Efficiently Driving F1 Molecular Motor in Experiment by Suppressing Nonequilibrium Variation

<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi mathvariant="normal">F</a:mi></a:mrow><a:mrow><a:mn>1</a:mn></a:mrow></a:msub></a:mrow></a:math>-ATPase (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mrow><d:msub><d:mrow><d:mi mathvariant="normal">F</d:mi></d:mrow><d:mrow><d:mn>1</d:mn></d:mrow></d:msub></d:mrow></d:math>) is central to cellular energy transduction. Forcibly rotated by another motor <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:msub><g:mrow><g:mi mathvariant="normal">F</g:mi></g:mrow><g:mrow><g:mi mathvariant="normal">o</g:mi></g:mrow></g:msub></g:mrow></g:math>, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:msub><k:mrow><k:mi mathvariant="normal">F</k:mi></k:mrow><k:mrow><k:mn>1</k:mn></k:mrow></k:msub></k:mrow></k:math> catalyzes adenosine triphosphate (ATP) synthesis by converting mechanical work into chemical free energy stored in the molecule ATP. The details of how <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mrow><n:msub><n:mrow><n:mi mathvariant="normal">F</n:mi></n:mrow><n:mrow><n:mi mathvariant="normal">o</n:mi></n:mrow></n:msub></n:mrow></n:math> drives <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mrow><r:msub><r:mrow><r:mi mathvariant="normal">F</r:mi></r:mrow><r:mrow><r:mn>1</r:mn></r:mrow></r:msub></r:mrow></r:math> are not fully understood; however, evaluating efficient ways to rotate <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mrow><u:msub><u:mrow><u:mi mathvariant="normal">F</u:mi></u:mrow><u:mrow><u:mn>1</u:mn></u:mrow></u:msub></u:mrow></u:math> could provide fruitful insights into this driving since there is a selective pressure to improve efficiency. Here, we show that rotating <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mrow><x:msub><x:mrow><x:mi mathvariant="normal">F</x:mi></x:mrow><x:mrow><x:mn>1</x:mn></x:mrow></x:msub></x:mrow></x:math> with an angle clamp is significantly more efficient than a constant torque. Our experiments, combined with theory and simulation, indicate that the angle clamp significantly suppresses the nonequilibrium variation that contributes to the futile dissipation of input work.