Department of Food Science, Chenoweth Laboratory, University of Massachusetts, Amherst, MA 01003, USA.
Crit Rev Food Sci Nutr. 2011 Dec;51(10):917-45. doi: 10.1080/10408398.2011.570463.
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.
大多数食品中微生物生长的模型都是经验性的代数模型，其中最著名的是 Gompertz 模型。速率方程主要是 Verhulst 逻辑模型的变体，或者是种群动态模型，可以是确定性的和连续的，也可以是随机的和离散的。前两种模型只考虑净生长，因此不能解释在生长的任何阶段可能发生的细胞死亡。几乎无一例外地，所有三种类型的模型都可以描述相同的一组实验生长数据。这种缺乏唯一性本身就是一个质疑仅通过曲线拟合获得的生长参数的机械解释的理由。正如所争论的那样，包括 Baranyi-Roberts 模型在内的 Verhulst 模型的所有变体都是形式为速率方程的经验现象学模型。它们都没有提供任何机械上的见解，也没有比其他模型更具优势。原则上，所有三种类型的模型都可以根据等温数据预测非等温生长模式。因此，模型构建者应该选择最简单和最方便的模型来达到这个目的。没有理由假设“最大比生长速率”对温度、pH 值、水分活度或其他因素的依赖性遵循原始或修改后的 Arrhenius 模型，正如 Ratkowsky 平方根模型检验所证明的那样。大多数 S 型等温生长曲线需要三个可调参数来描述其数学表达式，而至少有一个峰的生长曲线需要四个。尽管经常观察到，但没有理论上的理由表明这些生长参数应该总是一致地随着外部条件的变化而上升或下降。因此，量化环境因素对微生物生长的影响需要考虑所有的生长参数，而不仅仅是“最大比生长速率”。确定“迟滞时间”的不同方法通常会产生不同的值，这表明它是一个定义不明确的生长参数。几个因素（如温度、pH 值或 aw）的联合效应不一定是“乘法”，因此应该通过实验来揭示。这可能并不总是可行的，但牢记这一点将消除难以证实的理论假设。现代数学软件可以对同时发生细胞分裂和死亡的生长或死亡微生物种群进行建模，并且可以用于解释不同的生长模式是如何出现的。但至少在不久的将来，像将变化的温度转换为相应的微生物生长曲线这样的实际问题，将通过经验性的速率模型来解决，尽管这些模型不是“机械的”，但非常适合这个目的。
