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The effect of the growth environment on the lag phase of Listeria monocytogenes
International Journal of Food Microbiology 44 (1998) 83–92
The effect of the growth environment on the lag phase of Listeria monocytogenes Tobin P. Robinson*, Maria J. Ocio, Anu Kaloti, Bernard M. Mackey Institute of Food Research, Earley Gate, Whiteknights Road, Reading, Berks. RG6 6 BZ, UK Received 3 March 1998; received in revised form 20 July 1998; accepted 6 August 1998
Abstract The duration of lag in Listeria monocytogenes was examined in relation to the physico–chemical properties of the growth environment. It was supposed that lag would be determined by two hypothetical quantities, the amount of work that a cell has to perform to adapt to new conditions and the rate at which it can perform that work. If the rate at which the cell can perform the necessary work is a function of the maximum specific growth rate in the new environment, the hypothesis predicts that lag time should be related in some way to growth rate, provided cells are initially in approximately the same physiological state. Literature data suggest this is true for many organisms when temperature is the sole growth limiting factor. However, lag times of L. monocytogenes displayed an unusual response to temperature in which lag times of cells precultured at 378C were shorter at 158C than at 208C or 258C. Analysis of data from the Food Micromodel in which growth of L. monocytogenes was controlled by combinations of pH, NaCl concentration and temperature, showed that there was a linear relationship between lag time and mean generation time although there was much scatter in the data. When the effects of pH, solute type and concentration were investigated individually in this work the correlation between lag time and mean generation time was often poor. It would thus appear that the relationship between growth environment and lag time is more complex than the corresponding relationship between growth environment and maximum specific growth rate. 1998 Elsevier Science B.V. All rights reserved. Keywords: Lag; Listeria monocytogenes
1. Introduction The lag phase of microbial growth was defined by Penfold (1914) as the interval between the inoculation of a bacterial culture and the time of commencement of its maximum rate of growth. It has *Corresponding author. Tel.: 1 44 118 9357230, fax: 1 44 118 9357222, e-mail: [email protected] 0168-1605 / 98 / $ – see front matter PII: S0168-1605( 98 )00120-2
been conventionally measured as the point at which the slope of the exponential phase of growth (on a semi-logarithmic plot) intercepts a horizontal line drawn from the initial cell concentration (Lodge and Hinshelwood, 1943). Several other definitions of lag have been employed depending on the mathematical model or curve fitting procedure applied to the growth data (Buchanan and Cygnarowicz, 1990; Zwietering et al., 1991, 1992). In physiological
1998 Elsevier Science B.V. All rights reserved.
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terms, lag represents a transition period during which cells adjust to their new environment. Pirt (1975) recognized the following causes of lag: (i) change in nutrition, (ii) change in physical environment, (iii) presence of an inhibitor, (iv) spore germination and (v) state of the inoculum. The early literature was reviewed by Penfold (1914), Winslow and Wilson (1939) and Hinshelwood (1946). The effect of inoculum age, inoculum size, nutrient content of media, carbon dioxide concentration was established in these studies at least on a broad qualitative basis. More recent work has also examined the effect of cellular injury (Mackey and Derrick, 1982, 1984; Tsuchido et al., 1989). Lag times and growth rates of the major foodborne pathogens and some spoilage organisms have been measured under a wide range of growth conditions to develop methods for predicting microbial behaviour in foods. The data have been incorporated into mathematical models that allow growth rates of many foodborne bacteria to be predicted with a fair degree of accuracy from a knowledge of temperature, pH, solute content or water activity, gas atmosphere and preservative content (reviewed by McMeekin et al., 1993). Lag is inherently more difficult to predict than growth rate because it depends on the physiological state of the inoculum as well as growth conditions. Pre-adaptation to inimical growth conditions can shorten lag times dramatically (Hudson, 1993; Kroll and Patchett, 1992; Buchanan and Klawitter, 1991; Dufrenne et al., 1997) and the magnitude of this effect is difficult to predict. Even when inoculum effects have been minimised, it has still proved difficult to obtain a clear picture of the way lag varies as a function of the external environment. However, several studies have demonstrated a relationship between lag time and growth rate (Smith, 1985; Mackey and Kerridge, 1988; Adair et al., 1989; Baranyi and Roberts, 1994) but the general validity of this relationship has not been fully explored. A better understanding of the determinants of lag and the relative importance of physiological state and environmental conditions would help define the accuracy limits of predictive models, and might also suggest ways of extending lag and so delaying or preventing growth of undesirable microbes. On the other hand, reducing lag times would have benefits
in improving use of starter cultures and in recovering bacteria from food and environmental samples. The aim of this work was to investigate systematically the effects of solute concentration, pH and temperature on lag times of the foodborne pathogen Listeria monocytogenes, in an attempt to find a quantitative relationship between the physicochemical properties of the growth environment and the duration of lag. The variation in lag time between individual cells in a population is an important aspect of the problem (Baranyi, 1998; Stephens et al., 1997) but is not considered here.
2. Materials and methods
2.1. Preparation of inocula Stationary phase cultures of Listeria monocytogenes NCTC 11994 were prepared by inoculating 10 ml tryptone soya broth, (TSB; Oxoid, Basingstoke, UK) from a slope and then incubating overnight, shaken at 378C. One hundred ml of this culture were then used to inoculate 10 ml TSB and this was incubated until an OD 680 of 0.15 was reached. The culture was then incubated for a further 17 h. Stationary phase cultures prepared in this way gave more reproducible results than log phase cultures (results not shown). The inoculum level used in the experiments was approximately 10 3 cells ml 21 .
2.2. Growth media Broths (TSB) containing different concentrations of solutes were prepared by adding glycerol or NaCl and then autoclaving. Where broths of varying pH were required, the pH of the broth was altered before autoclaving using HCl or NaOH and the pH measured again after autoclaving. All broths were preheated to the desired incubation temperature before inoculation.
2.3. Viable counts and growth curves Viable counts were assessed by spread plates, the culture being diluted in maximum recovery diluent (Oxoid) and 0.05 ml spread on TSA (tryptone soya agar, Oxoid), in duplicate. Eleven to 27 points were taken for each curve depending on the duration of
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the experiment. Experiments were repeated three times, except for those in broths with both NaCl and glycerol which were only repeated twice. Curves were fitted to the data using an IFR in-laboratory program Dmodel written by Jozsef Baranyi, which is based on the growth model of Baranyi and Roberts (1994), with m 5 0, n 5 1. The program provided estimates of lag times and growth rates from the fitted curves.
3. Results
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was that W will tend to increase and R decrease, as conditions in the new medium deviate farther from those under which the inoculum was grown. If we define the fitness of a medium to support growth in terms of the maximum specific growth rate possible in the medium, then the difference between media can be quantified as the difference in maximum specific growth rates, irrespective of the particular factors leading to those different growth rates. According to this argument, lag times of cells grown under standardised conditions would be related in some way to maximum specific growth rate ( m ) or mean generation time (mgt) in the new medium.
