Theoretical analysis of the $F_1$-ATPase experimental data

$F_1$-ATPase is a rotatory molecular motor fuelled by ATP nucleotides. This motor rotates in main discrete steps of $120^0$ with substeps of $\sim 80^0 + 40^0$. Different loads can be attached to the motor axis and experimental data show the dependence on the mean rotational velocity $\omega$ with respect to the external control parameters: the nucleotide concentration [ATP] and the friction of the load $\gamma_L$. In this work we present a theoretical analysis of the experimental data whose main results are: i) A derivation of a simple analytical formula for ${\omega}([ATP], \gamma_L)$ which compares favorably with experimental data; ii) The introduction of a two-state flashing ratchet model, exhibiting more specific experimental phenomenology ; iii) The derivation of an argument to obtain th e values of the substep sizes; iv) An analysis of the energy constraints of the model, and v) The theoretical analysis of the coupling ratio between the ATP consumend and the success of a forward step. Moreover, we also discuss the compatibility of our approach with recent experimental observations.

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