Ergosterol and Colony Diameter

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Fitting of colony diameter and ergosterol as indicators of food borne mould

growth to known growth models in solid medium

Sonia Marn, Dolors Cuevas, Antonio J. Ramos, Vicente Sanchis

PII: S0168-1605(07)00464-3

DOI: doi: 10.1016/j.ijfoodmicro.2007.08.030

Reference: FOOD 4118

To appear in: International Journal of Food Microbiology

Received date: 30 June 2006

Revised date: 3 July 2007

Accepted date: 10 August 2007

Please cite this article as: Marn, Sonia, Cuevas, Dolors, Ramos, Antonio J., Sanchis,Vicente, Fitting of colony diameter and ergosterol as indicators of food borne mouldgrowth to known growth models in solid medium, International Journal of Food Microbiol-ogy (2007), doi: 10.1016/j.ijfoodmicro.2007.08.030

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http://dx.doi.org/10.1016/j.ijfoodmicro.2007.08.030http://dx.doi.org/10.1016/j.ijfoodmicro.2007.08.030http://dx.doi.org/10.1016/j.ijfoodmicro.2007.08.030http://dx.doi.org/10.1016/j.ijfoodmicro.2007.08.030


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FITTING OF COLONY DIAMETER AND ERGOSTEROL AS INDICATORS OF FOOD

BORNE MOULD GROWTH TO KNOWN GROWTH MODELS IN SOLID MEDIUM

Running title: Fitting mould growth to models

Sonia Marn*, Dolors Cuevas, Antonio J. Ramos and Vicente Sanchis

Food Technology Department, Lleida University, CeRTA-UTPV, Rovira Roure 191, 25198

Lleida, Spain

*Corresponding author. Mailing address: Food Technology Department, Lleida University,

CeRTA-UTPV, Rovira Roure 191, 25198 Lleida, Spain. Phone: 34 973702555. Fax: 34

973702596. E-mail: [email protected]


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ABSTRACT

Growth of a range of 14 common food spoilage fungal species was evaluated along

time as a function of both colony diameter and ergosterol content on malt extract agar.

Growth was assessed under different environmental conditions following a central composite

design. The suitability of using either linear, Gompertzs or Baranyis models for primary

modelling of the results was tested. Regarding colony diameters, using either linear or

asymptotic Baranyis function gave better estimations of growth rate and lag phase when no

asymptotic trend was observed. When a decrease in growth rate was observed with time,

standard Baranyis model was chosen, although the search for new mechanistic models

specific for moulds would probably improve the estimations. The use of Gompertz equation

led, in general, to overestimated parameters. Ergosterol showed good performance as a

fungal growth indicator for the whole range of species. Finally, significant correlation

coefficients were found between ergosterol and colony diameters, suggesting that both

parameters may be useful for primary modelling and thus for subsequent secondary

modelling.

Keywords: fungi, food spoilage, growth, modelling, sigmoidal


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INTRODUCTION

Predictive microbiology has traditionally dealt with prediction of food spoilage by bacteria.

The non-pathogenic nature of moulds together with the lack of good methods for assessing

their growth are the reasons why they have been neglected in predictive microbiology

researches. However, moulds are important causative agents of economical losses mainly

regarding cereals and their derivatives. In indoor environments fungal volatiles/mycotoxins

have been shown to provoke adverse health effects (Samson et al., 1994). In addition, the

increasing concern regarding the presence of mycotoxins in foods, and the difficulty of

eliminating them from the foodstuffs once produced, has highlighted the importance of

preventing growth of toxigenic fungal growth as the main alternative for preventing mycotoxin

contamination in foodstuffs.

Mould growth (expressed as increase in colony diameter) was first empirically

modelled against time using the model of Baranyi et al. (1993) originally developed for

bacterial growth. This model has been successfully used to fit growth of bacteria and yeast,

and filamentous fungi such as Penicilliumroqueforti(Valik et al., 1999) andAspergillus flavus

(Gibson et al., 1994). The modified version of the Gompertz model (Zwietering et al., 1990)

has been sometimes selected for empirically modelling mould growth on the basis of its

proven flexibility to different asymmetrical growth data (Char et al., 2005). In addition, the

maximum growth rate (m) estimated by a modelling step is equivalent to the slope of the

straight line observed on the plot. From these primary models some parameters are usually

estimated such as m and lag phase (), which are subsequently used for secondary

modelling.

