Recent Developments of Predictive Microbiology Applied to the Quantification of Heat Resistance of Bacterial Spores

Transcription

1 Japan Journal of Food Engineering, Vol. 9, No. 1, pp. 1-7, Mar Recent Developments of Predictive Microbiology Applied to the Quantification of Heat Resistance of Bacterial Spores Ivan LEGUERINEL and Pierre MAFART Université de Bretagne Occidentale Laboratoire Universitaire de Microbiologie Appliquée de Quimper 6 rue de l Université, Quimper cedex, France All conventional heat processing calculations are based on as few as two equations: a primary equation which corresponds to the first order kinetic of microbial inactivation represented by a log-linear survival curve, and a secondaryequation which describes the effect of the heating temperature on the thermal resistance of target spores. Improvements of heat inactivation modelling consist in the extension of these equations into more general primary models which are able to fit typical non log-linear survival curves and multifactorial secondary models which take non only heating temperature, but also some new other environmental factors into account. A first models generation inputs only factors such as ph or water activity which are related to the heating phase regardless of recovery conditions. A second models generation further includes environmental factors linked to the recovery conditions of incubation for the calculation of heat resistance. These new trends lead to the main following consequences: i. the efficiency of a heat treatment is more suitably characterised by the bacterial inactivation ratio than by the traditional F-value which is no longer additive, ii. The lethality factor concept can be usefully extended to a more general function which would include not only heating temperature, but also main other environmental factors. Key words: predictive microbiology, heat resistance, thermal inactivation 1Introduction The early risk assessments concerning canned foods can be viewed as the early history of predictive food microbiology. This science was born as early as the 1920s, when heat destruction of spores was recognied to follow a first order kinetic and when the effect of temperature on the heat resistance of microorganisms was described by either the famous Arrhenius equation or the Bigelow model [1]. In the early 80s, the development of the fresh foodstuffs market carried predictive microbiology towards modelling microbial growth in foods, analysis and control of risk. This trend was largely enhanced by the availability of powerful microcomputers on every desk. Predictive microbiology may concern either bacterial pathogens in food or spoilage microorganisms : in the first case, food safety concerns consumershealth while in the second one, it concerns the nutritional value and the acceptability (Received 16 Nov. 2007: accepted 4 Feb. 2008) Fax: , guerinel@univ-brest.fr of foods. In both cases, models are supposed to allow the answers to two types of questions: the first one revolves round the risk assessment: what would happen if...? What would the shelf-life of my foodstuff be if stored at a certain temperature? What is the probability of a food becoming toxic at certain conditions? Etc. The second kind of questions is related to the optimisation of foodstuffsformulation and process: which combination of ph and water activity of a prepared meal would be likely to prevent the growth of a certain pathogenic bacteria? At which combination of time-temperature must a dish be cooked to get sufficient food safety without spoiling its nutritional value or its acceptability? A major difficulty is the selection of the microbial species and even of the strain, the characteristics of which must be input in the model. In the frame of health problems and of fresh foodstuffs, the fastest growing and most toxic or pathogenic strain would be selected as a reference. If it is a canned food, the most heat resistant and most toxic type of spore must be considered. Since the works of Esty and Meyer [2] Clostridium botulinum has

