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2-electron redox chemistry

The electrochemistry of 2-electron transitions underlies a number of phenomena crucial to biological energy conversion (which itself arguably is the very essence of life).
As a function of their environment (i.e. binding sites within proteins, type of solvent etc.) 2-electron redox compounds can undergo astonishingly different types of redox transitions ranging from widely separated and seemingly independent 1-electron reductions/oxidations to strongly cooperative n=2 transitions where both electrons come or go together.
The analytical description of the relationship between the individual 1-electron redox potentials (E1 and E2) and the observable redox transitions has been worked out as early as 1932 by Michaelis and is detailed as well as illustrated by empirical examples in W. Mansfield Clark's book "Oxidation-Reduction Potentials of Organic Systems".

Outline of the formalism

If we define

[O], [R] and [I] as the concentrations of the oxidised, reduced and intermediate states,

as well as

[I]2/[O][R] = KS as the stability constant of the semireduced form,

together with the Nernst-equations:

Eh = E1 + (RT/F) ln([O]/[I]) = E2 + (RT/F) ln([I]/[R])

Eh = Em + (RT/2F) ln([O]/[R]) with Em = (E1 + E2)/2

the following relationships can be deduced:

[O] = Suv/(uv+u+1)
[I] = Su/(uv+u+1)
[R] = S/(uv+u+1)


S = [O] + [I] +[R]
u = [I]/[R]
v = [O]/[I]

e.g. u = 10((Eh-E2)/59mV) (note that "59mV" corresponds to T = 20oC)

The Eh-dependences of all relevant observables in equilibrium redox titrations can thus be calculated. A few representative examples are shown in the figure to the right (with red, brown and blue standing for [O], [I] and [R], respectively, while dashed and dotted curves represent pure n=2 and n=1 dependences, respectively)


Pertinent formulae derived from the formalism

defining ΔE = E1 - E2 and Em = (E1 + E2)/2 one obtains:

logKS = ΔE/59mV

[I] = 1/(1+10(Eh-Em-ΔE/2)/59mV + 10(Em-ΔE/2-Eh)/59mV)

maximal fraction of [I] = KS0.5/(KS0.5+2)

The intermediate ("semiquinone") redox state

If you are using EPR to monitor 2-electron redox transitions then you will most frequently be observing the intermediate, semireduced/semioxidised compound.
Theoretical titration curves and useful relationships for this intermediate redox state [I] are shown in the figures below.

[I] vs. Eh [I] vs deltaE Width of [I]-curve vs deltaE

The left figure illustrates the Eh-dependence of [I] for ΔE = (E1-E2) values ranging from +400 mV to -150 mV. The maximal observable intermediate redox state (i.e. the maximum of the curves shown in the left figure) depends on ΔE as depicted in the top figure to the right. The half-hight values of the [I] vs. Eh dependences are indicated by blue circles in the left figure. As is obvious from the figure, these half-hight values tend towards a limiting value (see blue dashed line). This means that with decreasing size of the bell-shaped titration curve of [I], the width of the curve eventually becomes constant and the curve thus scale-invariant. This relationship is shown in the bottom figure to the right. Down to ΔE-values of roughly -100 mV, the width of the [I] vs Eh curve can be straightforwardly converted into KS values, ΔE or maximal intensities of the intermediate redox state. This approach was first suggested by Robertson et al. in 1984.

Observing the transition from positive to negative ΔE on [O] or [R]

[O] vs Eh

If the experimental approach allows to observe either the oxidised ([O]) or the reduced ([R]) state of the compound (or both), it may be useful to know that in the region -50 mV < ΔE < +50 mV, the observable titration curves deviate in defined ways from standard n=1 and n=2 Nernst curves (illustrated in the figure to the left in which continuous, dotted and dashed lines represent the theoretical dependences of [O] as well as n=1 and n=2 Nernst curves). Given sufficient accuracy of the titration data, KS and ΔE can then be extracted from the empirical results by fitting the obtained data to the theoretical dependence.

Relevance to bioenergetics and specific 2-electron systems

The interface between environmental redox gradients and bioenergetic chains: A substantial number of bioenergetic substrates (i.e. reducing and oxidising environmental redox molecules) are 2-electron compounds with strongly destabilised intermediate redox states (e.g. nitrate, CO2, formate, CH4, arsenic oxyanions, dimethylsulphoxides etc...). Due to this property, they react only extremely sluggishly with 1-electron redox partners, even if the overall reaction is strongly exergonic. Using (that is, oxidising or reducing) these environmental substrates requires the intervention of redox enzymes containing catalytic centres capable of 2-electron redox chemistry. Many studied cases of such redox enzymes feature quinones (see also our webpage dedicated to quinones), flavins or molybdenum and tungsten in their catalytic sites.