Modelling of colony diameter may be useful for research purposes; however, it is not

a measurable parameter in routine food analysis. Ergosterol analysis, which accounts for the

total fungal population in food samples, may be an alternative, although its determination

may be tedious and lengthy. In previous kinetic studies with Penicillium expansum,

ergosterol determination showed lower repeatability and sensitivity than colony diameters

measurements (Marn et al., 2006).


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The objective of this study was to compare the commonly used growth models for

primary modelling in order to assess their usefulness for estimation of growth parameters.

Also the use of ergosterol, besides colony diameters, as mould growth indicator for primary

modelling was assessed. Secondary modelling was not studied in the present work.

MATERIALS AND METHODS

Fungal isolates

The strains belonged to 14 fungal species representing general common food contaminants

found in intermediate moisture foods:Alternaria alternata (Fr.) Keissl. CECT2662,

Aspergillus carbonarius (Bainier) Thom CECT2086,A. flavus Link CECT2687,A. ochraceus

K. Wilh. NRRL3174,A. parasiticus Speare CECT2688, Cladosporium cladosporioides

(Fresen.) G.A. de Vries CECT2110, Eurotium amstelodamiL. Mangin CECT2586, Fusarium

graminearum Schwabe CECT2150, F. verticillioides (Sacc.) Nirenberg 25N, Mucor

racemosus Fresen. CECT2253, Penicillium chrysogenum Thom CECT2802, P. expansum

Thom CECT2278, P. verrucosum Dierckx CECT2906, and Rhizopus oryzae Went & Prins.

Geerl. CECT2339 (CECT: Spanish Type Culture Collection).

Experimental design

Experimental runs were generated by a Central Composite Design (circumscribed, alpha=2)

by means of The Unscrambler version 7.6. The factors entered were aw (0.85-0.95),

temperature (15-30C), pH (5-7) and potassium sorbate concentration (0.5-1.5%), and the

program generated a model with a centre point which was tested seven times as well as 24

test samples which were prepared and carried out in a random sequence (Table 1). The

levels of the factors were chosen to simulate those of intermediate moisture foods kept at

room temperature, thus susceptible of fungal spoilage. Five different sets of inoculated Petri

plates were prepared which were assessed for fungal growth diameters periodically and

analysed for ergosterol content when colonies attained approximately 15, 30, 45, 60 and 75


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mm of diameter (31 experiments x 14 isolates x 5 sampling times = 2170 ergosterol assays).

Experiments lasted for no more than 6 months.

Media

Malt Extract Agar (MEA) was used as medium. The pH of the medium was adjusted to pH

levels of 4-7 by using McIlvaines buffer consisting of 0.1M citric acid and 0.2 M Na2HPO4,

while pH 8 was achieved by means of NaOH. Glycerol was added to the media in order to

prepare media at 0.95, 0.90, 0.85 and 0.80 aw levels. Experimental curves were built in order

to calculate the amount of buffer solutions and glycerol to be added to the media. For the

later purpose initial medium was prepared with different glycerol concentrations and final aw

measured in each case with an Aqualab (Decagon, Pullman, USA), subsequently g of

glycerol added were plotted against aw and a suitable calibration curve was fitted. Finally,

potassium sorbate was added at the required concentrations. All 31 media were prepared

separately, autoclaved and plated onto 9-cm Petri plates. Water activity values were checked

in the prepared plates, as well as pH (Crison micropH2000 pH meter, Crison, Barcelona,

Spain).

Inoculation and incubation

The strains were grown on Malt Extract Agar (MEA) for 14 days and suspensions (105CFU

ml-1) were prepared in 0.005% Tween 80 solutions. Petri plates were single point inoculated

(101-102 CFU) in the middle for each fungal suspension. Petri plates with the same water

activity level were enclosed in sealed polyethylene bags and placed in suitable incubators

following the experimental design.

Measurement of colony diameters

Periodically, daily or as required, Petri plates were observed and colony diameters recorded.

When colonies achieved approximately 15, 30, 45, 60 and 75 mm of diameter, one Petri

plate per experiment and strain (434 in total) was taken and analyzed for ergosterol content.


