Demonstration of the Applicability of the Weibull–Log-Logistic Survival Model to the Isothermal and Nonisothermal Inactivation of Escherichia coli K-12 MG1655†

Abstract

Published isothermal semilogarithmic survival curves of Escherichia coli K-12 MG1655, in the range of 49.8 to 60.6°C, all had noticeable downward concavity. They could be described by the model log S(t) = −b(T)tn, where S(t) = N(t)/N0, N(t) and N0 being the momentary and initial number of organisms, respectively; b(T) is a temperature-dependent rate parameter; and n is a constant found to be about 1.5. The temperature dependence of b(T) could be described by the log-logistic model, b(T) = ln{1 + exp[k(T − Tc)]}, which had an almost perfect fit, with k = 0.88°C−1 and Tc = 60.5°C. The constants, n, k, and Tc were considered the organism's survival parameters in the particular medium. They were incorporated into a rate equation on the assumption that in nonisothermal heating, the momentary inactivation rate is the isothermal rate at the momentary temperature at a time that corresponds to the momentary survival ratio. This model's estimates matched the actual survival curves obtained in the same work under two different nonisothermal heating profiles, lending support to the notion that the Weibull–log-logistic model combination can be used not only to describe isothermal inactivation mathematically, but also to predict survival patterns under nonisothermal conditions.