Universal Poisson Statistics of mRNAs with Complex Decay Pathways

Area of Science:

• Molecular and Cell Biology
• Biophysics
• Systems Biology

Background:

• Single-cell mRNA dynamics are commonly modeled as memoryless birth-death processes.
• This model predicts a Poisson steady-state distribution, which aligns with experimental observations.
• However, mRNA decay is known to be a complex, non-memoryless process, creating a paradox.

Purpose of the Study:

• To resolve the paradox between simple models and complex mRNA decay.
• To explain the universality of the Poisson steady state in mRNA number distributions.
• To identify conditions under which deviations from the Poisson distribution occur.

Main Methods:

• Utilized queueing theory to map mRNA dynamics.
• Applied a nonlinear time rescaling to birth-death processes and complex decay variants.
• Analyzed deviations from Poisson distribution under promoter fluctuations and non-independent degradation.

Main Results:

• Demonstrated that various mRNA birth-death models, including complex decay, exhibit a Poisson steady state.
• Showed that this universality holds under a nonlinear time rescaling.
• Identified transcriptional bursting and non-independent degradation as key conditions causing deviations from the Poisson form.

Conclusions:

• The Poisson steady state is a robust feature of mRNA dynamics, generalizing beyond simple models.
• Single-cell experiments have limited power to distinguish between different microscopic mRNA dynamics models.
• Single-molecule measurements are crucial for probing complex mRNA decay mechanisms and promoter dynamics.