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Energy-based analysis of biochemical oscillators using bond graphs and linear control theory
Peter Gawthrop1,2, Michael Pan1,2,3,4,5
1Systems Biology Laboratory, School of Mathematics and Statistics, University of Melbourne, Melbourne, Victoria 3010, Australia.
Royal Society Open Science
|May 1, 2025
Summary
This study introduces a novel method for analyzing biochemical oscillators by integrating bond graph modeling with feedback control theory. The phase margin is proposed as a key indicator for understanding and designing oscillating biological systems.
Area of Science:
- Systems Biology
- Biochemical Engineering
- Control Theory
Background:
- Oscillation is crucial for many biological functions.
- Understanding biochemical oscillators is essential for systems biology.
- Existing models may lack a unified framework for analysis and synthesis.
Purpose of the Study:
- To develop a novel approach for analyzing and synthesizing biochemical oscillators.
- To integrate bond graph modeling with classical feedback control theory.
- To identify a simple indicator for oscillation presence and characteristics.
Main Methods:
- Energy-based modeling of biochemical systems using bond graphs.
- Application of classical feedback control theory, including frequency-response analysis.
- Formalization of active and passive feedback interplay.
- Utilizing phase margin as a scalar indicator for oscillations.
Main Results:
- Oscillation is shown to depend on the interplay between active and passive feedback.
- Phase margin is proposed as a simple scalar indicator for oscillation.
- Demonstrated how phase margin can assess the impact of system structure and parameters on oscillation.
- The combined approach offers a new methodology for analyzing and designing biochemical oscillators.
Conclusions:
- The integration of bond graph approach and feedback control theory provides a powerful new methodology for systems biology.
- This approach facilitates the analysis and potential synthesis of biochemical oscillators.
- Phase margin serves as a valuable metric for understanding and engineering biological oscillations.
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