Modelling the effect of ascorbic acid, sodium metabisulphite and sodium chloride on the kinetic responses of lactic acid bacteria and yeasts in table olive storage using a specifically implemented Quasi-chemical primary model R. Echevarria a , J. Bautista-Gallego b, ⁎, F.N. Arroyo-López c , A. Garrido-Fernández b a Departamento de Ecuaciones Diferenciales, Facultad de Matemáticas, Universidad de Sevilla, Avda\Reina Mercedes s/n. 41012-Sevilla, Spain b Departamento de Biotecnología de Alimentos, Instituto de la Grasa (C.S.I.C), Avda\Padre García Tejero no 4. 41012-Seville, Spain c Institut “Cavanilles” de Biodiversitat i Biología Evolutiva. Universitat de València, Edifici d'Instituts, Parc Científic de Paterna, P.O. Box 22085, E-46071 València, Spain abstract article info Article history: Received 26 March 2009 Received in revised form 26 November 2009 Accepted 26 January 2010 Keywords: Quasi-chemical model Table olive Primary modelling Yeasts Lactic acid bacteria Fermentation The goal of this work was to apply the Quasi-chemical primary model (a system of four ordinary differential equations that derives from a hypothetical four-step chemical mechanism involving an antagonistic metabolite) in the study of the evolution of yeast and lactic acid bacteria populations during the storage of Manzanilla– Aloreña table olives subjected to different mixtures of ascorbic acid, sodium metabisulphite and NaCl. Firstly, the Quasi-chemical model was applied to microbial count data to estimate the growth–decay biological parameters. The model accurately described the evolution of both populations during storage, providing detailed information on the microbial behaviour. Secondly, these parameters were used as responses and analysed according to a mixture design experiment (secondary model). The contour lines of the corresponding response surfaces clearly disclosed the relationships between growth and environmental conditions, showing the stimulating and inhibitory effect of ascorbic acid and sodium metabisulphite, respectively, on both populations of microorgan- isms. This work opens new possibilities for the potential use of the Quasi-chemical primary model in the study of table olive fermentations. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Table olives constitute an important part of the Mediterranean diet. Their world production reached a total of 1,762,000 tons in the 2005/2006 season (IOOC, 2007). Processing table olives always requires a phase of fermentation or storage which is also characterized by the presence of diverse microorganisms, mainly yeasts, lactic acid bacteria (LAB) and Enterobacteriaceae (Garrido Fernández et al., 1997). The use of starter cultures for directly brined olives has been assayed at laboratory or pilot scale (Tassou et al., 2002; Panagou et al., 2003) but usually these processes are carried out based on the presence of nat- urally occurring microorganisms. Regardless of the exact process applied in the fermentation/storage of table olives, the microbial evolution of particularly yeasts and LAB, follows a similar trend: there is an active growth phase followed by a decline phase (Garrido Fernández et al., 1997; Tassou et al., 2002; Panagou et al., 2003; Arroyo-López et al., 2008). The first phase is usually the period of greater interest and has been the most frequently studied. However, the existence of continuous phases of growth and decline has recently been considered when modelling the microbial growth in directly brined olives (Arroyo-López et al., 2008), with the combined logistic-Fermi function developed by Peleg (1996) or in the controlled fermentation of cv. Conservolea green olives, using a multilayer perceptron network which was compared with the same logistic-Fermi equation and a two term Gompertz function (Panagou et al., 2007). Several models have been proposed that account for microbial growth–decline. One of them is a three-step enzymatic kinetic model (Whiting and Cygnarowicz-Provost, 1992). Other models combine expressions for both growth and decay into a single equation, such as the logistic model with a superimposed Fermi term (Peleg, 1996), the Jones and Walker model (Jones and Walker, 1993; Jones et al., 1994), the Churchill model (Membré et al., 1997) or the model combining two Baranyi-type equations for yeast fermentations in a model wine system (Del Nobile et al., 2003). Bello and Sánchez Fuertes (1995) also developed a mathematical equation to describe the behaviour of the Lactobacillus species during the ripening of Spanish “chorizo”. Recently, Ross et al. (2005) showed that models based on equations for chemical reaction systems provide insight into the growth and decline processes of microorganisms, particularly the chemical mechan- isms used in understanding nonlinear chemical dynamic processes (Epstein and Pojman, 1998). The Quasi-chemical (QC) kinetics model (Taub et al., 2003) combines the concepts of chemical kinetics and International Journal of Food Microbiology 138 (2010) 212–222 ⁎ Corresponding author. Tel.: + 34 954 692516; fax: + 34 954 691262. E-mail address: joaquinbg@ig.csic.es (J. Bautista-Gallego). 0168-1605/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ijfoodmicro.2010.01.037 Contents lists available at ScienceDirect International Journal of Food Microbiology journal homepage: www.elsevier.com/locate/ijfoodmicro