Hinge-Bending Transitions during F1 ATPase Function: Ligand-Rocked Brownian Motion?

The $\beta $-subunit hinge of the F1-ATPase enzyme is a type of allosteric protein, with alternative (T-open) and [R-closed] states. In the absence of an inducing ligand, such as [ATP], the hinge is on a ground-state energy surface, whose minimum dictates the (open) state. In the presence of [ATP], it is on an excited-state surface, whose minimum now dictates the [closed] state. Thus, during the F1 ATPase catalytic cycle, the hinge undergoes two opposite bending transitions. First, it is driven by [ATP] into the excited-state force-balanced [closed] state. After loss of [$\gamma $-Pi], it relaxes back to the (open) state. We study these transitions by regarding the $\beta $-subunit hinge as a type of Brownian particle moving in a double-well potential energy function. We find that [ATP] binding rocks (tilts) this energy function ``forward,'' biasing diffusion of the particle towards the [closed] state. Likewise, loss of [$\gamma $-phosphate] rocks it ``back,'' biasing diffusion toward the (open) state. We conclude that regarding the $\beta $-subunit hinge as a ligand-rocked Brownian particle may yield physical insight into operation of this molecular motor.