6 JOURNAL OF FOOD SCIENCE—Volume 63, No. 1, 1998 Modeling Combined Effects of Temperature and pH on Heat Resistance of Spores by a Linear-Bigelow Equation P. MAFART and I. LEGUERINEL related to the quantitative effect of pH is scarce. Using the published data of Xezones and Hutchings (1965), Davey (1993) pro- posed a “linear Arrhenius model” to describe the combined effect of temperature and pH on heat resistance of Clostridium botulinum spores. 1n k = C 0 + (C 1 /T) + C 2 pH + C 3 pH 2 (4) where k is the death rate, T the absolute tem- perature, and C 0 , C 1 , C 2 and C 3 empirical constants. The Davey model has the advan- tages of satisfactory goodness of fit and pa- rameters that are easy to compute. However the four empirical coefficients of the model have no biological representation. As an alternative and following a similar approach, our objective was to propose a lin- ear-Bigelow equation with only three param- eters, each with a physical representation: log D = log D*–(1/z T )(T–T*)–(1/z 2 pH )(pH–pH*) 2 (5) where T* is the reference temperature (for example, 121.1°C), pH* is the pH of maxi- mal heat resistance of spores (pH 7), z T is the conventional thermal z-value, z pH is the distance of pH from pH* which leads to a ten fold reduction of the decimal reduction time. Lastly, D* is the D-value at T* and pH*. MATERIALS & METHODS THE MODEL WAS TESTED BY APPLYING three published sets of data respectively ob- tained from Clostridium botulinum (Xezones and Hutchings, 1965) with ranges from 110°C to 118.3°C and pH from 4 to 7, Clostridium sporogenes (Cameron et al., 1980) with ranges from 110°C to 121°C and pH from 5 to 7, and Bacillus stearothermo- philus (Lopez et al., 1996) with temperature ranges from 115°C to 135°C and pH from 4 ABSTRACT A generalized linear-Bigelow model was proposed to describe the effects of both temperature and pH on spore heat resistance. The model required only 3 param- eters, each having a physicochemical significance. In addition to the conven- tional z value, the effect of pH on thermal resistance of spores was characterized by a z pH value. Although the model neglected interactions between temperature and pH, its goodness of fit and its robustness enable it to be applied for optimiza- tion of heat treatments. Further experiments need to be undertaken to validate the model under industrial conditions. KEYWORDS: temperature, pH, heat resistance, spores. Laboratoire Universitaire de Recherche Agro- alimentaire de Quimper, Quimper, France. Address in- quiries to: Pr Mafart, I.U.P. Innovation en Industries Alimentaires, Pôle Universitaire P. Jakez Hélias, 29000 Quimper, France INTRODUCTION WHEN A MICROBIAL POPULATION IS EX- posed to a constant and lethal temperature, it is generally assumed that microbial death fol- lows the kinetics of first-order reaction (Etsy and Meyer, 1922) according to the equation: N = N 0 e -kt (1) where N is the number of survival cells, t is the exposure time and k the death rate. Equa- tion (1) is often rewritten as: N = N 0 10 -(t/D t ) (1 bis) where D T is the decimal reduction time at the T temperature and is a characteristic of the heat resistance of bacterial populations. The effect of temperature on rate of mi- crobial destruction can be described by two equations. Several researchers have used the Arrhenius equation: k = Ae -(E a /RT) (2) Others prefer the thermobacteriological approach originated from the observations of Bigelow (1921): DT = D T* 10 -(1/z)(T-T*) (3) where T* is a reference temperature. Temperature is not the only factor that af- fects spore thermoresistance. Particularly, pH is a major factor in microbial destruction. It has been recognized for several years that low pH value reduces spore resistance (Alderton et al., 1976; Townsend et al., 1938; Tsuji et al., 1960) However, available information to 7. D*, z T and z pH values were computed by a linear regression of log D (STATITCF soft- ware). RESULTS PARAMETERS OF EQ. (5) AND ASSOCIATED statistics were computed (Tables 1–3). Fam- ilies of graphs of D as a function of pH at constant values of temperature were devel- opped (Fig. 1–3). In each case, although the model was relatively simple, very satisfac- tory goodness of fit was obtained. Parameter values for Clostridium botuli- num spores appeared very stable regardless of type of food. Similarly, parameter values for Bacillus stearothermophilus spores were Table 1—Rate coefficient for Clostridium botulinum (equation 5) Multiple regres- Mean sion co- square z T Food n efficient error D*(s) (°C) z pH Spaghetti Tomato sauce and cheese 32 99.6% 4.68 8.34 9.32 3.61 Macaroni creole 32 99.7% 3.60 9.30 9.45 3.54 Spanish rice 32 99.3% 9.00 8.58 9.29 3.56 Table 3—Rate coefficient for Bacillus stearothermophilus (equation 5) Multiple regres- Mean sion co- square z T Food n efficient error D*(s) (°C) z pH 7953 20 99.0% 46.08 70.2 9.40 3.97 12980 20 99.3% 35.64 81.0 8.70 3.82 15951 20 99.5% 27.72 78.0 8.83 3.45 15952 19 99.6% 22.68 72.6 8.56 2.94 Table 2—Rate coefficient for Clostridium sporogenes (equation 5) Multiple regres- Mean sion co- square z T Food n efficient error D*(s) (°C) z pH Phosphate buffer 30 98.8% 9.72 123.6 12.2 4.29 Pea puree 30 99.1% 10.80 142.2 10.3 3.33 HYPOTHESIS PAPER