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~V
C Challenge of Food and
the Environment
Tim Brocklehurst
CONTENTS
5.1 Role of Food Heterogeneity
5.1.1 Aqueous Phase
5.1.2 Gelled Aqueous Phase
5.1.3 Oil-in-Water Emulsions
5.1.4 Water-in-Oil Emulsions
5.1.5 Gelled Emulsions
5.1.6 Surfaces
5.2 Modeling the Food Environment
5.2.1 Organic Acids
5.2.2 Dissociation
5.2.3 Partitioning into Oil Phases
5.2.4 Water Activity
5.3 Hurdle Concept
5.4 Competition with Other Microorganisms
5.4.1 Interactions Based on the End-Products of Metabolism
of One Species
5.4.2 Mixed Culture
5.5 Adaptation and Injury
5.5.1 Effects of Environment on Adaptation
5.5.2 Effects of Sublethal Injury
5.5.2.1 Enumeration of Sublethally Injured Bacteria
5.6 Validation in Foods
5.6.1 Bias and Accuracy
5.6.2 Validation Using Literature Values
5.6.3 Validation in Foods
References
5.1 ROLE OF FOOD HETEROGENEITY
Foods are typically not homogeneous. The structure of the food creates local chem-
ical or physical environments that affect the spatial distribution of microorganisms
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TABLE 5.1
Examples of the Heterogeneity of Foods
Structure of the Food
Liquid
Gel
Oil-in-water emulsion
Water-in-oil emulsion
Gelled emulsion
Examples of Food
Soups, juices (with some suspended
material)
Pate, jellies, skimmed milk cheeses,
such as cottage cheese
Dairy cream, milk, salad cream,
mayonnaise
Butter, margarine, low fat spread
Whole milk cheese
Surface
Vegetable tissues, meat tissues
Model Experimental Systems
Used to Mimic This Food
Structure
Broth culture medium
Cells immobilized in agar or gelatin
(including in a specifically designed
Gel Cassette System)
Alkanexulture medium emulsions
Culture medium:alkane emulsions
Alkanexulture medium emulsions,
where the aqueous phase is gelled
with agarose
Agar or gelatin (including a modified
version of the Gel Cassette System)
as well as their survival and growth. 197 Microorganisms occupy the aqueous phase
of foods, and structural features of this phase (Table 5.1) relevant to the length scale
of microorganisms can influence their growth. The effects of these structural features
on microbial growth include constraints on the mechanical distribution of water, 77 ' 78
the redistribution of organic acids, including those used as food preservatives, 3132
and constraints on the mobility of microorganisms. 30 ' 60 ' 61 ' 109 ' 110 ' 139 ' 152 ' 153 ' 201
Many foods will contain a number of microstructural features, and the behavior
of microorganisms is influenced differently in each. For example, Parker et al. 140
described the effect of microstructure on the distribution and growth of microorgan-
isms in Serra cheese. Some growth occurred in liquid regions, while other micro-
organisms formed colonies on surfaces and within the protein gel of the curd (Figure
5.1). Predictions based on data obtained from broth systems can be applied success-
fully to organisms growing in structured foods. However, where the structure of the
food results in a different behavior, this is described below, together with model
experimental systems for its study. In many cases growth is "fail-safe," in that
organisms grow more slowly in structured systems than in broths. Wilson et al. 197
suggested that this may explain the differences that food manufacturers sometimes
observe, where challenge testing of real foods indicates growth at a slower rate than
suggested from predictive models. Additionally, the complexity of food structure
has been identified as a major contribution to the "overall error" included in micro-
biological modeling predictions. 144
5.1.1 Aqueous Phase
Growth in a liquid aqueous phase is typically planktonic, with motility allowing
taxis to preferred regions of the food. Diffusive transport of nutrients to
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a)
b) I
FIGURE 5.1 Light micrographs demonstrating some structural heterogeneity in hard cheese,
and showing (a) a colony embedded within the gelled protein of the cheese curd and (b) a
colony growing on the surface. The black irregular shapes are embedded globules of milk fat.
microorganisms and of their metabolites away can result in a locally stable equi-
librium environment until accumulation of microbial biomass and metabolites
cause bulk chemical changes. This is typically manifested by changes in pH or in
gaseous composition. When broth culture medium is used in microbiological
experiments it is this environment that is mimicked, and, with few exceptions,
models for bacterial growth and death have been developed in such simple broth
systems. The complexity of foods has been recognized for many years, and it has
been suggested that the development of detailed models to account for all aspects
of microbial growth in foods may be too costly, and will not yield useful
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intermediate models. 14 Simplifying assumptions can be made, and models derived
in this way have proved useful. 14
However, with improving knowledge and the advent of mechanistic modeling
approaches it is possible to make predictions of the behavior of microorganisms in
structured foods.
5.1.2 Gelled Aqueous Phase
In gelled regions microorganisms are immobilized. This can occur as single isolated
cells, or when these multiply, they are constrained to grow as colonies. 60 ' 61,84 ' 88 ' 140 ' 201
Model experimental systems for studying colonial growth include agar 17124 and
gelatin in a specifically designed Gel Cassette System. 28 Immobilized growth as
colonies results in local depletion of oxygen 200 ' 201 and local accumulation of end-
products of metabolism, which results in a local decrease in pH within and around
the colonies. 104192201 Immobilized bacteria also differ from planktonic cultures in
their susceptibility to antimicrobial compounds, their energy metabolism, and their
metabolic end-products. 165193 Accordingly, in gelled regions of foods, the growth of
microorganisms will result in local changes in the concentration of their growth
requirements and metabolites. This results in growth at a slower rate and to a lower
yield than planktonic, or free-living cells. 30152 A unifying theory of microbial growth,
which includes proposed equations for a structured-cell mathematical model, influ-
ences of local environmental conditions on growth, influences of the microorganisms
themselves on the environment, transport of solutes between phases, and physical
expansion of colonies, 152 has been developed to attempt explanation of these growth
characteristics. 79 Experimental data demonstrate both a decrease in growth rate and
shrinkage of habitat domain in the case of Listeria monocytogenes, Listeria innocua,
and Bacillus cereus. In all of these cases, the use of a predictive model based on
data from the broth experiments would lead to a "fail-safe" prediction in the gelled
system. However, Wilson et al. 197 described the growth of Staphylococcus aureus as
a function of sucrose concentration. In the absence of sucrose, growth was slower
than in the broth cultures when the cells were immobilized in gel. However, as the
concentration of sucrose was increased, the growth rate in broth decreased, but
remained unaffected in gel. Hence, these authors identified conditions of a concen-
tration of sucrose above ca. 15% (w/v) at pH 6 where growth was faster in the case
of cells immobilized in gel than for cells in broth (i.e., "fail-dangerous" if a model
prediction was based on data from broth cultures).
Growth of cells immobilized in gelatin has been examined under nonisothermal
conditions. 28 This study showed that immobilized cells differ from planktonic bac-
teria during temperature cycling when stressed by high salt or low pH. A finite-
difference scheme has been used to combine thermal inactivation modeling with
thermal conduction modeling to simulate inactivation of bacteria immobilized within
agar blocks. 17
The local accumulation of metabolic end-products within and around colonies
can result in interaction between them. Such competition resulting from close spatial
distribution has been termed propinquity, and occurs up to a separation distance of
between 1400 and 2000 |im. 177 ' 201 The authors of these works go on to emphasize
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that a gap exists between model systems and food, and that to bridge it requires the
combined efforts of food microbiologists and microbial physiologists. 201
5.1.3 Oil-in-Water Emulsions
Here, structure is affected by the concentration and form of the oil phase. The
concentration of oil in food varies considerably, 32 and in milk is typically between
3 and 5% (v/v), but in mayonnaise may be between 26 and 85% (v/v). The oil phase
exists as polydispersed droplets with a mean diameter that is typically between 0.15
and 8 |i.m. In concentrated emulsions, the space of the interstices between the droplets
is of the same order of size, which is also the same order of size as many bacteria.
