Now it's time to look at this paper:
We can start with this image of the membrane part of complex I from Thermus thermophilus which shows the water channels of the antiporter-like pumping units. The NADH reduction site is not shown but is at the right hand end, above the membrane. Nqo8 is the equivalent of mitochondrial NuoH, the universal adaptor between the redox limb and the membrane section of all similar complexes:

Water channels are important if you want to move protons through a protein. The problem is that protons are hydrated, at their simplest they can be thought of as the hydronium ion, H3O+, but it seems more likely that 4-6 water molecules form a structure around this giving a large molecule restricted to channels where there are adequate ionised amino acids to form an hydrophilic environment rich in water molecules.
The sketch shows the three conventional water pathways through Nqo12, 13 and 14 and a less straight forward probable channel through Nqo8 where the proton exit route is shown as a dashed section of black line rather than the solid line associated with the clear cut water channels in Nqo12, 13 and 14.
The channels open and close in response to the protonation of key amino acids. This is the schematic of how this group feels complex I works:
I'll briefly go in to detail of the section marked within the red oval to look at the key mechanism:
The pumping function is driven by the protonation of an amino acid in Nqo8 affecting a lysine/glutamic acid pair within Nqo14. While Nqo8 is de-protonated the lysine (K)186 is electrostatically attached to the glutamate (E)112.
While Nqo8's amino acid is protonated it attracts the -ve charged glutamic acid and repels the +ve charged lysine.
When Nqo8 is de-protonated the lysine and glutamate return to their original electrostatic association. In detail it looks like this:
The process is repeated at the junctions between Nqo14-13 and 13-12. There is a typo in the diagram on the top line, lysines (K)345 and (K)385 are shown as protonated but clearly can't be for the scheme to work.
Aside: The junction 13-12 actually has a glutamine bumping up against aspartate/lysine electrostatic bonded couplet. This seems to work but is not as intuitive as the glutamate/lysine pairs. I'll leave it alone as the story is complicated enough as it is. End aside.
I've corrected these "blue +" symbols to open circles to make sense of it and have highlighted the repeats with ovals circles again:
Having got that sorted let's fade Nqo12 and 13 out and look at pumping in Nqo14. In the resting state the cytosol side water channels are open and this allows protonation of the central lysine residue:
Nqo8's amino acid then protonates
and separates the adjacent lysine/glutamate pair which pushes the orange-crossed proton from its lysine to another lysine adjacent to Nqo13. It closes the cytosolic water channels in the same action
This displaced orange-crossed proton binds to Nqo13's lysine/glutamine pair and so propagates the effect along the central water channel within the membrane arm
This movement also opens the periplasmic water channels
allowing protons to leave the cell. This allows the lysine/glutamine pairs to return to their starting locations as the yellow-crossed proton exits Nqo8
As the protons exit, the associated conformational changes open the cytosolic water channels and the cycle is ready to repeat
This is all very nice and neat, typos excepted, with four protons pumped per cycle. But there is a fly in the ointment. As the authors comment
"Despite a significant N-side entry channel, we observe no clear exit pathways to the P side of the membrane within Nqo8."
There is no route out of Nqo8, exactly as there is no route out for protons in NuoH of human mitochondria or the equivalent in any of the other membrane bound hydrogenases of strict anaerobes.
Which gives us insightful constraints on where the system might have come from.
Peter