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Ergosterol analysis

Colonies (on agar) were cut in small squares and extraction carried out. A modification of the

method by Gourama and Bullerman (1995) was applied. Recovery rates were calculated and

found to be around 84% for the concentrations found in the study; limit of detection was of 1-

2 g per plate. Briefly, fungal colony was extracted with 40 ml (or 20 ml in case of tiny

colonies) of 10% KOH in methanol by magnetically stirring for 30 min. A 10-ml aliquot was

transferred to a screw cap tube and placed in a hot water bath (55-60 C) for 20 min. The

tubes were then allowed to cool to room temperature. Three milliliters of water and 2 ml of

hexane were added to the tubes, which were then agitated in a Vortex mixer for 1 min. After

separation of layers, the upper layer (hexane) was transferred to a 10-ml vial. Hexane

extraction was repeated twice using 2 ml each time. The extracts were combined and

evaporated to dryness under a stream of nitrogen. The dry extracts were dissolved in 2 ml of

methanol, and forced through 0.45 m acetate filters. The HPLC equipment consisted of a

Waters 515 isocratic pump (Waters Associated, Milford, MA), a Waters 717plus autoinjector,

a Waters Spherisorb ODS2 C18 column (4.6 x 250 mm). The Waters 2487 variable

wavelength UV detector was set at 282 nm. The mobile phase was methanol at 1 ml min

-1

.

Ergosterol standard was purchased from Sigma (St. Louis, Mo) for calibration line (R2=0.99).

Statistical analyses

From the 434 experiments, those carried out with Fusarium species, C. cladosporioides, A.

alternata andA. carbonarius led to no-growth after 180 days in more than 74% of the cases,

and erratic under most of the remaining conditions, thus the authors decided not to use them

in this study. From the remaining strains (279 experiments), 142 experimental data

corresponded to growth kinetics, 137 to no-growth after 180 days.

Root-square ergosterol content and colony diameters were plotted against time. For

each treatment, diameters were adjusted to the sigmoidal Baranyis function [1] (Baranyi et

al., 1993), and to the Gompertz model modified by Zwietering et al. (1990) [2] by using


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Statgraphics Plus 5.1; also the linear model was adjusted using Microsoft Excel 2000.

Additionally, a biphasic Baranyis function was used in which the logarithmic term where Dmax

appears was deleted in order to omit the upper asymptote, as suggested by Valik et al.

(1999) [3].

[1]

+=

)exp(D

1-A)*exp(1log-A*diametercolony

max

mm

where [ ])**exp()*exp()*exp(log*1

mmmmm

tt

tA ++=

t=time (d)

m= maximum growth rate (mm d-1)

= lag phase before visible growth (d)

Dmax= maximum diameter attained, in most of the cases, the diameter of the Petri dish

[2]

+= 1)(*

*expexp*diametercolony

max

max tD

eD m

[3] [ ]

++= )**exp()*exp()*exp(log*1*diametercolony m mmmm

m

tt

t

Maximum growth rates, lag phases and final diameter attained were estimated from

the sigmoidal models, while maximum growth rates and lag phases were estimated from the

linear and Baranyis biphasic ones. In the linear case, lag phase was estimated through the

intercept of the regression line with the X-axis.

RESULTS

Primary modelling of colony diameters: comparison of sigmoidal, linear and Baranyis

biphasic models

Firstly, modelling was carried out in colony diameter data. In general, data plots showed,

after a lag phase, a linear trend with time. Only treatments 4, 13, 19 and 31 (0.85 aw) and


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those at 0.90 aw and 22.5C led in some cases to asymptotic curves (Fig. 1, 2), due to the

difficulty of maintaining a constant aw for such long periods of time. Thus under normal

circumstances convergence of the sigmoidal models relied on the diameter of the Petri dish

as upper asymptote; this means that the use of these models has no biological support as

growth functions in this case as the upper asymptote is an external parameter. Easier

convergence was found when using modified Gompertz model, than with Baranyis one.

However, the former led to overestimations of the final diameter, although this point is not

important due to the poor relevance of this parameter for practical issues, as long as it does

not interfere in m and estimations. Regarding linear model, plotting of the results against

time and manual (and subjective) selection of the straight part of the line (avoiding lag

phase and asymptotic one, if any) was required. Finally, Baranyis biphasic model seemed to

be the best choice in most of the cases (no subjectivity involved). R2 obtained for the 31

treatments and 9 strains ranged from 94 to 100%, 87 to 99%, 94 to 100%, and 78 to 100%

for the Gompertz, Baranyi, biphasic Baranyi and linear models, respectively. However, it is

known that, depending on the distribution of the experimental points, good R2 do not

necessarily mean accurate estimation of parameters.

