New Mathematical Modeling Approach for Predicting Microbial Inactivation by High Hydrostatic Pressure

Abstract

A new primary model based on a thermodynamically consistent first-order kinetic approach was constructed to describe non-log-linear inactivation kinetics of pressure-treated bacteria. The model assumes a first-order process in which the specific inactivation rate changes inversely with the square root of time. The model gave reasonable fits to experimental data over six to seven orders of magnitude. It was also tested on 138 published data sets and provided good fits in about 70% of cases in which the shape of the curve followed the typical convex upward form. In the remainder of published examples, curves contained additional shoulder regions or extended tail regions. Curves with shoulders could be accommodated by including an additional time delay parameter and curves with tails shoulders could be accommodated by omitting points in the tail beyond the point at which survival levels remained more or less constant. The model parameters varied regularly with pressure, which may reflect a genuine mechanistic basis for the model. This property also allowed the calculation of (a) parameters analogous to the decimal reduction time D and z, the temperature increase needed to change the D value by a factor of 10, in thermal processing, and hence the processing conditions needed to attain a desired level of inactivation; and (b) the apparent thermodynamic volumes of activation associated with the lethal events. The hypothesis that inactivation rates changed as a function of the square root of time would be consistent with a diffusion-limited process.When microbes are exposed to lethal agents such as heat, gamma radiation, or chemical disinfectants, the concentration of surviving organisms decreases more or less exponentially with time. This behavior has been interpreted in two different ways. The first views the inactivation process as being similar to a first-order reaction such that lethal events occur at random over time within a population of cells that are similar in their susceptibility to the agent (6). The second interpretation, sometimes referred to as the "vitalist" approach, supposes that the observed differences in survival time are the result of differences in resistance among individual cells (41).The simple first-order model has been applied very successfully for many years in the food industry to define safe thermal processes for canned foods (38). For cells heated under isothermal conditions, a plot of the logarithm of the surviving fraction against time yields a straight line, and inactivation rates are expressed in terms of the decimal reduction time, or D value, which is the reciprocal of the specific inactivation rate at a particular temperature. The relationship between D value and temperature is given by the z value, which is the temperature increase needed to change the D value by a factor of 10. These two parameters are also used to describe microbial inactivation by UV or ionizing radiation. However, there are many exceptions to the simple first-order type kinetics, especially when cells are ex...

Biological Approach to Modeling of Staphylococcus aureus High-Hydrostatic-Pressure Inactivation Kinetics

“…Deviations in survival curves under HHP are quite commonly reported in the literature, but the appearance of shoulders is rare (11,21,25); however, to the best of our knowledge, neither the different phases of the inactivation curve nor the events taking place in each phase have been studied separately. For this purpose, data should be fitted using an adequate model.…”

“…Most of the published survival graphs show pronounced tails (14,23,28,35,41) and sometimes also shoulders (21,25). Occasionally, both phenomena occur simultaneously, giving rise to graphs with sigmoid profiles (11,20,43).…”

“…On the other hand, several authors have suggested that permeabilization of the cell membrane could be an indirect cause of the inactivation, without the need for a drastic decrease in its integrity (21,29,38), since it would facilitate the interchange of components between the cytoplasm and the treatment medium. Therefore, the shoulder could represent the time needed to attain a sufficient (lethal) level of component interchange.…”

Role of the alternative sigma factor σBonStaphylococcus aureusresistance to stresses of relevance to food preservation

“…1c, it can be seen that the most relevant difference between both strains was the occurrence of a pronounced shoulder in the curve corresponding to the parental strain. It is remarkable that the presence of shoulders in HHP survival curves has been reported only occasionally (Klotz et al 2007). Tailing was observed for both micro-organisms at the same percentage of survival, which caused a diminution in the difference in resistance after prolonged treatments.…”

High-Pressure Processing Technologies for the Pasteurization and Sterilization of Foods

“…Since pressure-treated foods first appeared on the market, significant advances in the modeling of microbial inactivation have been accomplished (e.g., McMeekin et al 1993;Baranyi and Roberts 1995;Peleg and Cole 1998;Xiong et al 1999a;Ahn et al 2007b;Corradini and Peleg 2007;Klotz et al 2007;Koseki and Yamamoto 2007b;Black and Davidson 2008;Pérez Lamela and Torres 2008b). Many authors have reported that in thermal processes, the survival curves for microorganisms deviate from the expected linear behavior (Kamau et al 1990;Bhaduri et al 1991;Linton et al 1995Linton et al , 1996Anderson et al 1996;Buzrul 2007).…”