Mathematical modeling of area under the curve assessment criteria to quantify the antioxidant and pro-oxidant capacity: Coffee extracts as a case study

The development of a convenient mathematical application for testing the antioxidant and pro-oxidant capacity is essential in order to investigate potential sources of new agents and processes. In this regard, authors use the standardized values of the area under the curve of a kinetic profile of a dose–response agent, as a way to bypass the complex process of analyzing the kinetic variations of agents. In general, linear approaches are used, but such patterns frequently lead to unreliable results and misinterpretations, making it extremely difficult to compare the results from different assays. In this work, we have demonstrated the non-linearity of the dose–response area under the curve assessment criteria by means of simulations. A simple non-linear dose–response model was developed to describe the accurate response. As a case study, experimental data of extracts of unroasted coffee beans from five different country–climate locations for the two most common coffee varieties (Robusta and Arabica) were obtained using the β-carotene and crocin bleaching in vitro assays. Their antioxidant capacity was analyzed in detail and compared with commercial standards. The results show that the antioxidant capacity was greater than some of the commercial standards in terms of its maximum capacity, while when the analyses are based on rate parameters, the coffee extracts show between 6 and 40 times lower values than the standard antioxidants. In addition, to illustrate the advantages of using the standardized area units and the mathematical model developed, other more complex scenarios were recreated. We believe that the model application developed provides a simple alternative to summarize meaningful parameters that characterize the response, facilitates rigorous comparisons among the effects of different compounds and experimental approaches and helps to comprehend multi-variable scenarios. •The AUC represents a way of summarizing the kinetic part of a response.•Currently there is a lack of mathematical model to analyze the AUC dose–responses.•The criteria to test the anti- and pro-oxidant activities are developed.•The criteria are validated with data from common anti- and pro-oxidant assays.•Further capabilities of the criteria are illustrated to more complex responses.