Determination of mean growth parameters of bacterial colonies immobilized in gelatin gel using a laser gel-cassette scanner

International Journal of Food Microbiology 57 (2000) 75–89 www.elsevier.nl / locate / ijfoodmicro

Determination of mean growth parameters of bacterial colonies immobilized in gelatin gel using a laser gel-cassette scanner K.M. Wright, H.P. Coleman, A.R. Mackie, M.L. Parker, T.F. Brocklehurst, D.R. Wilson, B.P. Hills* Institute of Food Research, Norwich Research Park, Colney, Norwich NR4 7 UA, UK Received 29 April 1999; received in revised form 3 September 1999; accepted 15 January 2000

Abstract The potential of a laser gel-cassette scanner (LGS) for rapid, quantitative measurement of the effect of environmental factors such as pH, temperature and humectants on the lag and doubling times of microorganisms is explored. The quantitative relationships between the laser light scattering intensity and colony radius, mean lag time and doubling time are analysed and a measurement protocol is formulated and tested using the specific example of the effect of increasing salt concentration of the lag and doubling times of Salmonella typhimurium LT2. It is concluded that the LGS is a potentially valuable tool for the rapid determination of relative lag and doubling times, but that, because of the need for extensive calibration, it is not capable, at least in its present form, of reliably determining absolute values of lag and doubling times without at least one independent viable count measurement.  2000 Elsevier Science B.V. All rights reserved. Keywords: Bacterial colonies; Gel-cassette; Laser scanner; Growth rates; Salmonella typhimurium; Concentration gradient

1. Introduction The prevention of growth of pathogenic bacteria and spoilage organisms in foods is a major concern of food manufacturers and regulatory bodies. Considerable effort has been devoted to elucidating the effects of environmental factors such as temperature, pH, salt and organic acids on the growth, injury, resuscitation and death of pathogenic bacteria such as Salmonella, Listeria and Yersinia (Mackey and *Corresponding author. Tel.: 144-1603-255-207; fax: 1441603-507-723. E-mail address: [email protected] (B.P. Hills)

Derrick, 1982; Gibson et al., 1988; Cole et al., 1990). This is usually done by inoculating liquid growth media in shaken flasks and measuring the number of viable bacteria as a function of incubation time using conventional plate counting methods. In view of the large number of possible combinations of environmental factors that can affect the growth of microorganisms in synergistic ways, this conventional approach suffers from its extremely labour-intensive and time consuming nature. This necessitates the careful statistical design of experiments to try to sample the whole multidimensional space of environmental factors in an unbiased way (Gibson et al., 1988).

0168-1605 / 00 / $ – see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S0168-1605( 00 )00229-4

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Many methods can be used for determination of the rate of growth of bacteria. Besides plate counting techniques, the number of viable bacteria can be determined directly by measurement of the intensity of scattered light, the absorption of light or by some indirect measurement of cell concentration such as ATP, bioluminescence, or electroimpedence (Norris and Ribbons, 1969; Jarvis, 1982; Stewart, 1990). Few of these techniques are amenable to continuous monitoring and hence require repetitive sampling, which is often laborious and time consuming, and others are relatively insensitive and require the presence of large numbers of bacteria. Clearly there is an urgent need for more rapid, quantitative methods for determining the effects of environmental variables on the growth (and death) of microorganisms. The problem of the statistical sampling of the whole space of environmental variables can, to a large extent, be overcome by the use of gradient methods (Wimpenny and Waters, 1984; Wimpenny and Waters, 1987; McClure and Roberts, 1987; McClure et al., 1989) and laborious plate counting can, in principle, be replaced by optical detection methods. Automated differential light scattering techniques have been described by Wyatt (1973a). Such techniques have been used to determine the growth of bacteria as colonies on agar strips (Wretlind et al., 1973), and laser light has been applied to the measurement of bacterial suspensions (Wyatt, 1973b) and to the assay of the inhibition of growth of bacteria in agar (Blume et al., 1973). These ideas have been pioneered, in large part, by Wimpenny et al. who used a two-dimensional gradient plate method, in combination with image analysis of the transmitted light, to investigate the effects of environmental factors on the growth of Salmonella typhimurium (Thomas et al., 1991) and several other microorganisms (Wimpenny et al., 1986; Wimpenny and Waters, 1987). While their technique has many advantages, such as speed and ease of use, it suffers from a lack of sensitivity and from the semi-quantitative nature of the observed growth patterns. This is largely because it is based on measuring surface growth in units of optical density of the transmitted light. One possible way of overcoming these shortcomings is to use a laser scanner in combination with a gel cassette in which bacteria grow as colonies immobilized in gelatin gel. This combination has been called a ‘laser gel-casset-

