Learning stochastic reaction-diffusion models from limited data using spatiotemporal features.

Area of Science:

• Computational Biology
• Systems Biology
• Biophysics

Background:

• Biological pattern formation relies on stochastic reaction-diffusion systems.
• Current modeling relies on handcrafted stochastic partial differential equations (PDEs), requiring extensive tuning.
• Data scarcity and noise hinder data-driven modeling of these systems.

Purpose of the Study:

• To develop a data-driven solution for learning stochastic reaction-diffusion models from limited and noisy data.
• To address the inverse problem of inferring model parameters and structure from spatiotemporal data.
• To enable accurate modeling of biological pattern formation with interpretable components.

Main Methods:

• Optimized learning of spatiotemporal features, including stochastic dynamics and pattern formation.
• Incorporated sparsity enforcement to identify parsimonious model structures.
• Validated the approach on simulated excitable systems and real live-cell imaging data.

Main Results:

• Successfully learned stochastic reaction-diffusion models from data with varying scarcity and noise levels.
• Identified novel activator-inhibitor models with interpretable structures.
• Demonstrated robustness with noisy, low-resolution live-cell imaging data.

Conclusions:

• The developed method offers a generalizable approach to learning governing stochastic PDEs.
• Enhances the ability to model and understand complex biological spatiotemporal systems from limited real-world data.
• Facilitates deeper insights into critical cellular processes regulated by dynamic molecular waves.