In this case, the experiments were performed in duplicate. Quantification of persister fractions The fraction of persisters, death rates and switching rates between persister and normal states were calculated using a model motivated by Balaban et al. . In this model, cells switch between two states, normal and persister. The equations describing the dynamics of this switching is detailed in the Additional file 1, together with the exact solutions of these coupled differential equations. We used maximum likelihood to fit the
CFU count data, under the assumption that the error in the CFU counts results primarily from Poisson sampling, using the likelihood function: in which x t is the number of CFUs observed at time point t, δ t is the dilution at time point t, and N(t) is the number of cells predicted by the model (see Additional file 4). The values that these parameters can take are XAV-939 cell line restricted, as outlined in the Additional file 1. Likelihood maximization was done using optim() in the R statistical framework . Likelihood convergence was checked by using ten separate Kinase Inhibitor Library price starting values for the parameters and three optimization algorithms, Nelder-Mead,
SANN, and BFGS. The values of the a, b, m, and F0 (the initial fraction of persisters) were determined independently for each replicate, and we calculated confidence intervals assuming normally distributed error. Because the values of a, b, and m cannot be uniquely fit (see Additional file 1), we calculated them using the median value of F0; in most cases, the uncertainty in F0 is very low, with most minimum and maximum values of F0 ranging between 0.99 and 1. Thus, this approximation has little effect Urease on our data. All other statistical analyses were performed using R . Acknowledgments We thank Mike Sadowsky for providing the E. coli environmental isolates. Electronic supplementary material Additional file 1: Appendix. (PDF 157 KB) Additional file 2: Table S1: Minimum inhibitory antibiotic concentrations for each strain. The MICs ranged between 15-22.5 μg/ml
for ampicillin, between 0.008-0.030 μg/ml for ciprofloxacin and 3-7.5 μg/ml for nalidixic acid. This variation in MICs was considerably smaller than the variation in persister fractions exhibited by the selected strains and moreover, the fraction of persisters and their corresponding MICs showed no correlation, suggesting that the variation in MICs does not account for the one observed in the level of persister cells. No resistance to the three used antibiotics was evident for any of the examined. (XLS 8 KB) Additional file 3: Table S2: Estimated death rates and switching rates for all strains in the three antibiotics (ampicillin, ciprofloxacin, and nalidixic acid). The parameters are explained in the Additional file 1. Electronic supplementary material.