A model describing the relationship between regrowth lag time and mild temperature increase for Listeria monocytogenes.

In order to comply with the consumer demand for ready-to-eat and look 'fresh' products, mild heat treatment will be used more and more in the agrofood industry. Nonetheless there is no tool to define the most appropriate mild heat treatment. In order to build this tool, it is necessary to study and describe the response of a bacterial population to a mild increase in temperature, from the dynamic point of view. The response to a mild increase in temperature, defined by stress duration and temperature, consisted in a mortality phase followed by the lag time of the survivors and their exponential growth. The effect of the mild increase in temperature on the mortality phase was described in a previous paper (Bréand et al., Int. J. Food Microbiol., in press). The effect of the stress duration on the lag was presented in a previous paper (Bréand et al., Int. J. Food Microbiol. 38 (1997) 157-167). In particular, the biphasic relationship between the lag and the stress duration was observed and modelled with a four parameter nonlinear model: the primary model (Bréand et al., Int. J. Food Microbiol. 38 (1997) 157-167). The study presented in this paper deals with the effect of the stress temperature on the biphasic relationship between the lag time and the stress duration. The secondary models describing the effect of the stress temperature on this biphasic relationship, were empirically built from our experimental data concerning Listeria monocytogenes. This work pointed out that the higher the stress temperature, the narrower the range of stress duration for which the lag time increased. Since the primary and the secondary models of the lag time were available, the global model describing the effect of the mild increase duration and temperature directly on the lag was fitted. This model allowed an improvement of the parameter estimator precision. The potential contribution in mild heat treatment optimization of this global model and the one built for the mortality phase (Bréand et al., Int. J. Food Microbiol., in press) is discussed.

Model of the influence of time and mild temperature on Listeria monocytogenes nonlinear survival curves.

Heat treatment has long been regarded as one of the most widely used and most effective means of destroying pathogens in food. Up to now the linear relationship between the death rate and the temperature has been used when choosing the best heat treatment to apply. However, the information given by this linear relationship is no longer sufficient when nonlinear survival curves are observed. Consequently, the agri-food industry needs a tool to choose the best mild heat treatment to apply in the case of nonlinear survival curves. This study deals with the temperature-induced death of Listeria monocytogenes CIP 7831 in the stationary phase of growth. Eleven temperatures were tested. With the proposed primary and secondary models good fits of our data were obtained. A model describing both the effect of the duration of treatment and the temperature on the logarithm of the number of survivors was then built. A clear increase in the precision of the estimation of the parameters was obtained with this model. Moreover, with this model a new graphical strategy to choose a mild heat increase regarding a maximal survivor number has been proposed.

A model describing the relationship between lag time and mild temperature increase duration.

When a bacterial population undergoes an unfavourable increase in temperature for a given duration, called stress duration, a death phase followed by a lag and a growth phase are observed. The lag phase is actually of great interest in regard to foodstuff safety in choosing a suitable protocol for the detection of microorganisms which have undergone a mild heat treatment. The extension of lag time with the severity of the increase in temperature has been highlighted by previous papers. Our experimental results concerning Listeria monocytogenes and Escherichia coli revealed that a two phase relationship between lag time and stress duration is observed for a specific increase in temperature. The first phase consists of an increase in lag time up to a peak; the second one consists of a decrease from this peak to a steady threshold. The mathematical model presented, describing the relationship between lag time and stress duration was empirically built from our experimental data concerning L. monocytogenes and E. coli. The fit evaluation carried out led us to consider this model as a good description of the relationship studied. The potential contribution of our model in heat treatment optimization is discussed.

The particular behaviour of Listeria monocytogenes under sub-optimal conditions.

Listeria monocytogenes is a ubiquitous pathogenic microorganism which has been described as growing at temperatures of interest to food production and especially at low temperatures (-2 degrees to 8 degrees C) in storage process. However, the general relationship between the maximum specific growth rate, mumax and temperature has not often been studied for L. monocytogenes in the whole temperature range from minimal to maximal growth temperature. A global analysis of this relationship for temperatures between -2 degrees C and 42 degrees C was therefore done. The global shape of this relationship was that usually observed for microorganisms, especially in the neighbourhood of the optimal temperature, Topt. But a more detailed study showed the existence of a so-called "change temperature", occurring between 10 degrees and 15 degrees C, below which L. monocytogenes grows faster than one would expect. This implies that the minimal growth temperature of both studied strains of L. monocytogenes is lower than expected.

