Long-Range Hopping Conductivity in Proteins

Abstract

Single molecule measurements show that many proteins, lacking any redox cofactors, nonetheless exhibit electrical conductance on the order of a nanosiemen, implying that electrons can transit an entire protein in less than a nanosecond when subject to a potential difference of less than 1V. In the conventional fast transport scenario where the free energy barrier is zero, the hopping rate is determined by the reorganization energy of approximately 0.8 eV, which sets the time scale of a single hopping event to at least 1s. Furthermore, the Fermi energies of metal electrodes used in experiments are far-removed from the equilibrium redox states of the aromatic residues of the protein, which should additionally slow down the electron transfer. Here, we combine all-atom molecular dynamics (MD) simulations of non-redox active proteins (consensus tetratricopeptide repeats) with an electron transfer theory to demonstrate a molecular mechanism that can account for the unexpectedly fast electron transfer. According to our MD simulations, the reorganization energy produced by the energy shift on charging (the Stokes shift) is close to the conventional value of 0.8 eV. However, the nonergodic sampling of molecular configurations by the protein results in reorganization energies, extracted directly from the distribution of the electrostatic energy fluctuations, that are only ~ 0.2 eV, which is small enough to enable long-range hopping. Using the MD values of the reorganization energies we calculate a current decay with distance that is in agreement with experiment. SignificanceElectron transfer is fundamental to biology, facilitating a range of metabolic processes and efficient energy conversion. Conventionally, electron transfer through proteins is thought to occur via a chain of metal or organic co-factors connecting one side of the protein to another. Recent experiments, however, show that proteins lacking any co-factors can nonetheless transport electrons with high efficiency if properly connected to metal electrodes. This study provides a theoretical model of such cofactor-less transfer, showing that transient occupation of non-equilibrium states of the proteins aromatic residues reduces the barrier to electron hopping, facilitating long range and rapid transport. Our results widen the pool of proteins potentially involved in biological electron transport and provide theoretical underpinning to design of protein molecular electronics.