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Translational regulation in prokaryotes ensures efficient protein synthesis by controlling ribosome access to mRNA. This regulation is mediated by secondary RNA structures, including translational riboswitches, RNA thermometers, and small RNAs (sRNAs), which respond to intracellular and environmental signals to modulate gene expression.Translational RiboswitchesRiboswitches in the leader region of mRNAs can regulate translation by altering the accessibility of the Shine-Dalgarno (SD) sequence,...
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Base complementarity between the three base pairs of mRNA codon and the tRNA anticodon is not a failsafe mechanism. Inaccuracies can range from a single mismatch to no correct base pairing at all. The free energy difference between the correct and nearly correct base pairs can be as small as 3 kcal/ mol. With complementarity being the only proofreading step, the estimated error frequency would be one wrong amino acid in every 100 amino acids incorporated. However, error frequencies observed in...
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Negative feedback and oscillations in a model for mRNA translation.

Aliza Ehrman1, Thomas Kriecherbauer2, Lars Grüne2

  • 1Electrical Engineering-Systems, Tel Aviv University, Tel Aviv-Yafo, Tel Aviv District, Israel.

Journal of the Royal Society, Interface
|October 21, 2025
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Summary

The ribosome flow model (RFM) with negative feedback demonstrates periodic protein production. This study provides conditions for non-trivial periodic solutions in translation dynamics.

Keywords:
mRNA translationperiodic solutionsregulation of gene expression

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Area of Science:

  • * Molecular Biology
  • * Systems Biology
  • * Mathematical Biology

Background:

  • * The ribosome flow model (RFM) simulates particle flow on a 1D chain, widely used for mRNA translation dynamics.
  • * RFM models ribosomes as particles and mRNA sites as codon groups, crucial for understanding cellular translation.
  • * Networked RFMs analyze resource competition in large-scale cellular translation.

Purpose of the Study:

  • * To analyze the ribosome flow model (RFM) incorporating negative feedback from protein production to initiation rate.
  • * To investigate the conditions for non-trivial periodic solutions in this 2-cooperative dynamic system.
  • * To characterize initial conditions leading to convergence to these periodic solutions.

Main Methods:

  • * Analysis of the RFM as a 2-cooperative dynamical system.
  • * Application of tools from the theory of 2-cooperative dynamical systems.
  • * Characterization of initial conditions for convergence to periodic solutions.

Main Results:

  • * A simple condition is identified that guarantees at least one non-trivial periodic solution in the closed-loop RFM system.
  • * A significant set of initial conditions is explicitly characterized, ensuring solutions converge to a non-trivial periodic state.
  • * The periodic solution corresponds to oscillating ribosome densities and protein production rates.

Conclusions:

  • * The study establishes conditions for periodic behavior in a translation model with negative feedback.
  • * This work provides insights into the dynamic regulation of protein synthesis through feedback mechanisms.
  • * The findings reveal periodic patterns in ribosome distribution and protein output under specific feedback conditions.