Transcriptional dynamics with time-dependent reaction rates

Area of Science:

• Molecular Biology
• Biophysics
• Systems Biology

Background:

• Transcription is the initial, crucial step in gene regulation, enabling cells to adapt to environmental shifts.
• Gene expression involves mRNA synthesis and degradation, a dynamic process often modeled using stochastic methods.
• Environmental fluctuations introduce time-dependent variations in cellular processes.

Purpose of the Study:

• To develop and analyze a generic stochastic model for transcription with time-dependent reaction rates.
• To derive an exact analytical expression for the messenger RNA (mRNA) probability distribution.
• To investigate cellular responses to arbitrary time-dependent environmental protocols.

Main Methods:

• Stochastic modeling of transcription as a birth-death process.
• Derivation of exact analytical solutions for mRNA probability distributions.
• Stochastic simulations to validate analytical findings.
• Analysis of transcriptional machinery as a low-pass filter.

Main Results:

• An exact analytical expression for the mRNA probability distribution was obtained.
• The transcriptional machinery was confirmed to function predominantly as a low-pass filter.
• Cellular mRNA levels can exhibit synchronous or asynchronous fluctuations based on system parameters.
• Deviations from Poisson statistics in mRNA levels were observed.

Conclusions:

• The developed stochastic model accurately describes gene transcription under fluctuating environmental conditions.
• The low-pass filter behavior of the transcriptional machinery is a fundamental characteristic of cellular response.
• System parameters critically influence the nature of mRNA fluctuations and their statistical properties.