Irregular activity oscillations of a rotary molecular motor: A simple kinetic model of F1-ATPase

F 1 -ATPase is a catalytic part of the F 1 F o -ATP synthase molecular motor. The cooperative hydrolysis of ATP at three catalytic sites of F 1 -ATPase is accompanied by the rotation of the central γ-subunit inside a cylinder formed by three α-subunits and three β-subunits. Experimental works of different authors have shown that the γ-subunit rotates with irregular dwells. A simple kinetic model suggested in this article provides an explanation as to why dwells occur during the rotation of F 1 -ATPase. According to this model, rotation dwells happen as a result of deterministic chaos, which in turn occurs at rate constants that are close to those demonstrated experimentally. The time duration of dwells in the model is in agreement with that observed experimentally. Our model explains the known irregular occupancy of catalytic sites of F 1 -ATPase by nucleotides.