3.1. Experimental approach We may suppose a priori that the duration of lag will depend on (a) the amount of work that a cell needs to do to adapt to its environment and prepare for division and (b) the rate at which it is able to do that work. By work we mean the various biosynthetic and homeostatic processes needed to prepare for growth in a new environment. Since there is no convenient direct way of measuring the hypothetical quantities ‘‘work needed’’ (W ) and ‘‘work rate’’ (R) independently, we sought to determine whether the lag time of cells that were initially in approximately the same physiological state would vary in a regular way as the external environment was changed. Our working hypothesis
3.2. General relationship between growth rate and lag time The data base used to construct FoodMicromodel contains growth curves for L. monocytogenes obtained under a wide range of conditions. These data were used to examine the relationship between growth rate and lag time (the original data are not publicly available, and the derived growth rates have been reproduced here with the kind permission of MAFF (Ministry of Agriculture Fisheries and Food)). Fig. 1 shows that lag time and mgt of L. monocytogenes are linearly related with the average lag being equal to about eight-times the mgt. If lag time conformed to the simple relationship:
Fig. 1. The relationship between lag time and mean generation time for L. monocytogenes grown in media at different combinations of pH, water activity and temperature. Data taken from Food MicroModel database.
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lag time (L) 5 work needed (W ) / work rate (R), and if R is taken to be equivalent to m (see also Baranyi and Roberts, 1992), and is assumed to be constant for cells in the same initial state, we would expect plots of m versus 1 / lag, or mgt versus lag to yield straight lines, as observed. However, the considerable scatter in the data we analysed implies that these assumptions are oversimplifications and that lag was affected by factors additional to growth rate. Inspection of the original data in Fig. 1 showed that in general, the lag was shorter in comparison to the mgt when salt and pH were optimal and temperature low, and longer when NaCl levels were high. However, these trends were not exclusive and many exceptions were evident. To investigate the relationship further, the effects of solute concentration, pH and temperature were examined separately.
Fig. 3. Relationship between lag time of L. monocytogenes at 378C and osmolality of growth medium adjusted with NaCl (s) or glycerol (j).
3.3. Effect of solute concentration Two solutes were tested, sodium chloride which is ionic and is excluded by the cytoplasmic membrane and glycerol which is neutral and diffuses passively through the membrane. Growth rates of L. monocytogenes decreased approximately linearly with increasing osmolality with no significant difference (a 5 0.05, two-tailed F-test) in slope for glycerol and NaCl (Fig. 2). In contrast, glycerol had no discern-
ible effect on lag whereas, with NaCl, lag increased in a biphasic fashion as concentration increased (Fig. 3). Small changes in osmolality above 3.0 OsM NaCl produced very large increases in lag. There was thus no direct relationship between lag time and mgt for either NaCl or glycerol. The observation that increasing concentrations of glycerol slowed down growth but had no effect on lag suggested to us that adding glycerol to media containing salt should decrease the work rate (R) without increasing work load (W ). The addition of increasing amounts of glycerol to media containing a fixed concentration of salt would therefore be expected to increase lag in direct proportion to the effect on growth rate. Fig. 4 shows that this was true to a first approximation.
3.4. Effect of pH
Fig. 2. Relationship between growth rate of L. monocytogenes at 378C and osmolality of medium adjusted with NaCl (s) or glycerol (j).
The relationship between growth rate and pH was biphasic (Fig. 5). Although growth rate varied by about sixfold over the pH range tested, there was negligible effect on lag except close to the lower limit for growth, when a large increase in lag was observed. Under these conditions, where acidity was the sole variable, lag was not related to growth rate. Rather, there was a threshold value below which very long lags occurred.
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Fig. 4. Relationship between lag time of L. monocytogenes and growth rate controlled by increasing the concentration of glycerol in TSB containing no added NaCl (– + –), or NaCl added to 0.9 M (– j –) or 1.2 M (– m –).
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Fig. 6. The effect of temperature on lag times of L. monocytogenes growing in TSB containing no added NaCl (s) or NaCl added to a concentration of 0.9 M (j) or 1.2 M (m).
trations of salt viz TSB containing zero, 0.9 M or 1.2 M added NaCl. The result was unexpected as shown in Fig. 6. At each NaCl concentration, lag increased as temperature decreased from 378C to 258C, then decreased again to a minimum at 158C. Thereafter there was a sharp increase in lag as temperature decreased to 58C. The corresponding effects on growth rate are shown in Fig. 7 and Fig. 8. An Arrhenius plot of the
Fig. 5. The effect of pH on lag time (s) and generation time (j) of L. monocytogenes.
3.5. Effect of temperature In an attempt to vary the putative work rate (R) without altering the workload (W ), lag times were determined at different temperatures in TSB containing a fixed concentration of salt. To examine the effect of temperature at different initial workloads (W ), the procedure was repeated at three concen-
Fig. 7. Arrhenius plot of growth rates of L. monocytogenes growing in TSB containing no added NaCl (s), or NaCl added to a concentration of 0.9 M (j) or 1.2 M (m).
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4. Discussion
Fig. 8. The relationship between œm and temperature for L. monocytogenes growing in TSB containing no added NaCl (s) or NaCl added to a concentration of 0.9 M (j) or 1.2 M (m).
data was non-linear with increasing slope from 378C to 58C (Fig. 7). A plot of square root of growth rate against temperature (Ratkowsky et al., 1982), gave a linear response for temperatures between 58C and 258C, but a discontinuity above this temperature, particularly in media containing 0.9 M and 1.2 M NaCl (Fig. 8). The relationship between growth rate and lag can be seen in Table 1 in which values of the quantity (lag / mgt) are listed for each temperature. (This effectively expresses lag in units of generation time). There is little difference in the values at 58C, 108C, 158C and 378C, indicating that at these temperatures lag is approximately proportional to growth rate. However at 208C and 258C the values are appreciably larger indicating that lag is longer at these temperatures relative to growth rate.
Table 1 Effect of temperature and NaCl concentration on lag / generation time of L. monocytogenes Temperature (8C)
5 10 15 20 25 37
Lag / generation time 0 M NaCl
0.9 M NaCl
1.2 M NaCl
1.73 1.97 0.76 3.62 5.52 0.20
1.94 3.44 0.84 7.89 10.74 2.87
1.10 5.08 1.83 7.72 14.84 3.91
The work / rate model of bacterial lag described here may be compared with the relative rate concept of Olley and Ratkowsky (1973) where the rate of spoilage of flesh foods (a product of lag and growth rate) at any temperature, was divided by the rate at 08C to produce the relative rate. This gave an approximately straight line relationship, when compared to temperature (the determinant of rate). Similar ideas are inherent in the gamma model of Zwietering et al. (1994) in which a temperature shift during lag or growth perturbs the cell and hence induces an additional lag whose duration depends on temperature and a proportionality constant d. However it became apparent during this work that a simple relationship between lag and growth rate did not hold for all environmental conditions, hence the effect of pH, temperature etc., were investigated separately.
