Darwin at the molecular scale: selection and variance in electron tunnelling proteins including cytochrome c oxidase

Abstract

Biological electron transfer is designed to connect catalytic clusters by chains of redox cofactors. A review of the characterized natural redox proteins with a critical eye for molecular scale measurement of variation and selection related to physiological function shows no statistically significant differences in the protein medium lying between cofactors engaged in physiologically beneficial or detrimental electron transfer. Instead, control of electron tunnelling over long distances relies overwhelmingly on less than 14 A spacing between the cofactors in a chain. Near catalytic clusters, shorter distances (commonly less than 7 A) appear to be selected to generate tunnelling frequencies sufficiently high to scale the barriers of multi-electron, bond-forming/-breaking catalysis at physiological rates. We illustrate this behaviour in a tunnelling network analysis of cytochrome c oxidase. In order to surmount the large, thermally activated, adiabatic barriers in the 5-10 kcal mol-1 range expected for H+ motion and O2 reduction at the binuclear centre of oxidase on the 10(3)-10(5) s-1 time-scale of respiration, electron access with a tunnelling frequency of 10(9) or 10(10) s-1 is required. This is provided by selecting closely placed redox centres, such as haem a (6.9 A) or tyrosine (4.9 A). A corollary is that more distantly placed redox centres, such as CuA, cannot rapidly scale the catalytic site barrier, but must send their electrons through more closely placed centres, avoiding direct short circuits that might circumvent proton pumping coupled to haems a to a3 electron transfer. The selection of distances and energetic barriers directs electron transfer from CuA to haem a rather than a3, without any need for delicate engineering of the protein medium to 'hard wire' electron transfer. Indeed, an examination of a large number of oxidoreductases provides no evidence of such naturally selected wiring of electron tunnelling pathways.

Figure 1

Maximum distances required for tunnelling at certain rates for given activation energies (left scale). Corresponding driving force for endergonic electron transfer is shown on the right scale. With an activation energy barrier of 10 kcal mol⁻¹, a distance of less than 7 Å will be required to achieve electron transfer in a millisecond or less.

Figure 2

Distances between redox centres in cytochrome c oxidase, as described in the Protein Data Bank (PDB) crystal structure 1QLE (Harrenga & Michel 1999). Diatomic oxygen is modelled in the position of carbon monoxide as in the structure 1V54 (Tsukihara 2003).

Figure 3

Electron tunnelling simulation of oxidase using different estimates of the midpoint potentials of the individual redox couples of O₂. (a) Completely averaged O₂ redox couple values as if 100% moderated by the enzyme environment; the picosecond electron tunnelling reactions in this simulation would not be observed experimentally as they would be limited by the 10 μs O₂ diffusion rate (grey shading). (b) O₂ redox couple midpoints as in aqueous solution, but moderate 5% levelling by the protein. (c) O₂ redox couples as reported in aqueous solution, pH 7. Default reorganization energies for electron tunnelling are 0.7 eV throughout.

Figure 4

Electron tunnelling network simulation in a haem a knockout allows an examination of direct Cu_A to catalytic cluster electron transfer, which may short circuit important proton pumping action. Using the default reorganization energy and barrier for cluster reduction of 0.7 eV, Cu_A to cluster electron tunnelling is 0.4 ms (fine dashed lines). Increasing the cluster reduction reorganization energy of 1.7 eV slows this electron tunnelling to 0.2 s (medium dashed lines). A 2.5 eV reorganization energy slows this potential short circuit to about a minute.

Figure 5

Electron tunnelling network of completely reduced oxidase, with haem a present, using the 1.7 eV reorganization barrier for cluster reduction by haem a₃ as in figure 4. Oxygen reduction still takes place at the observed 30 μs rate.

Figure 6

Tunnelling simulation of the mixed valence state (i.e. Cu_A and haem a initially oxidized). (a) With average redox midpoint potentials, O₂ reduction is comparable to the O₂ reduction rate in the reduced system and not 10 times slower as experimentally observed. Electron back flow to haem a and a small amount of Cu_A are observed. (b) Raising the redox midpoint of haem a₃ and Cu_B to 320 mV, as expected for a partly reduced system, slows the O₂ reduction rate to 300 μs, comparable to the observed mixed valence rate. Only a small amount of haem a is reduced on the nanosecond time-scale.

Figure 7

According to a molecular scale of version of Darwin's principle of multiply utility (Darwin 1872), each amino acid in a protein may serve many functions, and is not in general optimized for any single function of a particular scientist's interest.