Tailored parameter optimization methods for ordinary differential equation models with steady-state constraints.

Area of Science:

• Systems biology
• Computational biology
• Mathematical modeling

Background:

• Ordinary differential equation (ODE) models are crucial for describing biological processes.
• Parameter estimation from experimental data enhances ODE model predictive power.
• Steady-state constraints from perturbation experiments are valuable but often cause optimization convergence problems.

Purpose of the Study:

• To propose novel methods for solving optimization problems with steady-state constraints.
• To improve convergence properties and computational efficiency in parameter estimation for biological models.

Main Methods:

• Developed two new methods: one using manifold optimization with a retraction operator, and another based on the continuous analogue of the optimization problem (an ODE).
• Methods exploit local geometry and stability properties of the steady-state manifold without requiring its parameterization.
• Evaluated methods using a toy example and two applications, including a novel dataset for Raf/MEK/ERK signaling.

Main Results:

• The proposed methods demonstrated superior convergence properties compared to state-of-the-art techniques in systems and computational biology.
• Achieved significantly lower average computation time per converged start.
• Analysis of the Raf/MEK/ERK signaling dataset yielded novel insights into feedback regulation.

Conclusions:

• The presented methods effectively address convergence issues in nonlinear steady-state constrained optimization problems.
• Offer a robust alternative to current methods in systems and computational biology, recovering convergence properties similar to those exploiting analytical steady-state expressions.