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Cytoskeletal filaments propelled by surface-bound motor proteins can be viewed as active polymers, a class of active matter. When constraints are imposed on their movements, the propelled cytoskeletal filaments show dynamic patterns distinct from equilibrium conformations. Pinned at their leading ends, propelled microtubules or actin filaments form rotating spirals, whose shape is determined by the interplay between motor forces and the mechanics of the cytoskeletal filaments. We simulated the spiral formations of microtubules propelled by kinesin motors in an overdamped dynamics framework, which in addition to the mechanics of the spiralling microtubule explicitly includes the mechanics of kinesin motors. The simulation revealed that spiral formation was initiated by localized buckling of microtubules near the pinned ends, and the conditions for occurrence of spiral formation were summarized in a phase diagram. The radius of the formed spirals scaled with the surface motor density with an exponent of approximately − 1/4, distinct from previous theoretical and simulation studies based on implicit modelling of motor proteins. This result can be understood as a consequence of the contributions of kinesin motors to the total elastic deformation energy, highlighting the importance of mechanics of motor proteins in the behaviour of the active polymers. These findings can be useful in accurate modelling of active polymers and in designing active polymer-based applications such as molecular shuttles driven by motor proteins. 

The catalytic performance of enzymes is largely perceived to be a property of the enzyme itself, altered by environmental conditions, such as temperature and pH. However, the maximal catalytic rates of enzymes differ up to 100-fold between in vivo and in vitro measurements, suggesting that a complex chemical system has additional effects on catalytic performance. In this work, we show that the initial rate of an enzyme can increase 3-fold due to the presence of a second enzyme, which uses the product of the first enzyme as its substrate. This enhancement may originate in an allosteric effect or result from binding competition for the product molecule by the second enzyme. 

Mechanical failure of biological nanostructures due to sustained force application has been studied in great detail. In contrast, fatigue failure arising from repeated application of subcritical stresses has received little attention despite its prominent role in engineering and potentially biology. Here, paclitaxel-stabilized microtubules are up to 256 times bent into sinusoidal shapes of varying wavelength and the frequency of breaking events are observed. These experiments allow the calculation of fatigue life parameters for microtubules. Repeated buckling due to 12.5% compression–equal to the compression level experienced by microtubules in contracting cardiomyocytes – results in failure after in average 5 million cycles, whereas at 20.0% compression failure occurs after in average one thousand cycles. The fatigue strength (Basquin) exponent B is estimated as − 0.054±0.009. 

Abstract Microtubules, cylindrical assemblies of tubulin proteins with a 25 nm diameter and micrometer lengths, are a central part of the cytoskeleton and also serve as building blocks for nanobiodevices. Microtubule breaking can result from the activity of severing enzymes and mechanical stress. Breaking can lead to a loss of structural integrity, or an increase in the numbers of microtubules. We observed breaking of taxol-stabilized microtubules in a gliding motility assay where microtubules are propelled by surface-adhered kinesin-1 motor proteins. We find that over 95% of all breaking events are associated with the strong bending following pinning events (where the leading tip of the microtubule becomes stuck). Furthermore, the breaking rate increased exponentially with increasing curvature. These observations are explained by a model accounting for the complex mechanochemistry of a microtubule. The presence of severing enzymes is not required to observe breaking at rates comparable to those measured previously in cells.