**DOI:**10.1128/AEM.02551-07

## ABSTRACT

The distributions of times to first cell division were determined for populations of *Escherichia coli* stationary-phase cells inoculated onto agar media. This was accomplished by using automated analysis of digital images of individual cells growing on agar and calculation of the “box area ratio.” Using approximately 300 cells per experiment, the mean time to first division and standard deviation for cells grown in liquid medium at 37°C and inoculated on agar and incubated at 20°C were determined as 3.0 h and 0.7 h, respectively. Distributions were observed to tail toward the higher values, but no definitive model distribution was identified. Both preinoculation stress by heating cultures at 50°C and postinoculation stress by growth in the presence of higher concentrations of NaCl increased mean times to first division. Both stresses also resulted in an increase in the spread of the distributions that was proportional to the mean division time, the coefficient of variation being constant at approximately 0.2 in all cases. The “relative division time,” which is the time to first division for individual cells expressed in terms of the cell size doubling time, was used as measure of the “work to be done” to prepare for cell division. Relative division times were greater for heat-stressed cells than for those growing under osmotic stress.

When modeling the behavior of bacterial populations under different environmental conditions, the key kinetic parameters of the growth curve are the duration of the lag phase and the maximum specific growth rate. Lag time depends on both the environmental conditions and the physiological state of the inoculum and is thus more difficult to predict than growth rate, which, for a given organism, is an autonomous property defined by the environment alone (16, 17). The lag times of cell populations are conventionally measured geometrically as the time at which a tangent to the point of maximum slope on a plot of log of bacterial concentration versus time crosses a horizontal projection of the inoculum concentration. However, when pathogenic bacteria are present in food, they are often found in very low numbers and the distribution of individual lag times within cell populations then becomes an important consideration in risk assessment.

Lag time distributions can be determined directly by observing single cells under the microscope (5, 11, 22, 25, 32) or indirectly by measuring the time to produce a detectable optical density change in replicate cultures inoculated with approximately one cell using an automated growth analyzer such as the Bioscreen apparatus (7, 12, 19, 26, 29, 31, 32). An alternative indirect method consists of measuring the time to reach a certain colony size from single cells inoculated on an agar plate (8). Indirect methods are more convenient than microscopic methods and are essential when studying severely stressed populations containing only a few viable survivors. Distributions of detection times are a very good measure of the distribution of lag times (20), but they do not always give accurate absolute values for single-cell lag times because extrapolation from population to single-cell levels amplifies the effect of small measurement uncertainties. For this reason, microscopic methods based on direct observation are often regarded as the “gold standard” for studying single-cell behavior. Growth and division of single cells have been monitored in agar slide cultures viewed by light microscopy (10, 23, 24) and in a flow chamber in which daughter cells are flushed away from adherent mother cells after cell division (5). These methods are complementary, but each has certain limitations. The flow chamber method of Elfwing et al. (5) allows large numbers of cells to be monitored and gives a clear-cut point of cell division, but, under some conditions, problems can arise with spontaneous detachment of cells during the period of observation (19). The slide culture method is simple and can be used with a wide range of organisms but is subject to uncertainty when used to measure lag times because it is difficult to decide consistently and objectively exactly when cells have divided. However, a method was recently described that enables the time to first cell division to be determined objectively using image analysis (22). The time of first cell division is calculated from the “box area ratio” (BAR), which is the area of the smallest rectangle that can be drawn around a cell divided by the area of the cell itself. The box area ratio was found to increase abruptly during cell growth at the point of cell division as judged by eye (22). This allows the time of division to be measured objectively and opens up opportunities for systematic studies of the effects of previous history and current growth conditions on lag time distributions.

The aim of this work was to use the box area ratio method to determine the times to first division of individual *Escherichia coli* cells and thus examine the effect of heat injury to the inoculum and the salt content of the growth medium on lag time distributions of cells growing on an agar medium. We also determined the relative division time (RDT), which is a measure of the “work to be done” during lag, from direct observation of single cells.

