Predictive model of the effect of temperature, pH and sodium chloride on growth from spores of non-proteolytic Clostridium botulinum

ELSEVIER

Food

international

Journal of

Microbiology

31 (1996) 69985

Predictive model of the effect of temperature, pH and sodium chloride on growth from spores of non-proteolytic Clostridium bo tulinum Ann F. Graham*,

David R. Mason, Michael W. Peck

Institute of’ Food Research, Norwich Laboratory, Norwich Research Park, Colney Lane, Norwich NR4 %!JA, UK Received

29 May

1995; revised

19 October

1995; accepted

20 October

1995

Abstract Non-proteolytic strains of Clostridium botulinurn are capable of growth at chill temperatures and thus pose a potential hazard in minimally-processed chilled foods. The combined effect of pH (5.0-7.3) NaCl concentration (O.l-5.0%) and temperature (4-30°C) on growth of non-proteolytic C. botulinurn in laboratory media was studied. Growth curves at various combinations of pH, NaCl concentration and temperature were fitted by the Gompertz and Baranyi models, and parameters derived from the curve-fit were modelled. Predictions of growth from the models were compared with data in the literature and this showed them to be suitable for use with fish, meat and poultry products. This model should contribute to ensuring the safety of minimally-processed foods with respect to non-proteolytic C. botulinurn. Keywords: Clostridium Temperature

botulinurn; Predictive

modelling;

Food

* Corresponding author. Institute of Food Research, Norwich Colney Lane, Norwich NR4 7UA, UK. Tel: + 44 1603 255000,

016%1605/96/$15.00

0 1996 Elsevier

PII SO168-1605(96)00965-8

Science B.V. All rights

safety;

pH; Sodium

chloride;

Laboratory, Norwich Research fax: + 44 1603 507723.

reserved

Park,

70

A.F. Graham et al. / Int. J. Food Microbiology 31 (1996) 69-85

1. Introduction Clostridium botulinum is an anaerobe which produces an extremely powerful neurotoxin, and its growth in foods often results in the production of sufficient toxin to cause severe illness or death. Thus it is imperative that the safety of all food is ensured with respect to this bacterium. Refrigerated processed foods of extended durability (REPFEDs), such as sous-vide foods, receive a mild heat treatment followed by chilled storage. Non-proteolytic strains of C. botulinum (types B, E, F), unlike proteolytic strains, are capable of growth and toxin production at chilled temperatures, and present a potential hazard in these foods, particularly if they are stored under vacuum or modified atmosphere (Lund and Peck, 1994; McClure et al., 1994a). It is important that combinations of preservative conditions are defined that provide an adequate degree of safety against growth of non-proteolytic strains of C. botulinum, but few data on suitable combinations are available. The effect of temperature, pH or NaCl concentration on growth, including a few studies of the effects of combinations of factors, has been reviewed by McClure et al. (1994a). However, many of these studies are only relevant to the product or conditions tested and do not allow interpolation between results or assessment of interactions between factors. In the last few years, mathematical modelling has been used to describe growth responses of microorganisms to combinations of preservative factors (Baker and Genigeorgis, 1992; McMeekin et al., 1993; McClure et al., 1994b). Modelling permits interpolation in the region of observations and provides information on interactions between two or more factors. If models can be used predictively they reduce the amount of challenge testing required to ensure product safety. Models have been used to describe the effect of a single factor such as temperature on the probability of growth in broth of type B and E strains (Jensen et al., 1987) and on the doubling time of a type B strain (Graham and Lund, 1993). Several models have been published which describe the combined effect of two or more factors on growth of non-proteolytic C. botulinum. Two of these are based on experiments in laboratory media. Lund et al. (1990) described the effect of temperature, pH and sorbic acid on the probability of growth from vegetative cells of type B strains, and Lawson and Adair (McClure et al., 1994a) described the effect of temperature and NaCl on time to toxin from spores. There are also models of the effect of temperature and atmosphere on growth from spores in fish (Baker and Genigeorgis, 1990) and the effect of temperature, NaCl and lactate on growth in turkey (Genigeorgis et al., 1991; Meng and Genigeorgis, 1993). The aim of the current work was to study the combined effect of temperature, pH and NaCl on growth from spores of non-proteolytic C. botulinum, to use the data to construct a growth model and to compare predictions from the model with growth reported in the literature, particularly growth in foods. Most of the experiments used a mixture of non-proteolytic type B strains because type B is less studied than type E, and because type B strains have been involved in more outbreaks of foodborne botulism than type F. Laboratory media was used rather than a food product in order to ensure that all factors other than those being tested

A.F. Graham et al. 1 hr. J. Food Microhiolog

31 (1996) 69- 85

71

were optimal. This permits quantification of the effect of the factors under study without interference from other, possibly unquantified, inhibitory factors which might be present in a food system.

