Investigating electron conductivity regimes in the bacterial cytochrome wire OmcS

TL;DR

This work addresses how long-range electron transport occurs in Geobacter OmcS cytochrome wires. It combines first-principles DFT to compute site energies $\varepsilon_N$ and effective couplings $V^{eff}_{N,N+1}$ with a Lindblad quantum diffusion model to capture both coherent and incoherent transport, including non-perturbative phonon-like disorder. The authors show that $\varepsilon_N$ and $V^{eff}_{N,N+1}$ are highly sensitive to inter-heme geometry and electrostatics, that dephasing and intra-heme vibrations dramatically enhance diffusion by mitigating static disorder, and that geometry and electrostatic tuning can modulate conductivity, offering design principles for bioinspired heme-based materials. Overall, the study provides a plausible mechanism for achieving conductivity at biologically relevant scales and highlights the role of dynamic disorder in reconciling theory with experiment.

Abstract

The anaerobic bacterium \textit{Geobacter sulfurreducens} produces extracellular, electronically conductive cytochrome polymer wires that are conductive over micron length scales. Structure models from cryo-electron microscopy data show OmcS wires form a linear chain of hemes along the protein wire axis, which is proposed as the structural basis supporting their electronic properties. The geometric arrangement of heme along OmcS wires is conserved in many multiheme c-type cytochromes and other recently discovered microbial cytochrome wires. However, the mechanism by which this arrangement of heme molecules support electron transport through proteins and supramolecular heme wires is unclear. Here, we investigate the site energies, inter-heme coupling, and long-range electronic conductivity within OmcS. We introduce an approach to extract charge carrier site information directly from Kohn-Sham density functional theory, without employing projector schemes. We show that site and coupling energies are highly sensitive to changes in inter-heme geometry and the surrounding electrostatic environment, as intuitively expected. These parameters serve as inputs for a quantum charge carrier model that includes decoherence corrections with which we predict a diffusion coefficient comparable with other organic-based electronic materials. Based on these simulations, we propose that dynamic disorder, particularly due to perturbative inter-heme vibrations allow the carrier to overcome trapping due to the presence of static disorder \textit{via} small frequency-dependent fluctuations. These studies provide insights into molecular and electronic determinants of long-range electronic conductivity in microbial cytochrome wires and highlight design principles for bioinspired, heme-based conductive materials.

Figures (4)

• Figure 1: (a) Charge carrier sites on a heme pair. The electron density is centered around the Fe atom of the heme and delocalized over the porphyrin ring. (b) Schematic of of our approach for obtaining electronic coupling: The coupled orbitals are split in energy due to inter-heme electronic interactions and static disorder. By flipping the spin on one heme with respect to the other, the orbitals are decoupled. Site energies and effective electronic coupling are then calculated as shown in Eq. \ref{['eqn:veff']}.
• Figure 2: a) The configuration of heme molecules (labeled 1$-6$) studied in this work, shown along the protein backbone of OmcS (plotted as ribbons) extracted from Ref. OmcS. b) (Top) An example of two heme molecules in the parallel and T-shaped configuration. (Bottom) Calculated $|V^{eff}|_{N,N+1}$ and $|\varepsilon_N - \varepsilon_{N+1}|$) for six possible heme pairs of OmcS (labeled as X). $2^{\circ}$ rotations of each heme along the Cartesian axes (+) and geometry-optimized structures in implicit solvent (triangles) are also shown.
• Figure 3: The impact of (a-c) inter-molecular and (d-f) intra-molecular distortions on DFT-predicted conductivity parameters. (a) Effective coupling and (b) site energy differences upon modifications of inter-heme distance and rotation for the type 4-5 heme pair. The original geometry is marked with an x and data points are shown as gray points. (c) The effective coupling as a function of dimer binding energy, showing a positive correlation between the two parameters. (d) Effective coupling and (e) absolute site energy differences upon rotation of the propionate group on one molecule (molecule 1) with respect to the other (molecule 2) for the geometry-optimized heme structure. (h) The site energy for the heme molecule containing the distortion $\varepsilon_A$ compared with the other molecule ($\varepsilon_B$). The isosurface plots were interpolated using a cubic spline method to create a smooth surface as described in the SI.
• Figure 4: (a) Diagram of repeating heme molecules where the red dash indicates the end of a six-heme unit. (b) Site energy as a function of heme index. Site 0 indicates the initial electron position on heme type 1. (c) Population dynamics without dephasing ($\gamma$ = 0 $ps^{-1}$) with the wavefunction spread $R^2(t)$ as an insert. (d) Population dynamics in the presence of dephasing with $\gamma$ = 50 $ps^{-1}$with the wavefunction spread $R^2(t)$ as an insert. (e) The diffusion coefficient as a function of site energy difference and electronic coupling scaled by $\lambda_{E}$ and $\lambda_{V}$, respectively. Two different dephasing parameters, $\gamma$, are shown.(f) Impact of randomization and rerandomization rate (f$_{R}$) on the diffusion coefficient (D) for $\gamma$ = 50 $ps^{-1}$. f$_{R}$ represents the time before site energies are randomized again.