4.1. Effect of solutes Our finding that the growth rate of L. monocytogenes was influenced more by osmolality than the type of solute agrees with results of Li and Torres (1993) and Christian and Scott (1953) obtained with a range of other psychrotrophic or mesophyllic organisms. The biphasic lag response of L. monocytogenes with increasing NaCl shows that, above a critical concentration, salt affects lag much more than growth rate. Either the rate at which the cell can perform the necessary adjustment work decreases dramatically above this critical concentration or different physiological processes (additional work tasks) become necessary. The nature of the additional tasks are not known but could include repair of cellular injury or accumulation of compatible solutes, all of which are very energy demanding (Knochel and Gould, 1995). Others (Buchanan et al., 1989; Buchanan and Philips, 1990) have also shown that lag times and mgt values increase with increasing concentration of salt and other preservatives but, since the experimental designs were multifactorial it is often difficult to discern the precise response to salt alone. Davey (1991) analyzed several sets of published lag time data and observed that lag was affected more than growth rate at low values of a w . The observation that glycerol had no detectable
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effect on lag was not anticipated, although others have shown that glycerol has a smaller effect on lag or growth rate than NaCl or sucrose (Li and Torres, 1993; Tapia de Daze et al., 1991; Farber et al., 1992; Nolan et al., 1992). This is thought to be due to the compatible solute-like behaviour of glycerol, i.e., it readily diffuses into the cell and has low toxicity at high internal concentrations (Csonka, 1989). Under our conditions growth in glycerol-containing broth required no period of adaptation i.e., no specific work was needed to adapt to the increased osmolality, although growth rate was reduced. Plasmolysis is transient when cells are transferred to glycerol (Christian, 1981; Kroll and Anagnostopuolos, 1981) whereas deplasmolysis in the presence of NaCl or other non-permeant solutes is expensive in terms of energy, requiring activation of potassium uptake systems and induction or activation of uptake systems for proline, betain and other compatible solutes (Patchet et al., 1992, 1994; Ko et al., 1994; Gutierrez et al., 1995). Interestingly, Amezaga et al. (1995) reported that growth of L. monocytogenes in brain heart infusion at high osmolality was preceded by a marked lag whereas no significant lag occurred in a defined medium at high osmolality. The addition of glycerol (which caused no lag on its own) to media containing a fixed concentration of NaCl, increased lag in proportion to the decrease in growth rate. Under these particular conditions therefore, the rate at which cells can adapt to the new conditions, and hence lag time, were proportional to growth rate as predicted by the hypothesis.
4.2. pH The growth rate of Listeria monocytogenes in broth varied in a biphasic manner with respect to pH. This differs from the results of Duffy et al. (1994) who found that growth rates of Listeria monocytogenes on vacuum-packed cooked meats containing different salt concentrations were linearly related to pH. However, they only examined a pH range of 5.8 to 6.8, whereas we found the change in slope occurred at a pH of 5.0. Surprisingly, we found that lag was little affected by pH except close to the limit for growth. As with glycerol, this implies that the specific work required to adapt to acid conditions is slight except at the limit where other factors, possibly including cell damage, exert an influence. Most
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modelling studies are multi-factorial and so the sole effect of pH cannot be easily extracted however, others have found a progressive increase in lag and mgt with decreasing pH (Duffy et al., 1994; Johansen et al., 1994). The difference may reflect differences in growth conditions: in our experiments pH was the main controlling factor, other conditions being optimal for growth, whereas in the work of Duffy et al., growth was also affected by the anaerobic conditions and the reduced water activity.
4.3. Temperature If temperature affects lag processes in the same way as it affects growth processes, one would expect lag to be proportional to growth rate at the different temperatures. Others have found this to be so for Salmonella typhimurium (Smith, 1985; Mackey and Kerridge, 1988). This simple relationship did not hold for L. monocytogenes growing in broth. By expressing lag in units of mgt, it was apparent that lag, relative to growth rate, was proportionately longer at 258C than at all other temperatures. Even when expressed in absolute terms, the lag at 158C was noticeably shorter than at either 208C or 258C. Several lines of evidence suggest that the lag in E. coli following a temperature downshift is caused by inhibition of translation (Jones and Inouye, 1994). The duration of lag appears to be related to cellular levels of guanosine 59 triphosphate-39 diphosphate and guanosine 59 diphosphate-39 diphosphate [(p)ppGpp] which in turn depend on the translational capacity of the cell and the supply of charged tRNA. Following a temperature down-shift the decreased levels of (p)ppGpp result in changes in gene expression and synthesis of transcriptional and translational proteins during the lag period. Cold-shock protein synthesis may also depend on levels of (p)ppGpp (Jones and Inouye, 1994). The reason for the shorter lags in L. monocytogenes at 158C compared with 208C and 258C is not known, but may be because the temperature change from 378C to 258C or 208C is insufficient to trigger a full cold shock response. Several cold shock and cold acclimation proteins have been identified in L. monocytogenes by twodimensional gel electrophoresis following a temperature down shift from 378C to 58C (Bayles et al., 1996), and it would be interesting to follow their
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rates of synthesis following downshifts to different temperatures. No deviations from monotonic behaviour in the response of L. monocytogenes to temperature have previously been reported. Schaffner (1995), for example, found that lag times of L. monocytogenes changed little between 468C and 158C but increased rapidly below this temperature. The data that were analyzed were restricted to cases where lag time increased with decreasing temperature so it is possible the effect reported here was overlooked. It may be relevant to the present observation that within the range 4–408C, the optimum temperature for growth of L. monocytogenes in high concentrations of salt is 158C (Farber et al., 1992). Interestingly, Bajard et al. (1996) found that L. monocytogenes showed a nonlinear relationship between œmmax and temperature, when other conditions were optimal. They found that the slope of such a plot had two linear parts separated at a temperature of around 10 to 158C. This unexpected result is reflected by the ability of this organism to grow well at refrigeration temperatures. Our results also show a biphasic pattern of growth rates, particularly in the presence of raised NaCl levels, although the break occurred at 258C. This shows closer agreement with the observations of Ratkowsky et al. (1982) who found an excellent straight line relationship for temperatures up to or just below the maximum growth rate for 14 bacterial species. Arrhenius plots of the psychrophile Pseudomonas fluorescens MF10 showed a change in slope at 178C such that the temperature characteristic for growth in the range 08C to 178C was twice that for the range 178C to 308C (Guillou and Guespin-Michel, 1996). This was attributed to an increase in protein degradation at temperatures above 178C. It is not known whether lag showed a similar discontinuous response with temperature in this organism. The appearance of the Arrhenius curve was similar to that commonly seen in other bacteria (Ratkowsky et al., 1982) in that the slope increased as temperature decreased. The discontinuity in the Ratkowsky square root plots in salt-containing media implies that, in relative terms, salt is more inhibitory to growth of L. monocytogenes at temperatures above about 208C. The accuracy with which lag can be predicted will depend on (a) knowing the state of the inoculum and
