Death rates of bacterial spores: mathematical models

Predicting heat inactivation of Listeria monocytogenes under nonisothermal treatments

The aim of this study was to find a model that accurately predicts the heat inactivation of Listeria monocytogenes (ATCC 15313) at constantly rising heating rates (0.5 to 9 degrees C/min) in media of different pH values (4.0 to 7.4). Survival curves of L. monocytogenes obtained under isothermal treatments at any temperature were nearly linear. Estimations of survival curves under nonisothermal treatments obtained from heat resistance parameters of isothermal treatments adequately fit experimental values obtained at pH 4.0. On the contrary, survivors were much higher than estimations at pH 5.5 and 7.4. The slower the heating rate and the longer the treatment time, the greater the differences between the experimental and estimated values. An equation based on the Weibullian-like distribution, log S(t) = (t/delta)p, accurately described survival curves of L. monocytogenes obtained under nonisothermal conditions within the range of heating rates investigated. A nonlinear relationship was observed between the scale parameter (delta) and the heating rate, which allowed the development of an equation capable of predicting the inactivation rate of L. monocytogenes under nonisothermal treatments at pH 5.5 and 7.4. The model predictions were a good fit to the measured data independent of the magnitude of the thermotolerance increase. This work might contribute to the increase in safety of those food products that require long heating lag phases during the pasteurization process.

Growth and heat resistance kinetic variation among various isolates of Salmonella and its application to risk assessment

The abilities of cells of a particular type of bacteria to leave lag phase and begin the process of dividing or surviving heat treatment can depend on the serotypes or strains of the bacteria. This article reports an investigation of serotype-specific differences in growth and heat resistance kinetics of clinical and food isolates of Salmonella. Growth kinetics at 19 degrees C and 37 degrees C were examined in brain heart infusion broth and heat resistance kinetics for 60 degrees C were examined in beef gravy using a submerged coil heating apparatus. Estimates of the parameters of the growth curves suggests a small between-serotype variance of the growth kinetics. However, for inactivation, the results suggest a significant between-serotype effect on the asymptotic D-values, with an estimated between-serotype CV of about 20%. In microbial risk assessment, predictive microbiology is used to estimate growth and inactivation of pathogens. Often the data used for estimating the growth or inactivation kinetics are based on measurements on a cocktail--a mixture of approximately equal proportions of several serotypes or strains of the pathogen being studied. The expected growth or inactivation rates derived from data using cocktails are biased, reflecting the characteristics of the fastest growing or most heat resistant serotype of the cocktail. In this article, an adjustment to decrease this possible bias in a risk assessment is offered. The article also presents discussion of the effect on estimating growth when stochastic assumptions are incorporated in the model. In particular, equations describing the variation of relative growth are derived, accounting for the stochastic variations of the division of cells. For small numbers of cells, the expected value of the relative growth is not an appropriate "representative" value for actual relative growths that might occur.

Physiological and mathematical aspects in setting criteria for decontamination of foods by physical means

In heat processing, microbial inactivation is traditionally described as log-linear. As a general rule, the relation between rate of inactivation and temperature is also described as a log-linear relation. The model is also sometimes applied in pressure and in pulsed electric field (PEF) processing. The model has proven its value by the excellent safety record of the last 80 years, but there are many deviations from log-linearity. This could lead to either over-processing or under-processing resulting in safety problems or, more likely, spoilage problems. As there is a need for minimal processing, accurate information of the inactivation kinetics is badly needed. To predict inactivation more precisely, models have been developed that can cope with deviations of linearity. As extremely low probabilities of survival must be predicted, extrapolation is almost always necessary. However, extrapolation is hardly possible without knowledge of the nature of nonlinearity. Therefore, knowledge of the physiology of inactivation is necessary. This paper discusses the physiology of denaturation by heat, high pressure and pulse electric field. After discussion of the physiological aspects, the various aspects of the development of inactivation models will be addressed. Both general and more specific aspects are discussed such as choice of test strains, effect of the culture conditions, conditions during processing and recovery conditions and mathematical modelling of inactivation. In addition to lethal inactivation, attention will be paid to sublethal inactivation because of its relevance to food preservation. Finally, the principles of quantitative microbiological risk assessment are briefly mentioned to show how appropriate inactivation criteria can be set.

Occurrence of a Highly Heat-Sensitive Spore Subpopulation of Bacillus coagulans STCC 4522 and Its Conversion to a More Heat-Stable Form

The profile of the survival curves, at different heating temperatures, of B. coagulans STCC 4522 sporulated at 52(deg)C has been studied, focusing on the early moments of treatment. A highly heat-sensitive spore subpopulation that includes more than 90% of the total spore population has been found. This heat-sensitive spore fraction was inactivated after 2 s of treatment at 111(deg)C. Its heat resistance was as much as 200-fold lower than that of the heat-resistant spore fraction (D(inf111(deg)C) of 0.01 min for the heat-sensitive spore fraction compared with D(inf111(deg)C) of 2 min for the heat-resistant fraction). The shape of the survival curve at 108.5(deg)C was modified after a sublethal heat shock at 80(deg)C for 3.5 h, resulting in a straight-line survival curve. The temperature of treatment also influenced the shape of the survival curves. The conversion of the highly heat-sensitive spore subpopulation to a more heat-stable form is discussed.

Evaluation of the integrated time-temperature effect in thermal processing of foods

In this review, current methods used to evaluate the integrated impact of time and temperature upon preserving a food product by a heat treatment are considered. After identifying the basic premise any preservation scheme shall meet, the central role of a feasible description for the heat activation kinetics of microorganisms, their spores, and other quality attributes are stressed. Common concepts to quantify a thermal process are presented. Shortcomings of the prevalent evaluation methods are highlighted and attention is given to the development, restrictions, and possibilities of time-temperature-integrators as "new" evaluation tools to measure the impact of a "classical" in-pack heat treatment and more modern heating techniques such as continuous processing of solid/liquid mixtures on foods.

Effect of simultaneous application of heat and pressure on the survival of bacterial spores

The effect of simultaneous application of moderate hydrostatic pressure (10-300 atm) and heat on the survival of the Bacillus stearothermophilus spores in a flow-through system was investigated. A high heterogeneity of the sensitization of spores to heat by pressure was found. A higher degree of reduction of heat resistance was observed at the low than at the high temperatures tested. The simultaneous application of moderate pressure and heat can not be applied for the preservation of liquid foods due to the extreme heterogeneity of spore sensitization to heat by pressure.