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Experimental Design
and Data Collection

Maria Rasch

CONTENTS

1.1

1.2

1.3
References

Experimental Design

1.1.1

Complete Factorial Design

1.1.2

Fractional Factorial Design

1.1.3

Central Composite Design

1.1.4

Doehlert Matrix

1.1.5

Optimal Experimental Design

Data Collection

1.2.1

Strain Selection

1.2.2

Viable Count

1.2.3

Novel Methods

1.2.3.1 Turbidity

1.2.3.2 Flow Cytometry

1.2.3.3 Microscopy and Colony Size

1.2.3.4 Impedance

Conclusion

1.1 EXPERIMENTAL DESIGN

Assessments of the impact of environmental factors on the response of food-borne
microorganisms are the primary sources of data for the development of predictive
models. When investigating the influence of more than one factor and accurately
describing how those factors interact, it is important to consider how to design the
experiment. Unfortunately, in modeling bacterial growth in foods, the design is
commonly not accounted for, or it is chosen based on habit rather than the experi-
ment's specific purpose. But carefully considering the experiment's design is vital
to extracting the desired information (e.g., interactions) and to avoiding excessive
experimental work. Furthermore, researchers should be aware of the experimental
design in order to avoid extrapolation. 1-3 The following sections describe the most
common experimental designs used in modeling of microbial responses in food.

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1.1.1 Complete Factorial Design

A complete factorial design is one in which all combinations of the different
factors are investigated (Figure 1.1). This allows straightforward modeling of
interactions between, for example, environmental factors influencing growth or
inactivation of microorganisms. The experimental design is simple, easy to set up,
and easy to handle statistically. The main disadvantage is the large increase in
number of experiments for every new factor/level added to the experiment. A
simple example of a complete 3x3x3 factorial design was applied by Chhabra
et al. 4 for investigating thermal inactivation of Listeria monocytogenes in milk.
The factors were milk fat content, pH, and heating temperature; the experiment
was performed in triplicate, resulting in 3 4 = 81 experiments. A complete factorial
experimental design was also used by Uljas et al. 5 for modeling the combined
effect of different processing steps on the reduction of Escherichia coli 0157:H7
in apple cider. The response variable measured was binary (whether a 5-log 10 -unit
reduction was obtained or not), resulting in a logistic model. Three class variables
(cider from three different cider plants, a freeze-thaw treatment, and the preser-
vation agents potassium sorbate and sodium benzoate) and four continuous vari-
ables (cider pH, storage temperature, storage time, and preservation concentration)
were investigated. 5 This resulted in 1,596 treatments for each of the three types
of cider. As one type of cider was tested in duplicate and the other two in triplicate,
the total number of experiments was 12,768, which very clearly illustrates the
major drawback of complete factorial designs, namely, the very large number of
experiments required. However, complete factorial designs are still widely used
within predictive modeling of microorganisms, and have been used for different
purposes such as the effect of inoculum size, pH, and NaCl on the time-to-detection
(TTD) of Clostridium botulinum; 6 the effect of pH, NaCl, and temperature on
coculture growth of L. monocytogenes and Pseudomonas fluorescens; 1 the effect
of temperature, NaCl, and pH on the inhibitory effect of the antimicrobial com-
pound reuterin on E. coli; s and the growth of L. monocytogenes under combined
chilling processes. 9

5-,
4-
3-
2-
1 -
0-

♦
♦
♦
♦

♦
♦
♦
♦

♦
♦
♦
♦

♦

♦
♦

2

1

FIGURE 1.1 Example of a complete factorial design for the simple case with two variables
(k = 2), e.g., temperature and pH, each at four levels.

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1.1.2 Fractional Factorial Design

In order to reduce the number of experiments, several different alternative experi-
mental designs can be applied. Among these are fractional factorial designs,
described in this section. In contrast to the complete factorial designs, the fractional
factorial designs are not as easy to construct, and thus different software packages
are often used for determining which combinations of the different parameters to
include in the experimental setup. Examples of software programs used for fractional
factorial designs are the Screening Design procedure from STATGRAPHICS Plus
(Manugistics, Rockport, MD) 10 and Modde (Umetri, Umea, Sweden). 11 Farber et
al. 10 used a fractional factorial design for modeling the growth of L. monocytogenes
on liver pate. The factors investigated were temperature, salt, nitrite, erythrobate,
and spice, each at two different levels. The fractional factorial design yielded a total
of 16 experiments (= 2 5_1 ), where a complete factorial design would have resulted
in 32 different experiments. Juneja and Eblen 12 also obtained a large reduction in
number of experiments (compared to the number of experiments in a complete
factorial design) when they modeled thermal inactivation of L. monocytogenes. They
investigated 47 combinations of four different environmental factors (temperature,
NaCl, sodium pyrophosphate, and pH, each at five levels), where a complete factorial
design would have resulted in 5 4 = 625 experiments. Fractional factorial designs
have also been applied for investigating the heat resistance of E. coli 0157:H7 in
beef gravy. 13