In general, higher growth rates and lag phases were obtained when using modified

Gompertz model than with the others, the confidence intervals (P


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biphasic model is the best alternative, while complete Baranyis model may be the best when

an asymptotic stage is achieved.

Fig 4 shows two examples of the variability of the observed data and their respective

adjusted functions for the 7 replicates of the centerpoint (0.90 aw, 22.5C, pH 6, 1%) adjusted

to biphasic Baranyis model. Coefficients of variation of the observed values along time were

high around the lag phase but they decreased to less than 18% after 13-15 days of

incubation.

Primary modelling of ergosterol content

Ergosterol content did not show an exponential trend versus time, but a potential one (Fig 5).

Thus log transformation of the data was less useful than root-square one, which led to both

homogenisation of variance and linearisation of the data versus time. Data were

subsequently adjusted to either Baranyis or Baranyis biphasic model, depending on each

set of data. In this case regression analyses were carried out with 6 observed values over

time, and this resulted in high error levels of the estimations when compared to diameter

models (Table 2 and 3). Fig 5 also shows two examples of the variability of the observed

data for the 7 replicates of the centerpoint adjusted to either standard or biphasic Baranyis

model.

Fig 6 shows the experimental points adjusted to either standard or biphasic Baranyis

model for 4 different treatments. Ergosterol accumulation along time followed a similar trend

to diameter increase for the different treatments.

Correlation between colony diameters and ergosterol content

Significant Pearson correlation coefficients were found between colony diameters and root-

square (ergosterol content) of colonies of each of the strains tested under the 31 treatments

tested ranging from 0.66 to 0.91. The rate root-square(ergosterol)/diameter was rather

constant (between 0.20-0.24 forAspergillus species, 0.18-0.21 forPenicillium species, 0.16


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forE. amstelodami, while R. oryzae and M. racemosus, with a few observations, showed

rates of 0.13 and 0.29, respectively) (Fig. 7).

DISCUSSION

One challenge when working with moulds is their explorative and exploitative nature for

colonising solid substrates (Robinson et al., 1993), thus using liquid media for modelling their

growth (as generally done for bacteria) is not realistic. In the literature, the most common

used method to assess mould growth in solid substrates is colony diameter measurement,

with some authors using CFU counts (Vindelov and Arneborg, 2002), although it has been

shown that this latter parameter is linked to sporulating abilities of the species tested and has

poor correlation to biomass weight (Marn et al., 2005). Although easily assessed, colony

diameter measurement is difficult to be applied to real food substrates. Alternatively,

ergosterol content has been used for mould contamination in cereals and other food products

(Gourama and Bullerman, 1995; Saxena et al., 2001). This parameter, which accounts for

total fungal biomass has been shown to be correlated to biomass dry weight for the same

strains tested in the present study; a ratio between 0.6 to 1.6 mg dry biomass per g

ergosterol was found depending on the species tested (Marn et al., 2005).

In this study the total pool of data obtained represent most of the situations one can

encounter when dealing with fungal growth kinetics (from optimum growth to no-growth,

through erratic growth under certain limiting conditions). The responses of the 9 strains to the

31 treatments assayed were observed to be either sigmoidal or just have a lag phase

followed by a linear one. In general mould colony diameters have been primary modelled in

the past by Baranyis, linear and modified Gompertz models, both linear and Baranyi

approaches being the most common, but no study has compared before the usefulness of

each of them. This study shows that under favourable growth conditions, the linear model

may be the best alternative, however if the experimental design includes suboptimal

conditions, the lag phase makes the linear model not convenient. On the other hand, both

Baranyi and Gompertz models have been taken from bacterial growth curves in which log


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(N/No) is plotted against time in the presence of limited nutrients; thus after an initial lag

phase, an exponential multiplication of bacterial cells is observed after which, and due to the

shortage of nutrients or the accumulation of toxic metabolites the growth rate becomes

constant and eventually decreases. In this study, and from our previous experience, when

plotting diameters (or radiuses) of a mould colony growing in an agar Petri plate against time,

a lag phase is observed, followed by a linear phase, but in most of the cases no decrease in

growth rate is observed before the edge of the Petri plate is reached. Under constant

conditions a fungal colony would then probably grow indefinitely, if the agar plate was

unlimited; thus, in the absence of the edge of the plate, the Baranyis biphasic model would

be probably the best one (or the linear one in the absence of lag phase). This hypothesis

contradicts the results obtained by Valik et al. (1999), who described forPenicillium

roquefortidiameter a growth curve typical of microbial growth with lag-phase, linear phase

and upper asymptote when using 17 cm Petri plates with asymptotic values between 2 and

12 cm, well before the edge was reached.