In model experimental systems a relationship exists between the concentration
of oil and the form of growth of microorganisms. 139 Where the concentration of lipid
phase was low (30% v/v) the growth of bacteria was as free-living (or planktonic)
cells. An increase in the concentration of the oil phase had no effect on the form of
growth of bacteria until it was increased to 83% (v/v). Here the bacteria became
immobilized between the close-packed oil droplets. This entrapment resulted in
growth not as planktonic cells, but as discrete colonies. The droplets within emul-
sions confer opacity, and hence visualization of microorganisms is difficult. A mix-
ture of chloroform and methanol was used to selectively remove the oil phase and
allow the examination of colonies in situ. 30 - 139 The investigators showed that the
colonies are formed from a single bacterium, and as they expanded they displaced
the emulsion droplets. Immobilization of bacteria by the lipid component and sub-
sequent growth as colonies resulted in a decreased rate of growth and a shrinkage
of the habitat domain compared with growth as planktonic cells — essentially,
similar results to the consequences of colonial growth in gels.
5.1.4 Water-in-Oil Emulsions
These consist of an internal aqueous phase dispersed as discrete spherical or irreg-
ularly shaped droplets within an outer oil phase, which may contain a mixture of
fluid and crystalline fats. In the case of margarines the droplets of aqueous phase
are typically irregular in shape, and can range between 0.3 and 30 \i in diameter. 186
Droplets can be contaminated with microorganisms at the point of emulsion
manufacture. 186 The proportion of droplets occupied by microorganisms is small,
and a model to predict microbiological contamination based on a function of the
initial contamination, and the numbers of droplets exceeding the minimum size for
occupancy, has been developed. 186
Classical theories to describe microbial growth rely on the maintenance of
discrete compartmentalized droplets that restrict the availability of water, space, and
nutrients for growth. On the basis of these assumptions, Verrips and Zaalberg 186 and
Verrips et al. 187 used a mechanistic approach to predict the growth of bacteria within
discrete droplets related to the dimensions of the occupied droplets. This was
expanded further by modeling the energy demands of the contained bacteria. 175
Models are useful here to predict states that are difficult to measure, and predictions
confirm that bacteria in the droplets can grow well, but that their numbers remain
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small when expressed per unit volume of emulsion (although their local number
density within a droplet is extremely high). Additionally, microorganisms cease to
grow when the concentration of metabolic end-products (typically organic acids)
becomes toxic or if a requirement for growth, such as oxygen or a carbon source,
is exhausted. Models confirm that bacterial growth is restricted when the food
structure remains intact (i.e., when coalescence of the droplets does not occur). This
was observed in model experimental systems where an increase in numbers of
bacteria in water-in-oil emulsions was always accompanied by coalescence of the
droplets of aqueous phase. 31
5.1.5 Gelled Emulsions
Many food emulsions are gelled. This can occur by the deliberate addition of gums
or thickeners to increase the bulk viscosity (such as in sausages) or the denaturation
of protein to form protein micelles (such as in cheese). Microorganisms are immo-
bilized and constrained to form colonies much as in gelled systems described
above. 60 ' 61 ' 140
5.1.6 Surfaces
The simplest form of food structure is the surface. Growth of bacteria on the surface
of food has been measured on Canadian wieners, 118 pate, 69 and vegetable tissues. 27
Model experimental systems are numerous and include agar gels, 53 ' 115 ' 168 ' 179 ' 199 ' 202
agar film, 115 two-dimensional gradient plates, 178-180 ' 203 ' 204 and a modification of the
Gel Cassette mentioned above. 29
Nicolai et al. 132 modeled surface growth with the assumption that it was in a
surface film of liquid. However, growth on a surface is typically colonial. Hence,
constraints on growth are similar to those described in the case of gels. Some key
differences are important in modeling. Crucially, diffusion limitations are greater at
a surface than within an enveloping gel. This was confirmed by Wimpenny and
Coombs, 200 Peters et al., 141 and Robinson et al. 155 who measured the depletion of
oxygen and accumulation of protons immediately beneath the colony and extending
into the substratum. Colonial growth on surfaces results in decreased growth rates,
and comparisons of the growth rates of Salmonella typhimurium affected by increas-
ing salt or sucrose followed the order: broth > immersed colonies > surface colo-
nies. 29 This suggests that the rate of growth on surfaces may not be well predicted
by models derived from broth systems. 29 Spatial distribution on a surface leads to
interactions between colonies. 176 Spatial and temporal variations have a major influ-
ence on the potential of surfaces to support bacterial growth. In foods, it is partic-
ularly the availability of water. 50 Drying of a food may be deliberate to inhibit growth,
and desiccation of microorganisms has been reviewed. 146 A solid surface model
system was developed to study the effect of gas atmosphere on growth of several
psychrotrophic pathogens. 21 This system demonstrated that increased C0 2 markedly
inhibited the growth of all pathogens. The model system can be applied to exami-
nation of the growth of pathogens on minimally processed produce under modified
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atmospheres. Radial growth of colonies of B. cereus on a solid agar surface was
dependent on interaction between agar concentration and water activity. 168
5.2 MODELING THE FOOD ENVIRONMENT
In order to predict the growth of microorganisms in foods reliably, it is vital to use
the correct initial chemical conditions. The structural heterogeneity of foods results
in a chemical heterogeneity, which is often complicated by dynamics within the
food that create a "new" chemical environment. Models of varying complexity exist
that can predict the true initial chemical state of foods. Microorganisms occupy the
aqueous phase of foods, 30184 and hence, it is the chemical composition of this phase
that requires accurate prediction.
Many foods rely for their preservation on the concentration of organic acids
(e.g., acetic, lactic, benzoic, or sorbic acid). In addition, the concentration of sugars
or salts can contribute to preservation. It is, therefore, no surprise that many predic-
tive models use combinations of pH and water activity (although often expressed as
concentration of NaCl) together with temperature as the three major determinants
of growth. What follows is a summary of available models that can predict the initial
environmental conditions within foods.
5.2.1 Organic Acids
Acetic, lactic, benzoic, and sorbic acid (and their salts) are added as preservatives
in many foods, although acetic and lactic acids are also produced in fermented foods
as end-products of microbial metabolism. Their preservative action is by virtue of
a combination of their effect on the pH of the food and the antimicrobial properties
of the undissociated form of the molecule. Accordingly, their antimicrobial effect is
influenced by the fundamental thermodynamic characteristics of dissociation and
partition. It is these that must be modeled to predict the potential of foods to inhibit
the growth of microorganisms.