2 2 Ivan LEGUERINEL and Pierre MAFART been selected as the reference spore for calculations of sterilisation processes of canned foods. In any case, even when a precise strain of microorganism can be retained as a reference for calculations, it is very difficult to associate fixed parameter values with it. Casolari [3] reviewed early papers related to the heat resistance of C. botulinum 62A and noted D values (decimal reduction time at 121.1) ranging from 0.13 to 0.80 min. Conventional calculations used in thermal processing in the food industry input a D value of 0.2 min and a -value (see below Bigelows model) of 10. That means that, more or less implicitly, standard parameter values of an «ideal strain» are retained. On account of the multiplicity of often uncontrolled factors and interactions affecting parameter values, this attitude seems to be the most rational and realistic. 2Classical Basis of Modelling 2.1 Theoretical and empirical models The ideal model to which every researcher longs is obviously the theoretical and explanatory (or mechanistic) model which is built from fundamental laws. The simplest example of this type of model, in the field of microbiology, is the exponential microbial growth kinetic which is based on a constant average generation time. Theoretical models involve only parameters having a physicochemical or biological significance and their fields of validity are much larger than those of empirical models. On the other hand, generally based on a number of simplifying assumptions, theoretical models can be simplistic with a poor predictive value. Because of the complexity of mechanisms involved in the field of biology, researchers have to be satisfied with purely descriptive empirical models. The approach consists then in fitting a set of experimental data on a mathematical function without any theoretical justification. The simplest example of this type of model, in the field of microbiology, is the exponential heat destruction kinetic of microbial spores which is based on the observation that, at a constant temperature, the logarithm of surviving cells follows an approximately linear relationship. Obviously, the field of validity of an empirical model is much narrower than that of a theoretical model because they can be applied only at specific experimental conditions and cannot be extrapolated out of the field of investigation. On the other hand, the main advantage of such models is that every experimental curve can be described by an empirical model such as a polynomial equation. Moreover, several models which can be very different, can be fitted on the same set of experimental data. For example, the models of Arrhenius and of Bigelow, in spite of their apparent incompatibility, both describe successfully the effect of temperature on heat resistance of microorganisms. Nowadays, nobody is able to decide whether one model is better than the other. That means that researchers can choose among a large palette of equations with the advantages and drawbacks of each. 2.2 The basic keystones of predictive modelling applied to heat inactivation of spores Before the early 80s, predictive food microbiology was mainly based on as few as two fundamental elementary models: a primary equation which described microbial kinetics, and a secondary equation which took into account the effect of temperature, the only considered factor until then, upon these kinetics. Madsen and Nyman [4] showed that the destruction of a homogeneous population of bacteria subjected to the action of a disinfectant followed an exponential law (first order kinetic). Further works showed the generality of this law, regardless of the cause of destruction. The general primary equation is then : NN 0 e -kt (1) where N 0 is the initial sie of the alive population and N the sie of the living population at t time. As late as 1943, Katin et al. [5] reparameterised this equation into NN t D (2) The logarithmic transformation of this last equation yields the following relationship: lognlogn 0 t (2) D whereas D is the decimal reduction time (average exposure time which is likely to cause a tenfold reduction of the number of surviving cells). The older secondary equation describing the effect of temperature on the growth or destruction rate is the famous Arrhenius equation (1889): - kk 0 e Ea RT (3) where T is the absolute temperature, R, the perfect gas constant, E a, the activation energy and k 0, an empirical constant. This historical equation showed an excellent goodness in a relatively large range of temperatures. As soon as 1910, Chick [6] found an alternative model

3 Thermal inactivation modelling 3 by observing a linear relationship between the logarithm of the inactivation rate and temperature. Comparing her equation with that of Arrhenius, she could not find any difference of goodness of fit. However, based on the same relationship, the well known conventional conceptwas introduced by Bigelow whose equation can be written as follows: D(T)D10 TT (4) where D* is the decimal reduction time at the reference temperature T*. In the early 20s, Ball [7] was the first to implement heat resistance models for the needs of food engineering in order to intrinsically compare the efficiency of heat treatments, regardless of the thermal resistance of target strains. He defined the F-value as the time (in minutes) of a heat treatment at the constant temperature T* (121.1), or any equivalent cycle which would yield the same