## MATERIALS AND METHODS

Strain and growth conditions.Cultures of *Escherichia coli* W3110 were stored at −70°C in Microbank vials (Pro-Lab Diagnostics, Neston, United Kingdom). Stationary-phase inocula were prepared for image analysis experiments by placing a single bead in 10 ml tryptone soya broth (TSB; Oxoid, Basingstoke, United Kingdom) and incubating for 6 h at 37°C. This culture was then used to inoculate a 100-ml volume of TSB (0.1% [vol/vol]) that was incubated for 18 h at 37°C with shaking.

Microscopic observation of growing cells.Estimates of the times to first division of individual cells were made following the observation of cells growing on an agar surface, as described previously (22). Coverwell Press-Seal imaging chambers (Z 365866; Sigma-Aldrich Company, Gillingham, United Kingdom) were used to carry a thin layer of tryptone soya agar (TSA; Oxoid, Basingstoke, United Kingdom). These consisted of a 0.8-mm-thick silicone spacer gasket, incorporating a 20-mm circular well bonded to a polycarbonate microscope slide. TSA (27.5 μl) was added to the well and left to dry for 20 min under aseptic conditions. The agar was then inoculated with a drop (5 μl) of stationary-phase culture of *E. coli*, and a coverslip was placed over the well. Slides were incubated at room temperature (ca. 20°C) during observation of bacterial growth by phase contrast using a Nikon Microphot-SA microscope equipped with a ×20 objective lens. Digital images were captured at 10- to 20-min intervals using a CoolSNAP-Pro cf monochrome camera incorporating a 1,392-by-1,040 pixel charge-coupled device and 12-bit 20-MHz digitization.

Determination of times to first division of individual cells.The time from inoculation to the first cell division was taken as the measure of individual cell lag time. This was determined by automated processing of digital images to calculate the BAR, as described previously by Niven et al. (22). Digital images in TIFF format showing growing cells on agar were analyzed using Image-Pro Plus V4.5 image analysis software (Media Cybernetics). This identified each cell in the field of view and measured the parameters required to calculate the BAR (cell area, length, and width). These data, along with the *x* and *y* coordinates of each cell in the image, were downloaded into Microsoft Excel for further processing. A time course of BAR values was produced for each observed cell from the series of images. Since each image contained a large number of cells, a Microsoft Visual Basic program written in house was used to “track” individual cells through the sequence of images using the *xy* coordinates and to generate an Excel file containing time courses of area, length, and width for each cell (22). Another in-house Visual Basic program was used to calculate the BAR values as (length × width)/area and to identify the inflection points in plots of BAR against time, which had previously been shown to indicate the point of division (22). In order to increase the number of cells observed in each experiment, four fields of view were selected and the same fields were examined at each time point during an experiment. Data were thus generated for approximately 300 cells per experiment.

Where distributions of times to first cell division are shown, these are the results of a single experiment but are typical of the data produced by several replicate experiments. The Anderson-Darling test was used as a measure of how well data fitted each distribution using a maximum likelihood estimation. This was carried out using Minitab release 14.20 software (Minitab, Inc.).

Determination of RDT.The time to first cell division divided by the cell size doubling time was taken as a measure of RDT. This was calculated for individual cells by image analysis, the time to first division being determined by the BAR method as described above, while the size doubling time was that of the two-dimensional cell area. The increase in cell area was observed to follow an exponential pattern after an initial period of accelerating growth rate, thus enabling the doubling time to be calculated from the gradient of the linear portion of plots of log cell area against time. The period of logarithmic growth was identified in the measured area data for individual cells, and the associated cell area doubling times were calculated using a Visual Basic program written for the purpose. The values quoted in the text refer to the average RDTs determined for all of the cells in the analyzed population.

## RESULTS

Measurement of lag time distributions by the BAR method.Figure 1 shows the distributions of the times to first cell division for three separate experiments in which stationary-phase *E. coli* cells grown in TSB at 37°C were inoculated onto agar medium and grown at 20°C. In each experiment, four fields of view were examined and the average number of cells for which division times were obtained was 387 per experiment. All three experiments gave similar results, confirming the reasonable reproducibility of the method. On the basis of a normal distribution, the mean and standard deviation of the times to first division (taking the means of the values obtained for the three data sets) were 3.0 h and 0.7 h, respectively. In each case, the distribution appeared slightly asymmetrical with tailing toward the higher values. This was confirmed by an average skew value of 1.05, determined using Microsoft Excel; a symmetrical distribution would return zero and a positive skew indicated a bias toward higher values. However, fitting a variety of distribution equations to these data revealed no particular model that could be selected with any certainty over the others on the basis of the Anderson-Darling test (Table 1). These tests showed that normal, lognormal Weibull, logistic, log logistic, and smallest extreme value distributions fitted the data with 95% confidence levels for all three data sets (data not shown). The gamma distribution fitted one of the three on this basis, while the exponential distribution fitted none, being included to illustrate a poor fit. There is yet no consensus on the most appropriate distribution function to apply to lag time distributions (see Discussion), so for purely empirical reasons we have used the normal distribution since it fits the data adequately.