(b) being able to predict how lag is determined by the separate effects of inoculum state and environmental conditions. Many models have been described that allow lag and growth rate to be predicted, but models that are most suitable for lag may differ from those that are best for growth rate (Zwietering et al., 1991; Ratkowsky et al., 1991; Duh and Schaffner, 1993; Buchanan, 1993) and in most cases no allowance is made for the effect of inoculum history on lag. The models of Baranyi et al. (1993) and Hills and Wright (1994) contain parameters that allow the state of the inoculum to be quantified and also assume that lag time and growth rate are dependent variables. These properties allow sets of differential equations to be used to predict growth and lag under conditions where temperature or other variables change with time. The modelling of continuously changing variables is impossible for example in the many models that employ the Gompertz function, which can however be applied to step changes in temperature (Zwietering et al., 1994). Many sets of published data indicate that lag time and growth rate are closely correlated when temperature is the sole variable (see Davey, 1991). Under these conditions predictions of lag should be reasonably accurate for cells in the same physiological state though, as demonstrated in this work, variation in the rate at which cells respond to cold shock at different temperatures may increase the uncertainty of predictions. When additional variables such as pH and salt concentration are introduced, growth rate and lag time are less closely correlated, though a general trend is still evident as shown in Fig. 1. Two types of effect may be envisioned that would account for the increased variation. First, even when cells are initially in the same physiological state, the act of inoculation will cause changes to that state, the extent of which will depend on the new growth conditions (i.e., both ‘‘work load’’ and ‘‘work rate’’ are affected independently). Second, the rate-limiting steps in adapting to new conditions may be specific to the conditions, depending on the physiological processes involved. Hence when the effects of individual variables such as type of solute or pH are considered separately, the correlation between growth rate and lag time may be poor. It would thus appear that the relationship between growth environment and lag time is more complex than the corresponding relationship between growth
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environment and maximum specific growth rate. Predictions of lag time will therefore inevitably be less accurate than those for growth rate and variation in the initial physiological state will introduce further uncertainty. However attempts to quantify responses of bacteria to changing conditions are important in identifying trends, identifying ‘‘typical’’ behaviour and setting ‘‘worst case’’ limits. In the model of Baranyi for example an ‘‘envelope’’ of prediction is given, representing the difference between typical behaviour and a worst case scenario where there is no lag. When tested with Brochothrix thermosphacta under conditions of changing temperature, the model provided surprisingly accurate predictions except when temperature changed very rapidly and other conditions were also inhibitory (Baranyi et al., 1995). Such models may be refined as the underlying physiology becomes better understood. Knochel and Gould (1995) commented that predictive microbiology should provide a useful tool to those assessing hazard and risk in HACCP operation and help to identify key areas where intervention to inactivate or inhibit microbes would be most profitable. This work has revealed several thresholds or discontinuities in the responses of Listeria monocytogenes to inimical conditions. For example lag times increased very rapidly at salt concentrations above 2–3 OsM or at temperatures below 158C. Significantly, soft cheese, such as camembert is ripened at a temperature of approximately 148C (Gay et al., 1996). The discovery of these transition points raises the exciting possibility that their position might be shifted by appropriate manipulation of conditions, leading to synergistic inhibitory effects of benefit in food preservation.
Acknowledgements This work was funded by The Ministry of Agriculture Fisheries and Food. M.J.O. was supported by the Spanish Ministry for Science and Education.
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Dufrenne, J., Delfgou, E., Ritmeester, W., Notermans, S., 1997. The effect of previous growth conditions on the lag phase time of some foodborne pathogenic micro-organisms. Int. J. Food Microbiol. 34, 89–94. Duh, Y.-H., Schaffner, D.W., 1993. Modelling the effect of temperature on the growth rate and lag time of Listeria innocua and Listeria monocytogenes. J. Food Prot. 56, 205– 210. Farber, J.M., Coates, F., Daley, E., 1992. Minimum water activity requirements for the growth of Listeria monocytogenes. Lett. Appl. Microbiol. 15, 103–105. Gay, M., Cerf, O., Davey, K.R., 1996. Significance of preincubation temperature and inoculum concentration on subsequent growth of Listeria monocytogenes at 148C. J. Appl. Bacteriol. 81, 433–438. Guillou, C., Guespin-Michel, J.F., 1996. Evidence for two domains of growth temperature for the psychrotrophic bacterium Pseudomonas fluorescens MF0. Appl. Environ. Microbiol. 62, 3319–3324. Gutierrez, C., Abee, T., Booth, I.R., 1995. Physiology of the osmotic stress response in microorganisms. Int. J. Food Microbiol. 28, 233–244. Hills, B.P., Wright, K.M., 1994. A new model for bacterial growth in heterogeneous systems. J. Theor. Biol. 168, 31–41. Hinshelwood, C.N., 1946. The Chemical Kinetics of the Bacterial Cell. Clarendon Press, London. Hudson, J.A., 1993. Effect of pre-incubation temperature on the lag time of Aeromonas hydrophila. Lett. Appl. Microbiol. 16, 274–276. Johansen, C., Gram, L., Meyer, A.S., 1994. The combined inhibitory effect of lysozyme and low pH on growth of Listeria monocytogenes. J. Food Prot. 57, 561–566. Jones, P.G., Inouye, M., 1994. The cold-shock response – a hot topic. Molecular Microbiol. 11, 811–818. Knochel, S., Gould, G., 1995. Preservation microbiology and safety: quo vadis?. Trends Food Sci. Technol. 6, 127–131. Ko, R., Smith, L.T., Smith, G.M., 1994. Glycine betaine confers enhanced osmotolerance and cryotolerance on Listeria monocytogenes. J. Bacteriol. 176, 426–431. Kroll, R.G., Anagnostopuolos, G.D., 1981. Potassium fluxes on hyperosmotic shock and the effect of phenol and bronopol (2-bromo-2-nitropropan-1,3-diol) on deplasmolysis of Pseudomonas aeruginosa. J. Appl. Bacteriol. 51, 313–323. Kroll, R.G., Patchett, R.A., 1992. Induced acid tolerance in Listeria monocytogenes. Lett. Appl. Microbiol. 14, 224–227. Li, K.-Y., Torres, J.A., 1993. Water activity relationships for selected mesophiles and psychrotrophs at refridgeration temperature. J. Food Prot. 56, 612–615. Lodge, R.M., Hinshelwood, C.N., 1943. Physicochemical aspects of bacterial growth. Part IX. The lag phase of bact. Lactis aerogenes. J. Chem. Soc., 213-219. McMeekin T.A., Olley, J.N., Ross, T., Ratkowsky, D.A., 1993. Predictive Microbiology: Theory and Application. Research Studies Press, Taunton. Mackey, B.M., Derrick, C.M., 1982. The effect of sublethal injury bt heating, freezing, drying and gamma-radiation on the duration of the lag phase of Salmonella typhimurium. J. Appl. Bacteriol. 53, 243–251. Mackey, B.M., Derrick, C.M., 1984. Conductance measurements of the lag phase of injured Salmonella typhimurium. J. Appl. Bacteriol. 57, 299–308.
