Application of rigid body mechanics to theoretical description of rotation within F0F1-ATP synthase

ATP synthase catalyses the formation of ATP from ADP and P(i) and is powered by the diffusion of protons throughout membranes down the proton electrochemical gradient. The protein consists of a water-soluble F(1) and a transmembrane F(0) proton transporter part. It was previously shown that the ring of membrane subunits rotates past a fixed subunit during catalytic cycle of the enzyme. However, many parameters of this movement are still unknown. In the present study the mutual protein movement in the membrane part of F(0)F(1)-ATP syntase has been analysed within the framework of rigid body mechanics. On the base of available experimental data it was shown that electrostatic interaction of two charged amino acids residues is able to supply quite enough energy for the rotation. The initial torque, which caused the rotation, was estimated as 3.7 pN nm and for this pattern the angular movement of c subunits complex could not physically have a period less than 10(-9)s. If membrane viscosity and elastic resistance were taken into account then the time of a whole turnover could rise up to 6.3 x 10(-3)s. It is remarkable that rotation will take place only under condition when the elasticity (Young's) module of the central stalk (gamma subunit and other minor subunits) is less than 5.0 x 10(7)N/m(2). Thus, for generally accepted structural parameters of ATP synthase, two-charge electrostatic interaction model does not permit rotation of the rotor if elastic properties of the central stalk are tougher than mentioned above. In order to explain the rotation under that condition one should either suppose a shorter distance between subunit a and c subunits complex or assume interaction of more than two charged amino acids residues.