A bit of physical chemistry

Stimulated by this fascinating book.

I note that ‘alkaline’ means what I learned as ‘basic’ as opposed to acidic. An alkaline pH is between 7 and 14. The concentration of OH ions is much greater that that of H+. The density of H+ is 10−pH and the density of OH is 10pH−14. In pure water pH=7 and about one water molecule in 107 is broken into a H+ and a OH. These two populations occasionally run into each other and combine but at concentration 10−7 they break up as often as they rejoin. While I am at it an OH or H+ is a big deal. It reorients thousands of nearby water molecules so as to decrease the energy it would otherwise take to separate the two ions of a broken water molecule. The mobility of such ions is decreased due to the hassle of reorienting these molecules. When an ion wants to move it must coordinate with its retinue of nearby water molecules. The retinue does not tag along but as an ion moves all newly nearby water molecules pay attention.

If a charged ion approaches some membrane that membrane can react in one of two ways. It might be willing to arrange its polar components to accommodate the potential gradient produced by any nearby ion like water does, in which case the ion can approach closer even as the membrane retains its integrity. On the contrary it can refuse and the ion sees a electrical mirror image of itself in the membrane and is repelled and will not cross.

A pH of 0 means very acid but it does not imply a positive charge in the solution. If I add some hydrochloric acid, HCl, to water those molecules break into H+ and Cl. There are then more H+’s than OH’s and pH < 7 but it is still electrically neutral overall.

I think that the energy that runs the ATP synthase is a true potential difference, not a mere difference in pH. I think an electrical engineer would call it a capacitor. I think the diagrams and text obscure this vital difference.


At L 1106: (in the book) Lane says: Lane cites a potential gradient, measured in volts/meter. I can believe that nature can create such potential gradients. But don’t confuse a pH gradient with a potential gradient. If I separate aqueous solutions of HCl and NaOH by a thin barrier, I do not produced a potential gradient. An ATP synthase installed in that barrier (Figure 10) won’t spin. A proton that finds itself half way thru will feel no pull. For every proton below pushing, there is a Cl pulling back just as hard. For every OH above pulling the proton, there is a Na+ pushing back! But if it is a real capacitor it will feel a strong force to move up and spin the rotor. To do that there must more positive charges below than above. That is just what a capacitor arranges. Nature can do this and I suppose it does.

L 2186: “The problem is that protons cross the membrane much faster than chloride ions, so there is an influx of positive charge that is not offset by an influx of negative charge.” Good point. This can turn a pH gradient into a potential gradient. My intuition is that this is not enough however. It won’t cause the potential necessary for ATP synthase; that would be a perpetual motion machine, I think.

I quibble with Lane’s definition of “proton gradient”:

I think that the difference in H+ concentration counts for about 0.00001% of the force that turns ATP synthase.
Another curiosity may be relevant here. When a charged conductor is at equilibrium, the excess (or deficit of) electrons is at the boundary of the conductor. Otherwise there would be a potential gradient within the conductor which is impossible. If the conductor is not close to any other mater and you solve the Laplace equations for empty space outside the conductor, using a constant potential on the conductor surface as boundary condition, the lines of force will meet the conductor in varying densities, unless the conductor is a sphere. The charge is concentrated just where those lines meet the surface of the conductor.

The capacitor proposal means that the positive charges on one side of the membrane are within Ångstroms of the membrane; ditto negative ions on the other side.


I look at the 100 places where Lane uses “proton”, in order to imagine how better to word things.

L 223: “Essentially all living cells power themselves through the flow of protons (positively charged hydrogen atoms), in what amounts to a kind of electricity – proticity – with protons in place of electrons.”

I would say that like uses ordinary electricity and that can be carried by and charged mass. It is true that most electric circuits that people design carry electricity by mobile electrons and most atomic nuclei stay put. Bad things generally happen when they move. Electroplating, however, thrives on moving ions of any sort. I can believe that ATP synthase is driven by protons which (I would say) extract power from a capacitor by moving charge from a higher to lower electric potential. That potential difference is due to ions including protons but other ions as well.

L 225: “The energy we gain from burning food in respiration is used to pump protons across a membrane, forming a reservoir on one side of the membrane.” I bet it is better to say “... is used to pump ions across an insulating membrane causing a charge separation—like a loaded spring which stores energy.