On validation and invalidation of biological models

Area of Science:

• Mathematical Biology
• Systems Biology
• Computational Biology

Background:

• Multiple mathematical models often describe the same biological system, leading to confusion about their correctness.
• Model validation is a misnomer; models can only be invalidated, not validated, against experimental data.
• Complex nonlinear models are difficult to invalidate through simulation, leading to the process being overlooked.

Purpose of the Study:

• To develop methods for invalidating competing ordinary differential equation (ODE) based models of biological systems.
• To address the challenge of invalidating nonlinear models with parametric uncertainty using experimental data.
• To establish a framework for distinguishing between correct and incorrect biological models.

Main Methods:

• Emphasized the interplay between system identification and model invalidation.
• Developed a method to obtain a lower bound on the error between model predictions and experimental data.
• Formulated an algorithmic methodology for discrete-time and continuous-time model invalidation using Semidefinite Programming.

Main Results:

• Demonstrated approaches to invalidate competing ODE models using experimental data.
• Showcased that exhaustive simulation is intractable and inconclusive for complex nonlinear models.
• Presented a framework for invalidating ODE models using convex optimization techniques.

Conclusions:

• Biological models derived from data can never be definitively validated.
• Invalidating models incompatible with data is crucial for understanding biological function.
• The presented convex optimization framework provides an exact solution for model invalidation with polynomial time complexity.