A particular class of fractional factorial designs has been widely used for mod-
eling of bacterial growth, namely, the Box-Behnken designs. These designs are
formed by combining two-level factorial designs with balanced incomplete block
designs (Figure 1.2). 14 Often, more than one experiment is performed at the central
point of the experimental design in order to evaluate the repeatability of the model.
A Box-Behnken design was applied for three studies of spoilage of cold-filled ready-
to-drink beverages investigating the bacteria Acinetobacter calcoaceticus and Glu-
conobacter oxydans, 15 the molds Aspergillus niger and Penicillium spinulosum, 16
and the yeasts Saccharomyces cerevisiae, Zygosaccharomyces bailii, and Candida

6 -|

5 -

4 -

3 -

2 -

1 -

-

♦

©

~r
2

"T -

3

"T -

4

5

1

6

FIGURE 1.2 Example of a Box-Behnken design for the simple case with two variables
(k = 2), e.g., temperature and pH. The circle denotes the central point.

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UpolyticaP In each study, the effect of pH, titratable acidity, sugar content, and
concentrations of the preservatives sodium benzoate and potassium sorbate were
tested at three different levels each. 15-17 The Box-Behnken design was constructed
by using the JMP software (SAS Institute, Cary, NC), with two points at the center
of the design, resulting in 42 experiments. 15-17 A Box-Behnken design has also been
used to show that the C0 2 concentration in the water phase of a model food system
was the most important factor when describing modified atmosphere packaging and
its inhibitory effect towards microorganisms. 18 The C0 2 concentration in the water
phase was investigated as a function of gas/product ratio, initial C0 2 concentration
in the gas phase, temperature, pH, and lard content. 18

1.1.3 Central Composite Design

A central composite design consists of a complete (or fraction of a) 2 k factorial design,
n center points, and two axial points on the axis of each design variable at a distance
of a from the design center (Figure 1.3). The number of experiments for k variables
is 2 k + 2k + n Q , where n denotes the number of experiments at the central point (n
> l). 14 For k = 2 and 3 and n Q = 2, this results in 9 and 16 experiments, respectively.
In a validation study by Walls and Scott, 19 the effect of temperature, pH, and
NaCl on the growth of L. monocytogenes was described by the use of a central
composite design. The experiment was repeated six times at the design center in
order to estimate the experimental variance. Guerzoni et al. 20 used central composite
design to optimize the composition of an egg-based product in order to prevent
survival and growth of Salmonella enteritidis. The factors studied were pH, NaCl,
and pressure treatment. Lebert et al. 21 used a central composite design to study the
growth of L. monocytogenes in meat broth. Three variables were studied: pH, a w ,

r

(-i>i)

(-a,0)

(0,a)

(0,0)

(-1.-1)

(0,-a)

(1-1)

(a,0)

1 (L-1

-1)

FIGURE 1.3 Example of a central composite design for the simple case with two variables
(k = 2), e.g., temperature and pH.

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and temperature. Two experiments were performed at the central point, resulting in
16 experiments. Later, a similar design was used to study the mixed growth of
Pseudomonas spp. and Listeria in meat, where the three variables were NaCl,
temperature, and pH. 22

A combination of two central composite designs and a factorial design has been
applied to study the effect of osmotic and acid/alkaline stresses on L. monocytogenes.
The two central composite designs were set up in the acid and alkaline pH range,
i.e., one covered the pH range from 5.6 to 7 and the other from 7 to 9.5. 23,24 As
pointed out by Pin et al., 2 the risk of extrapolation can be very high when using
central composite design as the vertices of the nominal variable space (the unit cube)
are far from the interpolation region (the minimal convex polyhedron). The shape
of the minimal convex polyhedron is determined by a convex linear combination of
the environmental factors at which the experiments were performed for the model
development. If a prediction is made randomly in the unit cube, the risk of extrap-
olation is as high as 75 %. 2