te scanner’ (LGS). The idea is to continuously scan an inoculated gel cassette and relate the increase in fixed angle laser light scattering intensity to the increase in the diameter of the individual nearlyspherical bacterial colonies within the controlled environment of the gel-cassettes. The increase in colony diameter can then be related to cell numbers within the colony and hence to lag and doubling times. In principle this combines the advantages of gradient methods with the sensitivity and quantitative nature of laser light scattering techniques. In this paper we explore to what extent the LGS can be used in this way for rapid, quantitative determination of the effect of environmental factors, such as pH, humectants and temperature, on the lag time and doubling time of food-borne pathogenic bacteria. To do this we have chosen the example of the effect of salt and pH on the lag time and doubling time of Salmonella typhimurium and we compare our results with those of conventional plate counting methods. Both the gel-cassette and the LGS are the subject of a patent (Brocklehurst et al., 1993).

2. Materials and methods

2.1. Gel-cassette The LGS has been described elsewhere (Hills et al., 1993) and is the subject of a patent (Brocklehurst et al., 1993). The gel cassette itself consists of a 2-mm thick acetal frame sealed within a sleeve of polyvinyl chloride (PVC) film (15 mm thickness) which can be sterilised by autoclaving. The bacterial growth medium in the cassette consisted of Trypticase Soy broth (Baltimore Biological Laboratory) with added yeast extract and glucose (TSBYG) and gelatin (approximately 225 bloom from bovine skin, Sigma). This medium was inoculated with Salmonella typhimurium LT2 (NCIMB 10248) and poured, while warm into the cassette, where is sets as a gel on cooling to 208C. The TSBYG was prepared at twice the final concentration and was sterilised by filtration. The gelatin was prepared as a 20% (w / v) solution, adjusted to pH 7.0 by the addition of NaOH, 5 mol l 21 , sterilised by autoclaving at 1218C for 20 min, cooled to 328C and mixed in appropriate volumes with concentrated TSBYG. In some cases the composition

K.M. Wright et al. / International Journal of Food Microbiology 57 (2000) 75 – 89

of the culture medium was modified by the addition of appropriate volumes of solutions of NaCl or by adjustment of the pH by the addition of HCl (1 mol l 21 ). The gelatin / TSBYG medium was inoculated at a concentration of approximately 10 3 viable bacteria ml 21 . At this concentration the bacteria, and hence the colonies derived from them, were on average 1 mm apart. One cassette was mounted in the LGS system (Hills et al., 1993) in a room strictly controlled at 208C. Other cassettes, prepared and incubated in parallel, were used for the determination of the numbers of viable bacteria, using conventional plating techniques or for the measurement of colony diameter using a light microscope fitted with differential interference contrast optics. The original inocula were obtained by incubating Salmonella typhimurium LT2 in TSB (10 ml) at 258C for 24 h and then at 208C for another 24 h. The A 650 of the second culture was measured in a spectrophotometer (SP600, Pye Unicam) and the concentration of viable bacteria determined from the calibration curve. Inocula were prepared by dilution of a sample of the culture in peptone salt dilution fluid (ICMSF, 1978) to give a final concentration within each cassette of 10 3 viable bacteria ml 21 . Numbers of viable bacteria were determined by cutting about 10 g of gel from the cassette, weighing this and then adding measured volumes of diluent. This mixture was stomached and plated in duplicates

77

onto plate count agar (PCA, Oxoid, Basingstoke, Hampshire, UK) and incubated at 328C for 24 h.

