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This study presents analytical solutions for generalized two-state models of transcriptional regulation, enabling calculation of mRNA moments. These findings offer insights into gene expression mechanisms and aid statistical inference from experimental data.

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Area of Science:

  • Molecular biology
  • Biophysics
  • Systems biology

Background:

  • Transcriptional regulation involves complex molecular events.
  • Generalized two-state models simplify these processes.
  • Analytical solutions for such models are challenging.

Purpose of the Study:

  • To analytically solve a generalized two-state model for transcriptional regulation.
  • To derive formulas for mRNA burst-size distributions.
  • To develop methods for calculating mRNA moments.

Main Methods:

  • Developed analytical formulas for burst-size distributions.
  • Derived an iterative equation for the mRNA moment-generating function.
  • Applied phase-type waiting-time distributions for special cases.

Main Results:

  • Provided analytical formulas for burst-size distributions.
  • Enabled calculation of any order of mRNA raw and binomial moments.
  • Demonstrated utility in special cases of phase-type distributions.

Conclusions:

  • The generalized two-state model can be analytically solved.
  • The derived methods facilitate the study of complex transcriptional regulation.
  • The approach aids statistical inference from experimental data.