Evidence for a bimodal distribution of Escherichia coli doubling times below a threshold initial cell concentration
- Peter L Irwin^{1}Email author,
- Ly-Huong T Nguyen^{1},
- George C Paoli^{1} and
- Chin-Yi Chen^{1}
DOI: 10.1186/1471-2180-10-207
© Irwin et al; licensee BioMed Central Ltd. 2010
Received: 28 January 2010
Accepted: 2 August 2010
Published: 2 August 2010
Abstract
Background
In the process of developing a microplate-based growth assay, we discovered that our test organism, a native E. coli isolate, displayed very uniform doubling times (τ) only up to a certain threshold cell density. Below this cell concentration (≤ 100 -1,000 CFU mL^{-1} ; ≤ 27-270 CFU well^{-1}) we observed an obvious increase in the τ scatter.
Results
Working with a food-borne E. coli isolate we found that τ values derived from two different microtiter platereader-based techniques (i.e., optical density with growth time {=OD[t]} fit to the sigmoidal Boltzmann equation or time to calculated 1/2-maximal OD {=t_{m}} as a function of initial cell density {=t_{m}[C_{I}]}) were in excellent agreement with the same parameter acquired from total aerobic plate counting. Thus, using either Luria-Bertani (LB) or defined (MM) media at 37°C, τ ranged between 17-18 (LB) or 51-54 (MM) min. Making use of such OD[t] data we collected many observations of τ as a function of manifold initial or starting cell concentrations (C_{I}). We noticed that τ appeared to be distributed in two populations (bimodal) at low C_{I}. When C_{I} ≤100 CFU mL^{-1} (stationary phase cells in LB), we found that about 48% of the observed τ values were normally distributed around a mean (μ_{τ1}) of 18 ± 0.68 min (± σ_{τ1}) and 52% with μ_{τ2} = 20 ± 2.5 min (n = 479). However, at higher starting cell densities (C_{I}>100 CFU mL^{-1}), the τ values were distributed unimodally (μ_{τ} = 18 ± 0.71 min; n = 174). Inclusion of a small amount of ethyl acetate to the LB caused a collapse of the bimodal to a unimodal form. Comparable bimodal τ distribution results were also observed using E. coli cells diluted from mid-log phase cultures. Similar results were also obtained when using either an E. coli O157:H7 or a Citrobacter strain. When sterile-filtered LB supernatants, which formerly contained relatively low concentrations of bacteria(1,000-10,000 CFU mL^{-1}), were employed as a diluent, there was an evident shift of the two populations towards each other but the bimodal effect was still apparent using either stationary or log phase cells.
Conclusion
These data argue that there is a dependence of growth rate on starting cell density.
Background
Understanding the behavior of bacterial growth parameters (duration of lag phase, specific growth rate, and maximum cell density in stationary phase) under various environmental conditions is of some interest [1]. In particular, knowledge about growth parameter population distributions is needed in order to make better predictions about the growth of pathogens and spoilage organisms in food [1–3]. In fact, probability-based methods, such as microbial risk assessment [1], have to take into account the distribution of kinetic parameters in a population of cells [4]. There is a paucity of growth parameter distribution data because of the large number of data points required to obtain such results. The utilization of traditional microbiological enumeration methods (e.g., total aerobic plate count or TAPC) for such a body of work is daunting. For this reason various methods have been developed which enable more rapid observations related to one, or more, growth parameters. Recently, growth parameter distribution characterization has mainly focused on the duration of lag phase [4–8]. For instance, Guillier and co-workers studied the effects of various stress factors (temperature, starvation, salt concentration, etc.) on individual cell-based detection times in Listeria monocytogenes[5, 6]. Additionally, reporting on improved methods, various workers [4, 7, 8] have presented frequency distribution information concerning lag phase duration of individual bacterial cells (Escherichia coli, L. monocytogenes, and Pseudomonas aeruginosa) on solid media. However, similar population-based information on specific growth rate is lacking.
The findings presented herein developed from work associated with the attachment of various Gram-negative bacteria to anti-Salmonella and anti-E. coli O157 immunomagnetic beads or IMBs [9–11]. For these IMB investigations microplate (OD-based) MPN methods were utilized because of the low limits of bacterial detection [12, 13] necessary to characterize the non-specific attachment of background food organisms to various capture surfaces. Because of large inter-bacterial strain variability in the time requisite to reach a measurable level of turbidity, we found it necessary to characterize the growth rate and apparent lag time (time to 1/2-maximal OD or t_{m}) [12] of certain problematic organisms. Toward this end we began a routine investigation into the best microplate reader method to determine doubling time (τ). However, while performing this work we noticed that our test organism, a native E. coli isolate which non-specifically adheres to certain IMBs [11], seemed to display very uniform τ values only up to a certain threshold initial or starting cell density (C_{I}) beyond which we observed an obvious increase in the scatter. A larger number of observations were then made after various physiological perturbations (media used, growth phase, etc.) which have lead to the results discussed in this report.
