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Analysis of spontaneous oscillations for a three-state power-stroke model
Takumi Washio1, Toshiaki Hisada1, Seine A Shintani2
1Graduate School of Frontier Sciences, The University of Tokyo, 178-4 Wakashiba, Kashiwa, Chiba 277-0871, Japan.
Physical Review. E
|March 17, 2017
Summary
This study reveals that molecular motor oscillations depend on rate constants tied to elastic element strains, not just detachment rates. Our three-state model accurately predicts oscillatory behavior using experimentally validated parameters.
Area of Science:
- Biophysics
- Molecular Biology
- Mechanobiology
Background:
- Spontaneous oscillations in molecular motors are crucial for biological functions.
- Previous models often focused on detachment rates, limiting explanatory power.
Purpose of the Study:
- To elucidate the mechanism of spontaneous oscillations in molecular motors driven by the power stroke principle.
- To identify the key factors governing these oscillations using a three-state model.
Main Methods:
- Linear stability analysis around a stationary solution.
- Rank-1 updated matrix system to couple molecular and sarcomeric dynamics.
- Derivation of analytical representations for Jacobian matrix eigenmodes.
Main Results:
- Essential oscillation conditions derived in terms of rate constants for power and reversal strokes.
- Demonstrated that strains in elastic elements, not detachment rates, are key.
- Numerical model successfully reproduced experimentally observed oscillatory behavior.
Conclusions:
- The three-state power stroke model provides a more accurate mechanism for molecular motor oscillations.
- Oscillations are characterized by two eigenmodes correlating to sarcomeric lengthening and shortening speeds.
- Hopf bifurcation analysis reveals the origin of these oscillatory modes.
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