Characterizing control between interacting subsystems with deep Jacobian estimation.

Area of Science:

• Neuroscience
• Control Theory
• Computational Biology

Background:

• Biological systems function through complex, dynamic interactions between subsystems.
• Current methods often use linear models, failing to capture nonlinearities crucial for biological complexity.
• Control theory offers a framework to understand directed interactions, but requires advanced methods for nonlinear systems.

Purpose of the Study:

• To develop a data-driven, nonlinear control-theoretic framework for characterizing subsystem interactions.
• To address limitations of linear methods in modeling complex biological dynamics.
• To enable precise inference and manipulation of control within dynamical systems.

Main Methods:

• Devised a nonlinear control-theoretic framework using the Jacobian of dynamics.
• Proposed JacobianODE, a deep learning method to estimate Jacobians from time-series data.
• Validated JacobianODE on complex systems, including high-dimensional chaos.

Main Results:

• JacobianODE significantly outperforms existing Jacobian estimation methods.
• Demonstrated increased control of a "sensory" area over a "cognitive" area in a trained recurrent neural network (RNN).
• Successfully used JacobianODE to precisely control the RNN's behavior.

Conclusions:

• The JacobianODE provides a powerful tool for understanding nonlinear interactions in biological subsystems.
• This framework bridges theory and data for analyzing complex dynamical systems.
• Enables new possibilities for dissecting and manipulating biological computation.