Data-driven identification of biological systems using multi-scale analysis.

Area of Science:

• Computational Biology
• Systems Biology
• Nonlinear Dynamics

Background:

• Biological systems exhibit complex multi-scale dynamics, posing challenges for traditional system identification methods.
• Existing techniques often require explicit equations, limiting their use with purely observational data.
• Accurate system identification is crucial for understanding and modeling biological processes.

Purpose of the Study:

• To develop a data-driven framework for accurate system identification of biological systems with multi-scale dynamics.
• To overcome limitations of traditional methods by integrating Sparse Identification of Nonlinear Dynamics (SINDy), Computational Singular Perturbation (CSP), and neural networks (NNs).
• To enable system identification from observational data without requiring explicit equations.

Main Methods:

• A novel framework integrating SINDy, CSP, and NNs was developed.
• Neural networks estimate the gradient of the vector field for CSP.
• CSP partitions data into subsets with similar dynamics, facilitating SINDy model identification.

Main Results:

• The framework successfully identified reduced models for the Michaelis-Menten model, outperforming SINDy on the full dataset.
• The method demonstrated robustness with stochastic data, accurately identifying models from noisy datasets.
• The algorithmic nature of the framework ensures system identification is independent of dataset dimensionality.

Conclusions:

• The proposed data-driven framework effectively addresses challenges in identifying multi-scale biological dynamics.
• Integration of SINDy, CSP, and NNs provides a powerful tool for data-driven system modeling.
• This approach enhances the applicability of system identification to complex biological data.