Energy And Torque Of Rotation

Isolated F1-ATPase hydrolyzes ATP at a rate of about 300 molecules/s. For the load-free motor this would correspond to 100 revolutions/s because 3 ATP molecules are hydrolyzed per full rotation. The rotation of subunit y was shown to be a three-step process [35-39], with each step corresponding to the hydrolysis of 1 ATP molecule. At low ATP concentrations (1 /M) even smaller rotational substeps of 90° and 30° were resolved [39] that were attributed to the binding of ATP and the release of ADP. Using the F1-actin filament construct with 1 /m filament length and low ATP concentrations that only allow slow rotation, Yasuda et al. [40] observed distinct steps where the actin filament rested in 120° intervals.

Calculated from the rotational velocity, the torque reached during rotation is >40 pN-nm. By comparison, the sliding force that linear motors like myosin and kinesin (that were mentioned in the Introduction) generate is much smaller. Myosin produces a sliding force of 3-6 pN [41, 42] and kinesin a force of 5 pN [43]. The energy required to generate the torque in Fx is about 8 x 10-20 J for a 120° rotation step. The free energy that is provided by the hydrolysis of one ATP (one ATP is hydrolyzed for a 120° rotation) is about 9 x 10-20 J. In other words, Nature has designed here a nanomotor, the ATP synthase, which runs at more than 90% efficiency. The efficiency may even be higher if the viscoelastic mechanics of the ATPase-actin construct are considered.

In two "head-to-head" papers [44, 45], Junge and coworkers studied the effects of slow viscoelastic relaxation of the actin filament on the torque generated by the F0F1 holoenzyme. The construct they used is depicted in Figure 6.

Figure 6. Diagram of an experiment to determine the torque generated by the ATPase (for more details see [44]). The basis of the experiments to determine the torque generated by the F0F1-ATP synthase is as described in the legend to Figure 3. The F1 part is fixed to glass slides using oligo-histidine tags and a Ni-NTA-coated surface. The ring of c subunits carries Strep-tags that allow the actin filament to bind. The analysis of the viscoelasticity of the actin filament was performed using video microscopy in an inverted fluorescence microscope.

Figure 6. Diagram of an experiment to determine the torque generated by the ATPase (for more details see [44]). The basis of the experiments to determine the torque generated by the F0F1-ATP synthase is as described in the legend to Figure 3. The F1 part is fixed to glass slides using oligo-histidine tags and a Ni-NTA-coated surface. The ring of c subunits carries Strep-tags that allow the actin filament to bind. The analysis of the viscoelasticity of the actin filament was performed using video microscopy in an inverted fluorescence microscope.

The results of these experiments and theoretical analysis suggest that indeed the torque that is generated by the syn-thase (here being powered by the electrochemical proton gradient) exceeds 40 pN • nm and was estimated to be more in the range of 50 ± 6 pN • nm. There were only very small variations in the torque output of the motor, implying a soft, elastic power transmission between the two parts of the motor, F0 and Fx. This elastic transmission seems to be an essential feature to allow this biomotor to perform under such high turnover rates. The higher torque value that was calculated also shows that indeed this nanomotor works with almost perfect energy efficiency.

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