efficiency. The most popular way of characterising the heating efficiency is the decimal reduction ratio defined by: nlog N 0 (5) N The target F-value to be applied depends obviously on the aimed level of safety (n) and on the heat resistance of the spores to be destroyed (D). The combination of transformation of Eq. (2) and (5) yields: tnd (6) At the reference temperature, by definition of the F-value, Eq. (6) becomes: t FnD (7) Eq. (7) allows calculating a target F-value but doesnt indicate how to reach the aimed value. At a constant heating temperature, the combination of Eqs. (4), (6) and (7) yields another expression of the F-value: TT F10t (8) The reached F-value is then the product of the heat exposure time and a function of temperature, generally denoted L(T) and sometimes called lethality factor At dynamic conditions of variable temperature, t TT F10dt 0 (9) 3Recent Trends of Inactivation Modelling Survival curves are conventionally assumed to be loglinear (see Eq. 2). However in reality, other patterns of curves are frequently observed [8], with either a curvilinear lag phase (shoulder) followed by a straight linear phase, or a first linear part followed by a curvilinear slow down phase (tail). Sometimes, curves may be entirely curvilinear, showing either an upward or downward concavity. Some survival curves corresponding to mild treatments can present a sigmoidal shape. In this context, the characterisation of the bacterial heat resistance by a single parameter (D value) is no longer possible. For this reason, a number of new primary models were proposed to describe non log-linear survival curves. On the other hand, the input lethality factorl(t) in conventional calculations includes only heating temperature as the single environmental factor taken into account. Traditional secondary modelling was then monofactorial, while it is well recognised that microbial heat resistance is also dependent on other environmental factors such as ph, water activity, chemical composition of the medium etc. The improvement of heating processes optimisation needs then the extension of classical secondary models towards multifactorials models. Lastly, it would be simplistic to reduce thermal inactivation of spores to a binary model which would include two populations corresponding to killed and surviving cells respectively. A fraction of the alive population is more or less injured and able or not to growth on a recovery medium, depending on the level of injury of cells and on environmental conditions of the recovery medium. It is widely admitted that the apparentdecimal reduction time (denoted D) depend not only on heating but also on recovery conditions. At non optimal environmental recovery conditions (acid, salted or dry medium) the Dvalue is systematically lower than the measured D value at optimal conditions. For this reason, secondary modelling has to take environmental recovery factors into account. 3.1 New primary models A number of empirical or more or less mechanistic models were proposed for describing non linear survival curves [9, 10]. A compromise has to be found between simplest models which are limited as they can describe only one shape of curve (for example, the biphasic Cerf model [8]) and more flexible but more complex models which are able to describe most of curve shapes (for example the Whiting model [11]). Among the lot of published equations, the Weibull frequency distribution model is more and more frequently chosen for its simplicity and its flexibility. Following Peleg and Cole [12], a number of authors explained the pattern of some curvilinear curves

4 4 Ivan LEGUERINEL and Pierre MAFART by a statistical Weibull distribution of individual life times of cells, the cumulative form of which yields: NN 0 e [-ktn ] (10) The characterisation of heat resistance needs then two parameters: the scale parameter k, and the shape parameter n. When n > 1, the curve representing the logarithmic form of Eq. (10) shows a downward concavity, while it shows an upward concavity when n <1. Obviously, the case where n1 correspond to the conventional log-linear curve. The major drawback of this last equation is the fact that the k parameter has not the dimensions of a time, but those of a time power - n, so that the simple -concept of Bigelow cant be applied for linking this parameter to the heating temperature. For this reason, Mafart et al. [13] preferred the following parameterisation of the same model: (13), was previously published by Geeraerd et al [9]. The main advantage of this model is its ability to fit survivor curves at dynamic condition of variable temperatures more easily than most of other models. In its static version, the Geeraerd model can be written as follows: N(N 0 N )e -kt e k N 1(e k 1)e -kt (14) where N has the same significance as in Eq. (13) and represents approximately the length of a lag phase preceding the sharp inactivation slope of the curve (shoulder). Indeed, Eq. (14) can be reduced for fitting simpler curves than a sigmoide. Without tail (N 0), the equation is reduced to e -(k-)t NN 0 1(e k 1)e -kt (15) while without shoulder (0), the equation is reduced to: NN 0 10 t p (11) N(N 0 N )e -kt N (16) where the scale parameter has the dimensions of a time and corresponds to time of first decimal reduction and varies with temperature according either to the Arrhenius equation or the -relationship. Unfortunately, the structure of this equation yields a strong self-correlation between parameters and p which can lead to difficulties of estimations. As it is generally observed that p values are little dependent on environmental conditions (heating temperature, ph of the medium), several authors recommended to circumvent this structural correlation by fixing p to an average value for a given strain. From the following logarithmic form: lognlogn 0 t p (12) parameters N 0 and can then be estimated from a simple linear regression. This last equation is able to describe downward and upward concavity curves and to fit with a good approximation survivor curves including a shoulder or a tail, however, but is not suitable for fitting sigmoidal curves. In order to allow the fitting of this last type of curve, Eq. (12) was modified by Albert and Mafart [14] into N(N 0 N )10N t p (13) The new added parameter N corresponds to a low asymptote reflecting the presence of a resistant sub-population which should not be destroyed by a heat treatment assumed to be mild. An alternative model which presents about the same level of simplicity without quite the same flexibility as Eq. 3.2 Secondary modelling At the present time, secondary modelling is almost exclusively linked to the conventional primary log-linear equation and concerns either the specific inactivation rate k (Eq. 1) or the decimal reduction time D (Eq. (2). However, the emergent popularity of the Weibull frequency distribution model is progressively leading to the modelling of the scale parameter of Eq. (12), while the shape parameter p is generally assumed to be characteristic of a strain and independent of environmental factors First generation models (ignoring recovery conditions) Davey et al. [15] were the first to propose an equation combining heating temperature and ph effects on the specific inactivation rate of spores of Clostridium botulinum: C LnkC 0 C 1 2 phc 3 ph 2 (17) T where T is the absolute heating temperature while C 0 -C 3 are empirical constants. By dropping the ph terms of the right side of the equation, it can be recognised the logarithmic transformation of Arrhenius equation, so that the authors regarded their model as an extension of Arrhenius equation. According to a similar approach, Mafart and Leguérinel [16] proposed an extension of Bigelow relationship from the same data sets as those which were input by Davey: TT log Dlog D T phph ph (18)

5 Thermal inactivation modelling 5 where T* represents the reference temperature (generally 121.1) and ph*, the reference ph (ph*7). Sensibility parameters are T (conventional -value) and ph (distance of ph from ph* which leads to a ten fold reduction of the decimal reduction time) respectively. D* corresponds to the D value at reference conditions (T* and ph*) The goodness of fit of both models is comparable. The major advantage of Davey model is its linearity which allows an easy estimation of parameters and their confidence intervals from a simple linear regression. In return, Eq. (17) includes 4 parameters instead of only 3 in Eq. (18). Moreover, by comparing both set of parameters, it can be seen that only Mafart parameters can be easily biologically interpreted. As an example, the same set of data regarding Clostridium botulinum yielded the following parameter estimates: Davey parameters : C C K C C Mafart parameters : D*0.139 min T 9.32 ph 3.61 A little later, a water activity term was added to Mafart model [17]: TT phph a W 1 logdlogd (19) T The common limit of both models is the fact that they ignore interactions between factors, while the existence of such interactions is well known. Investigating the heat resistance of Bacillus cereus, Gaillard et al. [18] attempt to circumvent this drawback by modifying Eq. (18) as follows: logdlogdc 1 ( TT ) C 2 ( phph) 2 C 3 ( TT )(phph) 2 (20) This modification produced a relatively poor improvement of the goodness of fit of the initial model (R instead of 0.977). Such an improvement was judged insufficient for justifying the addition of one more parameter and the loss of the biological interpretability of all parameters, except