S & P-Type Models: a Novel Class of Predictive Microbial Growth Models

Abstract

Food safety and quality are largely influenced by the presence and possible proliferation of pathogenic and spoilage micro-organisms during the farm-to-fork path of the product. In order to describe and predict the microbial evolution in foods, mathematical models are developed in the field of predictive microbiology. In this research a novel class of simple yet elegant models to describe single species microbial growth is discussed. In contrast with the currently used logistic-type models, the novel model class explicitly incorporates nutrient exhaustion and/or metabolic waste product effects. As such, these novel model types can be extended in a natural way towards microbial interactions in co-cultures and microbial growth in structured foods. Introduction Food safety and quality are largely influenced by the presence and possible proliferation of pathogenic and spoilage micro-organisms during the farm-to-fork path of the product. In order to decribe and predict the microbial evolution in foods, mathematical models are developed in the field of predictive microbiology. Single species microbial growth, whether in a bioreactor or in a (liquid) food product, normally passes three distinct phases. In a first phase, the so-called lag phase, the microbial cells adapt to their new environment and do not multiply. The total number of microbial cells remains constant during this phase. During the next phase, the exponential growth phase, the microbial cells multiply exponentially. Finally, the microbial cells cease multiplying and their total number remains constant at the maximum population density. This third and final phase is called the stationary phase. A typical growth curve is shown in Figure 1. Microbial growth can be considered as a self-limiting process principally due to either (i) the exhaustion of one of the essential nutrients, or (ii) the accumulation of metabolic (waste) products which inhibit growth (Lynch and Poole, 1979). The effect of both phenomena on the maximum population concentration is depicted in Figure 2. If an increase of the initial substrate concentration results in an increase of the maximum microbial population density attained (as in the left part of the plot), then the limiting factor is the substrate availability. If an increase of the initial substrate concentration (whether a C-source, N-source, essential element or a vitamin) does not affect the maximum microbial IUFoST 2006 DOI: 10.1051/IUFoST:20061134