5.2.2 Dissociation
Weak organic acids dissociate (or separate) into their component parts. In the case
of acetic acid, this occurs as:
CH3COOH
<^
CH3COO-
and
H +
acetic acid
acetate
hydrogen ion
(undissociated)
(dissociated)
(proton)
This dissociation is key to prediction of the concentration of the undissociated form
of the acid, which has the predominant antimicrobial effect in foods. 11 ' 65 ' 166
The Henderson-Hasselbalch equation relates the pH of the food to the pK a and
the relative proportions of dissociated and undissociated acid in foods have been
predicted 198 as follows:
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[acid].. . t ,
pH = pK + \Og w . 'dissociated ^ ^
\acid\ ,. . t ,
L ■* undissociated
Rearrangement gives the concentration of weak acid in its undissociated (i.e., micro-
biologically active) form, [HA] aq , given the pH, ipK a , and total concentration of weak
acid, [HA] T , as follows:
[HA] = [HA } T K : (5.2)
q 1 + 10 a
where [HA] aq is the concentration of undissociated organic acid in the aqueous phase
and [HA] T is the total concentration of organic acid. pK a is the negative logarithm
of the dissociation constant K a , which is a thermodynamic constant controlling the
dissociation equilibrium shown above:
p£=-log(£ a ) (5.3)
K a is typically a small number, and published values are available. 205 ])K a varies
slightly with temperature, and an empirical equation that predicts this variation has
been published 154 :
V K a =(^)-B + (CT) (5.4)
where T is the temperature in Kelvin (K), and A, B, and C are shown in Table 5.2.
Such predictions are important preliminaries in dealing with the challenge of food
and the environment. Without such knowledge it is quite simple to apply an incorrect
initial environmental condition when using predictive microbiology tools, and this
can easily result in erroneous predictions.
Predictions must also be reiterative. For example, once dissolved, the organic
acid will dissociate depending upon local pH, but will then perturb this pH. The
dissociation is also dependent on local buffering capacity of the food, and this is
TABLE 5.2
Values of A, B, and C to Be Inserted into
Equation 5.4 for Calculation of the Effect
of Temperature on p^ a 154
Acid ABC
Acetic
1170.48
3.1649
0.013399
Lactic
1286.49
4.8607
0.014776
Benzoic
1590.2
6.394
0.01765
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extremely difficult to predict. However, Wilson et al. 198 developed a method for
performing calculations describing the reiterative dissociation of organic acids, and
hence predicting the true chemical composition of foods. This not only allows
microbial growth models to predict growth, but also allows the changes in pH caused
by microbial metabolism to be predicted. These authors used a theory describing
the behavior of weakly dissociating systems, and knowledge of dissociation con-
stants and concentrations. They make the point that food is too complex for solutions
to be achieved through complex calculation. Hence, the authors characterized the
buffering behavior of food by a titration with a strong (i.e., completely dissociating)
acid, and then used knowledge of the dissociation constants of weak acid preserva-
tives to predict the behavior of these in the food. Their calculation scheme may also
be applied to a mixture of weak acids including polyacid species such as the
tricarboxylic acids (e.g., citric acid). 198
5.2.3 Partitioning into Oil Phases
In biphasic foods, which contain aqueous and lipid phases, the antimicrobial undis-
sociated acids partition between the aqueous and lipid components. 32 This decreases
the concentration of undissociated acid in the aqueous phase. Partition coefficients
of acetic, lactic, and sorbic acids between sunflower oil and water have been reported
as 0.02, 0.033, and 2.15, respectively, 32 demonstrating the potential for, particularly,
the undissociated form of sorbic acid to decrease in the oil phase of biphasic foods.
As a complication, the pH of foods preserved using organic acids is typically
in a region where weak organic acids are present in both the undissociated and the
dissociated forms. Calculation of the residual concentration of the undissociated
form following partition is thus difficult because the concentration is subject to the
effects of partition, and to the dissociation equilibrium based on the new pH of the
system and the new residual concentration of undissociated acid.
A modified form of the Henderson-Hasselbalch equation has been developed, 198
which takes these effects into account and gives the proportion of the total weak
acid in a two-phase system that is present in its undissociated form in the aqueous
phase, given the pH, the volume fraction of oil, and the partition coefficient for the
undissociated weak acid. It was cast as:
[HA] an 1_
4>
= - — (5.5)
[HA] T
l + K<
vl"*y
+ 10
(pH-ptf a )
where K P is the partition coefficient and <|) is the fraction volume of the oil phase.
Predictions have been validated in aqueous and biphasic foods. 198
5.2.4 Water Activity
Water activity (a w ) is a measure of the concentration of available water in a food
and can be defined as the tendency of water to escape from a solution relative to its
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ability to escape from pure water at a specific temperature. Water activity is equal
to the equilibrium relative humidity divided by 100. Pure water has an a w of 1.000,
and an environment where water is absent has an a w of 0.000. 49 ' 182 Most microor-
ganisms require a high a w for growth, and a w is included in many predictive micro-
biology models. The a w of foods can be adjusted by the addition of solutes (humec-
tants), such as sodium chloride, sucrose, or glycerol. In some cases, the solute itself
may have toxic effects, and the inhibition of growth of microorganisms when sodium
chloride is used to adjust a w can be greater than when glycerol is used, due to the
toxicity of high concentrations of sodium chloride. 1275182 Care must be taken, there-
fore, to use only those predictive models that use the same humectant as the food
of interest. Prediction of the initial a w of the food can be achieved from first principles
using a variety of equations, such as Raoult's law, 4993 which was derived by
Christian 49 as:
t -vmty
Log e «. = — (5.6)
where m is the molal concentration of the solute, v is the number of ions generated
by each molecule of the solute, and <|) is the molal osmotic coefficient. Commercial
software to predict water activity from a list of food ingredients in a recipe is available
(e.g., ERH CALC™).
5.3 HURDLE CONCEPT
Hurdle technology involves the use of combinations of physical or physicochemical
preservation techniques at subinhibitory levels to control the growth of food-borne
microorganisms. 98 This has the effect of conferring microbial safety and stability
while maintaining acceptable nutritional and sensorial attributes, 160 an approach that
is important for minimally processed extended shelf life foods. 108 With the develop-
ment of new food products that depend on multiple barriers to ensure safety, it
becomes necessary to develop the means to apply predictive microbiology to hurdle
technology. 43 ' 97 Careful definition of the conditions defining the boundaries of growth
or survival will allow industry to design foods with the appropriate level of
safety; 149 ' 160 however, there have been few attempts to provide a quantitative assess-
ment of hurdles. 160
Examples of interactions include C0 2 , pH, and NaCl on L. monocytogenes', 71
temperature, pH, citric acid, and NaCl in reduced calorie mayonnaise on Salmonella
spp.; 121 pH, acid, and salt on Staphylococcus aureus; 64 salt, pH, and nitrite on
Escherichia coli 0157:H7 in pepperoni; 151 temperature and pH on E. coli 0157:H7
in Lebanon bologna; 66 and nisin and leucosin on L. monocytogenes . 138
While it is clear that combinations of hurdles can influence food-borne micro-
organisms, it is not clear to what extent these factors interact. When the square root
model is used to describe the effect of several hurdles such as temperature, pH, and
a w , these factors are usually considered to act independently, with no interactions. 119
Ratkowsky and Ross 149 described a combined probability /kinetic model for Shigella
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flexneri in which temperature, pH, a w , and nitrite were shown to act individually. It
would be expected, however, that interactions must occur between certain hurdles.
