Elimination of the initial value parameters when identifying a system close to a Hopf bifurcation

Area of Science:

• Biochemistry
• Systems Biology
• Dynamical Systems Theory

Background:

• System identification of biological systems is often hampered by incomplete measurements.
• Estimating initial states and kinetic parameters simultaneously is a common challenge.
• Current methods for initial state estimation can be complex and prone to local minima.

Purpose of the Study:

• To generalize the steady-state approach for initial parameter estimation in biological systems.
• To develop a method applicable to systems starting on the centre manifold near a Hopf bifurcation.
• To simplify the estimation of initial state parameters in oscillatory biochemical systems.

Main Methods:

• Generalization of the steady-state approach to systems near a Hopf bifurcation.
• Utilizing centre manifold and normal form reduction to reveal system structure.
• Solving initial value parameters within an optimization sub-problem at each estimation step.
• Demonstrating the method on the Brusselator model.

Main Results:

• A novel method for estimating initial state parameters in biological system identification.
• The approach simplifies parameter estimation for systems exhibiting stationary oscillations.
• The method avoids the need for differential equation integration and mitigates local minima problems.
• Successful application and validation using the Brusselator model.

Conclusions:

• The generalized approach offers a significant advantage for system identification of biological systems, particularly those near Hopf bifurcations.
• This method provides a more straightforward and robust way to handle initial state estimation in oscillatory systems.
• The technique has potential applications in analyzing real-world biochemical data, such as from yeast glycolysis.