Single-Cell and Population Lag Times as a Function of Cell Age

After inoculation, the times to the first divisions are longerand more widely distributed for those Escherichia coli singlecells that spent more time in the stationary phase prior toinoculation. The second generation times are still longer thanthe typical generation times in the exponential phase, and thisextended the apparent lag time of the cell population. The greaterthe variability of the single-cell interdivision intervals,the shorter are both the lag time and the doubling time of thepopulation.

INTRODUCTION

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INTRODUCTION

It has been shown experimentally (1, 15, 17) and theoretically(13) that the lag parameters of a bacterial population do notcarry much information about the lag time of the individualcells. Single-cell measurements (6, 8, 10, 11, 14, 16-19) havemade it possible to study the effect of the environment on thedistribution of single-cell lag times, underlining the needfor the quantification of growth parameters and their variabilityat the single-cell level.

We used the flow chamber technique of Elfwing et al. (5) toinvestigate how the age of the cells, quantified as the incubationtime in the preinoculation culture, affects the distributionof the generation (i.e., interdivision) times of single Escherichiacoli K-12 cells. LB media with 0.2% glucose was inoculated withca. 10³ cells/ml and incubated at 25°C. Stationary-phasecells after ca. 53, 77, 83, 144, 151, 193, 218, 360, and 602h of incubation were removed from this culture and immediatelyused to inoculate the flow chamber. Thus, the age of the cellswas defined as the time at which the cells were sampled fromthe primary culture. The generation times for single cells werecalculated by observing the time intervals between two successivedivisions after the first division occurred. The first divisiontime (FDT) was considered to be the sum of the lag time andthe first generation time.

Figure 1a shows the distributions of the natural logarithm ofthe FDTs of single cells of different ages. The older the cells,the greater are the averages of their FDTs. The FDTs continuouslyincrease with the age of the cells (except for the unexpectedlyhigh division times observed when inoculating the 144-h primaryculture; this was attributed to experimental error). The standarddeviations of the FDTs were not constant but increased withthe average. However, the coefficient of variation (CV) (theratio of the standard error to the mean) did not change withthe age (Table 1).

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FIG. 1. Box-and-whiskers plots representing the distributions of the logarithm of the FDT (a) and of the second generation time (b) of single cells kept in the stationary phase for different periods of time prior to inoculation. A "+" represents the average; a notch represents the median. Outliers that were more than 1.5 or 3 times the interquartile range above or below the box are shown as small squares or small squares with "+" signs through them, respectively.

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TABLE 1. Average FDTs of single cells measured in the flow chamber and growth parameters of populations simulated with the same single-cell measurements for inocula of various ages

Figure 1b shows that the age of the cells did not affect thedistribution of the second generation time (the time intervalbetween the first and second division). This indicates thatthe main effect of the age of the cells is on the lag periodprior to the first division.

Pin and Baranyi (13) developed a stochastic model to simulatethe growth of the population resulting from the single-celldivision times. This approach proved to predict the growth ofthe population accurately. Simulations were carried out to studythe following three main questions.

What is the relationship between the single-cell division times measured in the flow chamber and the growth parameters of the population generated by those cells, for each inoculum age, based on 100 simulated growth curves?

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What is the relationship...

Figure 2 compares the sum of the lag and the doubling timesof the population with the average FDTs of the single cellswithin that population. The two were practically equal. Theoretically,the FDTs of single cells should be longer than the time at whichthe population doubles for the first time (2, 3). However, inthese articles, it was assumed that, after the FDT, the cellswere immediately in the exponential phase. Our observationsdisprove this hypothesis, as do other studies (12, 13). We foundthat the generation times decreased gradually after the firstdivision. For example, for single cells inoculated on the slideafter 53 h spent in the primary culture, the averages of thesecond, third, and fourth generation times were 0.74, 0.66,and 0.58, respectively. The fact that the second, third, andmaybe even the fourth generation times are still longer thanthose in the exponential phase causes a further delay in thelag of the population. From a physiological point of view, thisindicates that cells do divide before the adaptation processin the new environment is complete.

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FIG. 2. Relationship between the average of the single-cell FDTs and the sum of the lag (L) and doubling times of the population (Dt_p) (L + Dt_p). The growth of a population with 100 initial cells was simulated for each inoculum age based on the distributions of the observed single-cell generation times as described in reference 13.

What effect did the variability of the single-cell division times have on the lag time observed at the population level?

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What effect did the...

We generated, on computer, several series of single-cell first-divisiontimes according to the gamma distribution with 2.5 h as theirmean (as measured for the cells incubated after 602 h in theprimary culture) and standard deviations that varied from ca.0.1 to 2 times their expected values. The initial number ofcells in the population was 100. Each batch was simulated 100times. Figure 3a shows that the population lag time is determinednot only by the mean of the single-cell FDTs but also by theirvariability. The larger the variability of the single-cell FDTs,the greater the number of cells with short FDTs, which shortenedthe lag time of the population (Fig. 3a). According to our flowchamber measurements, the CV values observed for single-cellFDTs were between 0.3 and 0.4, independently of the age of thecells (Table 1). Similar values have been reported by Guillierand Augustin (7). Note that D'Arrigo et al. (4) reported greaterCV values (0.76) for the lag time of single cells stressed previously.The CV values for single-cell FDTs were ca. 10 times largerthan the respective parameters of the populations (Table 1).The simulations showed that the CV value of the population lagtime increased as the CV values of the single-cell FDTs withinthat population increased (Fig. 3b), keeping a ratio that wasca. 10-fold greater, until a maximum value was reached.

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FIG. 3. Effect of the variability of the single-cell FDTs on the population lag time (a) and the relationship between the CV (coeff. variation) values of the population lag time and of the FDTs of the single cells (b).

What effect did the variability of the generation time of single cells have on the exponential growth rate of the population?

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A population in which all cells divide synchronously and exactlyevery 0.66 h was also simulated and compared to the situationwhen the generation times were distributed as described above,with an expected value of 0.66 h. Figure 4 shows that if allcells divide exactly at the same time (single-cell generationtimes with a standard deviation of zero), then the doublingtime of the population is equal to the single-cell generationtime, i.e., 0.66 h. As the variance of the single-cell generationtimes increases, the population doubling time becomes shorter,in agreement with reference 9. This is because the random appearanceof cells with shorter generation times has an unexpectedly bigeffect on the overall population due to the exponential growth.

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FIG. 4. Relationship between the population doubling times and the variability of the generation times of single cells in the exponential phase. Comparison of scenarios when all cells divide synchronously and exactly every 0.66 h and when the generation times are distributed according to a gamma distribution with an expected value equal to 0.66 h and a standard deviation that varies from ca. 0.1 to 2 times the mean value.

ACKNOWLEDGMENTS

This paper was prepared under the funding of the EU, projectno. QLK1-CT-2001-01145 (BACANOVA), and BBSRC core strategicgrant 42266A.

We express our thanks to Anders Elfwing and András Ballagifor setting up the flow chamber in our laboratory and theirconstant help.

FOOTNOTES

* Corresponding author. Mailing address: Institute of Food Research, Norwich Research Park, Colney, Norwich NR4 7UA, United Kingdom. Phone: (44) 1603 255021. Fax: (44) 1603 255288. E-mail: carmen.pin{at}bbsrc.ac.uk

Published ahead of print on 22 February 2008.

REFERENCES

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