Parametric Sensitivity Analysis of Oscillatory Delay Systems with an Application to Gene Regulation

Area of Science:

• Mathematical Biology
• Dynamical Systems
• Computational Biology

Background:

• Delay-differential equations (DDEs) model complex biological systems, including gene expression networks.
• Periodic solutions in DDEs are crucial for understanding oscillatory behaviors.
• Parametric sensitivities are vital for analyzing model robustness and evolutionary dynamics.

Purpose of the Study:

• Develop a parametric sensitivity analysis method for periodic solutions of DDEs.
• Address challenges posed by phase shifts in sensitivity calculations.
• Apply the method to a gene expression model to explore evolutionary implications.

Main Methods:

• Focus on sensitivities of extrema and period to circumvent divergence issues caused by phase shifts.
• Compute amplitude sensitivities from extrema sensitivities.
• Utilize a specific oscillatory protein synthesis model with three delays.

Main Results:

• Successfully computed parametric sensitivities for periodic solutions, focusing on extrema and period.
• Demonstrated the utility of sensitivity analysis in characterizing the evolutionary landscape of a gene expression model.
• Identified directions of gradual evolutionary change based on computed sensitivities.

Conclusions:

• The developed sensitivity analysis provides a robust framework for studying DDEs with periodic solutions.
• This approach offers insights into the evolutionary trajectories of biological systems modeled by DDEs.
• Parametric sensitivities are valuable tools for understanding genotype-phenotype relationships and evolutionary adaptation.