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Recent experimental evidence shows that when a protein (or peptide) binds toits ligand pair, the protein effectively "switches on" enabling long-rangecharge transport within the protein. Astonishingly, the protein-ligand complexexhibits conductances in the order of nanosiemens over distances of manynanometers and macroscopic Ohm's law emerges. Here, we investigate thisemergent phenomenon via the framework of many-body (fermionic) quantumstatistical principles. We propose a simple model which gives rise to an Ohm'slaw with vanishing quantum effects in its thermodynamic limit (with respect tolength scales). Specifically, we consider protein-ligand complexes as atwo-band 1D lattice Hamiltonian system in which charge carriers (electrons orholes) are assumed to be quasi-free. We investigate theoretically andnumerically the behavior of the microscopic current densities with respect tovarying voltage, temperature and length within reasonable physiologicalparameter ranges. We compute the current observable at each site of theprotein-ligand lattice and demonstrate how the local microscopic chargetransport behavior generates the macroscopic current. The overall frameworkcontributes to the search for unifying principles for long-range chargetransport and associated emergent laws in protein complexes, which is crucialfor bioelectronics.

A First Rigorous Attempt to Explain Charge Transport in a Protein-Ligand complex