Mulkidjanian is a co-worker with Skulachev and extremely wedded to the primacy of Na+ bioenergetics, which is good. He has been looking at NuoH and NuoN subunits of complex I and their phylogenetics. In contrast to this, in the past I've discussed similarities between NuoH and NuoL. You just have to accept we're never going to be certain which component of complex I is most closely related to another... Anyway, I like this paper:
Phylogenomic Analysis of Type 1 NADH:Quinone Oxidoreductase
"Two recently published works independently noted the structural similarity between the NuoH and NuoN subunits and suggested their origin by some ancestral membrane protein duplication [13, 14]. Our analysis does not exclude the possibility that this duplication may have occurred even before the LUCA stage. In this case the initial NDH-1 form [proto-Ech in my terminology] had only one type of membrane subunit (the ancestor of NuoN and NuoH), which could function as a sodium transporter. The duplication of the gene would result in a different subunit, which improved the kinetic effectiveness of the redox-dependent sodium export pump (that participated in maintenance of [K+]/[Na+] greater than 1 in a primal cell) by facilitating proton translocation in the reverse direction".
Bear in mind that none of us can be certain exactly what a given protein might have been doing based on these family trees of genes.
I think there is general agreement that ancestor of NuoH and NuoN is a membrane pore and that it is primordial. In Mulkidjanian's scenario that pore is associated with a redox driven hydrogenase. His idea is that the hydrogenase is using preformed ferredoxin, or something similar, to extrude Na+ ions from the cell. This requires an external source of energy and his concept is for ZnS catalysed photosynthesis giving a localised organic "soup", ie heterotrophy. The refs are here and here. The source of K+ for the primordial cell cytoplasm is suggested here. I have to say, I'm not a convert to these aspects of his ideas, I'm staying more aligned with autotrophic thinking...
My own view is that the pore was a duct to localise oceanic acidic pH tightly to an NiFeS hydrogenase within alkaline vent "cytoplasm" to allow the hydrogenase to reduce ferredoxin, the primary energy currency of the proto-cell. The power source is the pH differential across an internal FeNiS moiety within the hydrogenase, combined with molecular hydrogen as the electron donor to reduce ferredoxin and so, eventually, CO2.
Given the almost certain ancestral gene duplication it is not difficult to make an antiporter out of NuoH/NuoN, whether you consider the ancestor to have been a proton pore or part of a Na+ pump. Even today, the membrane component of Complex I functions as an antiporter for Na+/H+ provided you separate it off from the hydrophilic matrix section:
The deactive form of respiratory complex I from mammalian mitochondria is a Na+/H+ antiporter
Given an antiporter sitting in a Na+ opaque membrane we can antiport a ton of Na+ out of the cell using a geological proton gradient to give us the result of a low intracellular Na+ concentration. Excess Na+ extrusion can be converted, by electrophoresis, to an elevated K+ inside giving the modern intracellular composition. In the early days the electrophoresis might not have been K+ specific, theoretically any positive ion other than Na+ would do. K+ is the long term preferred option.
As soon as we leave the vent there is no free antiporting so we need to have a system which provides energy to generate a Na+ potential (buffered by K+ electrophoresis). The power available to do this becomes very limited in the absence of a geothermal proton gradient, when all that is available is the reduction of CO2 using H2, the Wood–Ljungdahl pathway. The Na+ chemiosmotic circuit then comes in to it's own as a system for combining small amounts of free energy in to units large enough to generate one ATP molecule. Recall how the modern pyrophosphatase Na+ pump requires the hydrolysis of four PPi to give one ATP via chemiosmotic addition. Until the advent of photosynthesis and the possibility of heterotrophy, all free living prokaryotes would have been autotrophic and living on a meagre energy budget.
The switch from luxurious hydrothermal vent conditions to lean autotrophic conditions goes a long way to explaining the universality of chemiosmosis. Alkaline hydrothermal vents may be stable on geological time scales but not for 4 billion years of un-interrupted flow and if the Wood–Ljungdahl pathway is all there is to replace the vent power supply it's going to be chemiosmosis all the way...