Physical Principles of Size and Frequency Scaling of Active Cytoskeletal Spirals

Cytoskeletal filaments transported by surface immobilized molecular motors with one end pinned to the surface have been observed to spiral in a myosin-driven actin 'gliding assay'. The radius of the spiral was shown to scale with motor density with an exponent of -1/3, while the frequency was theoretically predicted to scale with an exponent of 4/3. While both the spiraling radius and frequency depend on motor density, the theory assumed independence of filament length, and remained to be tested on cytoskeletal systems other than actin-myosin. Here, we reconstitute dynein-driven microtubule spiraling and compare experiments to theory and numerical simulations. We characterize the scaling laws of spiraling MTs and find the radius dependence on force density to be consistent with previous results. Frequency on the other hand scales with force density with an exponent of ~1/3, contrary to previous predictions. We also predict that the spiral radius scales proportionally and the frequency scales inversely with filament length, both with an exponent of ~1/3. A model of variable persistence length best explains the length dependence observed in experiments. Our findings that reconcile theory, simulations, and experiments improve our understanding of the role of cytoskeletal filament elasticity, mechanics of microtubule buckling and motor transport and the physical principles of active filaments.