2-electron gates: Bioenergetic systems use the trick of dramatically slowing exergonic redox reactions through low KS values of intermediate redox states to control the flux of reducing equivalents through the entire chains. A prominent example is the redox couple NADH/NAD+ which features an extremely destabilised intermediate redox state. This fact enables NADH to float calmly in the cytoplasm next to a great number of 1-electron acceptors with more positive redox potentials while only getting oxidised at predestined redox enzymes featuring the appropriate 2-electron redox proporties. Obviously, bioenergetic chains also contain many 1-electron compounds (think cytochromes, ferredoxins, cupredoxins ...) and mediating between 2- and 1-electron redox reactions is therefore a major task of many bioenergetic enzymes. In these cases, the redox properties of intervening 2-electron centres are generally tuned so that their intermediate redox state is neither very stable nor very unstable enabling them to perform both 2- and 1-electron reactions. Examples are the QB-site in purple bacterial reaction centres (cf. the highly stabilised semireduced state of the QA-quinone which is designed for exclusively 1-electron redox chemistry) or the Qi-site in those Rieske/cytb complexes that don't contain heme ci.

Energy conversion through electron bifurcation: The fact that a strongly destabilised intermediate redox state means that E2 becomes substantially more positive than E1 ("crossed" or "inverted" potentials, see the first figure of this webpage, bottom panel) entails the possibility of redox-energy-augmenting electron bifurcations. This principle is famously used by the Qo-site of Rieske/cytb complexes (as rationalised by Peter Mitchell, 1975) giving rise to the phenomenon of "oxidant-induced reduction" of low potential electron acceptors (Wikström & Berden, 1972). In this case, the electron bifurcating agents are quinones in binding sites imposing extreme destabilisation of the intermediate (semiquinone) redox state. More recently it has been shown that flavin-based enzymes perform very similar electrochemical reactions (Herrmann et al., 2008, Buckel & Thauer, 2013, Chowdhury et al. 2016). In contrast to the quinone-mediated Qo-site reaction (which occurs in the membrane), the flavin-based electron bifurcations seem to involve water-soluble redox partners. A recent review (Baymann et al., 2018) compares quinone- and flavin-based 2-electron properties and proposes a common framework for the phenomenon of electron bifurcation. We have tried to visualise the principle of electron bifurcations in the figure below.



Michaelis, L. (1932) Theory of the reversible two-step oxidation. J. Biol. Chem. 96, 703-715

Clark, W.M. (1960) Oxidation-reduction potentials of organic systems. Williams and Wilkins Company, Baltimore

Robertson, D.E., Prince, R.C., Bowyer, J.R., Matsuura, K., Dutton, P.L., Ohnishi, T. (1984) Thermodynamic properties of the semiquinone and its binding site in the ubiquinol-cytochrome c (c2) oxidoreductase of respiratory and photosynthetic systems. J. Biol. Chem. 259, 1758-1763

Mitchell, P. (1975) Protonmotive redox mechanism of the cytochrome bc1 complex in the respiratory chain: protonmotive ubiquinone cycle. FEBS Lett. 56, 1–6 (doi:10.1016/0014-5793(75)80098-6)

Wikström, M.K., Berden, J.A. (1972) Oxidoreduction of cytochrome b in the presence of antimycin. Biochim. Biophys. Acta 283, 403–420. (doi:10.1016/0005- 2728(72)90258-7)

Herrmann G, Jayamani E, Mai G, Buckel W. (2008) Energy conservation via electron-transferring flavoprotein in anaerobic bacteria. J. Bact. 190, 784-91

Buckel, W., Thauer, R.K. (2013) Energy conservation via electron bifurcating ferredoxin reduction and proton/Na(+) translocating ferredoxin oxidation. Biochim. Biophys. Acta 1827, 94-113 doi: 10.1016/j.bbabio.2012.07.002

Chowdhury, N.P., Klomann, K., Seubert, A., Buckel, W. (2016) Reduction of Flavodoxin by Electron Bifurcation and Sodium Ion-dependent Reoxidation by NAD+ Catalyzed by Ferredoxin-NAD+ Reductase (Rnf). J. Biol. Chem. 291, 11993-2002 doi: 10.1074/jbc.M116.726299.

Baymann, F., Schoepp-Cothenet, B., Duval, S., Guiral, M., Brugna, M.,
Baffert, C., Russell, M.J. and Nitschke, W. (2018)
Frontiers in Microbiology 9, 1357
On the natural history of flavin-based electron bifurcation

Last update: September 22, 2020
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