Designing multi-parameter optimal control of a rotary molecular motor

Organisms use molecular machines to transduce energy between different forms, often at high efficiency. An example present in nearly every cell is the rotary motor F1-ATPase, which is crucial to converting energy from 'food' into a spendable energy currency, adenosine triphosphate (ATP). An energy-efficient design for this system ought to provide a selective advantage, and it is is indeed highly efficient in vivo. F1's dynamics can be imaged and controlled with single-molecule in vitro experiments, making it a powerful tool for understanding efficient design principles of molecular machines. Optimal-control protocols which vary a single control parameter have been designed previously for these experiments. However, in other systems, it has been found that accessing multiple control parameters can vastly improve efficiency. Here, we theoretically design multi-paramter control protocols for an F1 driving experiment. We find that the key design principles governing efficient control can be satisfied either by dynamic control of both parameters, or by dynamic control of a single parameter and a static control of the second. These results illustrate that accessing a new degree of dynamic control provides varying performance improvement in different systems.