Mackey, B.M., Kerridge, A.L., 1988. The effect of incubation temperature and inoculum size on growth of Samonellae in minced beef. Int. J. Food Microbiol. 6, 57–65. Nolan, D.A., Chamblin, D.C., Troller, J.A., 1992. Minimal water activity levels for growth and survival of Listeria monocytogenes and Listeria innocua. Int. J. Food Microbiol. 16, 323– 335. Olley, J., Ratkowsky, D.A., 1973. Temperature function integration and its importance in the storage and distribution of flesh foods above the freezing point. Food Tech. Aust. 25, 66–73. Patchet, R.A., Kelly, A.F., Kroll, R.G., 1992. Effect of sodium chloride on the intracellular solute pools of Listeria monocytogenes. Appl. Environ. Microbiol. 58, 3959–3963. Patchet, R.A., Kelly, A.F., Kroll, R.G., 1994. Transport of glycine-betaine by Listeria monocytogenes. Arch. Microbiol. 162, 205–210. Penfold, W.J., 1914. On the nature of bacterial lag. J. Hygiene 14, 215–241. Pirt, S.J., 1975. Principles of Microbe and Cell Cultivation, Blackwell, London. Ratkowsky, D.A., Olley, J., McMeekin, T.A., Ball, A., 1982. Relationship between temperature and growth rate of bacterial cultures. J. Bacteriol. 149, 1–5. Ratkowsky, D.A., Ross, T., McMeekin, T.A., Olley, J., 1991. Comparison of Arrhenius-type and Belehradek-type models for prediction of bacterial growth in foods. J. Appl. Bacteriol. 71, 452–459. Schaffner, D.W., 1995. The applicationof the WLF equation to predict lag time as a function of temperature for three psychrotrophic bacteria. Int. J. Food Microbiol. 27, 107–115. Smith, M.G., 1985. The generation time, lag time and minimum temperature of growth of coliform organisms on meat, and the implications for codes of practice in abattoirs. J. Hygiene 94, 289–300. Stephens, P.J., Joynson, J.A., Davies, K.W., Holbrook, R., LappinScott, H.M., Humphrey, T.J., 1997. The use of an automated growth analyser to measure recovery times of heat-injured Salmonella cells. J. Appl. Microbiol. 83, 445–455. Tapia de Daze, M.S., Villegas, Y., Matinez, A., 1991. Minimal water activity for growth of Listeria monocytogenes as affected by solute and temperature. Int. J. Food Microbiol. 14, 333–337. Tsuchido, T., Koike, T., Takano, M., 1989. A modified assessment of growth-inhibition from growth-delay time in a cell population exposed to an environmental stress. J. Ferment. Bioeng. 67, 132–134. Winslow, C.-E.A., Wilson, H.H., 1939. The earlier phases of the bacterial culture cycle. Bacteriol. Rev. 3, 147–186. Zwietering, M.H., de Koos, J.T., Hasenack, B.E., de Witt, J.C., van’t Riet, K., 1991. Modelling of bacterial growth as a function of temperature. Appl. Environ. Microbiol. 57, 1094– 1101. Zwietering, M.H., Rombouts, F.M., van’t Riet, K., 1992. Comparison of defenitions of the lag phase and the exponential phase in bacterial growth. J. Appl. Bacteriol. 72, 139–145. Zwietering, M.H., de Witt, J.C., Cuppers, H.G.A.M., van’t Riet, K., 1994. Modelling of bacterial growth with shifts in temperature. Appl. Environ. Microbiol. 60, 204–213.
The effect of the growth environment on the lag phase of Listeria monocytogenes Tobin P. Robinson*, Maria J. Ocio, Anu Kaloti, Bernard M. Mackey Institute of Food Research, Earley Gate, Whiteknights Road, Reading, Berks. RG6 6 BZ, UK Received 3 March 1998; received in revised form 20 July 1998; accepted 6 August 1998
Abstract The duration of lag in Listeria monocytogenes was examined in relation to the physico–chemical properties of the growth environment. It was supposed that lag would be determined by two hypothetical quantities, the amount of work that a cell has to perform to adapt to new conditions and the rate at which it can perform that work. If the rate at which the cell can perform the necessary work is a function of the maximum specific growth rate in the new environment, the hypothesis predicts that lag time should be related in some way to growth rate, provided cells are initially in approximately the same physiological state. Literature data suggest this is true for many organisms when temperature is the sole growth limiting factor. However, lag times of L. monocytogenes displayed an unusual response to temperature in which lag times of cells precultured at 378C were shorter at 158C than at 208C or 258C. Analysis of data from the Food Micromodel in which growth of L. monocytogenes was controlled by combinations of pH, NaCl concentration and temperature, showed that there was a linear relationship between lag time and mean generation time although there was much scatter in the data. When the effects of pH, solute type and concentration were investigated individually in this work the correlation between lag time and mean generation time was often poor. It would thus appear that the relationship between growth environment and lag time is more complex than the corresponding relationship between growth environment and maximum specific growth rate. 1998 Elsevier Science B.V. All rights reserved. Keywords: Lag; Listeria monocytogenes
1. Introduction The lag phase of microbial growth was defined by Penfold (1914) as the interval between the inoculation of a bacterial culture and the time of commencement of its maximum rate of growth. It has *Corresponding author. Tel.: 1 44 118 9357230, fax: 1 44 118 9357222, e-mail: [email protected] 0168-1605 / 98 / $ – see front matter PII: S0168-1605( 98 )00120-2
been conventionally measured as the point at which the slope of the exponential phase of growth (on a semi-logarithmic plot) intercepts a horizontal line drawn from the initial cell concentration (Lodge and Hinshelwood, 1943). Several other definitions of lag have been employed depending on the mathematical model or curve fitting procedure applied to the growth data (Buchanan and Cygnarowicz, 1990; Zwietering et al., 1991, 1992). In physiological