2. Materials

and methods

2.1. Strains The strains used were non-proteolytic C. botulinum types B, E and F. Type B strains used were: 17B, FT50, 2B and Colworth 151 obtained from J. Crowther (Unilever, Colworth, UK); 4762U-1 obtained from C. Hatheway (CDC, Atlanta, USA); 2129B obtained from V. Scott (NFPA, Washington DC, USA). Type E strains used were: Hazen 36208 obtained from NCIB (Aberdeen, UK); VH obtained from C. Hatheway; Sebald P34 obtained from J. Crowther. Type F strains used were: 202F, FTIO, and Craig 610, obtained from J. Crowther. Cultures were maintained in Robertson’s cooked meat broth with added glucose (Southern Group Laboratories, Corby, UK). 2.2. Production

of’ spore suspensions

A two-phase medium was used for spore production. The solid lower layer contained 300 ml Robertson’s cooked meat medium with double the usual quantity of meat (Southern Group Laboratories), 0.3 g glucose and 4.5 g agar (Oxoid, Basingstoke, UK). The liquid upper layer was deoxygenated distilled water. Preparation and inoculation were as described by Peck et al. (1992). Spore suspensions were prepared of each of types B, E and F, and these contained equal numbers of spores of each strain. 2.3. Experimental

procedure

The medium used for growth experiments was PYGS (Lund et al., 1985) containing the appropriate amount of NaCl. This was boiled for 15 min, cooled under a headspace of C0,/H2/N, (5:10:85 v/v), and dispensed in 100 ml volumes into 125 ml capacity glass vials in an anaerobic cabinet (Don Whitley Scientific, Leeds, UK) containing the same gas mixture. The pH was adjusted anaerobically before dispensing using HCI or KOH. PYGS for dilution of samples for plate counts was prepared without CO,, under a gas mixture of Hz/N, (lo:90 v/v). An aliquot of the type B, E or F spore suspension was pasteurised at 60°C for 30 min and inoculated into 100 ml of the test medium to give a final concentration of 10’ spores/ml. Vials of test medium were pre-incubated overnight at the temperature under test and were held on ice to ensure that no rise in temperature took place during inoculation and sampling. Samples were removed for viable count at the time of inoculation and at appropriate intervals thereafter. At the first three sampling times a further sample was removed for pH measurement and the

A.F. Graham et al. / Int. J. Food Microbiology 31 (1996) 69-85

12

average of the three measurements was taken as the pH of the test medium. The three measurements did not differ by more than 0.03 units, VL agar (Barnes and Impey, 1968) containing 5% (v/v) oxalated horse blood (Oxoid) was used for viable counts (VLB agar). Samples were diluted in PYGS, plated onto VLB agar and incubated at 30°C for 2 days in anaerobic jars containing CO,/H, (lo:90 v/v). Inoculated test vials were incubated for up to 3 months. Strict anaerobic technique was used for all sampling and dilution (Holdeman et al., 1977). 2.4. Experimental

design

A total of 78 growth curves were constructed using different combinations of the following conditions: temperature, 4-30°C; pH, 5.0-7.3; NaCl, O.l-5.0% (w/w) (Fig. 1). The type B spore suspension was used for 72 combinations, the type E suspension for one combination, and the type F suspension for five combinations. As non-proteolytic C. botulinurn is of particular concern in foods held at chilled temperature, 50 of the 78 combinations were at 10°C or less. 2.5. Temperature

monitoring

Test vials were incubated in low temperature incubators (Astell-Hearson, UK.) and the temperature was recorded at intervals of 15 min using a series 400 data acquisition and control system with Scan 1000 software (Anville Instruments, Camberley, Surrey, UK.). Two platinum resistance thermometers (l/l0 DIN, Anville Instruments) were placed in each incubator, one near the top and one near the bottom. These were in held in vials containing 100 ml of water in order to mimic the test media. At the end of each growth curve the temperature data were analysed in order to determine mean, maximum and minimum temperature, and also to quantify variation in temperature. 2.6. Modeiling

