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Thermodynamically Consistent Modeling of ATP-Driven Cross-Bridge Dynamics in Muscle Contraction
1Department of Mathematics, University of California, Riverside, Riverside, CA, 92521, United States.
Biophysical Journal
|August 15, 2026
Summary
This study integrates ATP hydrolysis energy into muscle contraction models using the Energetic Variational Approach. The new framework thermodynamically links molecular cycling to macroscopic force generation, improving muscle mechanics understanding.
Area of Science:
- Biophysics
- Mechanobiology
- Computational Biology
Background:
- Muscle contraction is a complex chemomechanical process driven by ATP hydrolysis.
- Existing models face challenges in thermodynamically linking molecular-level ATP energy to macroscopic force generation.
- A unified framework is needed to connect microscopic cross-bridge cycling with macroscopic muscle function.
Purpose of the Study:
- To develop a thermodynamically consistent framework integrating ATP hydrolysis energy into cross-bridge models.
- To connect microscopic motor cycling to macroscopic force generation in muscle contraction.
- To derive effective cross-bridge kinetics from fundamental principles.
Main Methods:
- Utilized the Energetic Variational Approach (EnVarA).
- Formulated a three-state Fokker-Planck-jump model for cross-bridge densities on free-energy landscapes.
- Treated ATP, ADP, and Pi as reacting and diffusing chemical species coupled to cross-bridge dynamics.
Main Results:
- Developed a unified framework combining Hill's cycle-affinity and Huxley's sliding-filament mechanics.
- Reduced the model to a two-state molecular motor description and a Huxley-type transport-reaction equation.
- Derived effective attachment/detachment rates from underlying physics, showing strain, ATP, and phosphate dependence.
- Reproduced key velocity-dependent trends and a Hill-like force-velocity relation.
Conclusions:
- The EnVarA framework provides a thermodynamically consistent method to model muscle contraction.
- The derived cross-bridge kinetics offer a more fundamental basis than phenomenological parameters.
- The model successfully bridges molecular energetics to macroscopic muscle mechanics, advancing understanding of chemomechanical energy transduction.
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