Ensemble velocity of non-processive molecular motors with multiple chemical states

Theoretical efficiency limits and speed-efficiency trade-off in myosin motors

Muscle myosin is a non-processive molecular motor generates mechanical work when cooperating in large ensembles. During its cyle, each individual motor keeps attaching and detaching from the actin filament. The random nature of attachment and detachment inevitably leads to losses and imposes theoretical limits on the energetic efficiency. Here, we numerically determine the theoretical efficiency limit of a classical myosin model with a given number of mechano-chemical states. All parameters that are not bounded by physical limits (like rate limiting steps) are determined by numerical efficiency optimization. We show that the efficiency is limited by the number of states, the stiffness and the rate-limiting kinetic steps. There is a trade-off between speed and efficiency. Slow motors are optimal when most of the available free energy is allocated to the working stroke and the stiffness of their elastic element is high. Fast motors, on the other hand, work better with a lower and asymmetric stiffness and allocate a larger fraction of free energy to the release of ADP. Overall, many features found in myosins coincide with the findings from the model optimization: there are at least 3 bound states, the largest part of the working stroke takes place during the first transition, the ADP affinity is adapted differently in slow and fast myosins and there is an asymmetry in elastic elements.

Embedding dual function into molecular motors through collective motion

Protein motors, such as kinesins and dyneins, bind to a microtubule and travel along it in a specific direction. Previously, it was thought that the directionality for a given motor was constant in the absence of an external force. However, the directionality of the kinesin-5 Cin8 was recently found to change as the number of motors that bind to the same microtubule is increased. Here, we introduce a simple mechanical model of a microtubule-sliding assay in which multiple motors interact with the filament. We show that, due to the collective phenomenon, the directionality of the motor changes (e.g., from minus- to plus- end directionality), depending on the number of motors. This is induced by a large diffusive component in the directional walk and by the subsequent frustrated motor configuration, in which multiple motors pull the filament in opposite directions, similar to a game of tug-of-war. A possible role of the dual-directional motors for the mitotic spindle formation is also discussed. Our framework provides a general mechanism to embed two conflicting tasks into a single molecular machine, which works context-dependently.

Working stroke of the kinesin-14, ncd, comprises two substeps of different direction

Single-molecule experiments have been used with great success to explore the mechanochemical cycles of processive motor proteins such as kinesin-1, but it has proven difficult to apply these approaches to nonprocessive motors. Therefore, the mechanochemical cycle of kinesin-14 (ncd) is still under debate. Here, we use the readout from the collective activity of multiple motors to derive information about the mechanochemical cycle of individual ncd motors. In gliding motility assays we performed 3D imaging based on fluorescence interference contrast microscopy combined with nanometer tracking to simultaneously study the translation and rotation of microtubules. Microtubules gliding on ncd-coated surfaces rotated around their longitudinal axes in an [ATP]- and [ADP]-dependent manner. Combined with a simple mechanical model, these observations suggest that the working stroke of ncd consists of an initial small movement of its stalk in a lateral direction when ADP is released and a second, main component of the working stroke, in a longitudinal direction upon ATP binding.