The match implies 100% efficiency for the conversion of the Gibbs free energy of ATP hydrolysis into mechanical work performed on the elastically strained filament. This is not surprising given the approximate thermodynamic equilibrium of the enzyme (long)-filament construct. It is more informative to say that there is no slip between ATP hydrolysis in F1 and rotation in FO under the given conditions.2 Rotary slip in FOF1 in chloroplasts and bacteria has been detected, but only under single-site occupancy, that is, at nucleotide concentrations significantly below 100 nM. The momentary torque can be larger (for example, during a particular power stroke) or smaller (during a kinetic dwell) than its equilibrium average. This may account for the still puzzling independence of the torque from the ATP concentration in the nanomolar to millimolar range (see ref. 2 for a review). It is worth mentioning that the other technique for determining the torque from the rate of rotation underestimates its magnitude because it neglects viscous flow coupling between the filament and the enzyme-supporting surface.
The mismatch of gear ratios may actually make the machine more efficient. “It has also shown that an elastic power transmission is indispensable for a high rate of coupled turnover under load,” they said. “It increases the rate by several orders of magnitude over that of a rigidly coupled double motor..... The elastic power transmission both increases the ‘kinetic efficiency’ of the coupled motors ... and allows the double motor to function with different gears in different organisms.” In conclusion, they noted five questions about ATP synthase that remain to be answered since the true mechanical nature of this rotary engine came to light around 1997 (and won its discoverers the Nobel Prize). Surrounding those questions were expressions of marvel at the design of this machine:
ATP synthase (FOF1) is a molecular machine that combines the electrical, mechanical and chemical aspects of enzyme function. These are neatly separated, readily attributed to its different subunits, and reasonably well understood thanks to a wealth of structural and kinetic data. However, understanding the enzyme fully at a molecular level will require considerable efforts, both experimental and theoretical. There are five outstanding issues.... Only when we have solved these problems will we come close to a full understanding of this remarkable piece of cellular machinery.
There are other examples of rotary engines in living cells, including the bacterial flagellum (which is an order of magnitude larger), and helicases (the machines that unwind DNA). There are also two other spinoffs of ATP synthase (if you’ll pardon the pun), built on the same principle, that perform other functions (see 02/24/2003 and 12/22/2003 for information on of them). Most other cellular machines, like the actins and kinesins, operate in a linear fashion. “The coupled operation of two rotary motors, one electrical (FO) and one chemical (F1), is unique,” the authors said. “In FOF1-ATPase there is no fine-tuning of the two stepping motors;3 instead, their coupled operation is smoothed and speeded by elastic power transmission, which accounts for its high kinetic efficiency and robust function..” Scientists used to believe life was incapable of utilizing the wheel. Now they know better. Speaking of elastic power transmission producing high kinetic efficiency and robust function, they mentioned something that should tempt a biophysicist to investigate: “Other nanomotors probably share this feature.”
1. Junge, Seilaff and Engelbrecht, “Torque generation and elastic power transmission in the rotary FOF1-ATPase,” Nature 459, 364-370 (21 May 2009) | doi:10.1038/nature08145. 2. F0 refers to the rotating part of the machine that runs on proton motive force. F1 refers to the top half that synthesizes ATP. 3. They refer not to design principles but to the non-integer gear ratio between the two parts which, as they explained, actually increases the yield by an order of magnitude. See also the 08/10/2004 entry: “ATP Synthase: Another Unexpected Case of Fine Tuning”.
We could form a pretty large stack of scientific papers with the following characteristics: (1) they express marvel at the engineering design of living things, and (2) they say absolutely nothing about evolution. This paper was another prime example. Somebody should make a project of that and carry the stack to school board meetings where the NCSE is giving their usual spiel that nothing in biology makes sense except in the light of evolution. The more you know about ATP synthase, the more you will be led to conclude that this is a wondrous device showcasing intelligent design. It’s mechanically perfect, irreducibly complex, 100% efficient, absolutely necessary for life, and capable of generating awe among scientists who study it. Notice that it was discovered 138 years after Charlie dreamed up his little myth about how design could invent itself.