2.2. The LGS system The LGS is illustrated in Fig. 1 and has been described elsewhere (Hills et al., 1993; Brocklehurst et al., 1993). It comprises a mounted plate in which the cassette was held vertically on a motorised X–Y stage (Micro-Control) (A in Fig. 1). The cassette is illuminated by a 30 mW He–Ne laser (Spectra Physics) (B in Fig. 1) at a wavelength of 632.8 nm. For the purposes of measurement, the scan window (area of the cassette to be interrogated) was broken into pixels the size of which were set by the laser beam diameter through the cassette. This was 200 mm, which was achieved by collimation of the laser beam through a 200 mm pinhole (P1 in Fig. 1) mounted 2 cm from the cassette. This provided a well-defined diameter and a sharp beam profile, and illuminated each pixel as evenly as possible. The laser beam passes through the cassette at an angle of 458 giving a path length in the gel of 2.8 mm. Light scattered through 908 from the laser beam was collected and focused by a 3 10 microscope objective (C in Fig. 1) placed 2 cm from the cassette. The scattering angle was set at 908 because this was the only way of maintaining a focused image of the laser beam throughout the thickness of the cassette and to keep the distance between the scattering centre and

Fig. 1. A schematic layout of the optical path used in the Laser Gel-cassette Scanner.

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detector as similar as possible along the length of the beam in the gel, thus providing a similar solid angle for light collection at all points along the beam. The lens focused the image of the laser beam going through the cassette onto a 400 mm pinhole (P2 in Fig. 1). Between the lens and the pinhole was a scanning mirror (D in Fig. 1) which could move the focused image of the laser beam across the pinhole. Directly behind the pinhole was a narrow band pass filter (E in Fig. 1) to remove any stray background light. Light passing through the filter was detected by a photo-multiplier tube (PMT) (Hamamatsu) (F in Fig. 1). At each pixel position the scanning mirror moved the laser beam image across the detector pinhole and back again. This scan was broken down into 100 separate readings but for reasons of phase lag only 60 were used. At each pixel position the minimum intensity value plus the threshold value were subtracted from all 60 data values and resultant negative values were set to zero. Any peaks in the remaining data were then stored so that the final data was in the form of an X-position, a Y-position and an intensity value. The growth of bacterial colonies was monitored by regular measurement of the light scattered through 908 from the colonies.

2.3. Measurement of growth in a concentration gradient As the laser scanning configuration collects data from the cassette as a function of position, the cassette does not have to be uniform in composition. Using a cassette with a concentration gradient along its length enables data for growth under a range of conditions (e.g. concentration of NaCl) to be collected in a single experiment. Gel-cassettes were filled in a stepwise manner using a series of preinoculated gelatin / TSBYG growth media with increasing salt concentration. Cassettes were filled in seven strips using growth medium containing 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 and 3.5% w / v NaCl. After filling each strip the cassette was cooled to set the latest layer before overlaying the next aliquot. Prepared in this way, the gradient rapidly established a smooth, linear gradient of salt concentration along the cassette. Decay of the gradient was measurable with a sodium ion electrode, 48 h after preparation. For experiments lasting longer than 48 h the gradient was maintained by mounting the cassette

in a clamp containing reservoirs of sterile growth medium at 0.5 and 3.5% w / v NaCl at the top and base, respectively. The intensity data were integrated separately over each horizontal strip of gel, to monitor bacterial growth under a range of salt conditions. In the initial experiments the data were averaged over the seven strips originally prepared, in order to obtain data from over 2000 colonies in each strip, but a finer grid could readily be used if required.

3. Results

3.1. Uniformly inoculated gel cassettes in the absence of imposed salt or pH gradients To determine the effect of a given environmental factor, such as salt concentration, on the lag time and doubling time of a particular microorganism using the LGS, a uniformly inoculated gel-cassette containing a gradient of the environmental factor is repeatedly scanned and the time dependence of the laser scattering intensity at each position in the gradient is determined. For this laser method to be useful it must then be possible for the dependence of the lag and doubling times on the environmental factor to be extracted from this raw scattering intensity data without need for repeated and time consuming calibration. Fig. 2 shows the dependence of the viable cell count, N(t) (in colony-forming units (cfu) ml 21 ) and laser light scattering intensity, I(t) integrated over a 10 cm 2 area of a cassette uniformly inoculated with Salmonella typhimurium in the absence of imposed salt or pH gradients. It is clear that the I(t) and N(t) curves differ substantially so that it does not appear to be possible to extract the true viable count lag and doubling times directly from the raw I(t) data. To investigate this problem systematically and find a reliable protocol for relating gradient scattering data to the viable count growth parameters we undertook measurements of the dependence of viable counts, N(t), laser scattering intensity, I(t), and average colony radius, r(t), on pH and salt concentration in uniformly inoculated gel-cassettes in the absence of imposed gradients. Each of these three types of plot was analyzed and compared, beginning with the viable count data.