Effect of heat shock on lag time distributions.To investigate the influence of preinoculation stress on the distribution of times to first division, stationary-phase cells were heated at 50°C for various times prior to inoculation onto agar. The resulting distributions are shown in Fig. 2. The mean time to first division increased with the duration of heat stress in a near-linear fashion, from 3.0 h with no heating to 5.7 h after heating for 80 min (Fig. 3). This degree of heating did not result in significant cell death, and therefore all treatments were sublethal. The spread of lag time values was also larger at higher levels of stress, the standard deviations ranging from 0.7 h to 1.5 h. The coefficient of variation values (mean/standard deviation) were similar at each of the heating times investigated at 0.22 ± 0.05 (Fig. 3). This indicated that the spread of the distribution was proportional to the mean time to first division.

Effect of salt concentration in growth medium on lag time distributions.The distributions of times to first cell division were determined for cells growing in the presence of various concentrations of NaCl incorporated into the TSA medium. In this case, therefore, the stress was applied during growth, rather than before inoculation. Representative lag time distributions on inoculation into media containing 0.5%, 2.5%, 3%, and 4% NaCl (wt/vol) are shown in Fig. 4. These data were obtained using an average of 300 cells per experiment. As with preinoculation heat stress, the time to first division increased with the level of stress (Fig. 5), although the relationship was less linear than with heat stress as little increase was observed below 3% NaCl. The coefficient of variation was relatively constant at 0.20 ± 0.05 and similar to that observed on preinoculation heat stress (Fig. 5), showing that the spread of values within the distribution was directly proportional to the mean lag time.

Calculation of relative division times.The two-dimensional area growth curves of individual cells constructed during this study were characterized by two phases: a period of no growth or accelerating growth followed by exponential growth at a constant rate (data not shown). This enabled an estimate of the two-dimensional area doubling time to be made for each cell from the gradient of the linear portion of the plot of log area against time. The RDT for each cell was then calculated as the time to first division divided by the area doubling time.

The mean RDT for unstressed cultures was estimated as 1.8. In cultures that were heat stressed prior to inoculation, the RDT increased with the severity of the stress, rising to 4.3 after heating at 50°C for 80 min (Fig. 6a). This followed the pattern already described for the increase in the time to first division with the relative increase in time to first division and RDT being similar. The influence of postinoculation salt stress on RDT was comparatively slight, with no increase observed at salt concentrations less than 2.5% and an increase to 2.7 in the presence of 4% NaCl (Fig. 6b). In this case, the proportional increase in the RDT was lower than that of the time to first division. This indicated that the reduced growth rate of cells in the presence of elevated salt concentrations was a significant factor in increasing the time to first division, rather than the increased amount of work required to adapt to the new growth conditions. As with the time to first division, the standard deviations of all the RDT values for a given population were proportional to the mean value. The coefficients of variation for heat- and salt-stressed cells were 0.27 ± 0.04 and 0.27 ± 0.03, respectively. The coefficients of variation were thus relatively unaffected by the stress imposed on the cultures (Fig. 6).

Influence of stress on cell size at division.The mean cell areas of individual cells at inoculation and division were calculated for the population in each experiment. The means and standard deviations reported here were determined from these values for two to four replicate experiments. The environmental stresses investigated in this study had no significant influence on cell size at inoculation, which was 2.4 ± 0.1 μm^{2} for unstressed populations. This was to be expected for the salt-stressed cultures as they were identical to control cultures at inoculation, but it was also the case for heat-treated cultures that had been subjected to preinoculation stress. The mean and standard deviation cell areas at division were 5.4 ± 0.3 μm^{2} for unstressed cells. As shown in Fig. 7, there was relatively little effect of postinoculation salt stress on area at division, the mean value for all experiments being 5.5 ± 0.3 μm^{2}. In contrast, preinoculation heat stress resulted in a progressive increase in the cell size at division with increased duration of heating, rising to 6.7 μm^{2} after heating at 50°C for 80 min.

