6 ± 0.708 min using a single Gaussian distribution function: this website i.e., Eq. 7 with α = 1 and β = 0; selleck kinase inhibitor Methods Section). However, when CI < ca. 100 CFU mL-1 there was a clear broadening in the range of observed τ values (ca. 10 to 34 min). At such low concentrations the CFUs per well should vary between 1 and 10 whereupon 44% of the wells should have 1 (± 1) CFU per well, 14% with 2 (± 1.4) CFUs per well, 8% with 3 (± 1.7) per well, 6% with 4 (± 2) per well, and 3% with between 5 (± 2.2) and10 (± 3.2) CFUs per well (assuming a Poisson distribution of CFU counts). The inset graph in Fig. 2 shows frequency of occurrence for all values of τ, which occur in the region of greatest scatter (CI< 100 CFU mL-1), with
the best fit bimodal Gaussian distribution (Eq. 7 ) represented by the solid, black curve. The least squares bimodal distribution curve fit contains a narrow component (α ~0.48; μτ1 ± στ1 = 18.0 ± 0.678 min) similar to the high cell concentration-associated unimodal distribution. Based upon area, there was also a nearly equivalent broad component (β ~ 0.52; μτ2 ± στ2 = 19.9 ± 2.48 min). Each constituent of this bimodal distribution is shown as a solid, grey curve. Figure 2 Plot of 653 observations of τ as a function of initial cell concentration (C I ; dilute stationary phase E. coli cells). Inset Figure: Frequency of occurrence of various values of τ (C I < 100 CFU mL -1 ) fit to Eq.
7. A similar increase in another https://www.selleckchem.com/products/H-89-dihydrochloride.html growth parameter’s scatter was also observed with the tm[CI]data at low CI (Fig. 3) whereupon we saw that tm values changed in a predictable way (e.g.,|∂tm/∂Log2CI| = τ) up to CI ~ 100 – 1,000 CFU mL-1 at which point they began to show an obvious large deviation in tm (between 6 and 11 hrs). These perturbations
in tm at low CI confirm the τ observations because tm is modulated, at least in part, by τ (Eqs. 5 – 6 : all tm & T-based equations are developed in the Methods Section) Ponatinib supplier and therefore large deviations in τ (Fig. 2) should result in increased scatter in tm as well. Working with stressed Listeria monocytogenes, Guillier and coworkers  observed numerous values of a lag time-related growth parameter with a similar asymmetric distribution pattern. Measuring the time of the first cell division in E. coli using a microscopic method, which should provide the true value of lag time, Niven and co-workers  were ableto make numerous observations (n = 434) which showed a very broad (μT~ 184 ± 45 min; our calculation assuming a unimodal distribution) asymmetric distribution. Asymmetry might be interpreted as weakly bimodal. Other workers  using a different method of observation showed that the distribution of individual times to the first cell division varied greatly based on salt concentration. In fact, at high salt concentrations, the distribution pattern appeared distinctly bimodal. However, in earlier work , such asymmetric population distributions were interpreted as being Gamma-distributed.