Estimating the Heat Resistance Parameters of Bacterial Spores from their Survival Ratios at the End of UHT and other Heat Treatments

Abstract

Accurate determination of bacterial cells or the isothermal survival curves of spores at Ultra High Temperatures (UHT) is hindered by the difficulty in withdrawing samples during the short process and the significant role that the come up and cooling times might play. The problem would be avoided if the survival parameters could be derived directly from the final survival ratios of the non-isothermal treatments but with known temperature profiles. Non-linear inactivation can be described by models that have at least three survival parameters. In the simplified version of the Weibullian –log logistic model they are n, representing the curvature of the isothermal semilogarithmic survival curves, T_c, a marker of the temperature where the inactivation accelerates and k, the slope of the rate parameter at temperatures well above T_c. In principle, these three unknown parameters can be calculated by solving, simultaneously, three rate equations constructed for three different temperature profiles that have produced three corresponding final survival ratios, which are determined experimentally. Since the three equations are constructed from the numerical solutions of three differential equations, this might not always be a practical option. However, the solution would be greatly facilitated if the problem could be reduced to the solution of only two simultaneous equations. This can be done by progressively changing the value of n by small increments or decrements and solving for k and T_c. The iterations continue until the model constructed with the calculated k and T_c values correctly predicts the survival ratio obtained in a third heat treatment with a known temperature profile. Once n, k, and T_c are established in this way, the resulting model can be used to predict the complete survival curves of the organism or spore under almost any contemplated or actual UHT treatment in the same medium. The potential of the method is demonstrated with simulated inactivation patterns and its predictive ability with experimental survival data of Bacillus sporothermodurans. Theoretically at least, the shown calculation procedure can be applied to other thermal preservation methods and to the prediction of collateral biochemical reactions, like vitamin degradation or the synthesis of compounds that cause discoloration. The concept itself can also be extended to non-Weibullian inactivation or synthesis patterns, provided that they are controlled by only three or fewer kinetic parameters.

Keywords:

• survival curves
• non linear kinetics
• Weibull-log logistic model
• predictive microbiology
• ultra high temperature (UHT)

ACKNOWLEDGEMENTS

The contribution of the Massachusetts Agricultural Experiment Station at Amherst is gratefully acknowledged. The authors would also like to express their gratitude to Professor Murray Eisenberg of the Mathematics and Statistics Department at the University of Massachusetts for his help in making the Mathematica® programs work.

The four appendices mentioned in the text can be accessed at the following URL: http://www-unix.oit.umass.edu/∼aew2000/three_points_method/UHT_Appendices.html

Notes

¹From ter Steeg et al. (2008). The actual temperature profiles are shown in Fig. 6

¹The experimental results are from ter Steeg et al. (2008). The corresponding temperature profiles are shown in Fig. 6. The predictions were made by the incremental method using Eq. 6 as the survival model