Scaling of microtubule spirals driven by dyneins: collective effect of microtubule and motor mechanics.

Molecular motor-driven spirals of actin filaments pinned at one end while driven along their length were seen to be scale-independent. The spiral radius and frequency dependence on force was predicted to follow a universal law, validated by actin-myosin experiments. However, the theory was primarily compared to acto-myosin spirals, assuming no effect of filament length and that motor velocity is additive with density. Here, we reconstitute microtubule spirals driven by dynein transport and end-pinning and find that spiral size scales with force with an exponent α approximately -1/3, consistent with theoretical predictions. However, spiral radius scaling with length deviates from the theory and can be explained by a 'variable persistence length' model. The previously predicted exponent of frequency scaling with force β approximately 4/3 is not observed in experiments. A model that assumes constant collective transport velocity of motors regardless of density predicts the scaling exponent β approximately 1/3, comparable to that observed experimentally. Our work demonstrates that microtubule motor systems deviate from the general scaling laws of cytoskeletal spirals predicted previously, based on both detailed mechanics of microtubules and collective force generation of motors.