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Fig. 2. A comparison of the dependence of the laser light scattering intensity I(t) (arbitrary units), and viable cell count N(t) (cfu ml 21 ) on incubation time for Salmonella typhimurium incubated in a gel-cassette containing 10% gelatin, pH 7, 0.5% NaCl at 208C (data set 1 in Table 1).

3.1.1. Analysis of viable count data The viable count growth curve, N(t), for each uniform pH and salt concentration was first fitted with a growth function derived using a two-compartment kinetic cell model (Hills and Wright, 1994). This has the simple bi-exponential form, N(t) 5 N(0) hk n exp(At) 1 A exp(2k n t)j /(k n 1 A) (1) where the doubling time, t d , is related to A as t d 5 ln 2 /A

(2)

and the lag time, t lag , to both A and k n as t lag 5 A21 ln(1 1 A /k n )

gathered in Table 1 where they are compared with the corresponding values derived by fitting with an alternative growth function derived by Baranyi et al. (1993). The slight differences in the two sets of times results from the different fitting criteria; nevertheless the results illustrate the expected lengthening of the lag and doubling times with increasing salt concentration and lower pH. We now turn to the dependence of the colony radius on pH and salt concentration since, as we will show, this is related to the light scattering intensity.

(3)

The resulting values of t d and t lag (obtained by least-squares fitting of the data to Eq. (1)) are

3.1.2. Analysis of colony size data The dependence of the radius of the spherical colonies on incubation time was measured by direct examination of the optically transparent inoculated gel-cassettes with light microscopy. A representative plot of the mean colony volume (as computed from

K.M. Wright et al. / International Journal of Food Microbiology 57 (2000) 75 – 89

80 Table 1 Data set a

1 3 4 6 9 11 12 a

Experimental

Barayani Model

2-Compartment Model

conditions

Viable count

Viable count

LGS protocol

[NaCl] (%)

pH

Lag time (h)

Doubling time (h)

Lag time (h)

Doubling time (h)

Lag time (h)

Doubling time (h)

0.5 1.0 1.0 2.0 3.0 0.5 0.5

7 7 7 7 7 6 5

2.20 2.77 1.84 4.20 4.44 1.31 16.52

1.30 1.41 1.46 1.57 2.76 1.67 4.78

3.26 3.89 1.85 5.21 9.62 0.20 17.49

1.12 1.33 1.49 1.51 2.07 1.67 4.92

5.5 3.0 3.5 8.5 12.1 6.6 33.2

0.9 1.4 1.3 1.3 1.9 1.2 3.5

Data sets 2,5,7,8 and 10 are incomplete and were omitted.

the experimental root-mean-cube colony radius) for 0.5% NaCl and pH 7 at 208C is shown in Fig. 3 where it is compared with the corresponding viable count data. Provided the mean cell number density within a colony is a constant, one might expect a

relationship between the mean colony volume and the viable count of the general form N(t) 5 N(0)r v(t) p

(4)

where v(t) is the mean colony volume, v(t) 5 (4p /

Fig. 3. A comparison of the mean colony volume, v(t), and the viable count data, N(t) for Salmonella typhimurium at pH 7, 0.5% NaCl at 208C (data set 1 in Table 1). Each v(t) value is the mean volume of 10 colonies, deduced from colony diameters measured using a microscope fitted with differential interference contrast optics and a scale micrometer.

K.M. Wright et al. / International Journal of Food Microbiology 57 (2000) 75 – 89

3)r(t)3 , with r(t) the the root-mean-cube colony radius; and r is a proportionality constant equal to the mean cell number density within a colony if, as expected, the exponent p can shown to be 1. Assuming that each colony grows from a single cell, N(0) is the number of colonies. Taking logs this becomes log 10 Nstd 5 log 10sNs0d rd 1 p log 10 vstd

(5)

But in Appendix A it is shown that for t.t lag , Eq. (1) can be approximated by N(t) 5 N(0) ? 2 t

(6)

where t is a normalised, dimensionless incubation time defined as

t 5st 2 t lagd /t d

(7)

The t values are computed in what follows using the viable count lag and doubling times from Table 1. Taking logs of Eq. (6) and substituting the result

81

into Eq. (5) gives the dependence of the mean colony volume on incubation time, log 10 vstd 5 2slog 10 r /pd 1slog 10 2 /pdt

(8)

