Scaling Laws of Motor Driven Spiraling Microtubules

In a gliding assay, molecular motors drive the directed transport of filaments. When the leading tip

of a filament is translationally constrained but retains a rotational degree of freedom (i.e., a pinned fil-

ament), it undergoes a spiraling motion. In the actin–myosin system, the radius of a spiraling filament

scales with force density as r ∼ f^−1/3, while the frequency is predicted to scale as ν ∼ f^4/3, assuming

motors act as tangential force generators. These results, proposed as universal, have not been tested

in microtubules, which are elastically anisotropic and whose persistence length(ℓ_p), whether constant

or variable, remains debated. To investigate the universality of these scaling relationships, we use

theory and numerical simulations to reconcile the scaling behavior of spiraling microtubules

driven by cytoplasmic dynein. We show that while radius scaling agrees with previous reports,

frequency instead scales as ν ∼ f^1/3, due to simplified assumptions in prior studies. Both spiraling

radius and frequency scale with filament length, r ∼ ℓ_p^1/3 and ν ∼ ℓ_p^−1/3, and are better explained by

a variable persistence length. Our work refines the understanding of scaling in motor-driven filaments

and provides new insights into microtubule mechanics.