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# Optimal control of the F${_1}$-ATPase molecular motor

Oct 2022

F$_{1}$-ATPase is a rotary molecular motor that \emph{in vivo} is subject tostrong nonequilibrium driving forces. There is great interest in understandingthe operational principles governing its high efficiency of free-energytransduction. Here we use a near-equilibrium framework to design a non-trivialcontrol protocol to minimize dissipation in rotating F$_{1}$ to synthesize ATP.We find that the designed protocol requires much less work than a naive(constant-velocity) protocol across a wide range of protocol durations. Ouranalysis points to a possible mechanism for energetically efficient driving ofF$_{1}$ \emph{in vivo} and provides insight into free-energy transduction for abroader class of biomolecular and synthetic machines.

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