This is an interesting result since it predicts that a plot of log 10 v(t) against the normalized incubation time, t, should be universal with a slope log 10 2 /p. The universality of this relationship (at least for Salmonella typhimurium) is verified in Fig. 4 for all values of pH and salt concentration. Fig. 5 shows an expanded plot of the exponential growth phase which confirms the log-linear form of Eq. (8) and gives a value of 1.1 for the exponent p. This is very close to the value of unity expected for a constant cell packing density within the colony and verifies the form of Eq. (4). Knowing p and N(0) we can use Eq. (4) to estimate r, the mean cell number density in a colony. The result is r 50.03 cells mm 23 , which implies a mean cell diameter of about 4 mm. It is interesting to note that, according to Eq. (4),

Fig. 4. A plot of log 10 (v(t) / mm 3 ) against normalized time (t 5(t2t lag ) /t d ) for the seven sets of salt and pH values listed in Table 1.

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82

Fig. 5. An expanded plot of the exponential phase of Fig. 4. The slope of the best fit line gives p51.1 in Eq. (8).

the viable count growth curve, N(t), can be determined in the gel-cassettes simply by observing the colony radius, r(t), with light microscopy. This is certainly a faster method than conventional plate counting but is still very demanding, especially if gradients are used in the gel-cassettes since large numbers of colonies would need to be examined in each region of the gradient. Automatic scanning with a laser is obviously faster and more efficient, provided the light scattering intensity, I(t), can be reliably related to cell populations. To this we now turn.

3.1.3. Analysis of the laser scattering intensities As a first approximation we assume that the intensity of light scattered is proportional to some power q of the mean colony cross-sectional area a(t), I(t) 5 Ib 1 c a(t)

q

(9)

where Ib is the background scattering intensity

observed in the absence of colonies; c is a proportionality constant; and q is an exponent to be determined. The background scattering arises mainly from small particles in the growth medium and from scattering off the PVC–water interfaces of the cassette. We have found that Ib varies considerably from one experimental run (change of gel-cassette) to another. An examination of Fig. 2 shows that the onset of growth is detected later in the laser intensity data than in the viable count data, because it takes time for the second term on the right-hand side of Eq. (9) to become significant with respect to Ib ; thus I(0)5Ib . The exponential phase of growth is reflected in the laser data. Fig. 6 shows that over a wide range of experimental conditions, it is always possible to find a ‘reference time’ t ref during the exponential growth phase such that I(t ref )2I(0)5 Iref 2Ib 5some constant arbitrary reference level, which we call DI. In Fig. 6, log 10 DI is chosen to be 5.25. From Eq. (9) it follows that q DI 5 c ast refd q 5 c a ref

(10)

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83

Fig. 6. A plot of log 10 hI(t)2I(0)j versus incubation time for the combinations of salt and pH indicated in Table 1. The dotted line corresponds to log 10 hI(t)2I(0)j5log 10 DI55.25. Values of t ref are read off where the growth curves cross this line.

where a ref is the mean colony area at the reference level. It then follows from Eqs. (9) and (10) that q hIstd 2 Is0d j / hIref 2 Is0d j 5 (a /t) /a ref )

(11)

After choosing DI, t ref can be read off from the experimental plots of I(t), as shown in Fig. 6. The

values of t ref are listed in Table 2, together with the corresponding values of Nref 5N(t ref ), obtained by interpolation of the viable count data using Eq. (1) with the fitted values of the parameters. If we put a(t)5 p r(t)2 and, according to Eq. (4), N(t)5 constant ? r(t)3p , it follows that hIstd 2 Is0d j / hIref 2 Is0d j 5 (N(t) /Nref )

(2q / 3p)

(12)

Table 2 Data set

Reference time t ref (h)

Nref 5 N(t ref )

N(0)

a

Lag time t lag (h)

Doubling time t d (h)

1 3 4 6 9 11 12

16.0 20.0 18.0 25.0 35.0 21.5 72.0

2.19310 6 2.88310 6 1.74310 6 9.55310 6 4.07310 6 4.37310 6 2.00310 6

8.32310 2 6.61310 2 9.77310 2 1.07310 3 8.13310 2 6.46310 2 9.12310 2

12.3 16.2 9.8 53.7 22.9 24.5 11.2

5.5 3.0 3.5 8.5 12.1 6.6 33.2

0.9 1.4 1.3 1.3 1.9 1.2 3.5

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K.M. Wright et al. / International Journal of Food Microbiology 57 (2000) 75 – 89