Results and Discussion
Doubling Times from both TAPC and Microplate Observations
Comparison of doubling time (= τ) observations based on total aerobic plate counting with growth time (= TAPC[t]), time to 1/2-maximal OD with growth time (= t_{m}[t]), and optical density at 590 nm with time (= OD[t]) in either LB broth or MM at 37°C.
Method | τ (min) -- LB | ||||
---|---|---|---|---|---|
Exp. 1 | 2 | 3 | average | F_{2,4} | |
TAPC[t] | 18.6 | 17.3 | 18.1 | 18.0 | 3.43 |
t_{m}[Φ_{i}] | 17.1 | 17.4 | 16.8 | 17.1 | P > 0.1 |
OD[t] | 17.9 | 17.9 | 17.7 | 17.8 | |
Method | τ (min) --MM | ||||
Exp. 1 | 2 | 3 | average | F2,4 | |
TAPC[t] | 52.7 | 50.1 | 51.9 | 51.6 | 0.886 |
t_{m}[Φ_{i}] | 50.8 | 59.9 | 52.1 | 54.3 | P >> 0.1 |
OD[t] | 50.1 | 53.8 | 49.4 | 51.1 |
Effect of Initial or Starting CFU Concentration on τ
It is important to keep in mind throughout this work that by the time we begin to observe an increase in OD (and therefore measure τ via Eq. 1), somewhere between 2 and 20 doublings will have occurred. This fact implies that the values we observe are somehow modulated based upon initial conditions. It should also be noted that low bacterial C_{I}s (i.e., ≤ 5 CFU mL^{-1}) would result in at least some single CFU occurrences per well (i.e., the average probability of observing 1 CFU per well should be about 32.0 ± 6.65%) at which point the first few events of cell division could modulate characteristics of both τ and true microbiological lag time (T). Thus, some of the increase in τ and T scatter we observe at low C_{I} could result from the random selection of isolates with particularly slow growth rates which would otherwise be masked by other isolates in the media with faster rates. However, arguing against such a stochastically-based explanation is the fact that a significant fraction of the scatter in τ (Figs. 2 and 4) occurs between C_{I} = 10-100 CFU mL^{-1} whereupon the probability of observing 1 CFU per well only ranges from 18.1 to ca. 0%. Under these conditions the random selection of one particular τ-component would be overwhelmed by the sheer number of other cells present. At slightly higher concentrations (e.g., 2 or 3 CFUs per well), any well which has 2 or 3 cells with τ values differing more than about 4 or 5 min would be obvious in the ∂OD[t]/∂t curves as additional peaks. Nevertheless, we just don't observe such behavior at these low C_{I}s. What we do observe are relatively uniform, monotypic growth curves (examples in Methods Section) indicative of one component (or, if more than one, the Δτs are small). The fact that we see much greater τ-based scatter at a relatively large threshold C_{I} argues that there is some other controlling factor in determining such binomial-based population growth rates.
Comparison of doubling time distribution parameters (Eq. 1) for E. coli, E. coli O157:H7, and Citrobacter in LB, LB + ethyl acetate (EA, 75 mM), or MM at 37°C; S = Stationary phase, L = Log Phase.
C_{I} ≤ 100 CFU mL^{-1} | C_{I} ≥ 1000 CFU mL^{-1} | ||||||
---|---|---|---|---|---|---|---|
Organism (phase) | Medium LB | α | μ_{τ 1} ± σ_{τ1} | β | μ_{τ2} ± σ_{τ2} | Δμ_{τ} | μ_{τ} ± σ_{τ} |
E. coli (S) | LB | 0.48 | 18.0 ± 0.678 | 0.52 | 19.9 ± 2.48 | 1.87 | 17.6 ± 0.708 |
E. coli (L) | LB | 0.35 | 18.2 ± 0.660 | 0.65 | 20.0 ± 2.11 | 1.79 | 17.9 ± 0.645 |
E. coli (L) | LB+EA | 0.15 | 19.6 ± 0.999 | 0.85 | 21.7 ± 2.25 | 2.13 | 21.4 ± 2.06 |
E. coli (L) | MM | 0.30 | 51.1 ± 1.75 | 0.70 | 56.9 ± 8.32 | 5.77 | 52.0 ± 2.09 |
E. coli O157:H7 (L) | LB | 0.40 | 18.5 ± 0.401 | 0.60 | 20.1 ± 2.01 | 1.60 | 18.1 ± 0.438 |
Citrobacter (L) | LB | 0.6 | 42.5 ± 3.75 | 0.40 | 50.7 ± 6.50 | 8.24 | 42.4 ± 3.72 |
Comparison of doubling time distribution parameters (Eq. 1) for E. coli in LB, or in LB with sonicated and heat-killed cells at 37°C; S = stationary phase, L = Log phase.
