|MadSci Network: Biochemistry|
This is an extremely complex question! For a decent answer I would suggest lifting original papers on the structure and mechanism of ATP synthase. These papers can be readily found via e.g. pubmed with proper keywords, write me if you can't find where to start reading.
Motive force for the ATP synthase is provided through Brownian motion, however if Brownian motion were the only factor, ATP synthase won't be able to function since that would have violated the energy conservation law as well as the laws of thermodynamics. So, obviously, some sort of energy is involved and that's where the proton gradient comes in - ATP synthase works as a miniature turbine driven by the flow of H+.
Chances are, you alread knew that, right ?
The gradient of protons ensures that the random action of Brownian motion is applied only in one direction, i.e. in simplest terms it acts as a spring loaded unidirectional locking pin. There is more to this story because protonation causes conformational changes in the protein, and so forth, which is why simple thermodynamics is insufficient to describe this system. Abstracting amino acids from their environment for simple calculations is also dangerous because their behavior is usually radically affected by the protein structure of which they are parts.
I hope this helps.
Keep in mind that when ATP is available in excess and one end of the ATP synthase is fixed to some sort of substrate, it does act as a small motor and can rotate macroscopic objects (which is shown on a world-famous video depicting fluorescently labeled actin filaments being 'twirled' around by immobilize ATP synthase units). Try to find this online, if you want extra excercise.
Liu H, Schmidt JJ, Bachand GD, Rizk SS, Looger LL, Hellinga HW, Montemagno CD. (2002) Control of a biomolecular motor-powered nanodevice with an engineered chemical switch. Nat Mater. 1:173-7.
Yasuda R, Noji H, Kinosita K Jr, Yoshida M. (1998) F1-ATPase is a highly efficient molecular motor that rotates with discrete 120 degree steps. Cell.93:1117-24.
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