But during the exponential phase of growth (t. t lag ) Eq. (A.2) in Appendix A can be written in the form N(t) 5 constant ? exp(At)

(13)

and when t5t ref , N(t)5Nref so that Nstd 5 Nref exp h Ast 2 t refdj

(14)

Substituting Eq. (14) into Eq. (12) we obtain the desired form of I(t), ln( hI(t) 2 I(0) j / hIref 2 I(0) j) 5 (2q / 3p) A(t 2 t ref ) (15) or ln( hI(t) 2 I(0) j / hIref 2 I(0) j) 5 (2q / 3p)(ln2)tlas (16) where we have introduced a dimensionless, normalized time, tlas , such that

tlas 5st 2 t refd /t d

(17)

tlas measures the number of population doublings before or after t ref . Eq. (16) is an important relationship since it implies that a plot of log 10 h(I(t)2I(0)) / (I(t ref )2I(0))j against tlas should be a universal straight line (at least for any particular micro-organism) of slope (2q / 3p) ? log 10 2 provided that the light scattering process is independent of environmental factors. That this is the case in Fig. 7, where the data is compared with the theoretical straight line corresponding to q53 / 2. The data matches the theory well for at least four doubling times at and after t ref , so it is reasonable to equate q in Eq. (9) to 3 / 2. Thus the scattering intensity is actually proportional to the mean colony volume rather than the cross sectional area. This can be understood by substituting 2q / 3p5 1 in Eq. (12), which then implies that the signal I(t)2I(0) due to the colonies is proportional to the viable count. More specifically, it implies that the ratio of the signal from the colonies at time t, I(t)2I(0), to the signal from the colonies at time t ref , I(t ref )2I(0), is equal to the ratio of the total cell count at time t to cell count at t ref

Fig. 7. The test of Eq. (16) showing a plot of log 10 (hI(t)2I(0)j / hIref 2I(0)j) against the dimensionless, normalized time tlas defined by Eq. (17). The data sets are listed in Table 1.

K.M. Wright et al. / International Journal of Food Microbiology 57 (2000) 75 – 89

hIstd 2 Is0d j / hIst refd 2 Is0d j 5 hIstd 2 Ib j / hIref 2 Ib j 5 Nstd /Nref

(18)

This makes good physical sense. The incident radiation penetrates the colonies and is able to scatter off any of the cells in each colony, possibly undergoing multiple scattering processes. Since the size distribution of the individual cells remains unchanged during exponential growth (Cooper, 1991), the total scattered intensity is proportional to the cell population. This relation only holds during the exponential growth phase, because in the stationary phase the mean cell size usually decreases and the composition (and hence the refractive index) of the culture medium can change as the nutrients are depleted. Eq. (18) can be rearranged to give the viable count in terms of the laser intensity, Nstd 5 a hIstd 2 Ib j

In a gradient experiment on a single cassette doubling times and lag times can be deduced by rearranging Eq. (15) using Eq. (2) and assuming 2q / 3p51. This gives, log 10 hIstd 2 Ib j 5 constant 1 (log 10 2 /t d )t

(21)

A plot of log 10 hI(t)2Ib j against t will be a straight line of slope |0.3 /t d . The slope is measured where the growth curve crosses the intensity reference level. Lag times can be calculated but we also need to know Nref and N(0), because, it is shown in Appendix B, that t lag 5 t ref 2 A21 lnhNref /N(0)j

(22)

(19)

Viable count measurements of Nref and N(0) are required because we cannot see the onset of the exponential growth phase in the laser data; it is masked by the background signal (see Fig. 2).

(20)

3.2. Results for uniformly inoculated gel cassettes with an imposed salt gradient

where the calibration constant a is defined by

a 5 Nref / hIref 2 Ib j 5 Nref /DI

85

a measures the viable count per unit scattering intensity. Ideally it should be a constant for a particular experimental set-up, but unfortunately Table 2 shows that this is not the case and a can vary considerably between runs (changes of gelcassette). This may be due to systematic errors such as changes in the laser source intensity or detector sensitivity between runs and the precise positioning of the gel-cassette. However, since a is a constant for each uniformly inoculated gel-cassette, it is reasonable to assume that it is also constant across any particular cassette when there is a gradient of some environmental factor such as salt concentration. Such a gradient would not be likely to affect the laser scattering unless it caused a significant change in refractive index. Eq. (20) implies that Nref will also be uniform across the cassette, provided we use the same reference level DI in each region. Since knowledge of Nref is prerequisite to determining lag times from the laser data (see below), to measure the lags it will be necessary to calibrate each gel-cassette by performing independent viable count measurements. This implies that the laser technique will only represent an advance over traditional methods when it is used for gradient experiments.

