A stochastic approach for integrating strain variability in modeling Salmonella enterica growth as a function of pH and water activity

Abstract

Strain variability of the growth behavior of foodborne pathogens has been acknowledged as an important issue in food safety management. A stochastic model providing predictions of the maximum specific growth rate (μ(max)) of Salmonella enterica as a function of pH and water activity (a(w)) and integrating intra-species variability data was developed. For this purpose, growth kinetic data of 60 S. enterica isolates, generated during monitoring of growth in tryptone soy broth of different pH (4.0-7.0) and a(w) (0.964-0.992) values, were used. The effects of the environmental parameters on μ(max) were modeled for each tested S. enterica strain using cardinal type and gamma concept models for pH and a(w), respectively. A multiplicative without interaction-type model, combining the models for pH and a(w), was used to describe the combined effect of these two environmental parameters on μ(max). The strain variability of the growth behavior of S. enterica was incorporated in the modeling procedure by using the cumulative probability distributions of the values of pH(min), pH(opt) and a(wmin) as inputs to the growth model. The cumulative probability distribution of the observed μ(max) values corresponding to growth at pH 7.0-a(w) 0.992 was introduced in the place of the model's parameter μ(opt). The introduction of the above distributions into the growth model resulted, using Monte Carlo simulation, in a stochastic model with its predictions being distributions of μ(max) values characterizing the strain variability. The developed model was further validated using independent growth kinetic data (μ(max) values) generated for the 60 strains of the pathogen at pH 5.0-a(w) 0.977, and exhibited a satisfactory performance. The mean, standard deviation, and the 5th and 95th percentiles of the predicted μ(max) distribution were 0.83, 0.08, and 0.69 and 0.96h(-1), respectively, while the corresponding values of the observed distribution were 0.73, 0.09, and 0.61 and 0.85h(-1). The stochastic modeling approach developed in this study can be useful in describing and integrating the strain variability of S. enterica growth kinetic behavior in quantitative microbiology and microbial risk assessment.