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A New Look at Models of the Combined Effect of Temperature, pH, Water Activity, or Other Factors on Microbial Growth Rate

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Abstract

A popular approach to mathematical modeling of the combined effect of temperature, pH, water activity, oxygen tension, and the concentration of salts, sugars, alcohol, and/or antimicrobials on microbial growth rate is known as the gamma hypothesis. It is based on the notion that the growth rate, however defined, can be expressed as a multiplication product of algebraic terms each constructed from the individual factors’ cardinal parameters, i.e., their minimal, optimal, and maximal levels. These three alone, however, need not define a unique mathematical relationship, an issue that can be resolved by the terms’ redefinition or amendment. Offered are simulated examples where the roles of temperature, pH, or oxygen tension, which have an optimal level, are represented by a term that for the same three cardinal parameters can produce either curve having different maxima or different curves having the same maximum. Where a growth factor’s effect can be considered as rising or falling monotonically, as in water activity or inhibitory salt concentration, it can be represented by a single exponential or stretched exponential term. The resulting models can be used to simulate static and dynamic growth patterns to reveal how different cardinal parameter combinations may affect the growth kinetics.

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  1. Department of Food Science, University of Massachusetts, Amherst, MA, 01003, USA

    Micha Peleg

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Appendix

Appendix

The momentary γ[T(t)] and γ[pH(t)] expressed as a function of the corresponding cardinal parameters*

figure a

*Notice that in static growth, i.e., at constant temperature and/or pH, T(t) = T and pH(t) = pH, these two formulas produce plots of the kind shown in Figs. 12 and 13, that is peaking at Topt and pHopt, respectively, with a peak height γ(Topt) = γ(pHopt) = 1.

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Peleg, M. A New Look at Models of the Combined Effect of Temperature, pH, Water Activity, or Other Factors on Microbial Growth Rate. Food Eng Rev 14, 31–44 (2022). https://doi.org/10.1007/s12393-021-09292-x

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