1.1.4 Doehlert Matrix

The Doehlert matrix is another form of experimental design that to some extent
resembles the central composite design. The Doehlert matrices consist of points
uniformly spaced on concentric spherical shells, and are therefore also called uniform
shell designs (Figure 1.4). 14 The number of experiments for k variables is k 2 + k +
n , i.e., for n = 1 this gives 13 experiments for k = 3 and 21 experiments for k = 4.
The experiment performed at the center of the experimental domain (n ) can be
repeated several times in order to estimate residual variance. An advantage of

-1,5

-1

-0,5

1,5 -r

1 -

0,5

■^■

-0,5-

-1 -

-1.5-

0,5

1,5

FIGURE 1.4 Example of a Doehlert matrix design for the simple case with two variables
(k = 2), e.g., temperature and pH.

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Doehlert matrices is that they are easy to expand. Expansion can be done both by
investigating new variables (provided that these variables were set to their central
point during the first experiments) and by enlarging the range of the parameters
tested without having to repeat the former experiments. 25

The Doehlert matrix has been used by Terebiznik et al. 26 to investigate the effect
of combinations of nisin and pulsed electric fields on the inactivation of E. coli. The
experiments were designed with three variables, namely, nisin concentration, electric
field strength, and number of pulses. In a later study by the same group, the effect
of water activity in combination with nisin and electric field strength was studied. 27
Bouttefroy et al. 28 ' 29 used Doehlert design to study the inhibition of L. monocytogenes
at different combinations of NaCl, pH, incubation time, and the inhibitory effect of
the bacteriocins nisin and curvaticin 13, respectively. Doehlert design has also been
applied to investigate the conidial germination of Penicillium chrysogenum at dif-
ferent combinations of temperature, water activity, and pH. 30

1.1.5 Optimal Experimental Design

A new approach within mathematical modeling of growth or inactivation of micro-
organisms is optimal experimental design. The basic idea is to optimize the exper-
imental conditions with respect to parameter estimation by the use of an established
methodology from bioreactor engineering. 31 Ideally, the optimal design of dynamic
experiments will result in increased information content from each experiment, and
thereby to more accurate parameter estimates from a smaller number of experiments.
In the approach by Bernaerts et al., 32 ' 33 the growth data are modeled directly by the
square root model of Ratkowsky et al. 34 (see Chapter 3) integrated into the dynamic
model of Baranyi and Roberts 35 (see Chapter 2). Thus, the so-called secondary model
parameters are estimated directly from the population density data. Optimal dynamic
experimental conditions are then obtained by a stepwise change in temperature,
which is first shown with a one-step change 32 and later with three smaller temperature
increments in order to avoid an intermediate lag phase. 33 The optimization process
was performed by designing the optimal step -temperature profile in order to mini-
mize the standard deviation of the parameter estimates and the correlation between
parameters. 3233 Grijspeerdt and Vanrolleghem 36 used optimal experimental design
for optimizing sampling times for the Baranyi growth model. This resulted in lower
error on the parameter estimates and decreased correlation between them. 36

1.2 DATA COLLECTION
1.2.1 Strain Selection

There are several different approaches that one can use when choosing which strain
to use for model building purposes. Furthermore, there is the choice between using a
single strain or a mixture of different strains (i.e., cocktail). Before choosing which
strain to use it is important to clarify the intended use of the model: is the model going
to be used for prediction of possible growth of one particular pathogenic species, or
is it a model of the spoilage flora of a specific food product? Using a strain (type strain

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or other) that has previously been used for several studies or maybe even modeling
purposes gives the benefit of the previously accumulated knowledge on the particular
strain. On the other hand, a strain isolated from the particular food product which is
the goal for the application of the model gives the advantage of relevance for the
product, and being able to grow the strain at the environmental conditions investigated.

