Corradini Maria G, Peleg Micha
Department of Food Science, 228 Chenoweth Laboratory, 100 Holdsworth Way, University of Massachusetts, Amherst, MA 01003, USA.
Int J Food Microbiol. 2006 Apr 15;108(1):22-35. doi: 10.1016/j.ijfoodmicro.2005.10.011. Epub 2006 Jan 5.
Resumed growth of the survivors of a heat or chemical treatment after cooling or a disinfectant dissipation is not an uncommon phenomenon. Similarly, the inverse, the onset of mortality in a growing microbial population as a result of exposure to increasing temperature or concentration of an antimicrobial agent, is also a familiar scenario. Provided that in either regime, the organism has no time to adapt biologically, the continuous transition from growth to inactivation or vice versa can be simulated with conventional growth and inactivation models, whose rate constant is allowed to change sign. Where both the growth and inactivation follow first-order kinetics, the sign change has no effect on the model equation's solutions. The same applies when the growth and inactivation patterns are described by a rate model, like the differential logistic equation or its various variants. However, determination of such models' coefficients from experimental isothermal growth and inactivation data can be difficult for technical reasons, unless the model can be integrated analytically. If not, or when the model itself is unknown a priori, then the rate equation would have to be derived from the fit of empirical models like the Weibull, modified versions of the logistic function and the like. But this may create a new kind of problem as a result of that the log and certain power operations cannot be used for negative numbers. For certain models at least, the problem can be solved through modification of the procedure by which the rate equation is solved numerically. This is demonstrated in simulated transitions between growth and inactivation and between inactivation and growth based on the log linear and Weibullian-power law models and three logistic patterns based on a shifted logistic function, the Baranyi-Roberts model and a shifted arctan model.
经过冷却或消毒剂消散后，受热处理或化学处理的存活者恢复生长并非罕见现象。同样，相反的情况，即不断增长的微生物群体因暴露于不断升高的温度或抗菌剂浓度而开始死亡，也是常见的情形。只要在这两种情况下，生物体都没有时间进行生物学适应，那么从生长到失活或反之的连续转变就可以用传统的生长和失活模型来模拟，其速率常数允许改变符号。当生长和失活都遵循一级动力学时，符号变化对模型方程的解没有影响。当生长和失活模式由速率模型描述时，如微分逻辑方程或其各种变体，情况也是如此。然而，由于技术原因，从实验等温生长和失活数据确定此类模型的系数可能很困难，除非该模型可以进行解析积分。如果不能，或者当模型本身先验未知时，那么速率方程就必须从经验模型（如威布尔模型、逻辑函数的修正版本等）的拟合中推导出来。但这可能会产生一种新的问题，因为对数和某些幂运算不能用于负数。至少对于某些模型，该问题可以通过修改数值求解速率方程的程序来解决。这在基于对数线性和威布尔幂律模型以及基于移位逻辑函数、巴拉尼 - 罗伯茨模型和移位反正切模型的三种逻辑模式的生长与失活之间以及失活与生长之间的模拟转变中得到了证明。