1998 Elsevier Science B.V. All rights reserved.
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terms, lag represents a transition period during which cells adjust to their new environment. Pirt (1975) recognized the following causes of lag: (i) change in nutrition, (ii) change in physical environment, (iii) presence of an inhibitor, (iv) spore germination and (v) state of the inoculum. The early literature was reviewed by Penfold (1914), Winslow and Wilson (1939) and Hinshelwood (1946). The effect of inoculum age, inoculum size, nutrient content of media, carbon dioxide concentration was established in these studies at least on a broad qualitative basis. More recent work has also examined the effect of cellular injury (Mackey and Derrick, 1982, 1984; Tsuchido et al., 1989). Lag times and growth rates of the major foodborne pathogens and some spoilage organisms have been measured under a wide range of growth conditions to develop methods for predicting microbial behaviour in foods. The data have been incorporated into mathematical models that allow growth rates of many foodborne bacteria to be predicted with a fair degree of accuracy from a knowledge of temperature, pH, solute content or water activity, gas atmosphere and preservative content (reviewed by McMeekin et al., 1993). Lag is inherently more difficult to predict than growth rate because it depends on the physiological state of the inoculum as well as growth conditions. Pre-adaptation to inimical growth conditions can shorten lag times dramatically (Hudson, 1993; Kroll and Patchett, 1992; Buchanan and Klawitter, 1991; Dufrenne et al., 1997) and the magnitude of this effect is difficult to predict. Even when inoculum effects have been minimised, it has still proved difficult to obtain a clear picture of the way lag varies as a function of the external environment. However, several studies have demonstrated a relationship between lag time and growth rate (Smith, 1985; Mackey and Kerridge, 1988; Adair et al., 1989; Baranyi and Roberts, 1994) but the general validity of this relationship has not been fully explored. A better understanding of the determinants of lag and the relative importance of physiological state and environmental conditions would help define the accuracy limits of predictive models, and might also suggest ways of extending lag and so delaying or preventing growth of undesirable microbes. On the other hand, reducing lag times would have benefits
in improving use of starter cultures and in recovering bacteria from food and environmental samples. The aim of this work was to investigate systematically the effects of solute concentration, pH and temperature on lag times of the foodborne pathogen Listeria monocytogenes, in an attempt to find a quantitative relationship between the physicochemical properties of the growth environment and the duration of lag. The variation in lag time between individual cells in a population is an important aspect of the problem (Baranyi, 1998; Stephens et al., 1997) but is not considered here.
2. Materials and methods
2.1. Preparation of inocula Stationary phase cultures of Listeria monocytogenes NCTC 11994 were prepared by inoculating 10 ml tryptone soya broth, (TSB; Oxoid, Basingstoke, UK) from a slope and then incubating overnight, shaken at 378C. One hundred ml of this culture were then used to inoculate 10 ml TSB and this was incubated until an OD 680 of 0.15 was reached. The culture was then incubated for a further 17 h. Stationary phase cultures prepared in this way gave more reproducible results than log phase cultures (results not shown). The inoculum level used in the experiments was approximately 10 3 cells ml 21 .
2.2. Growth media Broths (TSB) containing different concentrations of solutes were prepared by adding glycerol or NaCl and then autoclaving. Where broths of varying pH were required, the pH of the broth was altered before autoclaving using HCl or NaOH and the pH measured again after autoclaving. All broths were preheated to the desired incubation temperature before inoculation.
2.3. Viable counts and growth curves Viable counts were assessed by spread plates, the culture being diluted in maximum recovery diluent (Oxoid) and 0.05 ml spread on TSA (tryptone soya agar, Oxoid), in duplicate. Eleven to 27 points were taken for each curve depending on the duration of
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the experiment. Experiments were repeated three times, except for those in broths with both NaCl and glycerol which were only repeated twice. Curves were fitted to the data using an IFR in-laboratory program Dmodel written by Jozsef Baranyi, which is based on the growth model of Baranyi and Roberts (1994), with m 5 0, n 5 1. The program provided estimates of lag times and growth rates from the fitted curves.
3. Results
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was that W will tend to increase and R decrease, as conditions in the new medium deviate farther from those under which the inoculum was grown. If we define the fitness of a medium to support growth in terms of the maximum specific growth rate possible in the medium, then the difference between media can be quantified as the difference in maximum specific growth rates, irrespective of the particular factors leading to those different growth rates. According to this argument, lag times of cells grown under standardised conditions would be related in some way to maximum specific growth rate ( m ) or mean generation time (mgt) in the new medium.
3.1. Experimental approach We may suppose a priori that the duration of lag will depend on (a) the amount of work that a cell needs to do to adapt to its environment and prepare for division and (b) the rate at which it is able to do that work. By work we mean the various biosynthetic and homeostatic processes needed to prepare for growth in a new environment. Since there is no convenient direct way of measuring the hypothetical quantities ‘‘work needed’’ (W ) and ‘‘work rate’’ (R) independently, we sought to determine whether the lag time of cells that were initially in approximately the same physiological state would vary in a regular way as the external environment was changed. Our working hypothesis
3.2. General relationship between growth rate and lag time The data base used to construct FoodMicromodel contains growth curves for L. monocytogenes obtained under a wide range of conditions. These data were used to examine the relationship between growth rate and lag time (the original data are not publicly available, and the derived growth rates have been reproduced here with the kind permission of MAFF (Ministry of Agriculture Fisheries and Food)). Fig. 1 shows that lag time and mgt of L. monocytogenes are linearly related with the average lag being equal to about eight-times the mgt. If lag time conformed to the simple relationship:
Fig. 1. The relationship between lag time and mean generation time for L. monocytogenes grown in media at different combinations of pH, water activity and temperature. Data taken from Food MicroModel database.
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lag time (L) 5 work needed (W ) / work rate (R), and if R is taken to be equivalent to m (see also Baranyi and Roberts, 1992), and is assumed to be constant for cells in the same initial state, we would expect plots of m versus 1 / lag, or mgt versus lag to yield straight lines, as observed. However, the considerable scatter in the data we analysed implies that these assumptions are oversimplifications and that lag was affected by factors additional to growth rate. Inspection of the original data in Fig. 1 showed that in general, the lag was shorter in comparison to the mgt when salt and pH were optimal and temperature low, and longer when NaCl levels were high. However, these trends were not exclusive and many exceptions were evident. To investigate the relationship further, the effects of solute concentration, pH and temperature were examined separately.
Fig. 3. Relationship between lag time of L. monocytogenes at 378C and osmolality of growth medium adjusted with NaCl (s) or glycerol (j).
3.3. Effect of solute concentration Two solutes were tested, sodium chloride which is ionic and is excluded by the cytoplasmic membrane and glycerol which is neutral and diffuses passively through the membrane. Growth rates of L. monocytogenes decreased approximately linearly with increasing osmolality with no significant difference (a 5 0.05, two-tailed F-test) in slope for glycerol and NaCl (Fig. 2). In contrast, glycerol had no discern-
ible effect on lag whereas, with NaCl, lag increased in a biphasic fashion as concentration increased (Fig. 3). Small changes in osmolality above 3.0 OsM NaCl produced very large increases in lag. There was thus no direct relationship between lag time and mgt for either NaCl or glycerol. The observation that increasing concentrations of glycerol slowed down growth but had no effect on lag suggested to us that adding glycerol to media containing salt should decrease the work rate (R) without increasing work load (W ). The addition of increasing amounts of glycerol to media containing a fixed concentration of salt would therefore be expected to increase lag in direct proportion to the effect on growth rate. Fig. 4 shows that this was true to a first approximation.
3.4. Effect of pH
Fig. 2. Relationship between growth rate of L. monocytogenes at 378C and osmolality of medium adjusted with NaCl (s) or glycerol (j).
