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Updated: May 27, 2026

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Published on: May 27, 2020
Periodic one-dimensional hopping model with transitions between nonadjacent states
1Shanghai Key Laboratory for Contemporary Applied Mathematics, Centre for Computational Systems Biology, School of Mathematical Sciences, Fudan University, Shanghai 200433, China. xyz@fudan.edu.cn
This study explores a modified hopping model for molecular motors, enabling jumps of ±1 or ±2 states. Researchers derived key motor functions, validating results with synthetic rotary molecular motors.
Area of Science:
- Physics
- Chemistry
- Materials Science
Background:
- Microscopic particle motion in thermal noise is often modeled using hopping models.
- Recent experiments reveal complex multi-step transitions in light-driven rotary molecular motors.
Purpose of the Study:
- To theoretically investigate a modified periodic one-dimensional hopping model.
- To analyze motor dynamics beyond simple nearest-neighbor transitions.
Main Methods:
- Developed a modified periodic one-dimensional hopping model with arbitrary period N.
- Analyzed the model to derive key kinetic parameters.
Main Results:
- Obtained expressions for mean velocity, effective diffusion constant, and mean dwell time per cycle.
- The model accounts for forward (i+1, i+2) and backward (i-1, i-2) state transitions.
Conclusions:
- The theoretical model accurately describes the behavior of synthetic rotary molecular motors.
- This work provides a framework for understanding complex molecular motor dynamics.
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