Optimal experimental design for improving the estimation of growth parameters of Lactobacillus viridescens from data under non-isothermal conditions

Abstract

In predictive microbiology, the model parameters have been estimated using the sequential two-step modeling (TSM) approach, in which primary models are fitted to the microbial growth data, and then secondary models are fitted to the primary model parameters to represent their dependence with the environmental variables (e.g., temperature). The Optimal Experimental Design (OED) approach allows reducing the experimental workload and costs, and the improvement of model identifiability because primary and secondary models are fitted simultaneously from non-isothermal data. Lactobacillus viridescens was selected to this study because it is a lactic acid bacterium of great interest to meat products preservation. The objectives of this study were to estimate the growth parameters of L. viridescens in culture medium from TSM and OED approaches and to evaluate both the number of experimental data and the time needed in each approach and the confidence intervals of the model parameters. Experimental data for estimating the model parameters with TSM approach were obtained at six temperatures (total experimental time of 3540h and 196 experimental data of microbial growth). Data for OED approach were obtained from four optimal non-isothermal profiles (total experimental time of 588h and 60 experimental data of microbial growth), two profiles with increasing temperatures (IT) and two with decreasing temperatures (DT). The Baranyi and Roberts primary model and the square root secondary model were used to describe the microbial growth, in which the parameters b and Tmin (±95% confidence interval) were estimated from the experimental data. The parameters obtained from TSM approach were b=0.0290 (±0.0020) [1/(h0.5°C)] and Tmin=−1.33 (±1.26) [°C], with R2=0.986 and RMSE=0.581, and the parameters obtained with the OED approach were b=0.0316 (±0.0013) [1/(h0.5°C)] and Tmin=−0.24 (±0.55) [°C], with R2=0.990 and RMSE=0.436. The parameters obtained from OED approach presented smaller confidence intervals and best statistical indexes than those from TSM approach. Besides, less experimental data and time were needed to estimate the model parameters with OED than TSM. Furthermore, the OED model parameters were validated with non-isothermal experimental data with great accuracy. In this way, OED approach is feasible and is a very useful tool to improve the prediction of microbial growth under non-isothermal condition.