Accurate estimation of cardinal growth temperatures of Escherichia coli from optimal dynamic experiments

Prediction of the microbial growth rate as a response to changing temperatures is an important aspect in the control of food safety and food spoilage. Accurate model predictions of the microbial evolution ask for correct model structures and reliable parameter values with good statistical quality. Given the widely accepted validity of the Cardinal Temperature Model with Inflection (CTMI) [Rosso, L., Lobry, J. R., Bajard, S. and Flandrois, J. P., 1995. Convenient model to describe the combined effects of temperature and pH on microbial growth, Applied and Environmental Microbiology, 61: 610–616], this paper focuses on the accurate estimation of its four parameters (Tmin, Topt, Tmax and µopt) by applying the technique of optimal experiment design for parameter estimation (OED/PE). This secondary model describes the influence of temperature on the microbial specific growth rate from the minimum to the maximum temperature for growth. Dynamic temperature profiles are optimized within two temperature regions ([15 °C, 43 °C] and [15 °C, 45 °C]), focusing on the minimization of the parameter estimation (co)variance (D-optimal design). The optimal temperature profiles are implemented in a computer controlled bioreactor, and the CTMI parameters are identified from the resulting experimental data. Approximately equal CTMI parameter values were derived irrespective of the temperature region, except for Tmax. The latter could only be estimated accurately from the optimal experiments within [15 °C, 45 °C]. This observation underlines the importance of selecting the upper temperature constraint for OED/PE as close as possible to the true Tmax. Cardinal temperature estimates resulting from designs within [15 °C, 45 °C] correspond with values found in literature, are characterized by a small uncertainty error and yield a good result during validation. As compared to estimates from non-optimized dynamic experiments, more reliable CTMI parameter values were obtained from the optimal experiments within [15 °C, 45 °C].