A theoretical note on estimating the number of recoverable spores from survival curves having an ‘activation shoulder’ Maria G. Corradini, Micha Peleg* Department of Food Science, Chenoweth Laboratory, University of Massachusetts, Amherst, MA 01003, USA Received 15 January 2003; accepted 21 July 2003 Abstract A ubiquitous feature of the survival curves of heat-treated Bacillus stearothermophilus and several other bacilli spores is the existence of a prominent ‘activation shoulder’. The shape of the survival curve alone, however, is insufficient to establish whether the observed initial increase in the number of ‘recoverable’ or ‘retrievable’ spores is due to heat activation, improved dispersion (‘de- clumping’) or both. But regardless of the mechanism, one can estimate a lower bound of the total recoverable spores using a crude empirical mathematical model. Estimates based on published data obtained with this model show that there can be 5–8 folds more recoverable spores in a heat-treated sample than the initial count would indicate, but this requires direct experimental verification. If correct, the model could serve as a tool to interpret the various possible shapes of ‘activation shoulders’ and to quantify the rate at which bacterial spores become ‘recoverable’. # 2003 Elsevier Ltd. All rights reserved. Keywords: Microbial survival; Heat inactivation; Sterilization; Bacillus stearothermophilus; Quantitative microbiology 1. Introduction The isothermal survival curves of certain bacterial spores, notably of Bacillus stearothermophilus (Le Jean, Abraham, Debray, Candau, & Piar, 1994; Rodriguez, Smerage, Teixeira, & Lindsay, 1988; Rodriguez, Smer- age, Teixeira, Lindsay, & Busta, 1992; Sapru, Teixeira, Smerage, & Lindsay, 1992, 1993) but also of others (e.g., Palop, Man˜as, & Condon, 1999) has a character- istic shape known as an ‘activation shoulder’ (Lewis & Heppel, 2000). In most survival curves, regardless of whether they are plotted on linear or semi logarithmic coordinates, the decline in the survival ratio is immedi- ately apparent, although its rate can vary dramatically among microbial cells and spores. In contrast, the counts of bacterial spores having an ‘activation shoulder’ initially rise with time and only after reaching a peak does the decline become evident. Or, in the cus- tomary semi logarithmic presentation of survival data, the logarithm of the survival ratio initially increases and assumes positive values and only after reaching a peak does it dive into a negative territory (Fig. 1). In at least some cases, the appearance of a short flat or ‘mild’ acti- vation shoulder can be attributed to the come-up time, i.e., to the fact that inactivation started only after a certain temperature had been reached. There are cases, however, where this cannot be a viable explanation. This is because the magnitude of the rise and the shoulder’s duration are a clear indication that the phenomenon is real and not an experimental artifact. The observed increase in the number of counted spores in such cases has been tradi- tionally attributed to their activation by heat and hence the term ‘activation shoulder’. According to this expla- nation, some of the spores are dormant and they would not germinate and produce countable colonies unless being activated first. Models to account for the different inactivation patterns of the dormant and active spores have been proposed by Rodriguez et al. (1988, 1992) and Sapru et al. (1992, 1993) who improved on a previous model suggested by Shull, Cargo, and Ernst (1963). An alternative explanation of the increase in the number of counted spores is that heat helps in their dispersion through de-clumping, i.e., by breaking their aggregates. Thus, spores clinging together would be 0963-9969/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.foodres.2003.07.003 Food Research International 36 (2003) 1007–1013 www.elsevier.com/locate/foodres * Corresponding author. Tel.: +1-413-545-5852; fax: +1-413-545- 1262. E-mail address: micha.peleg@foodsci.umass.edu (M. Peleg).