Stochastic models of gene expression with delayed degradation

Area of Science:

• Biochemistry
• Systems Biology
• Molecular Biology

Background:

• Cellular processes exhibit stochastic fluctuations due to low molecule numbers.
• Biological reactions often involve time delays, complicating dynamic modeling.
• Integrating stochasticity and time delays in cellular models presents significant challenges.

Purpose of the Study:

• To develop a systematic methodology for analyzing stochastic dynamics with time delays in biological systems.
• To investigate the combined effects of stochasticity and time delays in gene expression models.
• To rigorously analyze the impact of delayed protein degradation on cellular dynamics.

Main Methods:

• Proposed a novel analytical framework for stochastic models incorporating time delays.
• Applied the methodology to simple gene expression models with delayed degradation.
• Introduced an auxiliary stochastic process to handle consuming reactions like degradation.
• Analytically calculated variance and autocorrelation functions for protein molecules.

Main Results:

• Demonstrated that time delay in protein degradation does not inherently cause oscillations.
• Rigorous analysis indicates that other mechanisms are likely responsible for observed biological oscillations.
• Provided analytical calculations for key statistical properties of protein numbers in delayed degradation models.

Conclusions:

• Delayed protein degradation is not a direct cause of oscillations in gene expression.
• The developed methodology offers a robust approach for studying stochasticity and time delays in biological systems.
• Further research should explore alternative mechanisms driving oscillations in biological experiments.