86 C.E. Kosegarten et al. / Procedia Food Science 7 ( 2016 ) 85 – 88
Mathematical modeling tools, together with experimental data, are utilized for estimating microbial responses in
order to define processing and storage conditions for processed foods. Today, predictive microbiology considers
kinetic models that allow predicting microbial growth in a wide range of conditions. These models, however, are not
able to predict information under conditions that result in no growth1. With the aim of developing predictive models
that describe the growth/no-growth boundary, some probabilistic models have been evaluated as useful tools for
defining the combination of factors to prevent the growth of microorganisms2, 3. Furthermore, time-to-fail models
have been used to estimate the time at which microbial growth occurs4. Molds are toxicological and spoilage
microorganisms that may produce mycotoxins; particularly, Aspergillus species have the ability to grow in a wide
range of environmental conditions and foods. Mold growth in food products depends on several factors such as
product composition, pH, aw, temperature, composition of the atmosphere, presence and concentration of
preservatives, and storage time. Since aw and temperature are the most important factors for Aspergillus responses,
several approaches take into account such factors during the estimation of spoilage (failure) time5, 6. However, most
available models ignore factors such as food composition and structure, as well as potential microbial interactions
and the presence of antifungal agents7. In this work, the response of A. flavus in a food model system under different
conditions was obtained. Then, a probabilistic model that considers the combinations of studied factors (aw, pH, fat,
protein, cinnamon essential oil (CEO), and incubation temperature) was developed to predict the growth boundary
for A. flavus. The performance of the growth/no-growth and time-to-fail models are also presented, comparing the
obtained predictions with those obtained through traditional growth kinetics using the Gompertz equation.
2 Materials and Methods
2.1 Experimental design and inoculation procedure
A Box-Behnken design was used to evaluate the effect of different factors on A. flavus lag time and radial growth.
The studied variables were incubation temperature (15, 25, 35°C), casein concentration (0, 5, 10%), corn oil
concentration (0, 3, 6%), aw (0.900, 0.945, 0.990), CEO (0, 200, 400 ppm), and pH (3.5, 5.0, 6.5). Every
combination was evaluated by triplicate. For each experiment, model systems were prepared with a sucrose solution
to adjust aw, casein (Sigma Chemical Co., Steinheim, Germany), corn oil (Mazola, Monterrey, Mexico) and potato
dextrose agar (3.9 g /100 g solution). The pH was adjusted with 0.1 N HCl or NaOH solutions (Merck, Darmstadt,
Germany) as appropriate. In systems containing corn oil, Tween 20 at 2% (w/w) (Chemical Meyer, Tláhuac, Mex)
was added as emulsifier. Systems were poured into Petri dishes and depending on the experimental design, tested
CEO (Aromatic Chemicals Potosinos SA de CV, San Luis Potosi, Mex) was added. A. flavus (ATCC 18672),
obtained from the Food Microbiology Laboratory at the University of the Américas Puebla, was grown in PDA
(Becton Dickinson de Mexico SA de CV, Cuautitlan, Edo. Mex) at 25°C during 7 days. The culture surface was
washed and spores were recovered to obtain a suspension of §106 spores/mL. Petri dishes were inoculated with 5 μL
of the spore suspension and incubated at selected temperatures in sealed containers (avoiding anoxic conditions).
Mold growth was daily monitored and the diameter of the colonies was measured for 50 days.
2.2 Modeling of growth curves.
The mold growth curves were modeled by the Gompertz equation, Eq. (1), by fitting the model parameters using
ሻሻ where ߣ ൌ ሺܾ െ ͳሻȀܿ and ߤൌ
ሺܾ െ ͳሻȀߣ
where: ȝ is the maximum growth rate (1/h), A is the maximum growth, Ȝ is the phase of adaptation (h), D is the
colony diameter (mm) at time t (h), D0 is the initial diameter of the colony (mm), and a, b, c are Gompertz’s eq.
parameters. In order to determine the parameters dependence on the evaluated factors (temperature, aw, % protein, %
fat, pH, CEO concentration (ppm)), a response surface design was utilized for obtaining the coefficients of a
polynomial model for the significant (p<0.05) variables and interactions.