Two methods were used to model the data; the modified Gompertz model (Gibson et al., 1987) and the model of Baranyi (Baranyi and Roberts, 1994). The first stage of modelling was to fit sigmoid functions to the growth data. The parameters lag time and maximum specific growth rate (p) were derived from the Gompertz fit, and the parameters p and h, were derived from the Baranyi model. The parameter h, is the product of p and lag time. Variance of h, was greater in our experiments than that found by Baranyi and Roberts (1994), so the curves were not remodelled with h, as a constant as originally described. Doubling time (tD) can be calculated from p as follows: tD

=

On

WP

In the second stage, the derived parameters were modelled in terms of the environmental factors temperature, pH and NaCl concentration. A quadratic response surface was used which was represented by a polynomial of the form:

A.F. Graham et al. 1 Int. J. Food Microbiology 31 (1996) 69-85

9.5/1198/l

5

-1

4’ or 5-c 0

3

m

0

0 a

20

7’ or 8’C

4-

0

3-

0

0

2-

00

4I l-

0 0

0 7

6

5

I

0

.I

6

5

7

8

PH 51O’C 4-

l 00

3-

0

00

2-

0

0.0.

2

0

00

0

t 1-o.

0

1 t 0’5

0 II

10

6

7 PH

PH A 25’ or 30-C 0

1.0

0

0

I

I

6

7

0

PH Fig. I. Combinations

of pH and NaCl (% w/w) tested at each group

of temperatures.

8

A.F. Graham et al. / Int. J. Food Microbiology 31 (1996) 69-85

14

ln (j)

= cj + c,temp + c,pH*NaCl

+ c,pH

+ chNaC1 + c,temp*pH

+ c,temp*

+ c,pH2

+ c,temp*NaCl

+ c,,NaC12

where y is the dependent variable modelled, and clPc10 are the coefficients to be estimated. The dependent variables modelled were lag time and p in the case of the Gompertz model, and with the Baranyi model, /L was modelled as above and the multiplicative mean of h, was calculated and used as a constant (Baranyi and Roberts, 1994). The natural logarithm (In) was used to damp the variance of the dependent variables (McClure et al., 1993). In order to validate the model, i.e. determine for which food products predictions from the model compare well with observations of growth in the food, predictions from the model were compared with doubling times and times to toxin reported in the literature.

3. Results In total, 78 sets of conditions were tested, but growth was not observed in 20. A test resulting in no growth cannot be modelled using this technique, which leaves 58 growth curves to construct the model. In the first stage of modelling, the fitting of a curve to the original bacterial counts, good fits were obtained by both the Gompertz and the Baranyi models (Fig. 2). In the second stage of modelling, the fitting of a quadratic response surface to the quantities derived from the curve-fit, the R2 statistics for the Gompertz model were 88.5% for In (p) and 86.6% for In (lag time). The R2 statistic for the Baranyi model was 90.4% for In (h). The root mean square error (rmse) provides a measure of the goodness of fit of a model to the data used to produce it. The lower this figure, the closer the fit of the model to the data (Box and Draper, 1987). Values for the rmse of the Gompertz based models of In (g) and In (lag time) were 0.43 and 0.50 respectively. The rmse for In (,u) in the Baranyi model was 0.39, indicating a better fit to the experimental data. There was good agreement between experimental and predicted values for doubling time and lag time, examples from throughout the experimental matrix are shown in Table 1. Doubling times derived from the Baranyi model tended to be slightly higher than those derived from the Gompertz model. Both models predicted that optimal conditions for growth were temperatures between 25 and 28°C pH between 6.6 and 6.7 and a NaCl concentration less than 1%. Growth was not observed at pH less than 5.1 or at 5% NaCl.