For example, interactions between organic acids and pH would be expected (due to
the influence of pH on the extent of dissociation as described in Section 5.2) and
have been observed. 38121147 Effects on heat resistance of E. coli due to the interactions
between combinations of temperature, pH, NaCl, and sodium pyrophosphate have
been modeled. 86 ' 87
Polynomial models can be used to describe interactions between a wide variety
of hurdles. This is because the regression methods used facilitate the search for
quadratic or interactive effects. Combination effects have also been modeled using
Belehradek and Arrhenius models. 9091 The growth of L. monocytogenes at 9°C as
influenced by sodium nitrite, pH, sodium chloride, sodium lactate, and sodium
acetate has been modeled, 130 and predictions compared with the growth of organisms
in real sausage and predictions from Food MicroModel. Food MicroModel is a
software package developed in the U.K. that contains secondary models of the effects
of environmental factors (mainly pH, concentration of NaCl, and temperature) on
the survival, growth, and thermal death of major food-borne pathogenic bacteria in
broth. Predictions were on average within 20% of the Food MicroModel predictions
based on 10 experiments although predictions of growth in sausage were, on average,
16% below the observed values based on inoculation of four sausages. This is perhaps
related to the effects of structure as described in Section 5.1. The effect of previous
growth temperature, previous cell concentration, and previous pH on the lag time
and specific growth rate of Salmonella typhimurium. has been investigated using
response surface models. 135-137 In all cases the previous growth history did not
influence the predictions of the model.
Some authors contend that predictive models of the combined effects of tem-
perature and water activity and the combined effects of temperature and pH suggest
that the effect of the combinations on growth rate is independent. 120 However, these
authors go on to state that the factors are interactive at the no-growth interface (i.e.,
the point where growth ceases). Such interface models quantify the probability of
growth and define conditions at which the growth rate is zero or the lag time is
infinite. Such new growth interface or habitat domain models have been pub-
lished. 116 ' 181 Square root models and response surface models were developed to
look at the effects of interactions between dissolved carbon dioxide and water activity
on the growth and lag time of Lactobacillus sarcae. 52. The response surface models
showed the best correlation although at low water activities, predictions were illog-
ical. Both models, however, proved to be useful in the prediction of the shelf life
of meat products, and were validated by comparison with an existing model. 196
Similarly, a quadratic response surface model was built to predict the combined
effects of temperature and modified gaseous atmosphere on the growth of Yersinia
enterocolitica. 143
Predictive models have been used to predict the response of Listeria monocyto-
genes exposed to acid, alkaline, or osmotic shock at the time of inoculation on the
subsequent effects of temperature, concentration of NaCl, and pH. 47 The authors
found that predictive models were unreliable, highlighting potential problems of
variable conditions, but failing to consider the implications of adaptation of the
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organisms to osmotic or pH effects. An important development is the use of the
gamma concept, which assumes that the effects of controlling variables can be
multiplied and that the cardinal parameters of temperature, pH, and water activity
are not a function of other variables. 196 Accordingly, these authors developed a model
based on the prediction of growth rate as a function of temperature and water activity
and another where growth rate was predicted as a function of temperature and pH.
The two models were multiplied to produce one overall model, which was validated
against new experiments. Additive interaction between inhibitors has been
observed. 24 These authors used a response surface methodology to model the
response of L. monocytogenes to a bacteriocin (curvaticine) and sodium chloride:
the model showed that the combination of the two inhibitors was greater than the
effect of each individually. Interactions between inhibitory compounds were also
investigated 8 by using a series of secondary models 7 describing independently the
effects of environmental factors. 8 The authors of the latter work then went on to
show that, by taking into account interactions between environmental factors, the
model decreased the frequency of fail-safe growth predictions from 13.5 to 12.1%,
while the frequency of fail-dangerous no-growth predictions decreased from 16.1 to
7.1%. These findings suggest that interactions are occurring within the system, and
that the models were taking them into account. 8 However, even with multiplicative
models the predictions are less accurate to describe lag time and growth rate near
the limits of growth of microorganisms, 7 and lag time models were particularly
vulnerable to error.
Inactivation modeling is less common in response to a combination of hurdles.
Death kinetics as a function of pH, storage temperature, and concentration of essen-
tial oil have been described using a quadratic function, and used to predict success-
fully the death of Salmonella in home-made salads. 89 A regression model describing
the heat inactivation of L. monocytogenes was based on the Gompertz Equation. 48
The equation enabled separate characterization of the parameters of the shoulder,
the maximum slope, and the tail. Interactive effects were then derived from the
regression model. This showed that the shoulder region of the survival curve was
affected by pH, and the maximum slope by temperature, fat content, and interaction
of temperature and milk fat. Model validation was successful for temperatures only
above 62°C, however. The combined effects of pH and ethanol on the heat inacti-
vation of B. cereus, S. typhimurium, and Lactobacillus delbrueckii were modeled
using a series of second-order polynomial equations to describe variations in D
values resulting from changes in pH or added ethanol. 45 The heat inactivation of B.
cereus spores was modeled using a new concept of z- value modeling using a z(pH)
value, 96 where z(pH) was defined as the difference in pH from a reference pH value
required to effect a 10-fold reduction in the D value. A linear relationship between
the calculated z(pH) value and the lowest of the pK values of organic acids used to
effect heat resistance was found. The heat resistance of Listeria monocytogenes in
logarithmic phase cells that had been heat shocked at 42°C for 1 h and subcultures
of cells that were resistant to prolonged heating has been modeled. 9 A better fit for
the survivor curves was found using sigmoidal equations compared with the classical
log-linear models. Comparisons between models showed that an increase of thermal
tolerance was induced by sublethal heat shock or by the selection of the heat-resistant
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population. Both isothermal and nonisothermal heat inactivation effects on the ger-
mination and heat resistance of B. cereus spores have been modeled. 70 An inactivation
model was developed for Salmonella enteritidis. 96 It modeled the response of the
organism to a range of concentrations of oregano essential oil and temperatures at
two pH values. Quadratic functions were then used to predict the growth of this
organism in home-made salads. The inactivation kinetics of E. coll 0157:H7 were
modeled using the Baranyi model (based on a set of nonautonomous differential
equations) 13 as a function of time to estimate the kinetic parameters. 164 Quadratic
models were then developed with natural logarithms taken of the shoulder and death
rate as a function of temperature, pH, and concentration of oregano essential oil.
The predicted values from the model were validated using viable count measure-
ments made within real salads.
Modeling spore responses (other than inactivation) is unusual. The germination
kinetics of spores of proteolytic Clostridium botulinum. 56 A as a function of temper-
ature, pH, and concentration of sodium chloride have been modeled. 46 The germina-
tion kinetics were collected and expressed as the accumulated fraction of germinated
spores with time and each environmental condition, and this accumulated fraction
was then described by an exponential distribution. Quadratic polynomial models were
developed by regression analysis of the exponential parameter and the extent of
germination as a function of the variables under study. Validation experiments con-
firmed that the predictions were acceptable, and in most cases were fail-safe.
