  F$_{1}$-ATPase is a rotary molecular motor that \emph{in vivo} is subject to
strong nonequilibrium driving forces. There is great interest in understanding
the operational principles governing its high efficiency of free-energy
transduction. Here we use a near-equilibrium framework to design a non-trivial
control 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. Our
analysis points to a possible mechanism for energetically efficient driving of
F$_{1}$ \emph{in vivo} and provides insight into free-energy transduction for a
broader class of biomolecular and synthetic machines.
