Exactly solvable models of stochastic gene expression

Area of Science:

• Molecular Biology
• Systems Biology
• Biophysics

Background:

• Simple gene expression models (active/inactive states) inadequately represent biological observations in prokaryotes and eukaryotes.
• Real gene expression is influenced by complex factors like transcription factors, chromatin state, and DNA accessibility.

Purpose of the Study:

• To develop and solve generalized multistate models of gene expression.
• To capture the joint effects of regulatory factors on transcript abundance.
• To provide tools for analyzing and designing gene expression systems.

Main Methods:

• Analytical decomposition of complex multistate models into simpler, solvable processes.
• Approximation method using power series expansion of the stationary distribution for broader model classes.
• Investigation of model properties, including the absence of heavy-tailed distributions without extrinsic noise.

Main Results:

• A general analytical solution is provided for a class of multistate gene expression models.
• An approximation method is developed for an even wider range of models.
• Demonstration that extrinsic noise is necessary for heavy-tailed distributions in these models.

Conclusions:

• Generalized multistate models provide a more accurate framework for gene expression dynamics.
• The developed analytical and computational methods enable precise solutions for complex gene expression systems.
• These findings have implications for designing synthetic gene circuits and controlling cellular behavior.