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Circuit Reduction of Heterogeneous Nonequilibrium Systems
1Green Center for Molecular, Computational, and Systems Biology, Department of Biophysics, Center for Alzheimer's and Neurodegenerative Diseases, University of Texas Southwestern Medical Center, Dallas, Texas 75235, USA.
Physical Review Letters
|December 4, 2020
Summary
This study introduces a novel mapping of complex biological systems to battery-resistor circuits, revealing universal principles for predicting behavior in heterogeneous nonequilibrium systems. This approach simplifies complex dynamics and generalizes fundamental relations for system design and evolution.
Area of Science:
- Physics
- Biophysics
- Systems Biology
Background:
- Predicting heterogeneous nonequilibrium systems is analytically challenging.
- Complex biological systems lack unifying principles for behavior prediction.
Purpose of the Study:
- Introduce a new mapping from dynamical systems to battery-resistor circuits.
- Develop unifying principles for heterogeneous nonequilibrium systems.
Main Methods:
- Transforming dynamical systems into equivalent battery-resistor circuits.
- Analyzing system behavior using Thevenin equivalent resistors.
- Deriving steady-state relations from the circuit mapping.
Main Results:
- Arbitrary heterogeneous transitions reduce to a single Thevenin equivalent resistor.
- Resistors and driving sources fully describe system behavior.
- Directional symmetry of resistors yields universal nonequilibrium theorems.
- Derived two general steady-state relations, including a generalized Onsager reciprocal relation.
Conclusions:
- The mapping provides natural variables for studying heterogeneous nonequilibrium systems.
- The results offer a new perspective on biological complexity.
- The findings suggest principles for designing or evolving systems to maximize response.
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