Effect of temperature on microbial growth rate-mathematical analysis: the Arrhenius and Eyring-Polanyi connections

The objective of this work is to develop a mathematical model for evaluating the effect of temperature on the rate of microbial growth. The new mathematical model is derived by combination and modification of the Arrhenius equation and the Eyring-Polanyi transition theory. The new model, suitable for both suboptimal and the entire growth temperature ranges, was validated using a collection of 23 selected temperature-growth rate curves belonging to 5 groups of microorganisms, including Pseudomonas spp., Listeria monocytogenes, Salmonella spp., Clostridium perfringens, and Escherichia coli, from the published literature. The curve fitting is accomplished by nonlinear regression using the Levenberg-Marquardt algorithm. The resulting estimated growth rate (μ) values are highly correlated to the data collected from the literature (R(2) = 0.985, slope = 1.0, intercept = 0.0). The bias factor (B(f) ) of the new model is very close to 1.0, while the accuracy factor (A(f) ) ranges from 1.0 to 1.22 for most data sets. The new model is compared favorably with the Ratkowsky square root model and the Eyring equation. Even with more parameters, the Akaike information criterion, Bayesian information criterion, and mean square errors of the new model are not statistically different from the square root model and the Eyring equation, suggesting that the model can be used to describe the inherent relationship between temperature and microbial growth rates. The results of this work show that the new growth rate model is suitable for describing the effect of temperature on microbial growth rate. Practical Application:  Temperature is one of the most significant factors affecting the growth of microorganisms in foods. This study attempts to develop and validate a mathematical model to describe the temperature dependence of microbial growth rate. The findings show that the new model is accurate and can be used to describe the effect of temperature on microbial growth rate in foods.