D*. From the neperian version of the Weibull model, ph aw NN 0 exp t (21) Fernande et al. [19] modelled the scale parameter as follows: E a 1 1 Ln Ln (phph) R 1 1 (22) T T Microbial resistance depends not only on environmental factors, but also on the physiological state of cells and their thermal history. In particular, the sporulation temperature of bacteria has a dramatic impact on the thermal resistance of formed spores. Leguérinel et al, [20] pointed out, for different Bacillus species, a linear Bigelow type relationship between the logarithm of the decimal reduction time and the temperature of sporulation. The corresponding sensibility parameter value is variable but frequently close to Second generation models (taking recovery conditions into account) Because each environmental factor acts differently during the heating phase and during the recovery incubation following the heat exposure, in order to avoid any confusion, we denoted X any factor related to the heating and X, any factor related to the recovery. The notation D is reserved to the decimal reduction time measured at optimal recovery conditions, while D(the so called apparent decimal reduction time) corresponds to the same parameter measured at an environmental condition Xdifferent from X opt. All models developed in our laboratory present the common following form: 2 X'X' opt log D'logD (23) 'X It can be seen that three parameters have to be estimated from a non-linear regression: the optimum value of the considered factor X opt, the sensibility value X (distance of Xfrom X opt which leads to a ten fold reduction of the apparent decimal reduction time), and D which corresponds to the maximum Dvalue. This structure presents the advantage of simplicity, parsimony, and biological interpretability of parameters, but it imposes to fitted curves a symmetric pattern. Despite this constraint, observed goodness of fit are satisfying. Eq. (23) was successfully applied to incubation temperature of the recovery medium. As an example, it was found the following estimates for Bacillus cereus: D min ; T opt 23.6 ; T 33.7 [21]. The same equation is suitable for describing the effect of the recovery medium ph on the apparent resistance. Regarding the previously cited

6 6 Ivan LEGUERINEL and Pierre MAFART strain of Bacillus cereus, Couvert et al. [22] obtained the following estimates: D 95 2,33 min ; ph opt 6,78 ; ph 1,81. Lastly, the same model was also successfully applied for the same strain, to the water activity of the recovery medium: Coroller et al. [23] found an optimal water activity close to , while the sensibility parameter was dependent on the nature of the depressor: around 0.1 for dextrose and glycerol, closer to 0.07 for sucrose Modular combination of elementary models It is frequently assumed, in the field of predictive microbiology, a multiplicative effect of each inhibitory factor upon the specific growth rate of bacteria (see the Zwietering gamma-concept) [24]. The same assumption was retained concerning the bacterial heat resistance. As the logarithmic transformation of a product yields a sum, the combination of several monofactorial elementary models presents the structure of Eq. (19). More generally, it can be written as follows: X logdlogd i X i Xi n (24) where the exponent n may be equal to 1 or 2. X* i is not a free parameter, but correspond to a fixed reference value (for example, T*121.1; ph*7; a* w 1). Similarly, Eq. (23) can be extended into: 2 X' logd'logd i X' iopt (25) 'Xi Lastly, the combined effect of factors X related to the heating phase and Xrelated to the recovery conditions yields: X logd'logd (X,X' opt ) i X i Xi n 2 X' i X' iopt (26) 4Concluding Remarks The extreme variability of spore heat resistance is the consequence of a very complex group of factors and interactions, so that a perfect modelling is necessarily beyond reach. However, recent developments in heat resistance modelling are likely to allow large improvement in the area of heat processes calculations. The first consequence of the implementation of nonlog-linear primary models is the loss of relevance of the traditional F-value concept which keeps no longer additive [13], so that conventional algorithms are becoming no longer valid. Some authors proposed new algorithms from the Weibull model for calculating the efficiency of heat treatments in terms of decimal reduction ratio [25-26]. ' Xi However, further research would be necessary to elucidate the behaviour of the shape parameter of the model according to environmental conditions and physiologic state of target spores. In any case, the usefulness of comparative standard calculation based on reference strains and log-linear survivor curves would obviously remain intact, so that the F-value concept seems