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J Theor Biol. 2019 May 21;469:172-179. doi: 10.1016/j.jtbi.2019.01.042. Epub 2019 Mar 2.

Calculating stochastic inactivation of individual cells in a bacterial population using variability in individual cell inactivation time and initial cell number.

Author information

1
Graduate School of Agricultural Science, Hokkaido University, Kita-9, Nishi-9, Kita-ku, Sapporo 060-8589, Japan.
2
Graduate School of Agricultural Science, Hokkaido University, Kita-9, Nishi-9, Kita-ku, Sapporo 060-8589, Japan. Electronic address: koseki@bpe.agr.hokudai.ac.jp.

Abstract

The traditional log-linear inactivation kinetics model considers microbial inactivation as a process that follows first-order kinetics. A basic concept of log reduction is decimal reduction time (D-value), which means time/dose required to kill 90% of the relevant microorganisms. D-value based on the first-order survival kinetics model is insufficient for reliable estimations of bacterial survivors following inactivation treatment. This is because the model does not consider the inactivation curvature and variability in bacterial inactivation. However, although the D-value has some limitations, it is widely used for risk assessment and sterilization time estimation. In this study, stochastic inactivation models are used in place of the conventional D-value to describe the probability of a population containing survivors. As representative bacterial inactivation normally follows a log-linear or log-Weibull model, we calculate the time required for a specific decrease in the number of cells and the number of survival cells as a probability distribution using the stochastic inactivation of individual cells in a population. We compare the probability of a population containing survivors calculated via the D-value, an inactivation kinetics model, and the stochastic formula. The stochastic calculation can be approximately estimated via a kinetic curvature model with less than 5% difference below the probability of a population containing survivors 0.1. This stochastic formula indicates that the D-value model would over- or under-estimate the probability of a population containing survivors when applied to inactivation kinetics with curvature. The results presented in this study show that stochastic analysis using mathematical models that account for variability in the individual cell inactivation time and initial cell number would lead to a realistic and probabilistic estimation of bacterial inactivation.

KEYWORDS:

D-value; Individual cell heterogeneity; Poisson distribution; Probability theory

PMID:
30831174
DOI:
10.1016/j.jtbi.2019.01.042

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