[Time-killing curves of Pseudomonas aeruginosa strains exposed to polymyxin B]. / Etude de la courbe de mortalité de souches de Pseudomonas aeruginosa exposées à la polymyxine B.

The time-killing curves of three strains of Pseudomonas aeruginosa (PA01, ATCC10145 and ATCC27853) exposed to five concentrations of polymyxin B comprised: a latency phases, one or two decreasing phases and for the low polymyxin B concentrations a growth phasis. The five antibiotic concentrations were chosen to have a weak bactericidal effect such that decreasing exponential or biexponential models can be fitted to the data. In our experimental conditions, increasing Ca++ and Mg++ concentrations in the medium (Mueller-Hinton) reduced the bactericidal effect and increased the growth phases. Increasing inoculum (10(5) to 10(7) CFU/ml) decreased the bactericidal effect observed with polymyxin B.

[Mathematical study of the sensitivity curves of Escherichia coli exposed to polymyxins]. / Etude mathématique de la courbe de mortalité d'Escherichia coli exposé aux polymyxines.

The time killing curves of five strains of Escherichia coli (ATCC 25922, ATCC 29194, CIP 54125, CIP 54127, CIP 54117 (K 12)) exposed to five concentrations of polymyxin B are similar: latency phasis, two decreasing phasis and for the low polymyxin B concentrations growth phasis. In our experimental conditions, the Mg(+)+ and Ca(+)+ concentrations of the medium (Mueller-Hinton; medium A: Ca(+)+ = 9 mg/l, Mg(+)+ = 0.5 mg/l; medium B: Ca(+)+ = 35 mg/l, Mg(+)+ = 15.5 mg/l; medium C: Ca(+)+ = 60 mg/l, Mg(+)+ = 20 mg/l) have no time effect upon the killing curves. A decreasing biexponential model can be fitted to the data. Such a model is compatible with interaction between antibiotic and bacterium and can be formalized accorrding to the equation: T + ATB K1 in equilibrium of K2 T* - ATB K3----ATB + dead with ATB: Polymyxine B in excess, T: target bacterium and T*: modification target bacterium.

[A mathematical study of the mortality curve of Escherichia coli exposed to aminoglycosides]. / Etude mathématique de la courbe de mortalité d'Escherichia coli exposé aux aminosides.

The time killing curves of three strains of E. coli (CIP54117, ATCC25922 and ATCC29194) exposed to kanamycin, amikacin, netilmicin and dibekacin are decreasing exponentials. The absolute value of the killing rate m is related to the antibiotic concentration through a Michaelis-Henry equation. A maximum killing rate m max and an affinity constant Kc between bacteria and antibiotic can thus be estimated. m max is mainly strain dependent. On the contrary, Kc is related to the antibiotic. Kc is much higher (i.e. the affinity is much lower) for kanamycin and amikacin than for netilmicin or dibekacin. The dose-effect curve is a saturation curve. Increasing doses of antibiotic do not increase the mortality proportionally.

Early stages of in vitro killing curve of LY146032 and vancomycin for Staphylococcus aureus.

The early stages of the time-killing curves of vancomycin and LY146032 have been studied, by use of short sampling intervals, for three strains of Staphylococcus aureus. Both vancomycin and LY146032 killed S. aureus, but the time-killing curves differed: the effect of vancomycin was slow, limited, and not related to the concentration of the drug, whereas that of LY146032 was rapid, extensive, and related to concentration. When strains ATCC 25923 and CIP 6525 were exposed to LY146032, the population decreased exponentially with time. The killing rate was constant and linked to the concentration by a Michaelis-Menten relationship. The maximum killing rate and the affinity constant of LY146032, estimated from the data transformed by the Lineweaver-Burk method, differed for the two strains. The concentration of the antibiotic at which killing theoretically begins (estimated by linear regression using the logarithm of the concentration) is of the same magnitude as the MIC of LY146032, which indicates the pure bactericidal mode of action of the drug. S. aureus ATCC 12600 was more resistant to the bactericidal effect of the two drugs, and its killing curve did not conform to the model described here.

Gelatin and collagen binding to Staphylococcus aureus strains.

An interaction between the staphylococcal surface and gelatin is described. Out of 98 Staphylococcus aureus strains, 2 clumped in gelatin solution. Binding of collagen on the Staphylococcus aureus surface was also observed.