Are there any existing models of electron transport in biological systems?
Good question! The answer is yes, although they are not even mentioned in this unreviewed manuscript (which seems like hokum to me). Electron transfer in proteins is particularly well understood in the context of Marcus theory. The wiki article isn't great, but it has some good information and further references. A key insight is the "inverted driving force effect," an experimentally validated prediction of Marcus theory that electron transfer rates actually start to decrease if the transfer reaction is too exergonic (energetically favored).
Without going into a ton of detail, quantum effects are actually quite important for electron transfer, and some enzymes even encourage tunneling, mostly of electrons, as part of catalysis. Considering that the de Broglie wavelength of a 10 kJ electron is about 18 angstroms (biologically relevant scales), it's not really that surprising. Frequently, there are favored tunneling pathways through enzymes which electrons tend to follow.
Enzymes also sometimes utilize nuclear tunneling (i.e. tunneling proton/hydrogen/hydride), which is really, really cool. I am a fan of this paper which shows how tunneling is is encouraged through dynamic gating motions in a enzyme on the chlorophyll production pathway.