4. Discussion Both models gave a good fit to all the growth curves in the first stage of modelling. The fits were similar, in some cases almost indistinguishable (eg. curves A and F of Fig. 2), but the doubling times derived from the Baranyi model were

A.F. Graham et al. / Int. J. Food Microbiology

0

100

200

300

400

500

75

31 (1996) 69-85

600

700

800

Time (h) Fig. 2. Comparison of growth curves fitted by Gompertz and Baranyi models. Growth conditions were as follows: A, 15.O”C, pH 6.11, 2% NaCI; B, 9.9”C, pH 6.52, 0.1%1 NaCI; C, 8.2”C, pH 6.17, 2% NaCI; D, lO.O”C, pH 5.46, 2% NaCI; E, 5.O”C, pH 6.04, I% NaCl; F, lO.O”C, pH 5.95, 4% NaCI. Points are actual counts. Gompertz fit: - - - Baranyi fit.

slightly longer than those derived from the Gompertz model (eg. curve E of Fig. 2, and Table 1). This is because the Gompertz model fits a sigmoid function with a pronounced inflexion and thus tends to overestimate the growth rate while the Baranyi model has an approximately straight line in the exponential phase. This has been discussed in detail by Bardnyi et al. (1993). The fit in the second stage of modelling was slightly better for the Baranyi model, with an rmse for In (p) of 0.39 as compared to 0.43 from the Gompertz model, and comparisons between the original experimental data and predictions from the models indicate good agreement (Table 1). The Baranyi model was felt to be the more appropriate as the fit was better and it avoided the overestimation of ,U inherent in the Gompertz model. The goodness of fit of any model can be adversely affected by using spore inocula, which introduces the additional variable of the time taken for germination, and also by including experiments near the limits of growth, where growth tends to be less reproducible. Yet it is essential that spore inocula are used as this is the form in which the organism is likely to cause a hazard in minimally processed foods, and it is essential that combinations near the limits of growth are included if the model is to be useful over as wide a range of conditions as possible. It is not possible to make meaningful predictions outside the conditions under which growth was observed experimentally. The inoculum size (lo3 spores/ml, lo5 spores in total) was in the range commonly

A.F. Graham et al. / Int. J. Food Microbiology 31 (1996) 69-85

16

used in modelling studies (McClure et al., 1994b) and was chosen to ensure measurable growth rather than to reflect the likely level of natural contamination in foods. Various studies have indicated that where C. botulinurn is present, the level varies from l-2400 spores/kg in fish, 0.1-7 spores/kg in meat products and 0.6-2100 spores/kg in vegetables (Dodds, 1992). It is important however, that levels higher than this are used in growth experiments because under suboptimal conditions only a small proportion of the spores may be able to germinate, grow and produce toxin. For example, Jensen et al. (1987) demonstrated that only 1 in 10’ to 1 in IO* of various strains of type B and E spores were capable of growth at 5°C under otherwise optimal conditions. The inoculum level must therefore be a compromise between being low enough to allow enough doublings to measure ,u accurately, and high enough to detect growth under suboptimal conditions. The inoculum size used in the current experiments permitted a 4-5 log increase in the growth phase, while permitting growth to be detected at probability levels down to 1 in 105. To validate any model for use in making predictions in food products, estimates of growth observed in food must be compared with predictions from the model for the same temperature, pH and NaCl concentration. This was done for the Baranyi model. Data in the form of growth rate and data in the form of time to toxin/growth were considered separately. Growth rate data were taken from sources using type E strains (Ohye and Scott, 1957) and a type B strain (Graham and Lund, 1993) and in both cases growth was in laboratory media (Fig. 3). For points below Table 1 Sample experimental Temp

pH

(“C)

and predicted

NaCl

Doubling

values

time and lag time

time (h)”

Lag time (h)

W) Gompertz

5.0 5.0 5.0 7.0 7.9 8.2 9.9 10.0 10.0 15.0 19.9 24.9

for doubling

6.04 5.98 6.12 5.89 5.33 6.81 6.52 5.95 5.30 6.11 6.87 7.11

1 0.1 2 2

1 0.1 0.1 4 1 2 3 2

Gompertz

Baranyi

Baranyi

Exptl.b

Pred’

Exptl.

Pred

Exptl.

Pred

Exptl.

Pred

22 28 32 14 11 4.1 4.4 22 13 2.2 1.7 0.5

20 20 24 16 23 5.1 3.1 25 14 1.7 1.2 0.6

24 29 35 15 13 5.2 4.9 22 14 2.4 1.9 0.5

21 23 25 16 23 5.8 3.8 25 14 1.8 1.3 0.6

246 314 290 180 596 59 46 430 284 28 20 12

242 259 267 213 561 62 36 456 351 23 21 10

239 304 270 111 596 58 44 426 278 27 19 11

325 349 379 248 351 87 55 314 208 28 20 10

Exptl., Experimental “Doubling time was calculated as (In 2)/p. bTime derived from the curve fit. ‘Time predicted by the model.

