Non-Ergodic Electron Transfer in Mixed-Valence Charge-Transfer Complexes

Assessing Thermal Response of Redox Conduction for Anti-Arrhenius Kinetics in a Microbial Cytochrome Nanowire

A micrometers-long helical homopolymer of the outer-membrane cytochrome type S (OmcS) from Geobacter sulfurreducens is proposed to transport electrons to extracellular acceptors in an ancient respiratory strategy of biogeochemical and technological significance. OmcS surprisingly exhibits higher conductivity upon cooling (anti-Arrhenius kinetics), an effect previously attributed to H-bond restructuring and heme redox potential shifts. Herein, the temperature sensitivity of redox conductivity is more thoroughly examined with conventional and constant-redox and -pH molecular dynamics and quantum mechanics/molecular mechanics. A 30 K drop in temperature constituted a weak perturbation to electron transfer energetics, changing electronic couplings (⟨H_mn⟩), reaction free energies (ΔG_mn), reorganization energies (λ_mn), and activation energies (E_a) by at most |0.002|, |0.050|, |0.120|, and |0.045| eV, respectively. Changes in ΔG_mn reflected -0.07 ± 0.03 V shifts in redox potentials that were caused in roughly equal measure by altered electrostatic interactions with the solvent and protein. Changes in intraprotein H-bonding reproduced the earlier observations. Single-particle diffusion and multiparticle steady-state flux models, parametrized with Marcus theory rates, showed that biologically relevant incoherent hopping cannot qualitatively or quantitatively describe electrical conductivity measured by atomic force microscopy in filamentous OmcS. The discrepancy is attributed to differences between solution-phase simulations and solid-state measurements and the need to model intra- and intermolecular vibrations explicitly.

Protein electron transfer: Dynamics and statistics

Electron transfer between redox proteins participating in energy chains of biology is required to proceed with high energetic efficiency, minimizing losses of redox energy to heat. Within the standard models of electron transfer, this requirement, combined with the need for unidirectional (preferably activationless) transitions, is translated into the need to minimize the reorganization energy of electron transfer. This design program is, however, unrealistic for proteins whose active sites are typically positioned close to the polar and flexible protein-water interface to allow inter-protein electron tunneling. The high flexibility of the interfacial region makes both the hydration water and the surface protein layer act as highly polar solvents. The reorganization energy, as measured by fluctuations, is not minimized, but rather maximized in this region. Natural systems in fact utilize the broad breadth of interfacial electrostatic fluctuations, but in the ways not anticipated by the standard models based on equilibrium thermodynamics. The combination of the broad spectrum of static fluctuations with their dispersive dynamics offers the mechanism of dynamical freezing (ergodicity breaking) of subsets of nuclear modes on the time of reaction/residence of the electron at a redox cofactor. The separation of time-scales of nuclear modes coupled to electron transfer allows dynamical freezing. In particular, the separation between the relaxation time of electro-elastic fluctuations of the interface and the time of conformational transitions of the protein caused by changing redox state results in dynamical freezing of the latter for sufficiently fast electron transfer. The observable consequence of this dynamical freezing is significantly different reorganization energies describing the curvature at the bottom of electron-transfer free energy surfaces (large) and the distance between their minima (Stokes shift, small). The ratio of the two reorganization energies establishes the parameter by which the energetic efficiency of protein electron transfer is increased relative to the standard expectations, thus minimizing losses of energy to heat. Energetically efficient electron transfer occurs in a chain of conformationally quenched cofactors and is characterized by flattened free energy surfaces, reminiscent of the flat and rugged landscape at the stability basin of a folded protein.