ways not predicted by deterministic models.
• The derived formulae provide a theoretical framework for understanding noise in spatial stochastic systems.
• Findings underscore the importance of considering stochasticity and diffusion in biological systems like single cells and tissues.