Mathematical modeling and numerical analysis of the growth of non-O157 Shiga toxin-producing Escherichia coli in spinach leaves

Abstract

This study was conducted to investigate the growth of non-O157 Shiga toxin-producing Escherichia coli (STEC) in spinach leaves and to develop kinetic models to describe the bacterial growth. Six serogroups of non-O157 STEC, including O26, O45, O103, O111, O121, and O145, were used in the growth studies conducted isothermally at 4, 8, 15, 20, 25, 30, and 35°C. Both STEC and background microflora were enumerated to develop kinetic models. Growth of STEC in spinach leaves was observed at elevated temperatures (15–35°C), but not at 4 and 8°C.This study considered the dynamic interactions between the STEC cells and the background microflora. A modified Lotka–Volterra and logistic equation was used to simulate the bacterial growth. In combination with an unconstrained optimization procedure, the differential growth equations were solved numerically to evaluate the dynamic interactions between the STEC cells and the background microflora, and to determine the kinetic parameters by fitting each growth curve to the growth equations. A close agreement between the experimental growth curves and the numerical analysis results was obtained.The analytical results showed that the growth of STEC in spinach leaves was unhindered when the population was low, but the growth was suppressed by the background microflora as the STEC population approached the maximum population density. The effect of temperature on the growth of both STEC and background microflora was also evaluated. Secondary models, evaluating the effect of temperature on growth rates, were also developed. The estimated apparent minimum growth temperature for STEC was 11°C in commercial spinach leaves. The methodology and results of this study can be used to examine the dynamic interactions and growth between different bacteria in foods, and to conduct risk assessments of STEC in spinach leaves.