Abstract
Kinesin motors can induce a buckling instability in a microtubule with a fixed minus end. Here we show that by modifying the surface with a protein-repellent functionalization and using clusters of kinesin motors, the microtubule can exhibit persistent oscillatory motion resembling the beating of sperm flagella. The observed period is of the order of 1 min. From the experimental images we theoretically determine a distribution of motor forces that explains the observed shapes using a maximum likelihood approach. A good agreement is achieved with a small number of motor clusters acting simultaneously on a microtubule. The tangential forces exerted by a cluster are mostly in the range 0–8 pN toward the microtubule minus end, indicating the action of 1 or 2 kinesin motors. The lateral forces are distributed symmetrically and mainly below 10 pN, while the lateral velocity has a strong peak around zero. Unlike well-known models for flapping filaments, kinesins are found to have a strong “pinning” effect on the beating filaments. Our results suggest new strategies to utilize molecular motors in dynamic roles that depend sensitively on the stress built-up in the system.
Highlights
The propulsion of motile cells such as sperms relies on undulating bending of flagella, appendages of the cellular body able to perform periodic oscillations
We present experimental and theoretical results on a minimal system made of a single microtubule with a fixed end and a small number of kinesin-1 motor proteins that in the presence of ATP perform a continuous motion resembling flagellar beating
In this study we quantitatively analyze the buckling instabilities of single microtubules clamped at one end and subjected to the forces exerted by motor proteins
Summary
We report the quantitative analysis of buckling instabilities of clamped microtubules caused by compressive forces exerted by kinesin motors. We have the conjecture that the continuous buckling dynamics might be due to the reversible attachment of the motors to the surface, which was tailored to allow a binding that is sufficiently stable for activating the ’walk’ on the microtubule but so weak to dissociate under mechanical stimulus In this way the system self-organized by using the force of motor proteins that continuously rearranged by breaking and reforming bonds to the surface. We report an example of an autonomous molecular system that dynamically self-organizes through its elasticity and the interaction with the environment represented by the active forces exerted by motor proteins Assembling such minimal systems that can mimic the behavior of much more complex biological structures might help to unveil the basic mechanism underlying the beating of real cilia and flagella
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