Exact solution of stochastic gene expression models with bursting, cell cycle and replication dynamics

Area of Science:

• Molecular Biology
• Systems Biology
• Biophysics

Background:

• Stochastic gene expression models often simplify cell cycle dynamics, omitting cell age and explicit replication events.
• Implicit models approximate cell division as first-order decay, assuming bursty protein production leads to negative binomial distributions.

Purpose of the Study:

• To compare the accuracy of implicit stochastic gene expression models with detailed models that include cell age, replication, and variable cell division times.
• To identify conditions under which implicit models accurately represent protein distributions.

Main Methods:

• Derived the exact stationary solution of the chemical master equation for detailed stochastic gene expression models.
• Incorporated bursty protein dynamics, binomial partitioning at mitosis, age-dependent transcription, and replication.
• Modeled random interdivision times using Erlang or more general distributions.

Main Results:

• Implicit models (negative binomial) approximate detailed models when mean mRNA per cycle is low and cell cycle variability is high.
• Deviations occur when mean mRNA per cycle is high or cell cycle variability is low, leading to bimodal or flat-topped distributions.
• Protein noise depends on replication time and cell cycle variability, with different dependencies for lineage versus population measurements and low versus high transcription rates.

Conclusions:

• Implicit models of stochastic gene expression have limitations and are not universally accurate.
• Detailed models are necessary to capture complex dynamics, especially for genes with high transcription rates or under specific cell cycle conditions.
• Understanding these model discrepancies is crucial for accurate interpretation of gene expression noise and cellular processes.