Length dependence of displacement fluctuations and velocity in microtubule sliding movement driven by sea urchin sperm outer arm β dynein in vitro

Emergence of flagellar beating from the collective behavior of individual ATP-powered dyneins

“…Followed by this brief event, the dynein again attaches itself to the microtubule (i.e., another dynein in the dynein-coated bead in the experiments) and again starts applying the sliding force, which overcomes the spring force and slides the microtubule forward, see To understand the collective behavior of the dyneins and their interaction with the neighboring microtubules, various microtubule-motility/gliding assay experiments were carried out [25,[29][30][31][32][33][34]. In these gliding assay experiments, many dyneins coated on the substrate are interacting with (isolated) microtubules of various lengths [29,32]. The dyneinmicrotubule interaction and the cyclic conformational change of the dynein molecule leads to guided translocation of the microtubules over the substrate.…”

“…The dyneinmicrotubule interaction and the cyclic conformational change of the dynein molecule leads to guided translocation of the microtubules over the substrate. The sliding velocity of the microtubules has been found to increase with the length of the microtubules until a saturation velocity (U max ) is reached for large microtubule lengths [29,32]. As the number of dyneins that can interact with a microtubule is limited by the length of the microtubule itself (due to the regular spacing of the dyneins), the sliding velocity increases due to the increasing number of interacting dyneins [29][30][31][32].…”

“…The sliding velocity of the microtubules has been found to increase with the length of the microtubules until a saturation velocity (U max ) is reached for large microtubule lengths [29,32]. As the number of dyneins that can interact with a microtubule is limited by the length of the microtubule itself (due to the regular spacing of the dyneins), the sliding velocity increases due to the increasing number of interacting dyneins [29][30][31][32]. A step-size at the nanometer scale during the time period of a few milliseconds (typical for the ATP hydrolysis cycle) will lead to a microtubule velocity on the order of a few micrometers per second, as observed experimentally [27].…”

“…We assume here that the dyneins have a low duty ratio (f dynein = 0.15) and we account for the step-size per hydrolysis cycle (δ step = 8 nm) of a dynein molecule. [29][30][31][32]. The sliding velocity due to just one dynein can be theoretically approximated (without accounting for the viscosity) by δ step /t cycle , while the maximum sliding velocity U max = δ step /t a , which represents the condition that the maximum sliding velocity is limited by the rate of conformation change responsible for the dynein power stroke.…”

“…1b). The force-transduction of individual dynein molecules has been studied experimentally via optical-trap nanometry [23,[25][26][27][28] and their collective behavior has been analyzed through microtubule-motility assays [25,[29][30][31][32][33][34]. It has been generally accepted that the dyneins apply a sliding force during their working cycle leading to the generation of bending of the microtubules [8,10,[35][36][37].…”