## DISCUSSION

By using digital-image analysis to determine the times to first division of individual cells, we have been able to measure objectively both the mean lag time of the population and the variation in lag times among single cells growing on an agar surface. The mean lag times and the variation about the mean increased with increasing duration of heat treatment and increased concentrations of sodium chloride in the agar growth medium. With heat treatment, the mean lag times and variation increased progressively with duration of treatment but with sodium chloride there was a threshold concentration below which no increase in lag was observed. The coefficient of variation (standard deviation divided by the mean) remained constant at about 0.2, independent of the severity or nature of the stress.

There have been relatively few investigations of individual-cell lag using direct observation methods, and most of these have examined *Listeria monocytogenes* or *Listeria innocua* (5, 11, 25). The only other study that we are aware of in which lag times of stressed cells were measured directly using a slide culture method is that of Rasch et al. (25), who observed an increase in lag time and its variance in *L. innocua* cells growing on agar medium in the presence of the antimicrobial molecule reuterin (β-hydroxypropionaldehyde). Wu et al. (32) also determined lag time distributions in single cells of *L. monocytogenes* by microscopy but did not examine the effect of stress treatments.

The effects of sodium chloride on individual-cell lag times of *E. coli* have been examined using the microscope flow chamber and were found to increase with increasing sodium chloride concentration, but quantitative values were not presented (5). There are insufficient published data available to determine if lag times measured on a solid agar surface are similar to those in liquid under all conditions, but Wu et al. (32) found that lag times of unstressed *E. coli* cells in broth measured in the Bioscreen were longer than those of cells on agar. Interestingly, the mean lag times of unstressed *E. coli* measured using the flow chamber at room temperature were 5 h (21), somewhat longer than the 3 h observed with unstressed cells in the current study. To some extent, such differences in the absolute division times between studies may reflect the criteria used to objectively determine the point of cell division. The BAR method is based on the degree of flexibility at the point of attachment of daughter cells (22), while the flow chamber method requires physical separation of the cells with detachment of one daughter from the matrix (5). Liquid media are generally considered to provide more favorable conditions for recovery of injured cells than solid media, and growth rates on agar were shown to be slower than those in liquid (4). On the other hand, Guillier et al. (8) found no differences in the lag of stressed cells on agar and in broth media. Cells in foods are immobilized in a solid matrix rather than being present as planktonic cells in a liquid, so it seems important to determine whether the physical environment affects lag behavior of individual cells and under what conditions this may occur.

The *E. coli* distributions observed in the current study were slightly skewed toward higher division times, which is a common feature of lag distributions (6, 7, 9, 12, 20, 26, 31). It was not possible to assign any particular mathematical description to the distributions, since good fits to the data were found for a range of different functions and the histograms of division times lacked sufficient resolution to distinguish between them. A wide range of distributions have been examined in other studies, but no one distribution has proven to be best for all stress conditions and environments. These include, for example, gamma (1, 6, 19), exponential (6), Weibull (6), lognormal (12, 15), and extreme value (7, 9, 29) distributions. Given the diverse physiological effects of different stresses and the extreme sensitivity of stressed cells to small changes in their growth environment (13), it is not surprising that lag behavior fails to conform consistently to a mathematical ideal. In addition, it is likely that current methods for measuring individual cell lag times do not offer sufficient precision to enable different distribution functions to be adequately differentiated on the basis of experimental observations. However, this also implies that, for predictive modeling purposes, the exact function used to describe the distribution of lag times may not be critical as long as a reasonable basis exists for establishing values for the required variables. That being the case, it is perhaps more appropriate to have a method that is “good enough” and that has a satisfactory theoretical basis rather than attempting to use a range of different empirical fits to experimental data to accommodate different sets of conditions.

