Operon dynamics with state dependent transcription and/or translation delays

Area of Science:

• Molecular Biology
• Biophysics
• Dynamical Systems Theory

Background:

• Gene transcription and translation are fundamental cellular processes that operationalize genetic information.
• These biological processes are time-consuming and involve significant delays, which can influence cellular behavior.
• Goodwin models are commonly used to study gene regulatory networks, but often simplify delay mechanisms.

Purpose of the Study:

• To investigate the impact of state-dependent delays on the dynamics of inducible and repressible operons using Goodwin models.
• To provide a rigorous mathematical framework and detailed numerical analysis for these complex systems.
• To compare the behavior of operons with state-dependent delays against those with constant delays.

Main Methods:

• Derivation and justification of Goodwin models incorporating state-dependent delays.
• Analysis of the dynamical system's behavior within an appropriate mathematical setting.
• Extensive numerical simulations and parameter space exploration.
• Application of steady-state linearization and bifurcation theory.

Main Results:

• State-dependent delays introduce significant differences in operon dynamics compared to constant delay models.
• Inducible operon models exhibit stable periodic orbits.
• Repressible operon models demonstrate multistability and suggest the potential presence of Shilnikov-type homoclinic bifurcations.

Conclusions:

• State-dependent delays are crucial for accurately modeling gene regulatory network dynamics.
• The inclusion of realistic delay mechanisms can lead to novel phenomena like stable oscillations and multistability in gene expression.
• Further investigation into Shilnikov-type bifurcations in repressible operons is warranted.