5.4 COMPETITION WITH OTHER MICROORGANISMS
Existing published models include a wide range of environmental, physical, or
chemical factors; however, the competitive influence of microorganisms has not yet
been incorporated into them. Competition may not be an issue in many foods, since
interactions would not be expected until cell numbers had reached a potential hazard
or caused spoilage. 160 On the other hand, growth of L. monocytogenes in dairy
products is influenced by the natural microflora, and interactions may be difficult to
model. 33 Therefore, it has been suggested that competition must be considered in
the development of predictive models. 163
Competition between microorganisms in a solid matrix such as food depends to
a large extent on proximity of colonies to each other. 201 Cells growing on surfaces
generate gradients of redox potential, pH, oxygen concentration, and nutrients, which
can influence the growth of neighboring colonies. This phenomenon can be observed
in foods, for example, where "nests" of lactic acid bacteria in fermented sausage
influence the survival of food-borne pathogens, 201 and also in dairy products where
interactions between natural microflora and L. monocytogenes are influenced by the
nature of the food matrix. 33
A related concept is the idea of "maximum carrying capacity" of a food prod-
uct, 160 in which inhibition of pathogens by other microorganisms takes place when
the competing flora have reached numbers at which the environment can support
no further growth. This was observed with cocultures of L. monocytogenes and
Carnobacterium piscicola. 35 In this study, the maximum population density of L.
monocytogenes was reduced by the competing lactic acid bacteria, and this was
2004 by Robin C. McKellar and Xuewen Lu
1237_C05.fm Page 210 Wednesday, November 12, 2003 12:54 PM
attributed to nutrient depletion. It is by no means clear to what extent competition
is related to depletion of nutrients. The thermal tolerance of S. typhimurium was
enhanced by the presence of competing microflora, and it was suggested that the
presence of competitors may have influenced the pathogen to induce stationary-
phase gene expression. 62
The interaction of spoilage microorganisms has recently been quantitated by Pin
and Baranyi. 142 Polynomial models were developed for a number of microorganisms,
and the growth of groups of strains was compared individually and in the total
mixture. This approach allowed the identification of the dominant group on the basis
of its growth rate and lag time. These authors also showed that reduced growth rate
could be attributed to microbial interactions. Competition from naturally occurring
microflora has been documented. 94 Here, predictions of the growth of Pseudomonas
and Listeria in meat were made. Predictive models worked well in predicting the
growth of both organisms in decontaminated meat and in decontaminated meat
inoculated with each organism, together or individually. However, the presence of
naturally occurring microflora in non-decontaminated meat prevented the initiation
of growth of Listeria and the predictive models failed.
A related aspect of interaction is that of the potential for quorum sensing between
microorganisms. 101 At low inoculation concentrations, modifications to modeling
approaches were necessary to take into account inoculum size variation. Modeling
the effects of inoculum size stochastics, however, confirmed that the growth rate
was independent of inoculum concentration but that variability occurred as the
inoculum concentration decreased. 209 ' 210
5.4.1 Interactions Based on the End-Products
of Metabolism of One Species
This is a complex modeling task, but stoichiometric modeling can be used to relate
the end-products of metabolism to the inhibition of the same or an accompanying
organism. It assumes a "reaction scheme," and seeks to choose the simplest repre-
sentation of a system that embodies the behavior of interest.
Thus, a stoichiometric model can predict the local changes in weak acid con-
centration resulting from microbial growth. This must then be used to predict changes
in local pH. This can be done by an empirical characterization, merely by using a
titration of the growth environment with the acid of interest, and fitting a curve to
these data. Alternatively a quasi-mechanistically based approach may be taken, 132
or use made of a Buffering theory 198 described in Section 5.2. An advantage of the
latter is that the model may be easily applied to systems of differing buffering
capacity, and can combine the effects of mixtures of weak acids. Diffusion is an
integral part of such modeling, and a standard model of Fickian diffusion using
published diffusion coefficients in aqueous solution is usually appropriate.
For growth in liquid systems, a cardinal growth model has been combined with
cardinal pH data. 99 Cardinal models use the cardinal values (minimum, optimum,
and maximum values) of the environmental factors that constrain growth. Instanta-
neous growth rates from this model were used in a modified Baranyi growth model, 13
together with stoichiometric parameters determined from bioreactor experiments. 197
2004 by Robin C. McKellar and Xuewen Lu
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The change in pH from production of lactic acid was determined by use of a
Buffering theory. 198 Very close agreement was found between the model and the data.
5.4.2 Mixed Culture
Application of stoichiometric approaches to mixed cultures also works well. Wilson
et al. 197 showed the growth of a mixed culture of Lactococcus lactis and Listeria
innocua in a bioreactor at pH 4.5. Predictions used cardinal model parameters, 99
and stoichiometric parameters from bioreactor experiments. 197 A Buffering
theory 198 was used to predict changes in pH. Such an approach provided good
prediction of both the rate and extent of growth of the two organisms. Of interest
in these approaches is that a stationary phase was not incorporated into the primary
growth model, but emerged from the prediction in response to the accumulation
of metabolites.
Interactions resulting from the production of antimicrobial bacteriocins by lactic
acid bacteria in conjunction with the inhibition resulting from production of lactic
acid have been modeled. 44 These authors used a modification to logistical equations
that described the combined (although not additive) effects of two or more inhibitory
compounds. They then applied their findings to the inhibition of Leuconostoc
mesenteroides. The inhibition of growth of Enterobacter cloacae by Lactobacillus
curvatus resulted from the production of lactic acid by the latter, and the concomitant
decrease in pH, 105 which was also inhibitory to L. curvatus. This interaction has been
modeled using a set of first-order differential equations describing growth, consump-
tion, and production rates for both microorganisms. 107 Parameters were obtained from
pure culture studies and from the literature, and the equations were solved using a
combination of analytical and numerical methods. Predictions of growth of mixed
cultures used parameters from pure culture experiments, which were close to the
experimental data. The models also showed that interactions occurred when the
antagonistic bacterium, in this case L. curvatus, reached 10 8 cfu/ml.
5.5 ADAPTATION AND INJURY
5.5.1 Effects of Environment on Adaptation
Predictive microbiology should deal with bacterial stress within populations. 6 An
example is the extension of the lag time of Listeria monocytogenes under suboptimal
conditions when the inoculum was stressed. 6 More important, considerable interest
has arisen recently in the problems of adaptive responses of bacteria and in the cross-
resistance that this can confer. For example, adaptation of bacteria to methods of
preservation can result in survival or growth that is better than predicted if the
adaptive response is ignored. Accordingly, adaptation of bacteria can lead to unsafe
or spoiled food. 34 The implications of adaptation can be demonstrated by reference
to the acid tolerance response (ATR). The ATR in L. monocytogenes has been
attributed to the de novo synthesis of proteins (sometimes referred to as acid shock
proteins) when exposed to a decrease in extracellular pH. 134 Such biochemical
changes confer acid resistance on the organisms, but O'Driscoll et al. also noted
2004 by Robin C. McKellar and Xuewen Lu
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that L. monocytogenes that had been induced to show the ATR also had an increased
resistance to thermal, osmotic, and cold stresses. 134 ATR has been defined as the
resistance of cells to low pH when they have been grown at moderately low pH or
when exposed to a low pH for some time, 59 and is typically demonstrated in broth
culture, where a pH of 4.8 to 5.0 is reported to give an optimum ATR. 56 Many foods
fall into this region of pH, and, more important, many microorganisms can experi-
ence this pH transiently during food production or sanitation protocols. Adapted
populations could then result.
Additionally, it is clear from the above sections that one of the key effects of
food structure is the immobilization of microorganisms and their resultant growth
as colonies. This results in local changes in the concentration of substrates 201 and,
particularly, a local accumulation of acidic metabolic end-products leading to a
decline in pH within and around the colony 104 ' 192 with a pH gradient extending into
the surrounding menstrum. 192 ' 201 In the case of S. typhimurium, the pH gradient
extended from the original pH 7.0 in the surrounding medium to pH 4.3 inside the
colony. 192 Such a local decline in pH within the colony is greater than the change
required to stimulate an ATR in Salmonella and other Gram-negative enteric
bacteria 95 and in L. monocytogenes . 91 It is conceivable, therefore, that cells of food-
borne pathogenic bacteria immobilized as colonies embedded in a food matrix may
undergo a self-induced ATR stimulated by a localized pH that has declined by virtue
of the colony's own metabolic processes. It is known that acid shock proteins are
synthesized and exported from cells experiencing adaptation in broths. Should this
also be the case in colonies, it would result in cells within the colony becoming
acid tolerant.