Equivalent estimated parameters (m, ) were found using the different models except

for Gompertz one which was shown to overestimate both of them. Sigmoidal models other

than the ones traditionally used may have better potential to describe fungal growth process.

Under many circumstances, primary modelling yields reliable information on the value of m,

but poor estimates are often obtained for the lag time (McKellar, 1997).

Ergosterol was primary modelled for a range of food borne moulds for the first time.

Mould colonies, while growing at a constant growth rate in diameter, yield by branching an

exponential amount of biomass and consequently, of ergosterol amount. Thus ergosterol

content over time should show a lag phase, followed by an exponential increase phase, and

if log transformed, the curve should show a lag phase followed by a linear increase. In our

case, when ergosterol results were log transformed, a final phase in which ergosterol did not

increase exponentially anymore or even stopped was observed, while a clear decrease in

diameter growth rate was not observed, suggesting that even the colony extended in area, a

decrease in the rate of ergosterol accumulation occurred. This supports the work by Koch


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(1975), who reported that moulds form mycelium whose weight, except at the early stage of

growth, does not increase exponentially. For this reason, the square-root transformation was

chosen in the present work for data transformation in order to homogenise variance of

ergosterol data.

A previous work on growing colonies ofP. expansum and relationship with ergosterol

accumulation showed that ergosterol determination leaded to increased differences among

replicates compared to diameter measurements (Marn et al., 2006). However, in this study,

variation within replicates observed for colony diameters and ergosterol content was similar,

suggesting that the latter could be a good alternative. Also primary modelling of both square-

root ergosterol and colony diameters led to similar R2 values.

Primary models are the first step for estimation of parameters such as m, or time

for a certain colony size to be observed. Time for visible growth can also be directly observed

with no need for primary modeling. Lag phase and time for visible growth should have similar

values, the latter being slightly higher, and the former being always estimated through a

regression process. Dantigny et al. (2002) stated that lag time coincided with the completion

of the germination process; say more than 99% of germination. Germination has also been

studied by mycologists, from the predictive point of view, because prevention of germination

invariably leads to prevention of growth. However studies are lengthy and tedious, thus

prediction of lag time for growth would substitute parameters such as lag phase for

germination, germination rate and time for 10 or 90% germination.

This work has shown that, among the commonly used models, all of them showing

similar goodness of fit, Baranyis model, either biphasic or not, depending on the observed

kinetics, may be the best alternative for an accurate estimation of m and . Both growth rate

and lag phase have been used in the past for secondary modelling; m being used for

secondary modelling in about 75% of the publications. m may be a useful parameters to

compare treatments, and also complements lag phase data. However, when dealing with

prediction and prevention of fungal growth in food products, two parameters could be

considered: i) the lapse of time to reach a visible colony which makes a product rejectable,


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and ii) the lapse of time to reach a colony size which might be conducive to mycotoxin

accumulation; as it is not possible to establish such a correlation, in case of mycotoxigenic

species any growth should be prevented. Thus in this context growth rate may be of poor

application, and other parameters such as lag phase, time for a 2-3 mm visible colony, etc,

may be of interest. Secondary modelling will be the next step in this research. Also it is of

great importance the validation of secondary models obtained in real food matrices.

ACKNOWLEDGEMENTS

This work was supported by the Spanish Government (CICYT, Comisin Interministerial de

Ciencia y Tecnologa, project AGL 2004-06413/ALI, and Ramon y Cajal program).

REFERENCES

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chevalieri,Aspergillus fumigatus and Penicillium brevicompactum in Argentine milk jam.

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Dantigny, P., Soares Mansur, C., Sautour, M., Tchobanov, I., Bensoussan, M., 2002.

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Gibson, A.M., Baranyi, J., Pitt, I.J., Eyles, M.J., Roberts, T.A., 1994. Predicting fungal growth:

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Gourama, H., Bullerman, L.B., 1995. Relationship between aflatoxin production and mold

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technologie-foo 28, 185-189.

