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A model of temperature effects on microbial populations from growth to lethality
Author(s) -
Peleg Micha
Publication year - 1995
Publication title -
journal of the science of food and agriculture
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.782
H-Index - 142
eISSN - 1097-0010
pISSN - 0022-5142
DOI - 10.1002/jsfa.2740680114
Subject(s) - dimensionless quantity , constant (computer programming) , thermodynamics , bacterial growth , growth rate , spore , lethality , growth model , reaction rate constant , chemistry , kinetics , biology , bacteria , physics , microbiology and biotechnology , toxicology , mathematics , genetics , geometry , mathematical economics , quantum mechanics , computer science , programming language
The propagation/destruction rate constant of microbial populations over the entire temperature range from growth ( k ( T ) > 0) to lethality ( k ( T ) < 0) can be described by a single mathematical model in the from:\documentclass{article}\pagestyle{empty}\begin{document}$$ k(T) = \ln ((1 + b\exp - ((T - T_m)/a_1)^2))/(1 + \exp ((T - T_c)/a_2))) $$\end{document}where b is a dimensionless constant related to the height of the growth peak, T m and T c temperatures characteristic of the growth and lethal regimes and a 1 and a 2 constants (temperature units) indicating the span of the growth region and the steepness of k ( T ) in the lethal temperature region respectively. The fit of the model is demonstrated with published data on the effect of heat on two bacteria. Since bacterial spores, unless germinated, do not multiply, a reduced version of the model is sufficient to describe their destruction rate at moderate (almost no effect) and high (lethal) temperatures ie\documentclass{article}\pagestyle{empty}\begin{document}$$ k(T) = \ln ((1/(1 + \exp ((T - T_c)/a_2))) $$\end{document} . The fit of this equation is demonstrated with published data on the heat destruction kinetics of two bacilli spores. If the relationship between the model's constants and environmental conditions such as pH, a w , salts concentration, etc can be expressed algebraically the model can be used to describe the combined effect of the various factors within the frame work of a single mathematical equation. Although the model's applicability is only demonstrated with a limited number of microorganisms the concept that a single model can describe both the propagation and lethal regimes can be useful in other types of biological populations, eg insects.