We present a novel method for selecting important electron tunneling pathways in proteins by connecting important interatomic tunneling currents. Then, we constituted an electron tunneling route, called a "worm", which is formed by averaging over all of the interatomic tunneling currents. The method is applied to six kinds of Ru-modified azurins where the electron transfer takes place from the copper ion to the ruthenium ion linked to the surface of the azurin. We found that the worm is not straight but winds, reflecting the specific role of the microenvironment of the protein structure and ligands in the electron tunneling pathway and rather narrow radius of the worm, ca. 1.5 Angstrom at most. The donor-acceptor distance dependence of the electron-transfer rate k(e) is examined by taking into account the one-dimensional atomic density in the worm. We found that the Dutton plot, in which the logarithm of k(e) is in a linear relation with the donor-acceptor distance, which, in turn, depends somewhat an the one-dimensional atom density, is reproduced for a certain level of analysis by the worm model. Thus, we can consolidate the electron tunneling pathway model with the Dutton plot by using the worm model.