Despite the importance of adaptation in food microbiology, attempts to model
it are rare. Authors have acknowledged that organisms behaved differently when
exposed to changes in pH or sodium chloride concentration, and that exposure to
these agents during exponential phase had a more dramatic effect than during the
lag phase when adaptation was possibly induced. 47 However, no attempt to incor-
porate adaptive responses into models was made. A cross-resistance between high
hydrostatic pressure and mild heat, acidity, oxidants, and osmotic stresses was
demonstrated for E. coliO\51. 20 Differences were most dramatic in stationary-phase
cells; the only exception being acid resistance where differences were also apparent
in the exponential phase, although, again, no attempt to incorporate these into a
model was made. In one attempt to model adaptation, a model to describe the
influence of temperature and the duration of preincubation on the lag time of L.
monocytogenes was developed. 10
5.5.2 Effects of Sublethal Injury
Subjection of bacteria to inimical processes can result in the cumulative injury of
the bacteria, resulting in death. Sublethal injury is the reversible damage inflicted
on bacteria that is insufficient to cause a loss of viability, and from which the bacteria
can recover. 580 ' 150 It is an important phenomenon to recognize when collecting data
for modeling, because bacteria can often fail to form colonies on conventional
selective microbiological culture medium used for their enumeration. 2127 They can
2004 by Robin C. McKellar and Xuewen Lu
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also fail to respond positively to viability stains. 26 However, the cells can remain
viable and the injury can be repaired in foods, where the bacteria can then increase
in numbers. 82 ' 206 The severity of treatment that results in sublethal injury differs
between species, although serotypes of Salmonella have been found to respond
similarly to one another. 128
5.5.2.1 Enumeration of Sublethally Injured Bacteria
A range of methods have been used to determine the extent of injury of microorga-
nisms. These include differential plate counts on selective and nonselective agars 15 ' 150
or on minimal and more complex media, 102 extension of the lag phase, 4 ' 102 and
changes in bioluminescence. 67 Such methods can be used to optimize both the
recovery medium and the time and temperature of incubation. For example, it has
been shown that cells of L. monocytogenes that were subjected to sublethal injury
by heat exhibited a broad optimum temperature for recovery, with an optimum
between 20 and 25°C, but that incubation at 2 or 5°C failed to allow repair. 103 The
time taken for repair of injury to complete can be determined by measuring the time
before equivalent counts are found on a selective medium (which will not support
the growth of sublethally injured bacteria) and a nonselective culture medium (which
will allow the growth of sublethally injured bacteria). 103 Some modeling of resusci-
tation has been published. 117 Predictions of response might be possible: for example,
a relationship was found between the concentration of sodium chloride in the heating
menstrum and its concentration in the growth medium used for the resuscitation and
subsequent enumeration of S. typhimurium. 106
5.6 VALIDATION IN FOODS
One of the most important aspects of model development is ensuring that predictions
made by the model are applicable to real situations. This is the validation process.
It should involve comparisons of the predictions of the model with observed mea-
surements, which should be different data to those used to construct the original
model. Although some predictive models have been constructed in real foods (see
later in this chapter), the vast majority of models have been constructed from
experiments performed in laboratory culture media (typically broth). In all cases the
validation process should, ideally, include comparisons with the behavior of micro-
organisms in real foods or during real food processes. However, due often to cost
but also other factors, validation can be done in model systems, or using previously
published data. A validated model should be consistently "fail-safe," that is, predic-
tions should fail on the side of safety (i.e., predicted growth rate and lag time should
be faster and shorter, respectively, than experimental values). Predictive models can
be crucial aspects of HACCP protocols. Imaginary scenarios depicting the way in
which predictive models can be incorporated into HACCP concepts have been
published, 122 as has a useful review of the application of predictive food microbiology
in the meat industry. 113 Similarly, predictive microbiology is an important element
of Quantitative Microbial Risk Assessment (QMRA). Models are useful decision
support tools, but it should be remembered that models are, at best, only a simplified
2004 by Robin C. McKellar and Xuewen Lu
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representation of reality. The application of model predictions should be tempered
with previous experience and with knowledge of other microbial ecology principles
that may be experienced in the food by the organism. 158 Sources of data and models
relevant to the growth of L. monocytogenes in seafood and that could be part of a
QMRA have been published. 158
5.6.1 Bias and Accuracy
Some criticism of the term "validation" revolves around the difficulty in quantifying
just how well models perform their predictive role. Error occurs implicitly in the
use of data for modeling and the use of those models for the prediction of growth
of microorganisms. There are a number of potential sources of error: the homoge-
neity of foods; the completeness of the environmental factors used to collect the
data; conversion of empirical results to a mathematical function; and fitting the
models to the data. 159 For example, the overall errors in the application of growth
models to the growth of Pseudomonas species in food and in laboratory media have
been quantified. 144 The authors made the point that the error was small in the case
of culture medium but great in the case of food, and went on to quantify the influence
of food structure and composition on the overall error. Sutherland et al. 172 found
that much of the published work on E. coli 0157:H7 was done under conditions
outside of the experimental values used to develop their growth model. These
workers also reported that validation with data from cheeses and meats was difficult
because the original authors often did not report experimental conditions such as
NaCl content or pH. In these cases, poor predictions were often made. Similar
observations were made when a growth model for B. cereus was being validated. 170
It is clear in the above cases that some quantification of the deviation of the
predictions from the observed values would be useful. Many measures of such
quantification of error in the validation process have been made. 157 Additionally,
however, Ross 157 has proposed using simple indices of the performance of models
as a step towards an objective definition of the term "validated model." These indices
give an indication of the confidence with which those models can be used (accuracy
factor), and whether the model displays bias towards fail-dangerous predictions (bias
factor). The accuracy factor is defined as:
a
lo g( GT predicted /GT observed )| /n >
a r . ir\° predicted ooservea ' i ' /r '~i\
Accuracy factor = 10 (5.7)
where GT predicted is the predicted generation time and GT observed is the observed
generation time, and n is the number of observations. The less accurate the predic-
tions the larger the accuracy factor.
The bias factor is defined as:
Bias factor = i (Ilog<G W<' G W,, d >'<>> (J g)
If no disagreement between predicted and observed values occurs then the bias factor
is equal to l. However, a value of the bias factor greater than l indicates a fail-
2004 by Robin C. McKellar and Xuewen Lu
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dangerous model because it will predict generation times longer than actually
observed. It should be noted, however, that when rate values are used to compute
the bias factor, a fail-dangerous model will have a bias factor of less than 1.
As mathematical techniques advance, so does the process of comparing models.
The use of artificial neural networks has been identified as a useful alternative
technique for modeling microbial growth. Neural networks also lend themselves to
quantifying comparisons between models and suitable indices have been suggested. 85
5.6.2 Validation Using Literature Values
The most common method of validation is the use of literature data. This is based
on the assumption that if the published experiments were performed under well-
defined conditions that do not differ markedly from those used to develop the model,
then the model predictions should be reasonably reflected in the published data. A
large number of models have been validated using published information including
models for Y. enterocolitica 22 ' 100 ' 171 Aeromonas hydrophila, n2 Clostridium botuli-
num, 76 S. enteritidis 23 and E. coli 0157:H7, 23 ' 173 L. monocytogenes 71 ' 111 and a number
of other microorganisms. 55
There are, however, some potentially serious limitations to the use of literature
data for validation of predictive models. Additional food components are frequently
responsible for deviations between predicted and observed values in validation exper-
iments. For example, Tienungoon et al. 181 predicted the growth limits of L. monocy-
togenes as a function of temperature, pH, NaCl, and lactic acid. The authors used two
strains of L. monocytogenes, Scott A (a pathogenic strain) and L5 (a wild-type strain
isolated from cold-smoked salmon). Experiments were carried out in broth culture at
a wide range of environmental conditions. Aliquots of the inoculated media were
observed for a period of 90 days to determine whether the conditions supported growth.