A well-known strategy is to choose the fastest growing strain at the environ-
mental conditions investigated, as it is the fastest growing strain that will dominate
the growth in, e.g., food products. McMeekin et al. 37 recommended independent
modeling of several different strains before choosing the strain that grows fastest
under the environmental conditions of most interest. This strain then simulates a
worst-case scenario. 37 This strategy was followed by Neumeyer et al. 38 who, after
an initial screening of different Pseudomonas strains, chose the fastest growing strain
for modeling, and later during the validation stage confirmed that the chosen strain
was the fastest strain. 39 For modeling the growth of Bacillus cereus in boiled rice,
three different strains were examined and the fastest growing of the three chosen
for the modeling studies. 40 Miles et al. 41 examined four different strains of Vibrio
parahaemolyticus and found that one strain was the most resistant at all conditions
of temperature and water activity tested, and hence the growth data of this strain
were used for model development. A different method was employed by Lebert et
al. 22 who modeled the growth of three different strains, one fast and one slow growing
strain of Pseudomonas fragi and one slow growing strain of P. fluorescens. Any
growth was then assumed to be within a zone delimited by the predicted growth
curves of these three different organisms. 22 A similar approach was followed by
Benito et al., 42 who initially investigated the resistance of six different strains to high
hydrostatic pressure and heat before choosing one pressure- and heat-resistant strain
and one pressure- and heat-sensitive strain for further analyses.

The strains used for model development can also be isolated from the food that
is under investigation. For modeling the spoilage of ready-to-drink beverages,
strains of Saccharomyces cerevisiae, Z. bailii, and C. lipolytica were used. 17 These
strains were all isolated from spoiled ready-to-drink beverages. 17 Oscar 43 chose a
specific strain of Salmonella typhimurium as it exhibits the same growth kinetics
as Salmonella strains commonly found on chicken in the U.S. The use of strains
related to the food in question was also recommended by Hudson, 44 who used
strains isolated from smoked mussels and sliced smoked salmon to investigate the
growth of L. monocytogenes.

The importance of using more than one strain of a species in order to assess the
influence of strain variation has also been stressed. 44-46 According to Whiting and
Golden, 46 the between-strain variation should be equal to or smaller than the exper-
imental and statistical variation. However, when investigating the growth, survival,
thermal inactivation, and toxin production by 17 different strains of E. coli, they
found that the variations among the strains were larger than the uncertainties related
to the experimental error. 46 The variation among 58 strains of L. monocytogenes and
8 strains of Listeria innocua was examined by Begot et al. 45 Most of the strains had
been isolated from meat, meat products, and related industrial sites, and four addi-
tional strains that had been involved in outbreaks were also included. Large variations
in lag times were found between the strains, whereas the variations in generation

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times were less pronounced. 45 The opposite conclusion was reached by Oscar 47 when
studying 1 1 different strains of Salmonella. He found that the mean coefficients of
variation for four repetitions with the same strain were 11.7 and 6.7% for the lag
time (k) and the specific growth rate (|i), respectively, whereas the mean coefficients
of variation among the different strains were 9.4 and 5.7% for X and (I, respectively. 47

Salter et al. 48 compared the growth of the nonpathogenic E. coli M23 with the
growth of different pathogenic strains of E. coli and found only little difference in
the growth responses of the different strains. They also found that the model based
on E. coli M23 was able to describe the growth of pathogenic strains of E. coli,
including E. coli 157 :H7. 48 This result has practical value, as many research groups
do not have access to laboratory facilities suitable for work with E. coli 0157:H7.
However, the general suitability of nonpathogenic strains as models for the growth
or survival of pathogenic strains would have to be confirmed for each species.

Mixtures of different strains, so-called cocktails, have also been widely used.
The main arguments for using cocktails are as follows: first, that a mixture of several
different strains is more representative of the situation found in foods, where a flora
of strains is likely to be present. Second, it is not necessarily the same strain that
shows the fastest growth under all the investigated growth conditions, i.e., a strain
with a high salt tolerance might be the fastest growing at high salt concentrations
and high pH, but not necessarily at low salt and low pH conditions. For building
the Food Micromodel, which is a database software system for predicting growth
and survival of microorganisms in foods (see Chapter 6), it was decided to use a
cocktail of strains for the growth experiments, but a single strain for thermal inac-
tivation studies, as a cocktail of strains for the latter procedure could produce thermal
inactivation kinetics data that would be difficult to interpret. 49

A cocktail of five strains of Staphylococcus aureus was used for the determina-
tion of growth/no growth boundaries by measuring turbidity in microtiter plates 50
and Uljas et al. 5 used a mixture of three different strains to characterize the effect
of different preservation methods on the survival of E. coli in apple cider.

1.2.2 Viable Count

Viable count determinations by spreading on agar plates are still a very common
method for enumeration of microorganisms and it remains the method of reference.
To a certain extent it has been possible to automate viable count plating by the use
of automated platers such as the spiral plater and automatic colony readers.

