[A mathematical model of conformational changes in membrane protein part of F0F1-ATP synthase]

The transformation of the electrochemical membrane proton gradient into the energy of chemical bond in adenosinetriphosphate is one of the most important biological processes occurring in the living cell. The main enzyme that directly catalyzes the synthesis of ATP from ADP and Pi in aerobic conditions is F0F1-ATP synthase. In the present study, conformational changes in membrane protein part of ATP synthase during its catalytic cycle were described in terms of dynamic equations of solid state rotation. It was shown that this process should be considered in the framework of classical mechanics. The time dependences of the angle rotation for the protein complex rotates around its central axis were oobtained. Possible types of rotation were analyzed. It was proved that, considering the modern level of knowledge and understanding of ATP synthase structure and function are taken into account, the minimal period of rotor turnover cannot be less than 10(-9) s. With regard for viscous friction and elastic tension in the central axis, the calculated time of whole turnover varies from 10(-6) to 10(-3) and depends on the set of parameters used. These results indicate the essential contribution of friction and elastic tension to the rotation dynamics of the rotor. It is suggested that the proposed model can be used as a part of the entire algorithm for computer simulation of ATP synthase.