Data from the experimental program were modeled using a probability model for
growth. Figure 5.2 shows the growth boundary predicted by the model for the case of
no added lactic acid, and a water activity of 0.992 (representing 0.5% NaCl in a typical
culture medium) as a function of temperature and pH. This boundary is plotted
alongside the data from the literature (Table 5.3). Generally, the model predicted values
that were in good agreement with literature values. However, where deviation from
the observed measurements occurred, this was usually explained by additional iden-
tifiable preservative factors in the system, and these are described in Table 5.3.
A similar issue arises using the growth boundary model of McKellar and Lu, 116
which predicts the growth limits of E. coli 0157:H7 as a function of temperature,
pH, NaCl, sucrose, and acetic acid. These authors used five strains of E. coli 0157:H7
growing in broth culture for a period of 72 h to determine whether the conditions
supported growth. Data from the experimental program were modeled using a
probability model for growth.
This boundary is plotted alongside the data from the literature (Table 5.4) in
Figure 5.3. As above, the model predicted values that were in good agreement with
literature values. Again, however, deviation from the observed measurements
occurred, due to additional identifiable preservative factors, which are described in
Table 5.4.
2004 by Robin C. McKellar and Xuewen Lu
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Temperature (C)
FIGURE 5.2 The growth boundary predicted by the model of Tienungoon et al. 181 for the
case of no added lactic acid, and a water activity of 0.992 (representing 0.5% NaCl in a
typical culture medium) as a function of temperature and pH. This boundary is plotted
alongside the data from the literature described in Table 5.3.
Other sources of error associated with the use of literature data include lack of
information on preincubation conditions that might result in the development of acid
tolerance; use of selective media for enumerating microorganisms; lack of estimates
on variability; and presence of factors in foods that are not taken into account in
models (e.g., preservatives). 39 It appears that the most appropriate method for vali-
dation might be to use data derived under well-controlled conditions, so that the
model's performance will not be unfairly biased. 157 Unsafe predictions and lack of
published information on error also limit the usefulness of literature data, and
emphasize the need to validate against new data. 57
5.6.3 Validation in Foods
The most common method for validating models using new data is to carry out
experiments directly in the food product of concern. Thus, several models have been
validated directly in food products including survival of L. monocytogenes in
uncooked-fermented meat, 195 fishery products, 158 or pate; 69 survival of Campylo-
bacter jejuni in a variety of foods; 54 growth of L. monocytogenes in dairy products; 129
growth of L. innocua in Bologna-type sausage; 81 growth of Staphylococcus aureus
in sterile foods; 190 growth of E. coli 0157:H7 on raw ground beef; 188 growth of L.
monocytogenes in sterile foods; 189 growth of Shigella flexneri in sterile foods; 207
growth of E. coli on raw displayed pork; 73 growth of Y. enterocolitica in seafood; 143
and growth of Listeria in a range of foods. 174
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TABLE 5.3
Literature Values Used in the Validation of the Growth Boundary Model
Shown in Figure 5.2
Data
Temp.
Obs.
Ref.
(°C)
pH
Other Hurdles 3
Listeria monocytogenes -
Matrix b
— Growth Data
Ref.
Time"
1
6.4
Chicken broth
191
2
4
5.5
0.5% NaCl
TSBYG
71
3
4
6.5
4% NaCl
TSBYG
71
4
5
6
4.5% NaCl
Tryptose phosphate broth
42
5
5
6.27
0.05% NaCl
Minced beef
111
6
5
6.6
0.05% NaCl
UHT milk
111
7
5.3
5.6
0.05% NaCl
Vacuum packed lean beef
111
8
6
6.52
0.05% NaCl
Chicken legs
111
9
7
5.8
0.05 [0.004]% acetic acid d
Tryptose broth
3
10
7
5.8
0.05% citric acid
Tryptose broth
3
11
7
6.4
0.05% NaCl
Nonfat milk
111
12
8
5.8
0.05% NaCl
Minced beef
111
13
8
6.4
0.05% NaCl
Skimmed milk
111
14
10
4.5
TSBYE
181
15
10
4.6
Poised with citric acid
TSB
167
16
10
4.8
Poised with lactic acid
TSB
167
17
10
5.6
Tryptic meat broth
16
18
10
6.63
0.277% NaCl + 170 ppm nitrite
Vacuum packed ham
111
19
10
7
a w = 0.96
Listeria monocytogenes —
Tryptic meat broth
No Growth Data
16
20
4
5
TSBYG
72
28 d
21
4
6.5
8% NaCl
TSBYG
71
70 d
22
5
6
4.5% NaCl + nitrite
Tryptose phosphate broth
42
NS
23
7
4.4
0.2% citric acid
Tryptose broth
3
400 h
24
7
4.6
TSBYG
72
28 d
25
10
4.25
TSBYE
181
NS
26
10
4.4
TSBYG
72
28 d
27
10
4.4
Poised with citric acid
TSB
167
28 d
28
10
4.6
Poised with lactic acid
TSB
167
28 d
29
28
4
6 [5.12]% acetic acid
BHI
40
62 d
30
28
4
9 [3.78]% lactic acid
BHI
40
62 d
31
30
4
0.029% citric acid
TSBYE
51
42 d
32
30
4.5
0.068 [0.043]% acetic acid
TSBYE
51
42 d
33
30
4.5
0.043 [0.008]% lactic acid
TSBYE
51
42 d
Note:
NS = Not stated.
a These are responsible for the deviation of the data points from the growth boundary predicted by the
model.
b The following matrices refer to commonly used microbiological growth media: TSBYG; Tryptose-
phosphate broth; Tryptose broth; TSBYE; TSB; Tryptic meat broth; BHI.
c Time for which no growth was observed.
d Concentration of acetic and lactic acids expressed as total, with undissociated in square brackets.
2004 by Robin C. McKellar and Xuewen Lu
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8
7 -
6 -
5 -
4 -
+
11
■+
19
Growth
No Growth +
Lines: Model of McKellar and Lu (116),
0.5% NaCI, no acetic acid
90% growth probability
50% growth probability
10% growth probability
10
15
20
25
30
35
40
Temperature (C)
FIGURE 5.3 The growth boundary predicted by the model of McKellar and Lu 1 1 6 that predicts
the growth limits of Escherichia coli 0157:H7 as a function of temperature, pH, NaCI, sucrose,
and acetic acid. This boundary is plotted alongside the data from the literature described in
Table 5.4.
Dynamic modeling has also been validated, 25 where predictions from FoodMi-
croModel have been applied to the growth of L. monocytogenes and Salmonella in
a range of foods incubated under constant as well as fluctuating temperatures. The
authors found that generally the accuracy of prediction under the fluctuating tem-
peratures was similar to the isothermal conditions, although inhibition by natural
microflora did decrease the expected growth of L. monocytogenes in milk. Signif-
icant deviation of predictions of the growth of bacteria growing as colonies when
immobilized in gel occurred when predictions were made from isothermal growth
in broth. 125 ' 126
Validation of combined growth of the spoilage bacteria Pseudomonas,
Shewanella putrefaciens, Brochothrix therm osphacta, and lactic acid bacteria was
made in modified atmosphere packaged fish as a function of temperature and con-
centration of carbon dioxide. 91 Combined models based on polynomial, Belehradek,
and Arrhenius equations were developed and validated by comparison with experi-
mental growth rates of these bacteria obtained on three Mediterranean fish species.
