Protein molecular conductance has attracted attention from researchers for the possibility of constructing innovative flexible biocompatible nanoscale electronic devices and smart hybrid materials. Due to protein complexity, most evaluations of protein conductivity are based on the simple estimation of protein's molecular orbital energy levels and spatial distributions without analysing its protein interaction with electrodes and the calculation of the rates of electron transfer (ET). In the present work, we included in our density functional theory (DFT) analysis an approach based on the non-equilibrium Green's function (NEGF) allowing for calculation from the first principles the molecular interaction with electrodes and thus the role of electrode materials, Fermi level, the thermal distribution of electronic energy levels, and the coupling efficiency between the molecule and the electrodes. Compared to proteins studied so far, mainly artificial peptides, heme-containing cytochromes, and bacterial pili, we choose rubredoxin for our calculation. Rubredoxin contains a non-heme iron that, as we have discovered recently, can be involved in extracellular ET in electroactive bacterial biofilms (Yates et al., Energy Environ. Sci., 2016, 9, 3544-3558). Our calculations show that an iron atom incorporated into the protein structure as an iron-sulfur cluster opens a transmission path at the energy corresponding to the Fermi level of the electrodes. This allows the protein to become an extremely efficient conductor at very low bias voltages (<±350 mV). Calculation of the role of protein amino acids based on the local density of states and electron transfer paths reveals that neither aromatic amino acid Tyr nor Phe at any ring orientation participates in coherent ET through the FeS cluster of the protein. Moreover, direct ET through surrounding amino acids, bypassing FeS, is possible only at biases ±1.5 to ±2 V. The polar amino acid Asn might participate in ET at these bias voltages. The conductivity of the protein core substantially depends on the polarity of the applied electric field, allowing for unidirectional ET and operation of the protein as a molecular rectifier. These results can be used for a wise de novo design of proteins for molecular electronics and cellular energy converting devices, particularly for utilization of iron doping in the construction of conductive protein wires.