Complex I exists in various states, the two main ones being activated and deactivated. The deactivated form is convincingly a Na+/H+ antiporter. There is a pretty good case made in this paper, which has a number of flaws but is generally probably correct:
The deactive form of respiratory complex I from mammalian mitochondria is a Na+/H+ antiporter
As always, the suspect antiporter is thought to be NuoL, the distal "antiporter-like" subunit. You can see the logic for this which is supported by the stand-alone antiporting homologues of NuoL seen in nt-Nha and at least one archaeal MrpA subunit. Personally I'm not sure this is the case. The phenomenal difficulty in trying to interpret exactly what is happening in a structure as intricate and as minute as complex I allows many views of the available data.
It also appears to be the case that in bacteria which use menaquinone as their electron acceptor (rather than CoQ) some degree of Na+/H+ antiporting occurs under normal active NADH oxidation/proton pumping. That's in here
Respiratory complex I: A dual relation with H(+) and Na(+)?
and here's the energetics doodle from the same Fig 2 as I pinched the NADH:ubiquinone doodle from in the last post:
Because transferring two electrons from NADH to menaquinone only provides 480mV/2e- the complex uses Na+ moving down its concentration gradient to "top up" energy availability and so get the extra energy needed to pump the full four protons.
Aside: The paper has lots of good ideas but they are very wedded to the concept that NuoL, M and N are still antiporters and that loss of "control" by the redox cytoplasmic arm allows this antiporting to re establish. It's a very reasonable idea but I think it can be improved upon, especially now we have more detailed information about the Na+ pumping of the P furiosus MBH, where this is not what has happened. End aside.
Why on earth should it matter whether complex I pumps the full complement of four protons? If there is only enough Gibbs free energy for two or three protons, why not just pump two or three protons?
What occurred to me is that for complex I to pump the four protons it might be necessary to have a full "priming" of the membrane arm with enough Gibbs free energy for a full "push to the left", as in this doodle, discussed in a previous post:
What if you only have 480mV/2e- available, giving a half hearted "nudge" to the left when you need the full shove from 840mV/2e-? Is it possible that, under these circumstances, nothing at all happens? There is no flip of the glutamate/lysine pairs from together to apart, which triggers all of the opening/closing of water channels that allows proton translocation? Zero proton translocation?
If you wanted to restore the full "kick to the left" it might be a reasonable energetic top-up to supply the extra energy from Na+ ingress up near the Q binding site to allow the menaquinone plus Na+ ingress to generate the full Gibbs free energy for activation of the membrane arm. That needs a trans-membrane channel, so we are looking at the really complicated region around NuoH and NuoA/J/K. Not easy.
The best characterised Na+ channel in the whole related set of the complex I, MRP and MBH systems is the one in the MBH of P furiosus, described by Yu et al in
Structure of an Ancient Respiratory System
which gives the Na+ channel looking like
with the red blobs being the modelled Na+ binding sites. This is made up of proteins from four separate genes and is thought to be homologous to the Na+ channel of the MRP antiporter, also a multigene structure. They show them as identical in their discussion doodles, like this for the MRP multigene Na+ channel, simplified to the subunit shown as MrpG:
The equally multigene Na+ channel of the MBH of P furiosus (in this doodle the multiple Mbh genes are simplified to MbhC) is shown in exactly the same location with the same critical broken helix, in the same shade of green:
The final doodle in this figure is complex I. Here is their image:
which keeps things nice and simple between NuoH and the Nuo A/J/K region, where Nqo10 is shown but nothing else. So I wanted to know if there could be a Na+ channel which could be used to either top up the energy of the NADH:menaquinone couple or to allow the antiporting function to occur in deactivated standard CoQ based complex I. Of course no one is looking for Na+ channels in complex I in quite the same way as Yu et al were looking for one in MBH, where they knew it was crucial. Anyway, I went looking. In here
Structure and function of mitochondrial complex I
is where I found find this image (which is unfortunately left to right transposed in its view) that includes a rather nice broken helix shown in pink which I have circled in red:
If we take this broken helix, colour it green and transplant it in to Yu et al's complex I we get this:
Might it be the Na+ channel I need? No one knows (yet). It is known that there is a conformational change in the region of the CoQ binding pocket when complex I changes from the active to the deactivated state, close to the region of the broken helix head. I would suggest this conformational change might allow the Na+ antiporting function to occur when pumping in complex I is deactivated. Protons would be allowed to enter the cell/mitochondrion in exchange for Na+ expulsion (theoretically reversible but that seems unlikely physiologically unless you are a bacterium using menaquinone where some Na+ ingress is worth it to trigger the membrane arm). Logic says that this trade off would be preserved if antiporting provided a net benefit to the organism under which ever conditions might have favoured deactivation of complex I.
Addendum. Here are the three complexes lined up. Because PowerPoint lets you do it. No other reason.