Fast integration-based prediction bands for ordinary differential equation models.

Area of Science:

• Systems Biology
• Computational Biology
• Mathematical Modeling

Background:

• Mathematical models are crucial for understanding biological processes and diseases.
• Parameter uncertainties in models, arising from experimental data limitations, hinder accurate predictions.
• High-dimensional biochemical network models face computational challenges with traditional uncertainty propagation methods.

Purpose of the Study:

• To develop a computationally feasible approach for calculating prediction and confidence bands for mechanistic dynamic models.
• To provide reliable and smooth point-wise prediction and confidence bands across the entire time-course of model predictions.
• To enable better experimental design and model discrimination in systems biology.

Main Methods:

• Developed an integration framework with correction mechanisms for ordinary differential equation systems.
• Utilized a profile likelihood approach for calculating prediction and confidence intervals.
• Tested the framework on established cellular signaling models and performed efficiency analysis.

Main Results:

• Achieved reliable and smooth point-wise prediction and confidence bands for assessing model uncertainty over time.
• Demonstrated computational feasibility and efficiency compared to repeated profile likelihood calculations.
• Validated the approach on three established models for cellular signaling.

Conclusions:

• The proposed method provides accurate confidence and prediction intervals for high-dimensional nonlinear models.
• This approach overcomes the limitations of classical and sampling methods for uncertainty propagation.
• The framework is implemented in the freely available Data2Dynamics software package.