In our experiments, the mean single-cell lag time divided by the standard deviation was consistently around 0.2 for heat-shocked or osmotically stressed *E. coli* cells. Relatively mild stresses were examined of necessity because microscopic methods are not suitable for use after severe pretreatments when only a small proportion of the visible population is viable. Coefficients of variation for single-cell lag times reported in the literature tend to increase according to the severity of the stress, reaching values of 0.8 to >1.0 (6, 9). Guillier and Augustin (9) found that the logarithms of the means and standard deviations of individual cell lag times were linearly related for a wide range of conditions. These authors showed that the product of the growth rate and lag time at the single-cell level was constant and could be taken as representative of the physiological state of the cells.

If lag time is expressed as a multiple of the population doubling time during exponential growth under the same conditions, the resultant quantity, known as the relative lag time, is a means of comparing on the same basis lag times under different environmental conditions (18, 27, 28). Relative lag time can be regarded as a measure of the “work to be done” to prepare for cell division and is analogous to the physiological state parameter (*h*_{0}) in the model of Baranyi and Roberts (2). To allow comparison of work to be done at the single-cell level, the time to first division was expressed as a multiple of the single-cell biomass doubling time, as estimated from the exponential increase in cell area. We have called this the RDT. Determinations of RDT indicated that to a large extent the extension of lag time of cells in the presence of NaCl was due to a reduction in the rate at which cells could grow, rather than additional time required to adapt to the conditions. This contrasted with heat-treated cells where the higher RTD values observed suggested greater amounts of work required to repair heat damage. For heat-injured cells, the cell size at division increased progressively with increasing degree of stress. For unheated cultures, the cells grew on average by a factor of 2.2 before first division, but after the most severe heat treatment this increased to 2.8, the area at division being 23% greater than for unstressed cells. Part of the work to be done may therefore be the need to achieve a larger cell size before division could take place. It is possible to speculate that the increase in size at division may be a result of a limiting step in the repair process that prevented cell division but not cell growth. The cells therefore grew to a larger size due to the additional time required complete this step. Kutalik et al. (11) also noticed that heat-shocked cells of *L. monocytogenes* needed to increase their length to 2.2. times their size at inoculation before division occurred. They also found that heat treatment caused a reduction in cell size in *L. monocytogenes*, which we did not observe with *E. coli*. So far as we are aware, there are no similar published data on relative lag based on direct measurements of single cells.

Despite the increasing number of studies of population heterogeneity among microbes, we remain ignorant of the underlying reasons for cell-to-cell variability. We propose that two classes of effect could give rise to such variability. The first is physiological or nongenetic heterogeneity within the population (3, 30). This arises from random differences in the distributions of molecules and macromolecular assemblies among cells that affect their capacity to withstand stress, to recover from stress, or to adapt to new growth conditions. The second class of effects is the stochastic variation in the interaction of cells with their environment both during and after exposure to stress. For example, in a heated suspension of cells the chances of a cell component being damaged or inactivated will be a probabilistic process (14). During recovery, differences in the microenvironment may also occur at longer distance scales, especially in nonhomogenous food material. The net result is that cells in a population may start out with inherent differences, and those differences may be compounded by variation in the degree of stress actually experienced by individual cells and by differences in their local recovery conditions.

Recent studies have begun to reveal how the scatter of properties within populations of cells is influenced by inoculum history and current growth conditions. This will lead to improvements in predictive models that can be used in quantitative risk assessments. This is particularly important when low numbers of pathogens in food pose a significant risk, as with highly infective pathogens such as *E. coli* O157 or with an organism such as *Listeria monocytogenes* that can grow to infective levels even under refrigeration. Further work is needed to understand the physiological basis of heterogeneity and the sequence of events that occur during lag. Direct observations of single-cell behavior, including measurements of physiological heterogeneity, under different conditions will undoubtedly contribute to that understanding.

## ACKNOWLEDGMENTS

This work was funded by the European Union Programme “Quality of Life and Management of Living Resources,” project no. QLK1-CT-2001-01145 (BACANOVA).

We are grateful to Antony Vannard for the statistical analysis of distribution function fits and to Aline Métris for helpful discussions on lag time distributions.

## FOOTNOTES

- Received 12 November 2007.
- Accepted 11 April 2008.
↵▿ Published ahead of print on 18 April 2008.

- American Society for Microbiology