Estimating bacterial growth parameters by means of detection times

Abstract

We developed a new numerical method to estimate bacterial growth parameters by means of detection times generated by different initial counts. The observed detection times are subjected to a transformation involving the (unknown) maximum specific growth rate and the (known) ratios between the different inoculum sizes and the constant detectable level of counts. We present an analysis of variance (ANOVA) protocol based on a theoretical result according to which, if the specific rate used for the transformation is correct, the transformed values are scattered around the same mean irrespective of the original inoculum sizes. That mean, termed the physiological state of the inoculum, âlpha, and the maximum specific growth rate, mu, can be estimated by minimizing the variance ratio of the ANOVA procedure. The lag time of the population can be calculated as lambda = -ln âlpha/mu; i.e. the lag is inversely proportional to the maximum specific growth rate and depends on the initial physiological state of the population. The more accurately the cell number at the detection level is known, the better the estimate for the variance of the lag times of the individual cells.

FIG. 1

The intercept of the inoculum level with the tangent drawn to the exponential phase of the growth curve marks the end of the lag phase. The detection time, T_det, depends linearly on the lag, λ, if the detection level is in the exponential phase. The parameter μλ can be used to define a hypothetical inoculum level from which a growth curve, without lag, is able to catch up with the real curve with lag.

FIG. 2

Detection times from different inoculum levels obtained by a series of binary dilutions. The lower the inoculum level, the larger is the scatter of the detection times. x, measured detection times; –––, detection time predictions obtained by the new method.

FIG. 3

Physiological-state values, obtained by transforming the detection times by means of the respective dilution ratios and the estimated specific growth rate. x, physiological-state data; ■, group mean of the physiological-state data generated by the same inoculum level; –––, grand mean, ᾱ, the estimate for the mean physiological state of the initial population; ···, the expected theoretical deviation from the grand mean, calculated with X_det = 10⁷ detection level and assuming an exponential distribution for the individual lag times.

FIG. 4

Demonstration of the robustness of the method. If the maximum specific growth rates are slightly perturbed (μ = 0.95 h⁻¹ [A] or μ = 1.2 h⁻¹ [B] instead of the correct μ = 1.07 h⁻¹), the physiological-state values show a strong downward and upward tendency, respectively. For explanations of symbols, see the legend to Fig. 3.