Stiffness of γ subunit of F(1)-ATPase

F(1)-ATPase is a molecular motor in which the γ subunit rotates inside the α(3)β(3) ring upon adenosine triphosphate (ATP) hydrolysis. Recent works on single-molecule manipulation of F(1)-ATPase have shown that kinetic parameters such as the on-rate of ATP and the off-rate of adenosine diphosphate (ADP) strongly depend on the rotary angle of the γ subunit (Hirono-Hara et al. 2005; Iko et al. 2009). These findings provide important insight into how individual reaction steps release energy to power F(1) and also have implications regarding ATP synthesis and how reaction steps are reversed upon reverse rotation. An important issue regarding the angular dependence of kinetic parameters is that the angular position of a magnetic bead rotation probe could be larger than the actual position of the γ subunit due to the torsional elasticity of the system. In the present study, we assessed the stiffness of two different portions of F(1) from thermophilic Bacillus PS3: the internal part of the γ subunit embedded in the α(3)β(3) ring, and the complex of the external part of the γ subunit and the α(3)β(3) ring (and streptavidin and magnetic bead), by comparing rotational fluctuations before and after crosslinkage between the rotor and stator. The torsional stiffnesses of the internal and remaining parts were determined to be around 223 and 73 pNnm/radian, respectively. Based on these values, it was estimated that the actual angular position of the internal part of the γ subunit is one-fourth of the magnetic bead position upon stalling using an external magnetic field. The estimated elasticity also partially explains the accommodation of the intrinsic step size mismatch between F(o) and F(1)-ATPase.