The suggested candidate is inelastic electron tunneling. As I've discussed elsewhere, electrons can traverse a molecule through a second order tunneling process, and if enough energy is available to those electrons and the microscopic couplings work out right, they can leave behind a vibrational quantum of energy. In so doing, there is a kink in the current as a function of voltage, signifying the onset of this process.
I am very skeptical that true inelastic tunneling of that type is at work in your nose. First, the natural linewidth of IETS features is several times kT. At room temperature, that is several times 26 meV. The energetic difference between, e.g., the CH and CD stretch vibrations is around 125 meV. Basically, even with a laboratory setup and far higher currents than present in biological systems, and with the benefit of phase-sensitive detection, it would be very difficult if not impossible to use IETS to resolve that isotopic difference. That doesnt even take into account the complicated nature of electronic motion in biological conditions. That being said, I suppose there could be some weird physics where that vibrational frequency makes itself known through the noise in electronic motion - I am thinking along the lines of a fluctuation-dissipation effect like this one. Any mechanism has to be robust in the presence of environmental and thermal noise, and IETS is not, in my view. Still, it's a neat mystery!