It's an interesting area. It's clear enough that all cellular life has 'proticity' (more protons on one side of a membrane than on the other) and that in turn is driven by electron transport through the electron transport chain - and that chain relies on electron tunnelling (primarily complex I). In eucaryotes (complex life incuding us) that transport is done inside mitochondria; oxygen is used as an electron acceptor - bacteria and archaea can use other acceptors. So... if cells are using a quantum effect for one thing, why not another?
FWIW, one of the interesting things about mitochondria is that they have discarded almost all genetic material not directly part of controlling local respiration; parts of the ETC are made via nuclear (in the sense of in the nucleus) genetics, other parts via mitochondrial genetics - and those molecules need to fit within about 8 angstroms or the electrons stop tunneling. We eucaryotes have two sets of genetics, and if they drift apart... Nick Lane's team has done some interesting work with drosophila (fruit flies) and mitochondrial genetic drift. Their primary focus is around the beginning of life, how that probably came out of a situation where there was already a proton differential across something thin enough to function similarly to a lipid bilayer. The current leading candidate is undersea hydrothermic vents in an anoxic (so likely plenty of dissolved ferritin - just from looking at the ferric oxide that precipitated out once there was oxygen) ocean.
Meanwhile Luca Turin has been looking at smell receptors, how those are likely dependent on quantum effects - and there's a possibility that consciousness itself may be connected with proticity (and so electron tunneling). The one thing general anesthetics have in common is that the impair ECT I - even in protists(!) That's the only thing xenon gas and ether (both general anasthetics) have in common.
Are there any research papers on ferritin (and the possibility of transporting electrons via what I'd think of as a ferritin vessicle) that you could point me towards?
Not credentialed in this area, just fascinated with it...