Vast numbers of modeling studies have been based on viable counts. A few
studies have, however, observed problems with the viable count method compared
with other methods. As described in Section 1.2.3.2, enumeration of Brochothrix
thermosphacta by flow cytometry gave a more accurate result than with viable counts
when both were compared to manual counting by microscopy. 51

1.2.3 Novel Methods

Construction of models using viable count data is time-consuming and expensive,
and several alternative, more rapid methods for accumulating sufficient data for

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modeling have been explored. A novel method for data capture should either be
faster, cheaper, and less labor intensive or be able to provide more information on
the cells than do viable counts, e.g., physiological status or expression of different
phenotypic traits. In the following sections, four of these novel methods will be
described, namely, turbidity, flow cytometry, microscopy, and impedance. A num-
ber of other methods have been used to indirectly model bacterial growth, but
extensive development of these approaches has not been attempted. Some of these
include headspace measurements of evolved C0 2 by gas chromatography 5253 and
bioluminescence. 54,55

1.2.3.1 Turbidity

One of the simplest methods for data collection is the use of optical density (OD),
where growth can be related to the increase in turbidity of a bacterial culture. OD,
or absorbance, is a measure of the amount of light that is absorbed or scattered by
a solution of bacteria. The bacteria absorb or scatter light depending on their
concentration, size, and shape. According to Beer's law, absorbance is proportional
to concentration, and is related to the percent transmitted light (%T) by the fol-
lowing equation:

OD = 2-\og w {%T)

Some of the fundamentals of this approach have been discussed by McMeekin et
al. 37 There are some limitations associated with this approach to data collection.
Deviations from responses predicted by Beer's law occur at high cell densities,
requiring that dilutions be made to OD < 0.3 before accurate absorbance measure-
ments can be taken. 56 In addition, OD methods are comparative only, and cannot be
used to predict viable counts unless some attempt at calibration is made. Detectable
absorbance changes occur at a minimum bacterial concentration of 10 6 cfu ml -1 ,
depending on the sensitivity of the instrument, 56 and a linear relationship between
OD and viable count exists only between the detection limit and approximately 10 7 * 5
cfu ml -1 . With the maximum cell density in most growth media limited to approx-
imately 10 9 cfu ml -1 , the |i measured using OD will represent the rate towards the
end of the growth phase, and this will be less than the maximum specific growth
rate (|i max ) experienced during the midexponential phase of growth. Another draw-
back is the inability to distinguish between dead and living cells, which can lead to
an overestimation of the cell concentration. Furthermore, bacterial cultures that
change cell morphology under different environmental conditions, e.g., elongated
cells of L. monocytogenes at high salt concentrations, again lead to an overestimation
of the cell number. 57 Hudson and Mott 58 showed that the cell length of P. fragi
increased during lag phase, and consequently models based on OD measurements
underestimated X, unless a conversion equation was applied. 58 This method lends
itself particularly well to automation, and a number of studies have used automated
turbidimetric instruments such as the Bioscreen. 5759 ' 60

A number of attempts have been made to calibrate OD data. McClure et al. 57
used a simple quadratic equation to relate OD to viable counts. Dalgaard et al. 56

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used two equivalent methods for calibration: one in which stationary-phase cells
were diluted to the appropriate OD, and the other in which samples for OD and
viable count were taken during growth. Predicted generation times were lower with
viable count data, 56 and this factor has been taken into account in later studies. 41
Similar methods have been used to relate turbidimetric and viable count data. 58 ' 61,62

In some studies, the Gompertz equation was fitted directly to OD data; however,
no data were available at below the minimum detectable OD (ca. 10 6 cfu ml -1 ) and
thus the estimates for \i and |i. max should be questioned. 44 ' 58 A form of calibration
was achieved by relating X determined using OD measurements to that determined
with viable counts by a regression equation. 58 McMeekin et al. have discussed the
correct way to fit the Gompertz function to % transmittance data (Appendix 2A.9
of their book 37 ), and this method has been used to calculate generation times. 38

Other studies have been carried out without any apparent calibration. 59 X values
have been estimated from OD data by extrapolation of the exponential portion of
the curve back to the initial cell numbers; 63 however, this method may be inaccurate
since the |i estimated from the OD data may be lower than that obtained during the
period of maximum growth. 37 Lebert et al. 21 estimated X values of L. monocytogenes
with OD data, but the inoculation level during these experiments was kept at 10 7
cfu ml -1 , i.e., above the detection limit. This procedure, however, gives only a very
small dynamic range of growth of about 2 log units.

