Large redox molecules such as electron-transfer metalloproteins have a special relevance to scanning tunneling microscopy (STM) processes, since a redox state (RS) immersed therein provides a station of electron-hopping mediation for STM currents when they are adsorbed on the substrate. The currents flow when the tip is adjusted at the location of the RS on the substrate. Flowing into the RS, an electron induces both the inner sphere reorganization (in atomic arrangements in a prosthetic group that provides the RS) and the outer-sphere one (in amino-acid-residue arrangements in the protein matrix around the RS). The mediation is, therefore, accompanied by simultaneous emission of large-energy-quantum intramolecular phonons participating in the former and by relaxation along the coordinate of the latter. The intramolecular-phonon-assisted mediation is opened when the bias voltage exceeds a series of threshold values determined in conjunction with the latter. It is predicted, therefore, that the V-I characteristics should have a phonon-progressional staircase structure, It enables us to derive fundamental physical parameters for the RS due to the prosthetic group, such as its location with respect to both energy and height from the substrate, energies of inner-sphere and outer-sphere reorganization, and the energy quantum of intramolecular phonons participating in the former.