The ORAC Assay: Mathematical Analysis of the Rate Equations and Some Practical Considerations

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 (X-H) by examining the dependence of the rate of consumption of the probe (P-H) on the concentration of X-H; 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 X-H with ROO• (i.e. kx ) was much larger than that of P-H with ROO• (i.e. kp ). Using numerical solution 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 kx >> kp and the initial concentration of X-H was higher than that of P-H.