Interestingly, the TTD approach has not been used to any great extent. The TTD
for a turbidimetric instrument can be defined as the time required for a detectable
increase in OD. The difference between TTD for serial twofold dilutions gives the
doubling time, from which |l can be determined. 60 ' 64 X can be calculated subsequently
by the difference between the predicted TTD based on X, and the observed TTD. 60 ' 64
This method was used to estimate X for individual cells. 65 This method was also
used by Augustin et al. 61 for estimating |i max of 10 different strains of L. monocyto-
genes. They, however, observed large variations in the time separating the two
successive growth curves (i.e., doubling time).

In spite of the problems associated with the use of turbidimetric data for mod-
eling, there appears to be some value in this approach. Models based on viable counts
were compared with those obtained using either OD or transmittance data, and it
was concluded that turbidimetric methods may be used for reliably estimating |i max . 56

OD measurements have been used extensively for modeling purposes. This
includes modeling of the growth boundaries of S. aureus at different levels of relative
humidity, pH, potassium sorbate, and calcium propionate 50 and modeling the effect
of the antimicrobial compound reuterin on the growth of E. coli at different combi-
nations of temperature, pH, and NaCl. 8 OD has also been used to determine 5-log 10 -
unit reductions of E. coli in apple cider (see also Section l.l.l). 5 Cider inoculated
with 10 7 cfu ml -1 was exposed to the different treatments investigated, after which
a 10-J-il sample of the cider was transferred to a micro titer well containing Tryptic
Soy Broth and incubated. If a 5-log 10 -unit reduction occurred during the treatment,
the 10-J-il sample would contain <1 cfu and therefore no growth would be observed
in the well. 5

OD data have also been used for the determination of growth boundaries, i.e.,
the growth/no growth models (see Chapter 3). The growth boundaries of the spoilage

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organism Z. bailii were investigated at different combinations of salt, sugar, acetic
acid, and pH at a constant temperature of 30°C. Growth was measured by a Bio-
screen analyzer, but between measurements the Bioscreen plates were incubated in
closed containers in an incubator. 66 Masana and Baranyi 67 studied the growth bound-
aries of B. thermosphacta in multi-well plates, but inspected the wells visually for
growth. The interface between survival and death of E. coli 0157:H7 in a mayon-
naise model system was studied by McKellar et al. 68 A cocktail of five strains of
E. coli 0157:H7 was inoculated at a level of 10 7 cfu ml -1 into 5-ml tubes under
different environmental conditions, and growth was observed visually. In the case
of no growth, the samples were diluted 100-fold into Tryptic Soy Broth and incu-
bated again. Continued absence of growth was interpreted as a >5.7 log reduction
in viable cell numbers under the test conditions. Survival was hence defined as a
<5.7 log reduction in viable cell numbers. 68

1.2.3.2 Flow Cytometry

Flow cytometry is a rapid technique for measurement of single cells in suspension.
Individual cells confined within a rapidly flowing jet of water pass a measuring
window, in which several parameters can be simultaneously measured for several
thousand cells per second with high precision. 69 Light scattering reflects cellular size
and structure, while fluorescence measurements can determine the cellular content of
any constituent that can be labeled with a fluorescent dye. 70 In this way flow cytometry
combines the advantages of being a single cell technique with the power of being
able to measure a very large number of cells in a very short time. The resulting data
are not a mere average of the measured cells but a distribution of the measured
parameters for the cells. The possibility of measuring the distribution gives an estimate
of the heterogeneity of the microbial population and thereby also the possibility to
detect subpopulations that, e.g., are resistant to a treatment under investigation. With
a flow cytometer equipped with a cell sorter it is furthermore possible to sort cells
out on the basis of the parameters measured. These cells can then be sorted into
microtiter wells and be used for new growth experiments to monitor, e.g., X for the
single cells as shown by Smelt et al. 71 In general a good correlation between the
number of cells determined by plate counting and by flow cytometry has been found
for both bacteria 72 and yeast, 73 with detection limits of approximately 10 4 and 10 2
cells ml -1 determined for L. monocytogenes and Debaryomyces hansenii, respectively.
The use of flow cytometry for predictive microbiology is still very limited.
S0rensen and Jakobsen 73 used flow cytometry to enumerate viable cells of D. hans-
enii at different environmental conditions. The growth data were used to model X
and (l max as a function of temperature, pH, and NaCl. Rattanasomboon et al. 51
compared flow cytometry, turbidimetry, plate counts, and manual counts by micros-
copy for enumeration of B. thermosphacta. They found that turbidimetry overesti-
mated the cell number as the B. thermosphacta cells changed morphology during
growth, whereas flow cytometry gave a more accurate cell count than did plate
counts when both were compared to manual counts. 51 This overestimation of cell
number and hence |l could not be confirmed by Dalgaard and Koutsoumanis, 74 who
found that turbidimetric measurements estimated |i. max and X accurately.

