Theoretical Analysis of the F1-ATPase Experimental Data

F1-ATPase is a rotatory molecular motor fueled by ATP nucleotides. Different loads can be attached to the motor axis to show that it rotates in main discrete steps of 120° with substeps of ∼80° and 40°. Experimental data show the dependence on the mean rotational velocity ω with respect to the external control parameters: the nucleotide concentration [ATP] and the friction of the load γL. In this work we present a theoretical analysis of the experimental data whose main results are: 1), A derivation of a simple analytical formula for ω([ATP], γL) that compares favorably with experiments; 2), The introduction of a two-state flashing ratchet model that exhibits experimental phenomenology of a greater specificity than has been, to our knowledge, previously available; 3), The derivation of an argument to obtain the values of the substep sizes; 4), An analysis of the energy constraints of the model; and 5), The theoretical analysis of the coupling ratio between the ATP consumed and the success of a forward step. We also discuss the compatibility of our approach with recent experimental observations.