The relationship between growth rate and pH was biphasic (Fig. 5). Although growth rate varied by about sixfold over the pH range tested, there was negligible effect on lag except close to the lower limit for growth, when a large increase in lag was observed. Under these conditions, where acidity was the sole variable, lag was not related to growth rate. Rather, there was a threshold value below which very long lags occurred.
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Fig. 4. Relationship between lag time of L. monocytogenes and growth rate controlled by increasing the concentration of glycerol in TSB containing no added NaCl (– + –), or NaCl added to 0.9 M (– j –) or 1.2 M (– m –).
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Fig. 6. The effect of temperature on lag times of L. monocytogenes growing in TSB containing no added NaCl (s) or NaCl added to a concentration of 0.9 M (j) or 1.2 M (m).
trations of salt viz TSB containing zero, 0.9 M or 1.2 M added NaCl. The result was unexpected as shown in Fig. 6. At each NaCl concentration, lag increased as temperature decreased from 378C to 258C, then decreased again to a minimum at 158C. Thereafter there was a sharp increase in lag as temperature decreased to 58C. The corresponding effects on growth rate are shown in Fig. 7 and Fig. 8. An Arrhenius plot of the
Fig. 5. The effect of pH on lag time (s) and generation time (j) of L. monocytogenes.
3.5. Effect of temperature In an attempt to vary the putative work rate (R) without altering the workload (W ), lag times were determined at different temperatures in TSB containing a fixed concentration of salt. To examine the effect of temperature at different initial workloads (W ), the procedure was repeated at three concen-
Fig. 7. Arrhenius plot of growth rates of L. monocytogenes growing in TSB containing no added NaCl (s), or NaCl added to a concentration of 0.9 M (j) or 1.2 M (m).
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4. Discussion
Fig. 8. The relationship between œm and temperature for L. monocytogenes growing in TSB containing no added NaCl (s) or NaCl added to a concentration of 0.9 M (j) or 1.2 M (m).
data was non-linear with increasing slope from 378C to 58C (Fig. 7). A plot of square root of growth rate against temperature (Ratkowsky et al., 1982), gave a linear response for temperatures between 58C and 258C, but a discontinuity above this temperature, particularly in media containing 0.9 M and 1.2 M NaCl (Fig. 8). The relationship between growth rate and lag can be seen in Table 1 in which values of the quantity (lag / mgt) are listed for each temperature. (This effectively expresses lag in units of generation time). There is little difference in the values at 58C, 108C, 158C and 378C, indicating that at these temperatures lag is approximately proportional to growth rate. However at 208C and 258C the values are appreciably larger indicating that lag is longer at these temperatures relative to growth rate.
Table 1 Effect of temperature and NaCl concentration on lag / generation time of L. monocytogenes Temperature (8C)
5 10 15 20 25 37
Lag / generation time 0 M NaCl
0.9 M NaCl
1.2 M NaCl
1.73 1.97 0.76 3.62 5.52 0.20
1.94 3.44 0.84 7.89 10.74 2.87
1.10 5.08 1.83 7.72 14.84 3.91
The work / rate model of bacterial lag described here may be compared with the relative rate concept of Olley and Ratkowsky (1973) where the rate of spoilage of flesh foods (a product of lag and growth rate) at any temperature, was divided by the rate at 08C to produce the relative rate. This gave an approximately straight line relationship, when compared to temperature (the determinant of rate). Similar ideas are inherent in the gamma model of Zwietering et al. (1994) in which a temperature shift during lag or growth perturbs the cell and hence induces an additional lag whose duration depends on temperature and a proportionality constant d. However it became apparent during this work that a simple relationship between lag and growth rate did not hold for all environmental conditions, hence the effect of pH, temperature etc., were investigated separately.
4.1. Effect of solutes Our finding that the growth rate of L. monocytogenes was influenced more by osmolality than the type of solute agrees with results of Li and Torres (1993) and Christian and Scott (1953) obtained with a range of other psychrotrophic or mesophyllic organisms. The biphasic lag response of L. monocytogenes with increasing NaCl shows that, above a critical concentration, salt affects lag much more than growth rate. Either the rate at which the cell can perform the necessary adjustment work decreases dramatically above this critical concentration or different physiological processes (additional work tasks) become necessary. The nature of the additional tasks are not known but could include repair of cellular injury or accumulation of compatible solutes, all of which are very energy demanding (Knochel and Gould, 1995). Others (Buchanan et al., 1989; Buchanan and Philips, 1990) have also shown that lag times and mgt values increase with increasing concentration of salt and other preservatives but, since the experimental designs were multifactorial it is often difficult to discern the precise response to salt alone. Davey (1991) analyzed several sets of published lag time data and observed that lag was affected more than growth rate at low values of a w . The observation that glycerol had no detectable
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effect on lag was not anticipated, although others have shown that glycerol has a smaller effect on lag or growth rate than NaCl or sucrose (Li and Torres, 1993; Tapia de Daze et al., 1991; Farber et al., 1992; Nolan et al., 1992). This is thought to be due to the compatible solute-like behaviour of glycerol, i.e., it readily diffuses into the cell and has low toxicity at high internal concentrations (Csonka, 1989). Under our conditions growth in glycerol-containing broth required no period of adaptation i.e., no specific work was needed to adapt to the increased osmolality, although growth rate was reduced. Plasmolysis is transient when cells are transferred to glycerol (Christian, 1981; Kroll and Anagnostopuolos, 1981) whereas deplasmolysis in the presence of NaCl or other non-permeant solutes is expensive in terms of energy, requiring activation of potassium uptake systems and induction or activation of uptake systems for proline, betain and other compatible solutes (Patchet et al., 1992, 1994; Ko et al., 1994; Gutierrez et al., 1995). Interestingly, Amezaga et al. (1995) reported that growth of L. monocytogenes in brain heart infusion at high osmolality was preceded by a marked lag whereas no significant lag occurred in a defined medium at high osmolality. The addition of glycerol (which caused no lag on its own) to media containing a fixed concentration of NaCl, increased lag in proportion to the decrease in growth rate. Under these particular conditions therefore, the rate at which cells can adapt to the new conditions, and hence lag time, were proportional to growth rate as predicted by the hypothesis.
4.2. pH The growth rate of Listeria monocytogenes in broth varied in a biphasic manner with respect to pH. This differs from the results of Duffy et al. (1994) who found that growth rates of Listeria monocytogenes on vacuum-packed cooked meats containing different salt concentrations were linearly related to pH. However, they only examined a pH range of 5.8 to 6.8, whereas we found the change in slope occurred at a pH of 5.0. Surprisingly, we found that lag was little affected by pH except close to the limit for growth. As with glycerol, this implies that the specific work required to adapt to acid conditions is slight except at the limit where other factors, possibly including cell damage, exert an influence. Most
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modelling studies are multi-factorial and so the sole effect of pH cannot be easily extracted however, others have found a progressive increase in lag and mgt with decreasing pH (Duffy et al., 1994; Johansen et al., 1994). The difference may reflect differences in growth conditions: in our experiments pH was the main controlling factor, other conditions being optimal for growth, whereas in the work of Duffy et al., growth was also affected by the anaerobic conditions and the reduced water activity.
