Use of the Nernst Equation to Estimate the Spontaneity of a Redox Reaction (or, Here, the Reduction Potential for a "Composite" Half-Reaction)

This is not likely to be of interest to many people, but it's useful as a crude way of assessing the potential for a given reductant to reduce another species (which functions as the oxidant in the forward reaction). I was just realizing that one could also use the Nernst equation to estimate the upper or lower boundary for the reduction potential (an unknown, which is E0(sub1)) of the half-reaction for a reductant, as long as one knows that the overall reaction is occurring (deltaE > 0). In this article [Schafer and Buettner, 2001: (http://www.healthcare.uiowa.edu/corefacilities/esr/education/2003/appendix/FRBM-Redox-2001.pdf)(http://www.ncbi.nlm.nih.gov/pubmed/11368918)], the authors discuss the use of the Nernst equation (see below) to calculate deltaE for the reduction of a given species (Ox2, which in this case is ferryl heme) by a given reductant (in this case, a hydroxamate-based drug). In one article, the authors found that the rate constant was half-maximal at a ratio of reductant to ferryl heme of about 20:1 (200 uM reductant/10 uM ferryl heme), and [Hirst and Goodwin, 2000: (http://www.jbc.org/content/275/12/8582.full.pdf+html)(http://www.ncbi.nlm.nih.gov/pubmed/10722697?dopt=Abstract)] found that, until the H2O2 was consumed, the "initial steady-state" ratio of ferryl to ferric heme, for an in vitro system in which a cytochrome c peroxidase enzyme was functioning catalytically (the enzyme is "cycling" and has a supply of H2O2 or O2), was, at a maximum, ~0.6 (Hirst and Goodwin, 2000). Koppenol and Liebman (1984) [Koppenol and Liebman, 1984: (http://pubs.acs.org/doi/abs/10.1021/j150645a024)] estimated that the redox potential for the ferryl heme/ferric heme ["compound II/metmyoglobin" (Koppenol and Liebman, 1984, p. 100)] redox couple is about +990 mV (+0.99 V). E0(sub1) is the reduction potential for a "composite" of these two reduction reactions:

RNO(rad) (nitroxide) + e(-) ---> RNO(-) (hydroxamate)
RN+=O (nitrosonium) + e(-) ---> RNO(rad) (nitroxide)

That's the convention for writing the half-reactions. It's oxidant + n(electrons donated by the reductant to the oxidant) ---> reductant (Schafer and Buettner, 2001). This would work more effectively if there were only one possible reaction, instead of two, but it's still potentially useful. Some people approximate deltaE and say that deltaE = E0(sub2) - E0(sub1). E0(sub2) = (the reduction potential or redox potential for the compound or species that's being reduced in the forward reaction), and E0(sub1) is the reduction potential for the species being oxidized in the forward reaction shown below. That approximation gives slightly different numbers, but the numbers are sort of similar and can sometimes be similar enough to get a sense of things. The Nernst equation takes into account the stoichiometry (numbers of species taking part in the half reactions and overall reactions), and that takes into account entropy (as in GSSG ---> 2GSH, forming two molecules from one), etc. The Nernst equation also takes into consideration the temperature (in the 59.1 number) and concentrations. High concentrations of one species can sometimes affect the likelihood that deltaE will be greater than 0, meaning that the rxn will be spontaneous (as in E greater than 0 for an electrochemical cell). The less than/greater than symbol (blogger won't let me put those symbols in without confusing the html code or whatever, sometimes) reverses directions because it's necessary to multiply by a negative 1, as in "crayon-based third-grade math." Actually, I have to go the "crayon route" when I do math, to avoid making errors. When one plugs those numbers into the equation and applies the crayon method, one gets this: