Microbial growth curves: what the models tell us and what they cannot.

Most of the models of microbial growth in food are Empirical algebraic, of which the Gompertz model is the most notable, Rate equations, mostly variants of the Verhulst's logistic model, or Population Dynamics models, which can be deterministic and continuous or stochastic and discrete. The models of the first two kinds only address net growth and hence cannot account for cell mortality that can occur at any phase of the growth. Almost invariably, several alternative models of all three types can describe the same set of experimental growth data. This lack of uniqueness is by itself a reason to question any mechanistic interpretation of growth parameters obtained by curve fitting alone. As argued, all the variants of the Verhulst's model, including the Baranyi-Roberts model, are empirical phenomenological models in a rate equation form. None provides any mechanistic insight or has inherent advantage over the others. In principle, models of all three kinds can predict non-isothermal growth patterns from isothermal data. Thus a modeler should choose the simplest and most convenient model for this purpose. There is no reason to assume that the dependence of the "maximum specific growth rate" on temperature, pH, water activity, or other factors follows the original or modified versions of the Arrhenius model, as the success of Ratkowsky's square root model testifies. Most sigmoid isothermal growth curves require three adjustable parameters for their mathematical description and growth curves showing a peak at least four. Although frequently observed, there is no theoretical reason that these growth parameters should always rise and fall in unison in response to changes in external conditions. Thus quantifying the effect of an environmental factor on microbial growth require that all the growth parameters are addressed, not just the "maximum specific growth rate." Different methods to determine the "lag time" often yield different values, demonstrating that it is a poorly defined growth parameter. The combined effect of several factors, such as temperature and pH or aw, need not be "multiplicative" and therefore ought to be revealed experimentally. This might not be always feasible, but keeping the notion in mind will eliminate theoretical assumptions that are hard to confirm. Modern mathematical software allows to model growing or dying microbial populations where cell division and mortality occur simultaneously and can be used to explain how different growth patterns emerge. But at least in the near future, practical problems, like translating a varying temperature into a corresponding microbial growth curve, will be solved with empirical rate models, which despite not being "mechanistic" are perfectly suitable for this purpose.