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The ORAC Assay: Mathematical Analysis of the Rate Equations and Some Practical Considerations
Author(s) -
Arellano Juan B.,
MelladoOrtega Elena,
Naqvi K. Razi
Publication year - 2017
Publication title -
international journal of chemical kinetics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.341
H-Index - 68
eISSN - 1097-4601
pISSN - 0538-8066
DOI - 10.1002/kin.21086
Subject(s) - chemistry , oxygen radical absorbance capacity , reaction rate constant , ordinary differential equation , absorbance , kinetic energy , ode , thermodynamics , computational chemistry , analytical chemistry (journal) , antioxidant capacity , antioxidant , kinetics , organic chemistry , mathematics , differential equation , chromatography , quantum mechanics , physics
ABSTRACT ORAC (oxygen radical absorbance capacity), a method widely used for measuring the total antioxidant capacity of biological samples, can also be used for the determination of the relative reactivity of an antioxidant compound (XH) by examining the dependence of the rate of consumption of the probe (PH) on the concentration of XH; initial conditions are chosen in such a way that the rate of consumption of the starting reactants may be assumed to follow a drastically simplified kinetic scheme, and the steady‐state approximation for the concentration of the azo compound peroxyl (ROO • ) radical is invoked to simplify the analysis. Here we first attempted to find an analytical solution to the coupled first‐order ordinary differential equations (ODEs) of the minimal ORAC kinetic system, applying Lie symmetry group theory without any precondition. However, the Lie symmetry transformations applied to the Chini equation, which appeared after mathematical transformations, showed that the form of the coefficients of the Chini equation precluded the analytical solution of the minimal ORAC kinetic system through symmetry reduction. Consequently, an approximate analytical solution was sought, valid for the case when the bimolecular rate constant of XH with ROO • (i.e., k x ) was much larger than that of PH with ROO • (i.e., k p ). Using numerical solutions of the original set of ODEs of the ORAC kinetic system, the quality of the approximate solution was inspected under conditions that correspond to those employed in several ORAC methods together with a low initial concentration of the azo compound radical initiator. The simulations allowed us to conclude that the approximate analytical solution of the ODEs of the minimal ORAC kinetic system was not entirely devoid of academic interest, but its applicability was restricted to conditions where both k x ≫ k p and the initial concentration of XH was higher than that of PH.