to be far from being dropped. The development of multifactorial secondary models naturally leads to an extension of the lethality factor concept, the classical expression of which is: L(T )10 TT (27) It was proposed [16] to generalie this last equation into the following multifactorial expression: L(X 1, X 2... X n )10 X ix i Xi n (28) A further extension of the lethality concept to environmental factors linked to recovery conditions would need the replacement of free parameters X opt by fixed relevant reference X* value which remain to be determined from further research. References [1] W. D. Bigelow; The logarithmic nature of thermal death time curves. Inf. Dis., 29, (1921). [2] J. R. Esty, K. F. Meyer; The heat resistance of spores of Bacillus cereus and allied anaerobes. J. Inf. Dis., 31, (1922). [3] A. Casolari; About basic parameters of food steriliation technology, Food Microbiol., 11, (1994). [4] T. Madsen, M. Nyman; Zur theorie der desinfektion. Zeitschrift für Hygiene und Infectionskrankheiten, 57, (1907). [5] L. I. Katin, L. A. Sandholer, M. E. Stron; Application of the decimal reduction time principle to a study of the resistance of coliform bacteria to pasteuriation. J. Bact., 45, (1943). [6] H. Chick; The process of disinfection by chemical agencies and hot water. J. Hyg., 10, (1910). [7] C. O. Ball, C. W. F. Olson; Steriliation in food technology- Theory, Practice and Calculation, First ed, McGraw-Hill Book Company Inc. (1957). [8] O. Cerf; Tailing of survival curves of bacterial spores. J. Appl. Bacteriol., 42, 1-19 (1977). [9] A. Geeraerd, C. Herremans, J. Van Impe; Structural model requirement to describe microbial inactivation during a mild heat treatment. Int. J. Food Microbiol., 59, (2000)

7 Thermal inactivation modelling 7 [10] V. Valdramidis, A. Geeraerd, K. Bernaerts, F. Devlieghere, J. Debevere, J. Van Impe; Accurate modelling of nonloglinear survivor curves. Int. Dairy Fed. Bull., 392, (2004) [11] R. Whiting; Modeling bacterial survival in unfavourable environments. J. Ind. Microbiol., 12, (1993). [12] M. Peleg, M. Cole; Reinterpretation of microbial survival curves. Critic. Rev. Food Sci., 38, (1998). [13] P. Mafart, O. Couvert, S. Gaillard, I. Leguérinel; On calculating sterility in thermal preservation methods: application of the Weibull frequency distribution model. Int. J. Food Microbiol., 72, (2002). [14] I. Albert, P. Mafart; A modified Weibull model for bacterial inactivation. Int. J. Food Microbiol., 100, (2005). [15] K. Davey, S. Lin, D. Wood; The effect of ph on continuous high temperature/short time steriliation of liquids, Am. Inst. Chem. Eng. J., 24, (1978). [16] P. Mafart, I. Leguérinel; Modelling combined effect of temperature and ph on the heat resistance of spores by a nonlinear Bigelow equation. J. Food Sci., 63, 6-8 (1998). [17] S. Gaillard, I. Leguérinel, P. Mafart; Model for combined effects of temperature, ph and water activity on thermal inactivation of Bacillus cereus spores. J. Food Sci., 63, (1998). [18] S. Gaillard, I. Leguérinel, P. Mafart; Modelling combined effects of temperature and ph on the heat resistance of spores of Bacillus cereus. Food Microbiol., 15, (1998) [19] A. Fernande, J. Collado, L. Cunha, M. Ocio, A. Martine; Empirical model based on Weibull distribution to describe the joint effect of ph and temperature on the thermal resistance of Bacillus cereus in vegetable substrate. Int. J. Food Microbiol., 77, (2002). [20] I. Leguérinel, O. Couvert, P. Mafart; Modelling the influence of sporulation temperature upon bacterial spore heat resistance, application to heating process calculation. Int. J. Food Microbiol., 114, (2007). [21] I. Leguérinel, O. Couvert, P. Mafart; Modelling the influence of the incubation temperature upon the estimated heat resistance of heated bacillus spores. Lett Appl Microbiol., 43, (2006) [22] O. Couvert, I. Leguérinel, P. Mafart; Modelling the overall effect of ph on the apparent heat resistance of Bacillus cereus spores. Int. J. Food Microbiol., 49, (1999). [23] L. Coroller, I. Leguérinel, P. Mafart; Effect of water activities of heating and recovery media on apparent heat resistance of Bacillus cereus spores. Appl. Environ. Microbiol., 67, (2001). [24] M. Zwietering, T. Wijites, J. De Wit, K. Vant Riet; A decision support system for prediction of the microbial spoilage in foods, J. Food Protect., 55, (1992). [25] G. Chen, O. Campanella, C. Corvalan; A numerical algorithm for calculating microbial survival curves during thermal processing. Food Res. Int., 40, (2007). [26] P. Mafart, H. Ben Yaghlene, L. Coroller; A new algorithm for calculating thermal processes related to non-log-linear survival curves. 5 rd International Conference on Predictive modelling in Foods, September 16-19, 2007, Athens (Greece) (2007).