A.F. Graham et al. / Int. J. Food Microbiology 31 (1996) 69-85

17

observed doubling time (h) Fig. 3. Comparisons of doubling times derived from published data with predictions from the Baranyi model.

the line of unity the reported doubling time was greater than that predicted by the model, and the model has failed safe. Fig. 3 shows good correlation between literature data and model predictions, with most predictions slightly fail-safe. This can partly be explained by the fact that Ohye and Scott (1957) tested nine or ten strains individually at each temperature but only reported the mean growth rate whereas in the experiments reported here, a mixture of strains was used and the growth rate observed will therefore be that of the strain which grew fastest under each set of conditions. Doubling times reported by Graham and Lund (1993) were for a single strain, and although this strain was included in the suspension used in the current experiments it may not have been the fastest growing. Most of the data in the literature however, are in the form of time to toxin or to visible growth, quantities not included in the model, so some other predicted quantity must be used for the comparison. Time to a 2-fold increase indicates the time when growth has just started, while time to a lOOO-fold increase provides a less conservative comparison with reported times to turbidity or toxin. Predicted time to a 2-fold increase and time to a lOOO-fold increase are plotted against observed time to toxin/growth in Figs. 4 and 5 and examples are listed in detail in Table 2 with predictions from the Gompertz model also shown for comparison. These examples include observations of growth or toxin production after 7 days at 8°C after 6 days at 10°C and after 2 days at 12°C in foods under otherwise optimal conditions. There are 271 data points, from the references listed in Table 2 plus the following: Abrahamsson et al., 1966; Segner et al., 1966; Eklund et al., 1967a,b; Emodi and

78

A.F. Graham et al. / Int. J. Food Microbiology

31 (1996) 69-85

Lechowich, 1969; Read et al., 1970; Solomon et al., 1982; Lund and Wyatt, 1984; Lund et al., 1985; Jensen et al., 1987; Notermans et al., 1990; unpublished data. Most data are for fish, poultry, meat and media. In some cases where toxin production was faster than predicted time for a 2-fold increase or time for a lOOO-fold increase (Figs. 4 and 5), a large inoculum, i.e. lo6 or greater, was used (Cann et al., 1965; Eklund et al., 1967b; Emodi and Lechowich, 1969; Lund et al., 1985; Peck et al., 1995). Some of these are shown in detail in Table 2 (herring, Cann et al., 1965; homogenised minced beef, Peck et al., 1995). However, Fig. 4 (which contains only those data for which the inoculum size was clearly stated) does not indicate a clear relationship between inoculum size and predicted and observed times. This is presumably because the plot includes data from a large number of studies, involving quite different foods with varying potentials to support the growth of C. botulinum. Baker and Genigeorgis (1990) and Meng and Genigeorgis (1993) reported a significant effect of inoculum size on time to toxin in fish and poultry, but when comparing data from many studies testing different types of foods and conditions (Fig. 4), the effect of inoculum size may be obscured by the effect of other factors, for example anaerobiosis or presence of inhibitors. The model fails safe for the vast majority of points (Figs. 4 and 5) with more points crossing the line of unity in Fig. 5 which compares time to toxin with predicted time for a lOOO-fold increase rather than with time for a 2-fold increase. The points which lie above the line of unity include those discussed above where a

1

10

observed time to toxin (d) Fig. 4. Comparison of predicted time from inoculation to a 2-fold increase with observed time to growth or toxin formation. Data is taken from experiments where the inoculum size was 1- IO5 spores/sample (0) or 2 lo5 spores/sample (0).