Predictions of the models based on the Belehradek and Arrhenius equations were
judged satisfactory overall. This approach has been modified 90 to determine a pro-
cedure for modeling the shelf life of fish. Similarly, a quadratic response surface
model has been used to describe the maximum specific growth rate of Y. enterocolit-
ica. The model predicted growth rates as a function of refrigeration temperature and
2004 by Robin C. McKellar and Xuewen Lu
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TABLE 5.4
Literature Values Used in the Validation of the Growth Boundary Model
Shown in Figure 5.3
Data
Temp.
Obs.
Ref.
(°C)
pH
Other Hurdles 3
Matrix b
Ref.
Time'
£. co// — Growth Data
1
8.2
5.7
Ground mutton
83
2
10
4
0.5% NaCl
TSB
116
3
10
5.5
Poised with lactic acid
TSBYE
52
4
10
5.5
Poised with citric acid
TSBYE
52
5
10
5.5
0.5% NaCl
BHI
37
6
10
5.5
5% NaCl
BHI
41
E. coli — No Growth Data
7
4
4
TSBYE
52
21 d
8
5
3.6
"Condiments"
183
7d
9
5
4.8
a w = 0.99
w
TSB
156
48 h
10
5
6.5
5% NaCl
BHI
41
12 d
11
5
«7.2
Cucumber slices
1
10 d
12
8
5.5
0.5% NaCl
BHI
37
10 d
13
10
3.5
0.5% NaCl
TSB
116
72 h
14
10
4
Poised with acetic acid
TSBYE
52
21 d
15
10
4.5
5% NaCl
BHI
41
12 d
16
10
5
Poised with lactic acid
TSBYE
52
21 d
17
10
5
Poised with citric acid
TSBYE
52
21 d
18
12
5.5
30% sucrose, a w = 0.972
BHI
36
24 h
19
12
«7
Shredded carrot
1
10 d
20
15
4
0.5% NaCl
TSB
116
72 h
21
30
5.1
0.1 [0.03]% acetic acid as
vinegar 41
Nutrient agar
68
4d
22
37
4.5
Poised with lactic acid
TSBYE
74
14 d
Note: NS = Not stated.
a These are responsible for the deviation of the data points from the growth boundary predicted by the
model.
b The following matrices refer to commonly used microbiological growth media: TSBYE; TSB; BHI;
Nutrient agar.
c Time for which no growth was observed.
d Concentration of acetic acid expressed as total, with undissociated in square brackets.
modified atmosphere and comparisons of the model predictions were made with
growth rates obtained in seafood deliberately inoculated with Y. enterocolitica} 1
Validations of the growth of L. monocytogenes in tryptose phosphate broth and
in chicken and in beef have been made as a function of changing the pH and sodium
chloride concentration. 133 Predictions of the growth of L. monocytogenes were then
made using either a square root model 148 or a response surface polynomial model. 42
The square root model predicted growth rates at between and 25°C with a
2004 by Robin C. McKellar and Xuewen Lu
1237_C05.fm Page 220 Wednesday, November 12, 2003 12:54 PM
coefficient of determination of between 98.36 and 99.63%. The response surface
polynomial model, however, predicted generation times at 5 to 25°C with between
and 17.4% difference between the observed and expected generation times in
broth. Of greater significance in terms of validation in food here are the large
differences observed in the generation time at pH 5.6 and 8°C (25.5 h) and the
generation time predicted by the Pathogen Modeling Program (PMP) in these con-
ditions in tryptose phosphate broth (5.3 h). The PMP is a web-based package
developed in the U.S. that contains secondary models of the effects of environmental
factors (mainly pH, concentration of NaCl, and temperature) on the survival, growth,
and inactivation of major food-borne pathogenic bacteria in broth. A divergence
from predicted values was also shown at temperatures between and 3.5°C in the
square root model.
Predictions of the growth of Bacillus cereus from PMP were validated for its
growth from spores in boiled rice. 114 An analysis of variance showed that there was
no statistically significant difference between the observed and measured growth
rates in boiled rice and predictions made from PMP. Modeled predictions were fail-
safe for generation time and exponential growth rate at all temperatures. Although
the model was fail-safe for lag phase duration at 20 and 30°C, it was not at 15°C.
Modeling the growth of filamentous fungi is rare. The growth of three strains
of heat-resistant fungi, as influenced by water activity adjusted using sucrose was
modeled using the Baranyi model 13 to fit the changing colony diameter. 185 Modeling
the growth of filamentous fungi has also been done using a model derived from the
cardinal model family. The model was successfully fitted on data sets from a range
of filamentous fungi whose growth was affected by a range of humectants including
sodium chloride, glucose/fructose as a mixture, and glycerol and at different pH
values. Further cardinal values were extracted from the literature and the model was
used to predict the evolution of the radial growth of Penicillium rocqueforti and
Paecilomyces variotii. 162
In spite of the effort expended to develop and validate models, it is rare to find
a model developed in broth that accurately predicts behavior in food systems. Models
tend to fail-safe, and provide somewhat conservative predictions. 23 ' 54 ' 7381 ' 100 ' 114129 ' 170 ' 172
Indeed, the use of faster-growing strains has been suggested to provide a margin of
safety. 123 ' 131 ' 194 Although many validations of models show that there is a fail-safe
tendency and hence a margin of safety in growth prediction, some manufacturers
of foods find that the error is unacceptable and the margin of safety provided by
such models may well be more conservative than is desirable for many food appli-
cations. There are, however, examples of situations where the model makes what
are clearly unsafe predictions, and these usually involve an overestimation of the
extent of lag time. 69 ' 188 - 190
An alternative approach is to develop models directly in food products. This is
not possible in many cases, due to the requirement of appropriate facilities for
incorporating pathogens into the process under carefully controlled conditions. In
spite of this limitation, models have been developed for growth of L. monocytogenes
on vacuum-packed cooked meats 63 and liver pate; 69 inactivation of Salmonella typh-
imurium in reduced calorie mayonnaise; 121 inactivation of Enterobacteriaceae and
Clostridia 18 and growth of Lactobacillus spp. in dry fermented sausage; 19 growth of
2004 by Robin C. McKellar and Xuewen Lu
1237_C05.fm Page 221 Wednesday, November 12, 2003 12:54 PM
Clostridium botulinum in processed cheese; 169 thermal inactivation of L.
monocytogenes 145 and Enterococcus faecium 161 during high-speed short-time pas-
teurization; and the thermal inactivation of E. faecium during cooking of Bologna
sausage. 208 These models generally provide good estimates of the behavior of food-
borne pathogens in food processes. However, it is questionable if effort should be
expended developing models specific for all food processes. Improved validation
techniques for models derived in broth or other model systems would appear to have
more general applicability.
It has been suggested that models should only be regarded as first estimates of
the behavior of pathogens, and that additional studies with products giving poor
predictions should be undertaken. 195 Inclusion of additional data into models will
often improve their predictive ability 207 ; however, it is important that users of these
models take great care in their use, and ensure that predictions are carefully validated
in any product of concern.
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