Mathematical models based on transition state theory for the microbial safety of foods by high pressure

Abstract

Prior to the development of transition state theory, the Arrhenius equation was the principal relationship used in describing the temperature dependence of chemical reaction rates. Research into determining the theoretical basis for the Arrhenius parameters A (pre-exponential factor) and Ea (activation energy) led to the development of transition state theory and the Eyring equation, whose central postulate is a hypothetical transient state called the activated complex that forms through interactions between reactants before they can become products during the process of a chemical reaction. It is from the perspective of transition state theory that we develop two secondary models to reflect the effects of temperature and of high pressure on microbial inactivation by the emerging nonthermal technology of high pressure processing (HPP), and we designate these as transition state (TS) models TST and TSP, respectively. These secondary models are applied to data obtained with two primary models, the enhanced quasi-chemical kinetics (EQCK) differential equation model and the Weibull distribution empirical model, that were used to evaluate nonlinear inactivation kinetics for baro-resistant Listeria monocytogenes in a surrogate protein food system by HPP for various combinations of pressure (207–414 MPa) and temperature (20–50 °C). The mathematical relationships of TST and TSP involve primarily the unique model parameter called “processing time parameter” (tp), which was developed to evaluate inactivation kinetics data showing tailing. These detailed secondary models, as applied to the parameters of the EQCK and Weibull primary models, have important ramifications for ensuring food safety and the shelf life of food products and support the growing uses of HPP for the safe preservation of foodstuffs.