Estimation of the Temperature Dependent Growth Parameters of Lactobacillus Viridescens in Culture Medium with Two-step Modelling and Optimal Experimental Design Approaches

Abstract

In predictive microbiology, the model parameters has been estimated using the traditional two-step modeling approach (TS), in which primary models are fitted to the microbial growth data and secondary models represent the dependence of model parameters with environmental variables. The optimal experimental design approach (OED) has been used as an alternative to TS, mainly because the improvement of model identifiability and reduction of the experimental workload and costs. The fitting of mathematical model to experimental data in TS is sequential, whereas in OED is simultaneous. Lactobacillus viridescens is a lactic acid bacteria that is of great interest to the meat products preservation. The objective of this study was to estimate the growth parameters of L. viridescens in culture medium with TS and OED. For TS, the experimental data were obtained in six temperatures; for OED, the data were obtained in four optimal non-isothermal experiments, two experiments with increasing temperatures (ITOED) and two with decreasing temperatures (DTOED). The Baranyi and Roberts, and the Square Root models were used to describe the microbial growth, in which the b and T_min parameters (± 95% confidence intervals) were estimated from the experimental data. The parameters obtained for TS were b = 0.0290 (±0.0020) h^-0.5°C^-1 and T_min = -1.33 (±1.26) °C, with R² = 0.991; for ITOED were b = 0.0314 (±0.0019) h^-0.5°C^-1 and T_min = 0.12 (±0.71) °C, with R² = 0.995; for DTOED were b = 0.0295 (±0.0019) h^-0.5°C^-1 and T_min = -1.57 (±1.05) °C, with R² = 0.999. The parameters obtained in the OED approach presented smaller confidence intervals, higher R² and less experimental time than the parameters obtained in the traditional TS approach. In this way, it is possible to answer positively that OED approach is feasible and could be widely applied in predictive microbiology.