Simulation and evaluation of different statistical functions for describing lag time distributions of a bacterial growth curve

Abstract

The objective of this study was to simulate the lag time distribution of individual bacterial cells in a population incubated under an isothermal condition. Spores of Clostridium sporogenes PA 3679 inoculated to ground beef were incubated at 37 °C to develop a growth curve and determine its apparent lag time. The lag times of individual cells were simulated using normal, lognormal, Gumbel, gamma, Weibull, and exponential distributions. The growth process was modeled using the McKellar model. A 4th order Runge–Kutta method was used to solve the McKellar model in conjunction with the Nelder–Mead method. The objective of the numerical analysis was to search for the parameters in each lag time distribution model and the kinetic parameters (specific growth rate and mean lag time) of the growth model such that a minimized residual sum of squared errors (RSS) was found.Although different in shapes, the simulation results showed that the performance of normal, lognormal, Gumbel, and gamma distributions was practically the same when used to fit the growth curve, yielding the same estimates of initial and stationary phase bacterial concentrations, specific growth rate, and mean lag time as well as RSS. The lognormal, Gumbel, and gamma distributions of the lag times were slightly skewed to the right of the mean. The standard deviations of the lag times with these distributions were relatively small, suggesting that cells may leave the lag phase almost simultaneously. The Weibull and exponential distributions were also suitable for describing the distribution of lag times, but with larger standard deviations. In general, all these statistical distributions were found suitable for simulating the distribution of lag times of individual cells in a population.