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Water adsorbed onto both sides of the phospholipid bilayer release H+ by diffusion, as H+ in adsorbate is more mobile than OH- (and auto-ionization still happens). In lab experiments pOH of adsorbate shown to be 4 (with pH 5.5 upwards 10 mm out, and 0.3 mm thick adsorbate). The phosphate heads in the bilayer (the O- groups, i.e., deprotonated hydroxyl groups) will be protonated from these H+, and store them. On the outside, Na+ or K+ in equal charge proportions to the phosphate that stored H+ is what replaces the H+. The lipid bilayer is an insulator, thus electricity released when a positive charge is moved along concentration gradient (the Na+/K+ selective channels) is forced to travel via membrane proteins. This is the purpose of the machinery: provide electricity to membrane protein. The O2 consumed and released during the oxygen evolution and reduction reactions, 4 OH- -> 2 H2O + O2 + 4 e- and 4 H+ + 4 e- + O2 -> 2 H2O, is consumed and released near the phosphate heads, and can diffuse freely through - and be stored in - the lipid tail region, the center of the bilayer. The adsorbed water on top prevents the O2 from leaving the system.
The plasma membrane electrical circuit is built on top of the inherent electrical circuit of adsorbed water, which is what causes the mechanism of osmosis. THe asymmetry in mobility of H+ and OH- in the adsorbed phase of water, results in H+ spreading out by diffusion in all directions. If there is less adsorbate on one side of a mebrane than on the other, the H+ from the "exosmotic" side (the side water moves from) will tend to have net movement to the other side (the "endosmotic" side, where water moves to). The loss of positive charge from the "exosmotic" side, generates an electric field - voltage - and OH- in the adsorbate will tend to break down into electrons, molecular oxygen and water, and the electrons transfer over the "osmotic membrane" to combine with O2 and H+ on the other side, thus "moving" water by breaking it down on one side and producing it on the other (this requires externally supplied O2 on the "endosmotic" side). This inherent electrical circuit of water is why Sidney Fox's "protenoids" showed electrical activity so similar to the cell, despite not having any lipids (and thus clearly not lipid bilayer). The phospholipid bilayer of the cell is not producing the electricity, it is "taming" it. The addition of an insulator, controls where electrons can flow. The addition of the hydrophobic region also provides a way to control the O2, so that it does not diffuse away (and the storing-away of the H+ at the boundary of this O2 storage region forces the release and consumption of O2 in that position). And the Na+ and K+ substituting H+, makes the cation concentration gradient diffusion more easy to control. Na+ and K+ are larger than H+, more easy to selectively filter. And, they are two, providing one concentration gradient in either direction, providing a mechanism to also re-charge the battery.
The foundation of these insights is the realization that osmosis is an electro-chemical process, and that asymmetry of charge carrier mobility is the basis of it - the same physical principle that the transistor is built on (there, electrons are mobile wherees protons are not, whereas in adsorbed water it is the other way around).
These insights are built on the work of Gerald Pollack and Gilbert Ling. Ling, who invented the microelectrode and mentored Alan Hodgkin, devoted his career to defending the role of water and the "protoplasm". He did so at the cost of rejecting some contemporary advances, such as the discovery of the lipid bilayer. But Ling, from the work of Sidney Fox, that the electrical potential was not in the lipid bilayer but in th water itself. Gilbert Ling was right, but so was the "other side". Gerald Pollack advanced on Ling's work and discovered what the electrical activity of water was: it was a spontaneous separation of charges in the adsorbed water, where H+ would be released from it. Pollack saw this in his lab experiments, with a simple pH dye you see the H+ that has been released, and he measured the electrical behavior of the water during osmosis, and the fact that H+ was transferring (along concentration gradient) over the membrane from the side water moved from (exosmotic side) to where water moved to (endosmotic side). From their work, it was a small step to also realize that the electrical reactions Pollack had already noticed must happen, OH- breaking down into electrons, was also happening in osmosis and that osmosis actually only moved H+ and e-, and from there it was easy to document osmosis as the basis of most physiological systems, including the plasma membrane electrical circuit (an analogous circuit exists on protein, there ATP in the protein binding site is what stores away the H+, both combined behave as a base, and it releases the H+ when it is hydrolysed as it then leaves the binding site and is a much weaker base).
Osmosis, or "proto-respiration", is one of the most fundamental building-blocks of life. In the lungs, O2 does not get absorbed by diffusion, but, rather, it is produced in the capillaries surrounding alveoli, and water at the same time produced in the alvoeli. In the capillaries, H+ released from adsorbate cause net positive charge in lumen which propels blood, and an opposite flow on outside of capillary will bring back water produced on the end of the capillary (from the H+ that propelled the blood), while breaking it down at the start of the capillary (the release of e- from OH-). External O2 is required to sustain this, and it was shown in 1970s that ventilating lungs on a dog whose heart was incapacitated, you still had significant circultaion going on, the "vestigual circulation" they called it. Likewise, in the kidney, you have "repulsion osmosis" in the thin descending limb, the narrow lumen forces H+ released to instead diffuse outwards, across the thin epithelium, and you then have a separate loop to reabsorb the O2 (this loops water into the thin ascending limb and down the collecting duct, to be absorbed by pressure in collecting duct, so the O2 is moved back out of the tubules and brought via vasa recta to the thin descendning limb where it can osmotically reabsorb more water - concentrating the urine).