= Antioxidant reaction competition
\b[<Antioxidant reaction competition>] is competition between reactions that consume the same reactive intermediate, such as interception of a <radical (chemistry)> by an <antioxidant> and attack by that <radical (chemistry)> on a susceptible substrate. A large <reaction rate constant> alone does not establish which route dominates: the local <concentrations> of the reaction partners also enter the <reaction rates>.
For an original two-route model, let a radical react with donor $\mathrm{AH}$ or substrate $\mathrm S$. Hold both partner concentrations constant, with second-order rate constants $k_A,k_S$. The corresponding <pseudo-first-order reaction> rates per radical are
$$
a=k_A[\mathrm{AH}],\qquad b=k_S[\mathrm S].
$$
The probability of surviving without either event for time $t$ is $e^{-(a+b)t}$. Integrating the instantaneous interception probability gives
$$
f_A=\int_0^\infty a e^{-(a+b)t}\,\mathrm dt=\frac a{a+b},\qquad
\tau=\frac1{a+b},
$$
where $\tau$ is the mean waiting time for the first event. This is a <competing risks> calculation for the stipulated constant-rate reaction model.
Take chosen $k_A=10^6\,\mathrm{L\,mol^{-1}\,s^{-1}}$, $[\mathrm{AH}]=10\,\mathrm{\mu mol\,L^{-1}}$, $k_S=10^2\,\mathrm{L\,mol^{-1}\,s^{-1}}$ and $[\mathrm S]=0.10\,\mathrm{mol\,L^{-1}}$. Both effective rates are $10\,\mathrm{s^{-1}}$, so interception has probability $1/2$ and the mean waiting time is $0.050\,\mathrm s$. Raising only the donor concentration tenfold gives $f_A=10/11$ and $\tau=1/110\,\mathrm s$.
This fraction describes the first reaction, not necessarily final protection. If substrate attack regenerates another reactive radical, <radical chain propagation> can continue. In a simplified chain where each event either propagates with probability $1-f_A$ or terminates by trapping with probability $f_A$, the expected number of propagation events satisfies
$$
E=(1-f_A)(1+E),\qquad E=\frac{1-f_A}{f_A}=\frac ba.
$$
Depletion, additional termination and movement between phases alter this model.
An <inhibited autoxidation assay> measures a consequence of such chain chemistry under defined conditions. Primary work compared inhibited-oxidation measurements of lipid-soluble chain-breaking activity with independent chromatographic measurements of <vitamin E> in plasma and membrane preparations.<Is vitamin E the only lipid-soluble, chain-breaking antioxidant in human blood plasma and erythrocyte membranes? by G. W. Burton and others>[Abstract, inhibited-autoxidation and HPLC comparison]{ref} That independent comparison is stronger evidence than assigning protection from the chemical label <antioxidant> alone.
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