4.3. Temperature If temperature affects lag processes in the same way as it affects growth processes, one would expect lag to be proportional to growth rate at the different temperatures. Others have found this to be so for Salmonella typhimurium (Smith, 1985; Mackey and Kerridge, 1988). This simple relationship did not hold for L. monocytogenes growing in broth. By expressing lag in units of mgt, it was apparent that lag, relative to growth rate, was proportionately longer at 258C than at all other temperatures. Even when expressed in absolute terms, the lag at 158C was noticeably shorter than at either 208C or 258C. Several lines of evidence suggest that the lag in E. coli following a temperature downshift is caused by inhibition of translation (Jones and Inouye, 1994). The duration of lag appears to be related to cellular levels of guanosine 59 triphosphate-39 diphosphate and guanosine 59 diphosphate-39 diphosphate [(p)ppGpp] which in turn depend on the translational capacity of the cell and the supply of charged tRNA. Following a temperature down-shift the decreased levels of (p)ppGpp result in changes in gene expression and synthesis of transcriptional and translational proteins during the lag period. Cold-shock protein synthesis may also depend on levels of (p)ppGpp (Jones and Inouye, 1994). The reason for the shorter lags in L. monocytogenes at 158C compared with 208C and 258C is not known, but may be because the temperature change from 378C to 258C or 208C is insufficient to trigger a full cold shock response. Several cold shock and cold acclimation proteins have been identified in L. monocytogenes by twodimensional gel electrophoresis following a temperature down shift from 378C to 58C (Bayles et al., 1996), and it would be interesting to follow their
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rates of synthesis following downshifts to different temperatures. No deviations from monotonic behaviour in the response of L. monocytogenes to temperature have previously been reported. Schaffner (1995), for example, found that lag times of L. monocytogenes changed little between 468C and 158C but increased rapidly below this temperature. The data that were analyzed were restricted to cases where lag time increased with decreasing temperature so it is possible the effect reported here was overlooked. It may be relevant to the present observation that within the range 4–408C, the optimum temperature for growth of L. monocytogenes in high concentrations of salt is 158C (Farber et al., 1992). Interestingly, Bajard et al. (1996) found that L. monocytogenes showed a nonlinear relationship between œmmax and temperature, when other conditions were optimal. They found that the slope of such a plot had two linear parts separated at a temperature of around 10 to 158C. This unexpected result is reflected by the ability of this organism to grow well at refrigeration temperatures. Our results also show a biphasic pattern of growth rates, particularly in the presence of raised NaCl levels, although the break occurred at 258C. This shows closer agreement with the observations of Ratkowsky et al. (1982) who found an excellent straight line relationship for temperatures up to or just below the maximum growth rate for 14 bacterial species. Arrhenius plots of the psychrophile Pseudomonas fluorescens MF10 showed a change in slope at 178C such that the temperature characteristic for growth in the range 08C to 178C was twice that for the range 178C to 308C (Guillou and Guespin-Michel, 1996). This was attributed to an increase in protein degradation at temperatures above 178C. It is not known whether lag showed a similar discontinuous response with temperature in this organism. The appearance of the Arrhenius curve was similar to that commonly seen in other bacteria (Ratkowsky et al., 1982) in that the slope increased as temperature decreased. The discontinuity in the Ratkowsky square root plots in salt-containing media implies that, in relative terms, salt is more inhibitory to growth of L. monocytogenes at temperatures above about 208C. The accuracy with which lag can be predicted will depend on (a) knowing the state of the inoculum and
(b) being able to predict how lag is determined by the separate effects of inoculum state and environmental conditions. Many models have been described that allow lag and growth rate to be predicted, but models that are most suitable for lag may differ from those that are best for growth rate (Zwietering et al., 1991; Ratkowsky et al., 1991; Duh and Schaffner, 1993; Buchanan, 1993) and in most cases no allowance is made for the effect of inoculum history on lag. The models of Baranyi et al. (1993) and Hills and Wright (1994) contain parameters that allow the state of the inoculum to be quantified and also assume that lag time and growth rate are dependent variables. These properties allow sets of differential equations to be used to predict growth and lag under conditions where temperature or other variables change with time. The modelling of continuously changing variables is impossible for example in the many models that employ the Gompertz function, which can however be applied to step changes in temperature (Zwietering et al., 1994). Many sets of published data indicate that lag time and growth rate are closely correlated when temperature is the sole variable (see Davey, 1991). Under these conditions predictions of lag should be reasonably accurate for cells in the same physiological state though, as demonstrated in this work, variation in the rate at which cells respond to cold shock at different temperatures may increase the uncertainty of predictions. When additional variables such as pH and salt concentration are introduced, growth rate and lag time are less closely correlated, though a general trend is still evident as shown in Fig. 1. Two types of effect may be envisioned that would account for the increased variation. First, even when cells are initially in the same physiological state, the act of inoculation will cause changes to that state, the extent of which will depend on the new growth conditions (i.e., both ‘‘work load’’ and ‘‘work rate’’ are affected independently). Second, the rate-limiting steps in adapting to new conditions may be specific to the conditions, depending on the physiological processes involved. Hence when the effects of individual variables such as type of solute or pH are considered separately, the correlation between growth rate and lag time may be poor. It would thus appear that the relationship between growth environment and lag time is more complex than the corresponding relationship between growth
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environment and maximum specific growth rate. Predictions of lag time will therefore inevitably be less accurate than those for growth rate and variation in the initial physiological state will introduce further uncertainty. However attempts to quantify responses of bacteria to changing conditions are important in identifying trends, identifying ‘‘typical’’ behaviour and setting ‘‘worst case’’ limits. In the model of Baranyi for example an ‘‘envelope’’ of prediction is given, representing the difference between typical behaviour and a worst case scenario where there is no lag. When tested with Brochothrix thermosphacta under conditions of changing temperature, the model provided surprisingly accurate predictions except when temperature changed very rapidly and other conditions were also inhibitory (Baranyi et al., 1995). Such models may be refined as the underlying physiology becomes better understood. Knochel and Gould (1995) commented that predictive microbiology should provide a useful tool to those assessing hazard and risk in HACCP operation and help to identify key areas where intervention to inactivate or inhibit microbes would be most profitable. This work has revealed several thresholds or discontinuities in the responses of Listeria monocytogenes to inimical conditions. For example lag times increased very rapidly at salt concentrations above 2–3 OsM or at temperatures below 158C. Significantly, soft cheese, such as camembert is ripened at a temperature of approximately 148C (Gay et al., 1996). The discovery of these transition points raises the exciting possibility that their position might be shifted by appropriate manipulation of conditions, leading to synergistic inhibitory effects of benefit in food preservation.
Acknowledgements This work was funded by The Ministry of Agriculture Fisheries and Food. M.J.O. was supported by the Spanish Ministry for Science and Education.
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