Having formulated a possible quantitative protocol for analysing the laser gel-cassette scattering data, the technique was tested using a salt gradient to measure the effect of increasing salt concentration on the lag and doubling times of Salmonella typhimurium at 208C. A linear salt gradient was set up in the inoculated gel-cassette. The cassette was then scanned continuously and the scattering intensities from each part of the gradient were recorded. Fig. 8 is a plot of the raw data which was acquired over a 40-h period and which contains complete information on the effects of salt (%w / w NaCl) on the lag and doubling times at pH 7 and 208C in 10% gelatin. The resulting doubling times, t d , are listed in Table 3 and, surprisingly, are about three times longer than either the viable count doubling times in Table 1 or the laser calibration results on homogeneous cassettes in Table 2. This, we believe, is an artefact due to a change of laser, resulting in a different incident beam intensity. Failure of the beam to penetrate the colonies, and possibly interference effects, are expected to change the exponent q in the fundamental relationship relating scattering intensity to colony area and viable cell numbers. Because there is no simple way to control incident beam

K.M. Wright et al. / International Journal of Food Microbiology 57 (2000) 75 – 89

86

Fig. 8. The dependence of log 10 I(t) on salt concentration and incubation time for Salmonella typhimurium at 208C. The NaCl concentration is that of a linear salt gradient set up along the gel-cassette.

agree with the lag time determined in the viable count reference experiment for the same value of the environmental parameter (in this example, 0.5% NaCl). This is best done by adjusting the value of Nref in Eq. (22). The modified values of doubling times and lag times resulting from this scaling procedure are listed in Table 3. It is clear that the laser method has lower sensitivity than the direct plate counting method. Typically there are fewer data points on the exponential part of the laser intensity versus time plot, because the background signal obscures the early stages of growth. Determination of Ib and t ref is sometimes difficult because of the scatter on the background noise level. Both these problems could be partly overcome by replacing the photomultiplier detector used for these measurements with a more sensitive CCD detector which allows much faster scanning of the cassette. This would enhance the major advantage of the LGS, namely its speed, without compromising its accuracy.

Table 3 %w / w NaCl 0.5 1.0 1.5 2.0 2.5 3.0 3.5

t ref (h) 24.5 26.0 27.0 28.0 30.0 34.0 35.0

td (h) 4.2 4.2 4.6 5.1 5.3 6.4 5.4

4. Discussion

Modified t d (h)

t lag (h)

1.1 1.1 1.2 1.4 1.4 1.7 1.4

3.3 4.8 3.6 2.3 3.1 1.7 7.7

intensity between laboratories and experiments we are forced to abandon absolute measurements of doubling times and lag times in a gradient gelcassette laser experiment in favour of a less demanding protocol based on relative values. This is best done by scaling the doubling time determined from the laser experiment for a single value of the environmental variable (e.g. 0.5% NaCl) so that it agrees with the doubling time determined in the viable count reference experiment for the same value of the environmental parameter. All the remaining laser doubling times corresponding to different environmental parameters (in this case, salt concentrations) are then scaled by the same factor. In a similar way, laser lag times need to be adjusted to

The above analysis shows that the LGS has several, potentially important, advantages over conventional plate counting methods. For example, the data on the effects of salt on lag and doubling times were acquired in 40 h, rather than the weeks usually required with plate counting methods. However, it is somewhat disappointing that the technique does not give reliable, absolute values for lag and doubling times without at least one independent measurement of the viable cell count. Table 2 shows that the variation in the coefficient a (the viable count per unit scattering intensity) whenever the cassette is changed is quite considerable and this necessitates a viable count recalibration for each new experiment. It would therefore be of considerable future interest to investigate more deeply the physical reasons for this variation. Despite this shortcoming, the LGS is clearly capable of rapid measurement of relative lag and doubling times using gradients in environmental factors within the cassettes. So far, gradients in only one environmental factor (salt) have been investigated. However it is straightforward to set up counter gradients and parallel gradients in two or more environmental factors such as salt and pH, and