A.F. Graham et cd. / Int. J. Food Microbiology

31 (1996) 69-85

r

79

/

1

10 observed time to toxin (d)

100

Fig. 5. Comparison of predicted time from inoculation to a IOOO-fold increase with observed time to growth or toxin formation. Data is taken from experiments in: media ( n ); meat products (C); fish (+); poultry (0); milk (A) or vegetables (A).

high inoculum was used, and it may be that when the inoculum is very high, less than a lOOO-fold increase is required before toxin is detected, and time to a 2-fold increase is the more appropriate prediction to use for comparison in these cases. Other cases where observed times to toxin were shorter than predicted times to a IOOO-fold increase were data from crabmeat (Lerke, 1973) part of which is shown in Table 2 (Lerke, 1973). In this study, growth was reported at pH as low as 4.95 which is unexpected for non-proteolytic strains, particularly as a mixture of citric and acetic acids were used to adjust the pH. It is possible that the pH in the homogenates may not have been uniform and that there were pockets of higher pH where growth could be initiated. There were also two data points from experiments in poultry where the observed time to toxin was shorter than the predictions (Meng and Genigeorgis, 1993) but as growth occurred in one day or less, the difference between the observed and predicted time is not of any practical value. Predictions of time to a lOOO-fold increase in counts are intended purely to be an estimate of time to toxin for comparison with published data and are not therefore expected to consistently fail safe. The principal component of time to a lOOO-fold increase is

11

11

10

9

8

8

6 I

5 5

Ref.

8

fillet,

map Rockfish homogenised, map Salmon homogenised, v/p

8

16

8

12

map Rockfish

8 8

map“ fillet,

8

10

hoster-

10 8

12

ster-

map Herring, map Rockfish homogenised, map Salmon homogenised, v/p Salmon homogenised, map Salmon fillet,

VIP Crabmeat, ilised Crabmeat mogenate, ilised Cod fillet, Flounder

5 10

Herring, v/p’ Trout, smoked,

6.1

6.7

6.9

6.2

6.3

6.3

6.4 6.7

6.1 6.4

5.4

6.9

6.4 6

pH

,

0.85

0.85

0.85

0.85

E

E

B/E/F

B/E/F

B/E/F

B/E/F

0.85 0.85

B/E/F

0.85 0.85 E

0.6 4.0

0.4 2.6 7

3.0 4

7

0.9 6.0

4.8

6.3

7.0

6.6

2.2

3.5 6.0

6.0 6.3

12.4

2.1

17.5 10.9

Baranyi

0.7

5.2

5.6

4.6 3.1 7

4.1

5.2

4.3 2.9

7

4

1.8

1.5 2.6

7 7

1.4

4.0 4.1

2.6 2.7

1.0

4.8 4.9

8.1

11.3

2.8 4.8

16.1

1.4

1.8

13.0 10.8

11.5 7.1

1.0

6.9 6.6

Gompertz

lOOO-fold increase

Baranyi

to

2.3 4.0

8 23

E E

0.85 0.85

9

E

1.25

6

11 10

time (days)

increase

Gompertz

2-fold

Predicted

by the model

Observed time (days) to toxin”

