Assessment of distributions for fitting lag times of individual cells in bacterial populations

To develop mathematical models describing lag times of individual bacterial cells (τ), experimental τ data were fitted to a variety of continuous distributions using BestFit. Six strains of Escherichia coli O157:H7 were used, and serial dilutions were made in Bioscreen multi-well plates to get single cells per well. Detection times (td) for individual wells were converted to τ using the maximum specific growth rate (μ) for each strain. All strains were subject to 25 trials, with up to 100 replicate wells per trial. Some strains had significantly longer td, and lower μ, but the τ values were not significantly different. Distributions were best fit in the order Pearson V > Pearson VI > Extreme Value > Lognormal > Lognormal2 > Inverse Gaussian based on the Anderson–Darling statistic. The Lognormal distribution was selected because there was less variability in the parameter values, and parameters have specific biological meanings. Distributions could be fit to sample populations as low as six, with fittings and parameter values comparable to those obtained with larger samples (up to 89). Extreme Value, Pearson V, and Pearson VI distributions were more suitable for fitting τ values generated from a Lognormal distribution when the numbers of sample points were few, which suggested that there are similarities between the distributions. The results suggest that a Lognormal distribution can be used successfully to characterize τ.