K.M. Wright et al. / International Journal of Food Microbiology 57 (2000) 75 – 89

thereby examine synergistic effects (i.e. cross-terms in the effects of environmental factors on growth). This is important to the food industry when seeking optimum conditions for microbiological safety and food quality. The results presented in this paper have all been measured at a temperature of 208C. This is not, however, a necessary restriction and an apparatus has been designed to take the gel-cassette through any preprogrammed temperature–time profile during incubation. The results of such transient temperature experiments have been presented by Brocklehurst et al. (1996). Another potentially important application of the LGS is in the study of the effects of environmental factors on cell injury and resuscitation. The 2-compartment cell model (Hills and Wright, 1994) used in this paper has been generalised to include the phenomenon of injury, death and resuscitation (Hills and Mackey, 1995) and the LGS should greatly facilitate the testing of the theory. Some comment is needed about the ‘universality’ of the LGS calibration protocol proposed in this paper. Although the method has so far only been tested on Salmonella typhimurium, the underlying equations presented above are expected to remain valid for most colony forming microorganisms, where the colonies are spherical or nearly so. It will then be interesting to investigate the extent to which the coefficient a depends on the nature of the microorganism and on the composition of the growth medium. Besides salt, there are, of course, many other factors that can be examined such as pH, preservative concentration, organic acid concentration and bacteriocin concentration. In this paper only average quantities such as the mean colony volume and mean lag and doubling times have been used in the theoretical analysis of the laser scattering data and this necessitates integration of the scattering intensities over subregions of the gel-cassette so that large numbers of colonies are included. This averaging process is not, however, always necessary or desirable. Colonies of Salmonella typhimurium can grow from a diameter of a few microns up to several hundred microns in the course of incubation, and it is possible to track the growth of individual colonies by the laser scanner. This opens up the exciting possibility of measuring the statistical variations in the lag and doubling times which are known to exist in cell populations and

87

which can have a profound effect on our perception of safety tolerances in foods. The statistical aspects of the LGS measurements will be presented in a forthcoming publication.

Acknowledgements The authors wish to thank the Ministry of Agriculture, Fisheries and Food for funding this research as part of its Programme ‘Physiochemical principles underlying microbial growth in heterogeneous foods’. We are grateful to all our colleagues on the Programme for helpful discussions and collation of the data. We also thank Professor R.B. Leslie for help and encouragement during the course of the work, and the engineering staff at the Institute of Food Research, Norwich for assistance in the fabrication of the Laser Gel-cassette Scanner.

Appendix A Using the two compartment kinetic cell model (Hills and Wright, 1994) it has been shown that t lag 5 A21 ln(1 1 A /k n )

(A.1)

so that Eq. (1) in the main text can be approximated by Nstd 5 Ns0d exps Atd /(1 1 A /k n ) 5 N(0) exp(A(t 2 t lag ))

(A.2)

for t.t lag , and Nstd 5 Ns0d hk ns1 1 Atd 1 As1 2 k n tdj /sk n 1 Ad 5 Ns0d

(A.3)

to first order for t,t lag . But A5ln 2 /t d so that Eq. (A.2) becomes Nstd 5 Ns0d2 t

(A.4)

where t 5(t2t lag ) /t d .0. Eq. (A.4) is Eq. (6) of the main text.

K.M. Wright et al. / International Journal of Food Microbiology 57 (2000) 75 – 89

88

Appendix B According to the two compartment model (Hills and Wright, 1994), Nstd 5 Ns0d hk n exps Atd 1 A exps 2 k n tdj /sk n 1 Ad (B.1) But in the exponential phase k n t41 at t5t ref . Therefore Nref 5 Nst refd 5 Ns0dk n exps At refd /sk n 1 Ad

(B.2)

or (1 1 A /k n ) 5 (N(0) /Nref ) exp(At ref )

(B.3)

Substituting Eq. (B.3) into Eq. (2) of the main text, t lag 5 A21 hln(N(0) /Nref ) 1 At ref j

(B.4)

Since Nref .N(0), t ref 5 t lag 1 A21 ln(Nref /N(0))

(B.5)

which leads to Eq. (22) of the main text. Growth begins at around time t lag and continues up to (and after) t ref . During this time interval, the viable count increases from N(0) to Nref . Assuming that growth is exponential for most of this time, the interval is 21 | A ln(Nref /N(0)). This result is actually independent of the growth model Eq. (B.1) it would hold for any reasonable model incorporating an exponential growth phase.

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