E

E B

0.85 3

present

predicted

0.85

Types

and times to growth

NaCl %

times to toxin in foods

Temp

of published

Substrate

Table 2 Comparison

time

NaCl,

NaCl,

NaCI,

NaCl,

time

time

time

time

time

NaCI,

NaCl,

pH time

pH pH

pH

NaCl, NaCl,

NaCl, NaCl,

NaCl,

Estimated ablesb

vari-

8

%

2 2 g 9

% f 2 Z & 9

$

%

? %

1

0.4 0.85 0.85 1.75 1.75 2

2 0.96 0.52

6.2

6.2

5.8 6.3 6.3 6.25

6.25

6.8

6.8

5.8 5.9

12

8 15 10 16

12

10

4.4

8 8

1

2.25

I .47

1.8 2.8

16.7 7.0 6.0

1.4 2.2

11.1 6.0 4.8

4 6.9

34.6 8 16

B/E E

E

WE WE

B/E

E E

6.8 0.8 2.4 0.8

1.6

9.1

6.2

0.7

5.8 0.5 1.6 0.6

I.1

5.9

4.5

0.5

11 4 6 2

WE

WW=

WE

BE

2.4

10.3 1.2 3.7 1.3 2.8 4.3

25.4 10.7 9.1

9.6 1.0 3.0 1.1 2.4 3.8

20.3 10.0 8.1

13.8

9.4

1.1

2.0

10.8

8.0

1.0

PH

NaCl NaCl

time

“Time to toxin reported in the literature. ‘pH and NaCl were not reported in all papers, and were estimated. Where time has been estimated, there was a gap in the published data between the last -ve and the first +ve sample. Observed time to toxin was estimated as {sq rt (time of last -ve sample x time of first +ve sample)}. “Vacuum-packed. ‘Packed under modified atmosphere. References: I. Cann et al., 1965: 2. Cann and Taylor, 1979; 3. Solomon et al., 1977; 4. Lerke, 1973; 5. Post et al., 1985; 6. Taylor et al., 1990; 7. Lindroth and Genigeorgis, 1986; 8. Garcia and Genigeorgis, 1987: 9. Garcia et al., 1987; 10. Ikawa and Genigeorgis, 1987; 11. Baker et al., 1990; 12. Genigeorgis et al., 1991; 13. Peck et al., 1995; 14. Liicke et al., 1981; 15. Huss et al., 1980: 16. Huss et al., 1979; 17. Meng and Genigeorgis, 1993; 18. Lerke and Farber, 1971; 19. Meng and Genigeorgis, 1994.

19 19

18

18

17

14 15 16 17

13

13

6.3

6.3

6

8

vlp Beef, homogenised, sterilised Beef, homogenised, sterilised Ham, cured Herring, v/p Herring, v/p Chicken rolls, cooked, v/p Chicken rolls, cooked, v/p Crab, homogenised, pasteurised Crab meat, pasteurised Beef, sous-vide Chicken, sousvide

cooked,

vlp Turkey,

12

16

Table 2 (continued) 12 Turkey, cooked,

00

2

3

82

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often lag time, particularly for conditions close to the limits of growth where the lag time can be relatively long. For example, at 5°C pH 5.98 and 0.1% NaCl (Table l), predicted lag time, time to a 2-fold, lo-fold, 1OO-fold, lOOO-fold and lo4 increase in count are approximately 15, 16, 18, 21, 24 and 27 days respectively. There is a spread of data in Figs. 4 and 5, even within food commodities, indicating that in some cases a factor or factors other than pH, temperature or NaCl are contributing to growth limitation. At present, the model is suitable for use with fish, meat and poultry products as these have been thoroughly validated, but the use of the model with milk products requires further evaluation. When using the model it is important to understand that it provides information on the potential for growth in the worst possible case at particular levels of pH, temperature and NaCl, and that the information must be used in conjunction with an understanding of other inhibitory factors likely to be present in the food. The vast majority of the growth curves used to construct this model were carried out using type B strains. Type E or F strains were used for only a few curves. Yet from the validation studies, this does not seem to have compromised the usefulness of the models, indeed most of the data used in the validation relate to type E strains. The major difference between this and other published models for nonproteolytic C. hotulinum is that this is the first to use data from complete growth curves, permitting prediction of lag phase, growth rate or time to any increase in viable count up to 104. This could be used, for example, to predict different levels of increase for risk analysis. Other types of model include time to toxin (McClure et al., 1994a), and probability (i.e. the risk of one spore or vegetative cell resulting in growth and toxin formation) (Jensen used laboratory media as et al., 1987; Lund et al., 1990). These models the substrate. Genigeorgis and co-workers, in a series of publications, have modelled a combination of time to toxin and probability of toxin formation in fish (Lindroth and Genigeorgis, 1986; Ikawa and Genigeorgis, 1987; Garcia et al., 1987; Garcia and Genigeorgis, 1987; Baker and Genigeorgis, 1990) and in poultry (Genigeorgis et al., 1991; Meng and Genigeorgis, 1993). The different types of model provide different growth information and are thus complementary. The model detailed here should allow food processors to reduce the amount of challenge testing necessary to ensure food safety with regard to non-proteolytic C. botulinurn. This may prove useful in the development of minimally-processed foods which rely on storage at low temperatures for preservation, for example REPFEDs and sous-vide foods. These models were developed as part of the UK MAFF-funded programme on the predictive modelling of foodborne pathogens. The aim of this programme was to develop predictive models for inclusion in Food MicroModel, and the Gompertz model described here for growth of non-proteolytic C. botulinum is in version 1 of Food MicroModel. The Baranyi model may be included in future versions. Food MicroModel (for WindowsTM) for the personal computer was launched in 1994.

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Acknowledgements The authors wish to thank Dr. J. Baranyi for assistance with the modelling and many helpful discussions, and Dr. B.M. Lund for her contribution to the development of this project. This work was funded by the Ministry of Agriculture, Fisheries and Food. Food MicroModel software was developed by, and is available from, Food Micromodel Ltd., Leatherhead, Surrey, UK.

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