Negative feedback and oscillations in a model for mRNA translation

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.