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Possible applications of flow cytometry include enumeration of microorganisms
for both mono cultures and mixed cultures, 72 ' 75 direct measurement of lag phase as
described by Ueckert et al., 76 separation of intermediate states between dead and
culturable cells, 77 and detection of cell injury caused, e.g., by bacteriocins. 78

However, flow cytometry also has the potential to be used for gaining more
information on the microorganisms than just the number of cells. Garcia-Ochoa et
al. 79 recognized that in order to develop a structure kinetic model for the production
of xanthan by Xanthomonas capestris, they needed quantitative data on intracellular
compounds. They examined the DNA, RNA, and intracellular protein content by
flow cytometry and traditional biochemical methods, enabling them to set up stan-
dard curves and thereby quantify these intracellular compounds by flow cytometry.
It is also possible to determine other biochemical parameters such as intracellular
esterase, protease, glycosidase, and phosphatase activities. One of the limitations in
the use of flow cytometry is that it can be applied for liquid systems only. This
problem was, however, partly overcome by de Alteriis et al., 80 who studied the growth
dynamics of Saccharomyces cerevisiae cells immobilized in a gelatin gel. When the
cells were sampled for analysis, the gelatin was enzymatically liquefied with trypsin,
thus enabling the cells to be analyzed by flow cytometry.

1.2.3.3 Microscopy and Colony Size

Microscopy is another method that is gaining interest as developments in image
analysis programs and software tools for automation make the method more fea-
sible. Microscopy enables direct studies of single cells, which give new opportu-
nities for following the same cells for longer periods of time. One of the main
advantages of microscopy and the measurement of colony size is the possibility of
studying solid systems, which more closely resemble the situation in most food
systems. It is, however, also possible to investigate growth in a liquid system. By
the use of a microscope coverslip coated with, e.g., poly-L-lysine, it is possible to
obtain immobilized cells in a liquid system, as has been demonstrated for both
yeast 81 and bacteria. 82

Reports on the use of microscopy for predictive modeling of single cells are still
sparse. Wu et al. 83 recently compared the use of microscopy for determination of
lag phase duration for individual cells of L. monocytogenes with the TTD method
(described in Section 1.2.3.1). Microscopy has several advantages over the TTD
method for the determination of X of single cells. The method is a direct method
allowing visual observation of the first cell division, whereas the TTD method
depends on the time of detection, the growth rate, and extrapolation back to the
single cell. Furthermore, any treatment that results in cells not dividing will not be
detected by the TTD method. 83 A drawback when studying single cells by micros-
copy can be the difficulties in obtaining sufficient data for modeling purposes. Wright
et al. 84 used a gel-cassette in which bacteria grow as colonies immobilized in gelatin
gel, combined with a "laser gel-cassette scanner," to study the lag and doubling time
of Salmonella typhimurium at different concentrations of NaCl and pH. The inocu-
lated gel-cassette was continuously scanned, and the increase in fixed angle laser
light scattering intensity was related to the increase in diameter of the individual

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nearly spherical bacterial colonies within the controlled environment of the gel-
cassette. The system, however, needs extensive calibration; for example, it is nec-
essary to recalibrate for each new experiment in order to relate laser scattering
intensity to viable cell count. 84