Koch, A.L., 1975. The kinetics of mycelial growth. Journal of General Microbiology. 89, 209-

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Marn, S., Morales, H., Ramos, A.J. Sanchis, V., 2006. Evaluation of growth quantification

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Ergosterol content ofRhizopus oligosporus NRRL 5905 grown in liquid and solid

substrates. Applied Microbiology and Biotechnology 26, 456-461.

Robinson, C.H., Dighton, J., Frankland, J.C., 1993. Resource capture by interacting fungal

colonizers of straw. Mycological Research 97, 547-558.

Samson, R.A., Flannigan, B., Flannigan, M.E., Verhoef, A.P., Adan, O.C.G., Hoekstra, E.S.,

1994. Health implications of fungi in indoor environments. Elsevier, Amsterdam, The

Netherlands.

Saxena, J., Munimbazi, C., Bullerman, L.B., 2001. Relationship of mould count ergosterol

and ochratoxin A production. International Journal of Food Microbiology 71, 29-34.

Valik, L., Baranyi, J., Grner, F., 1999. Predicting fungal growth: the effect of water activity

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Vindelov, J., Arneborg, N., 2002. Effects of temperature, water activity, and syrup film

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FIGURE CAPTIONS

Figure 1. Run1 (0.90 aw, 22.5C, pH 6, 1% sorbate) and run14 (1.00 aw, 22.5C, pH 6, 1%

sorbate) colony diameters raw data and adjusted to (a) Baranyi, (b), Gompertz, and (c) linear

models forA. flavus (), A. ochraceus ({), P. expansum (), P. verrucosum (U), E.

amstelodami() and R. oryzae ().

Figure 2. Run3 (0.95 aw, 15C, pH 7, 0.5% sorbate) and run16 (0.95 aw, 30C, pH 7, 0.5%

sorbate) colony diameters raw data and adjusted (a) Baranyi, (b), Gompertz, and (c) linear

models forA. flavus (), A. ochraceus ({), P. expansum (), P. verrucosum (U), E.

amstelodami() and R. oryzae ().

Figure 3. Estimated m and through modified Gompertz (), Baranyis (z) and linear ()

models for 10 sets of raw data generated by (a) Baranyis biphasic function, (b) standard

Baranyis function and (c) modified Gompertz model (m=3; =10) with data points distributed

as a normal distribution with 1 variance. Error bars are the confidence intervals of the

estimated parameters (P


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sorbate) square-root ergosterol raw data and adjusted to Baranyis model forA. flavus (),

A. ochraceus ({), P. expansum (), P. verrucosum (U), E. amstelodami() and R. oryzae

().

Figure 7. Relationship between colony diameter and square-root ergosterol content for (a)A.

parasiticus and (b) P. chrysogenum.


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Table 1. Central composite design with 4 designed variables and 31 run samples.

Run Water activity Temperature

(C)

pH Potassium sorbate

concentration (%)

1 0.90 22.5 6 1.0

2 0.95 15.0 5 1.53 0.95 15.0 7 0.5

4 0.85 30.0 7 1.5

5 0.80 22.5 6 1.0

6 0.95 15.0 7 1.5

7 0.90 7.5 6 1.0

8 0.90 22.5 6 1.0

9 0.90 22.5 6 1.0

10 0.85 15.0 5 0.5

11 0.95 30.0 5 0.5

12 0.90 22.5 6 1.0

13 0.85 15.0 7 0.5

14 1.00 22.5 6 1.0

15 0.85 30.0 5 0.5

16 0.95 30.0 7 0.5

17 0.90 22.5 6 2.0

18 0.85 15.0 5 1.5

19 0.85 15.0 7 1.520 0.90 22.5 6 1.0

21 0.90 22.5 6 1.0

22 0.90 22.5 6 0.0

23 0.85 30.0 5 1.5

24 0.90 22.5 6 1.0

25 0.95 30.0 5 1.5

26 0.95 15.5 5 0.5

27 0.95 30.0 7 1.5

28 0.90 22.5 8 1.0

29 0.90 37.5 6 1.0

30 0.90 22.5 4 1.0

31 0.85 30.0 7 0.5


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Table 2. Examples of the estimated parameters (, growth rate, mm d-1; , lag phase, d; A, upper asymptote va

colony diameter by linear, Baranyis and Gompertz models forA. ochraceus, P. verrucosum, E. amstelodamian

