Protein electronics is a relatively new branch of molecular electronics which goal is to analyze the mechanism and utilize the gained knowledge for the construction of robust super small flexible protein- and biological cell-based electronic materials for bioinorganic hybrids, including sensors, actuators, electrochemical cell, and catalytic devices. Though widely discussed, the mechanism and the structural components controlling ET through multi-atomic proteins, which calculation requires unique software and high-performance computers, are not completely understood. In the present work, we calculate from first principles ET through two proteins, (a) helical region of PilA, an extracellular proteinaceous filament of Geobacter sulfurreducens with was reported to conduct electrons over long distances (>1 micron) and (b) through bacterial FeS protein, rubredoxin, a small non-heme protein widely used by biological cells as a soluble redox mediator. For comparison, we also calculate ET through an artificially designed carbon nanotube (CNT)-histidine-heme-histidine-CNT conjugate that mimics bacterial cytochromes. Our calculations show that iron atom incorporated into protein structure as a heme or an iron-sulfur cluster opens up a transmission path at the energy corresponding to the Fermi energy level of the electrodes that substantially (by several folds) increases efficiency of ET through the protein. Neither aromatic Tyr, nor Phe at any ring orientation can get the compatible effect, though bipolar Asn might participate in ET at high bias voltages. The conductivity of the proteins substantially depends on the polarity of applied electric field allowing for the protein operation of as a molecular rectifier. These data explain the origin of experimentally observed high conductivity of iron-containing native proteins and can be used for wise de novo construction of new proteins for molecular electronics and bio-inspired energy converting devices.