Radial growth of L. monocytogenes and Yersinia enterocolitica was studied on
agar surfaces under different modified atmosphere conditions. 85 Growth of visible
colonies was followed by image analysis and viable count per colony. A linear
relationship was found between log 10 viable cell number per colony and log 10 colony
radius and (I. 85 Dykes 86 used a similar method to investigate sublethal injury in L.
monocytogenes. Cells subjected to either starvation or heat stress were plated onto
Tryptic Soy Agar and incubated at 37°C for 48 h. The plates were photographed
using a digital camera and the areas (mm 2 ) of individual colonies were determined
using image analysis. The results were presented as histograms showing frequency
distribution of colony area. The colony areas from nonstressed cells were normally
distributed, whereas the colony areas from starved or heat-stressed cells had a skewed
distribution due to an increased proportion of small colonies. 86 The growth of
Bacillus cereus was also measured as radial growth at different concentrations of
agar, NaCl, and potassium sorbate. 87 Agar plates were incubated at 30°C and pho-
tographs were taken at 30-min intervals. The colony diameters were measured on
the slides, and the time to reach a diameter of at least 0.1 mm was called "time to
visible growth." Growth was then evaluated as time to visible growth or radial growth
rate. 87 Time to visible growth was also measured by Salvesen and Vadstein 88 ,
although they defined a colony as visible when it reached a diameter of 2 mm. They
studied seawater isolates and found an inverse relationship between the |i max deter-
mined in liquid culture and the time necessary to form visible colonies on agar. 88

In contrast to bacteria, the growth of molds is usually always measured as radial
growth since molds are not unicellular. Gibson et al. 89 first modeled |l and the time
to visible growth (diameter > 3 mm) for fungi, where the growth of Aspergillus
flavus was modeled at different water activities. Valik et al. 90 also modeled the effect
of water activity but on Penicillium roqueforti. The diameter of the colonies was
fitted to the model of Baranyi et al. 91 (see Chapter 2), and X and |i modeled as a
function of water activity. Later Valik and Pieckova 92 used the same approach to
model the effect of water activity on three different heat-resistant fungi, namely,
Byssochlamys fulva, Neosartorya flscheri, and Talaromyces avellaneus. Recently,
Rosso and Robinson 93 proposed a model to describe the effect of water activity on
the radial growth of molds. The model is of the cardinal model family (see Chapter
3) and fitted successfully the radial \i of six different Aspergillus species as well as
Eurotium amstelodami, Eurotium chevalieri, and Xeromyces bisporus.

1.2.3.4 Impedance

Microbiological impedance devices measure microbial metabolism in medium by
tracking the movement of ions between two electrodes (conductance), or the storage
of charge at the electrode-medium interface (capacitance). For bacterial growth, the
conductivity of the growth medium increases with bacterial numbers because of the
production of weakly charged organic molecules. 37 This production of charged

2004 by Robin C. McKellar and Xuewen Lu

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molecules is due to, for example, the conversion of proteins to amino acids, carbo-
hydrates to lactate, and lipids to acetate, all of which will increase the conductivity
(G) of the growth medium. 94 When electrodes are immersed in a conductive medium,
a dielectric field will build up at the electrode-solution interface. The medium will
display a capacitance due to the polarization of the electrode-solution interface. An
alternating sinusoidal potential applied to the system will therefore cause a resultant
current depending on the impedance (Z) of the system, which is a function of its
resistance (R, G = 1AR), its capacitance (Q, and the applied frequency (/). 94

Z =

\Gj

2

+

' 1 -

ylKfCj

Which signal should be measured (impedance, conductivity, or capacitance) depends
on the instrument, and the microorganism and its metabolism. Generation times may
be calculated based on TTD methods as described in Section 1.2.3.1, or from the
time required for a doubling of the change in conductance. 37 Impedimetric instru-
ments are often automated, allowing a large number of samples to run at the same
time. Conductance has been used for modeling the growth of Y. enterocolitica 95 and
impedance and conductance have been used for modeling the growth of S. enteriti-
dis. 96 ' 91 An indirect conductimetry method, in which C0 2 evolved during growth was
trapped and measured, was proposed for the modeling of food spoilage by yeasts. 98

1.3 CONCLUSION

It is important that a deliberate choice be made when choosing an experimental
design or a method of data collection. The outcome of an experiment, and the
ultimate value of the model, will be greatly influenced by the experimenter's choices.
Selection of a data collection method involves some trade-off. The novel methods
described above can roughly be divided into two groups, one that provides a possi-
bility of automation and thereby allows a higher number of experiments to be
analyzed, and another that gives additional information, e.g., on the physiological
state of the microorganisms compared with viable counts. Turbidity and impedimet-
ric methods are mainly in the first group, and flow cytometry and microscopy in the
second. Although the viable count method probably remains the method of reference
and of choice, it does not always give the correct answer, which was also pointed
out in Section 1.2.3.2. It is expected that novel techniques for data collection will
continue to increase in importance with the demand for more mechanistic models
based on microbial physiology.

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