Linear Baranyis biphasic Baranyi

run S.E. R2 S.E. S.E. R

2 S.E. S.E. A S.E. R

2 S.E

1 3.340.08 2.80 99.7 3.340.08 2.800.32 99.8 NC NC NC NC 4.300.3

14 5.130.10 0.12 99.7 5.180.13 0.210.19 99.7 NC NC NC NC 5.960.3

3 3.420.09 3.77 99.2 3.540.09 4.220.30 99.5 NC NC NC NC 4.170.0

16 8.210.08 1.19 100.0 8.210.07 1.190.05 100 NC NC NC NC 9.060.3

13 0.260.01 14.95 98.3 NC NC NC 0.330.01 21.411.47 83.30.4 99.7 0.380.

A. och

31 0.310.05 18.62 89.9 NC NC NC 0.590.17 24.822.47 9.30.4 94.8 0.820.2

1 0.570.02 18.04 98.3 0.570.02 17.951.63 97.9 NC NC NC NC 0.630.0

14 1.090.07 0.09 94.5 1.090.08 0.131.57 94.5 NC NC NC NC 1.550.6

3 2.500.06 2.59 99.4 2.860.17 3.560.69 97.0 NC NC NC NC 4.560.9

16 1.340.07 -3.15 94.6 1.320.07 -3.691.47 94.8 NC NC NC NC 1.750.

13 0.230.02 2.41 94.0 NC NC NC 0.290.02 11.253.95 42.12.0 98.4 0.360.

P. ver

31 - - - - - - - - - - -

1 1.370.09 23.63 95.5 NC NC NC 1.700.09 26.861.04 83.31.7 99.1 1.970.

14 - - - - - - - - - - -

E. 3 1.810.13 5.03 94.8 1.820.10 5.071.05 96.4 NC NC NC NC 2.730.


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16 6.210.19 2.11 99.3 6.0410.18 1.850.23 99.3 NC NC NC NC 6.630.2

13 - - - - - - - - - - -

ams

31 1.260.09 7.39 98.2 NC NC NC 1.530.08 13.791.40 83.31.7 99.5 1.930.

1 1.180.04 8.17 99.1 NC NC NC 1.200.03 8.730.74 74.01.4 99.6 1.480.

14 4.700.62 0.76 90.4 3.330.38 -1.681.47 92.4 NC NC NC NC 5.120.7

3 2.690.09 4.48 99.2 3.160.29 5.451.02 94.3 NC NC NC NC 10.727

16 1.080.01 -3.69 99.6 1.190.05 -2.031.11 96.5 NC NC NC NC 1.20.04

13 - - - - - - - - - -

P. exp

31 - - -- - - - - - -

S.E., standard error of the estimated parameters

-, no growth

NC, no convergence


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Table 3. Estimated parameters (, increase in root-square ergosterol per day; , lag

phase till ergosterol detection and A, maximum asymptotic value of root square

ergosterol) through modelling of root-square ergosterol by Baranyis (either biphasic or

standard) model forA. ochraceus, P. verrucosum, E. amstelodamiand P. expansum.

run S.E. S.E. AS.E. R2

1 1.470.07 5.280.28 17.950.22 99.9

14 1.300.28 -0.151.47 20.951.41 97.8

3 0.560.04 4.830.94 98.6

16 1.160.07 0.810.35 99.3

13 2.690.34 8.890.39 20.590.50 99.7

A. ochraceus

31 - - - -

1 0.240.08 23.1614.28 84.2

14 0.440.10 1.044.33 12.861.51 95.5

3 0.270.00 -2.440.25 100.0

16 0.270.05 -6.723.90 12.670.53 99.2

13 NC NC NC NC

P. verrucosum

31 - - - -

1 0.420.13 22.747.65 18.732.42 93.6

14 - - - -

3 0.210.04 -1.526.72 91.516 0.780.07 0.250.75 98.5

13 - - - -

E.amstelodami

31 0.570.04 15.090.80 15.170.12 100.0

1 0.740.67 14.6912.49 16.841.81 89.9

14 2.040.31 2.090.79 25.361.67 98.2

3 0.510.05 3.381.62 98.1

16 0.340.04 -10.544.00 19.121.58 98.9

13 - - - -

P. expansum

31 - - - -

S.E., standard error of the estimated parameters

-, no growth

NC, no convergence


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Ergosterol and Colony Diameter

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