Zinc-substituted cytochrome c (Zn-cyt c), in which the heme iron is replaced by redox-inactive Zn(II), is a classic platform for photoinduced electron transfer (ET) in proteins. A 2008 all-electron density-functional-theory computation of the intact 104-residue protein, combined with photocurrent measurements on electrodes, concluded that photoinduced intramolecular ET in Zn-cyt c is governed by hole transfer (HT) through occupied porphyrin orbitals to molecular orbitals localized on specific surface residues (Lys7, Asn54), with rates estimated using Fermi's golden rule. The unresolved problem is to establish this mechanism with quantitative accuracy: first-principles rates and lifetimes, with accurate excited-state energetics, that confirm or revise the proposed pathways and the implicated residues.

Background

Cytochrome c is a small (104 residues in the horse-heart protein), well-characterized mitochondrial electron carrier whose prosthetic group is a heme, an iron porphyrin coordinated by histidine and methionine axial ligands. Replacing the iron with Zn(II) yields zinc-substituted cytochrome c (Zn-cyt c): the central Zn(II) ion, unlike Fe, has no accessible metal-centered redox state, but the porphyrin is strongly photoactive, absorbing light in the Soret and Q bands and forming a long-lived excited triplet state. For this reason Zn-cyt c became a standard model for photoinduced long-range ET between proteins, for example with cytochrome c peroxidase (Conklin and McLendon, 1986) and with azurin or plastocyanin (Sokerina et al., 1999; Ivković-Jensen et al., 1999), where excitation of the Zn porphyrin drives interprotein electron transfer and leaves a Zn-porphyrin cation radical (a 'hole'). Zn-cyt c was also studied photoelectrochemically on nanoporous metal-oxide electrodes (Topoglidis et al., 2002). Porphyrin visible absorption is described by the standard four-orbital model of porphyrin electronic structure (Gouterman's model): two occupied and two unoccupied frontier π orbitals account for the Soret and Q bands. Long-range ET rates in proteins are conventionally treated with nonadiabatic Marcus-type theory, in which the rate is proportional to the square of the donor–acceptor electronic coupling TDAT_{\mathrm{DA}} times a Franck–Condon factor (FC), the nuclear-overlap term describing how readily the molecular geometry reorganizes during the transfer; 'hole transfer' denotes the equivalent process viewed as a positive charge moving through occupied orbitals, i.e. an electron from an occupied orbital of one site filling a hole on another. Tokita, Shimura, Nakajima, Goto, and Watanabe (2008) computed an all-electron density-functional-theory (DFT) wave function for the ground state of the entire intact Zn-cyt c molecule, assigned the four photoactive porphyrin orbitals using time-dependent DFT (TDDFT) on a chromophore model, and estimated ET rates between each of the four orbitals and all other protein molecular orbitals using Fermi's golden rule (the standard lowest-order perturbative rate expression). They found that the two occupied porphyrin orbitals couple by far most strongly to orbitals localized on the outermost surface residues Lys7 and Asn54, implying that intramolecular ET in photoexcited Zn-cyt c is governed by hole transfer through occupied orbitals. Immobilizing Zn-cyt c on a gold electrode through a carboxylic-acid-terminated self-assembled monolayer (SAM, an ordered organic monolayer that wires the protein to the metal), they measured photocurrents whose action spectrum (photocurrent versus wavelength) matched the absorption spectrum and whose voltage dependence was linear and bidirectional, like a photoconductor — interpreted as support for the computed HT mechanism. The 2008 conclusions rest on approximations whose accuracy for this system has not been independently established: the rates were estimated from Fermi's golden rule between molecular orbitals, and the porphyrin orbital assignment relied on TDDFT of a chromophore model, an approach with well-documented systematic errors for porphyrin Q-band excitation energies that affect the energetic alignment between chromophore and protein orbitals entering the rates. The authors presented the photocurrent measurements as strongly supporting the computed HT mechanism, but the residue-level assignments (Lys7 and Asn54) have not been subjected to targeted residue-specific experimental tests, and no subsequent first-principles rate study of this system has been reported.

Problem Statement

Establish the mechanism of photoinduced intramolecular electron transfer in Zn-substituted cytochrome c with quantitative accuracy. Concretely, determine, by first-principles electronic-structure and rate theory accurate enough to discriminate the actual mechanism, which orbitals and which surface residues (Lys7, Asn54, or others) carry the photoinduced transfer, and with what absolute rates or lifetimes — that is, confirm or revise the 2008 assignment of hole transfer through the occupied porphyrin orbitals to molecular orbitals localized on surface residues. The objective is a quantitative, mechanism-level account of how photoexcitation of the Zn porphyrin moves charge through the intact protein, with falsifiable rate and pathway predictions. Direct residue-level experimental tests of those predictions, and extension of the established mechanism to related metalloporphyrin-substituted proteins and to different electrode, solvent, and temperature conditions, would strengthen such an account; the core problem is the mechanism in intact Zn-cyt c.

References

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