C_{I} ≤ 100 CFU mL^{-1} | C_{I} ≥ 1000 CFU mL^{-1} | |||||
---|---|---|---|---|---|---|
Organism (phase) | α | μ_{τ1} ± σ_{τ1} | β | μ_{τ2} ± σ_{τ2} | Δμ_{τ} | μ_{τ} ± σ_{τ} |
Control LB (S) | 0.48 | 18.0 ± 0.678 | 0.52 | 19.9 ± 2.48 | 1.87 | 17.6 ± 0.708 |
Conditioned LB (S) | 0.21 | 17.8 ± 0.553 | 0.79 | 18.8 ± 1.99 | 1.03 | 17.5 ± 1.06 |
Control LB (L) | 0.35 | 18.2 ± 0.660 | 0.65 | 20.0 ± 2.11 | 1.79 | 17.9 ± 0.645 |
Conditioned LB (L) | 0.31 | 19.1 ± 0.627 | 0.69 | 20.1 ± 2.10 | 0.994 | 18.9 ± 0.700 |
Sonicated, Heat-killed Cells in LB (L) | 0.54 | 21.0 ± 0.690 | 0.46 | 21.3 ± 2.58 | 0.300 | 21.1 ± 0.646 |
Conclusion
Working with a native, food-borne E. coli isolate grown in either LB or MM, we found that microplate-based doubling times were bimodally distributed at low cell densities using either log or stationary phase cells as an initial inoculum. Qualitatively identical results were obtained for an E. coli O157:H7 and Citrobacter strain. When sterile-filtered 'conditioned' LB media (formerly contained relatively low concentrations of bacteria or sonicated/heat-killed cells) were employed as a diluent, there were apparent shifts in the two (narrow and broad) populations but the bimodal effect was still evident. However, the bimodal response was almost completely reversed when the growth media contained a small amount of ethyl acetate.
The clear doubling time-cell concentration dependency shown in these results might indicate that bacteria exude a labile biochemical which controls τ, or a need for cell-to-cell physical contact. The latter proposal seems unlikely inasmuch as the probability of random contact would be small at such low cell densities (C_{I} ~ 100-1,000 CFU mL^{-1}). Perhaps this anomalous bimodal distribution of doubling times is related to the recently proposed phenotypic switching [14, 15] which describes programmed variability in certain bacterial populations.
Methods
General
Escherichia coli (non-pathogenic chicken isolate) [11], E. coli O157:H7 (CDC isolate B1409), and Citrobacter freundii (non-pathogenic poultry isolate; identification based on 16 S rDNA analysis) [16] were cultured using LB (Difco) or MM (60 mM K_{2}HPO_{4}, 33 mM KH_{2}PO_{4}, 8 mM (NH_{4})_{2}SO_{4}, 2 mM C_{6}H_{5}O_{7}Na_{3} [Na Citrate], 550 μM MgSO_{4}, 14 μM C_{12}H_{18}C_{l2}Na_{4}OS [Thiamine•HCl], 12 mM C_{6}H_{12}O_{6} [glucose], pH 6.8). Liquid cultures were incubated with shaking (200 RPM) at 37°C for ca. 2-4 (for log phase cultures) or 18 hrs (stationary phase cultures) using either LB or MM. All total aerobic plate counts (TAPC) were performed using the 6 × 6 drop plate method [17] with LB followed by incubation at 20-22°C (lab temperature) for 16-18 hours. Using Microsoft Excel's formulaic protocol, the TAPC-based doubling time = 1/LINEST(LOG(TAPC_{1}:TAPC_{n},2),t_{1}:t_{n}) where the values TAPC_{1} through TAPC_{n} are log-linear with respect to associated growth times t_{1} to t_{n}; n was typically 6-8 points. All TAPC studies were performed using highly diluted stationary phase cells (initial colony forming unit [CFU] concentration or C_{I} ≥ 10^{3} CFU mL^{-1}) in either LB or MM.
Steady State Oxygen
O_{2} levels ([O_{2}], units of μM) were measured using a Clark-type oxygen electrode (Model 5300, Yellow Spring Instruments) connected to a Gilson water-jacketed chamber (1.42 mL; circulating water bath attached, 37°C) containing a magnetic stirring bar. Air-saturated 37°C water was used for calibration. To determine steady-state [O_{2}] in shaking/bubbled cultures, samples were withdrawn with a syringe from bacterial culture flasks at various time points during mid-to late-log phase growth, and the oxygen consumption (e.g., [O_{2}] dropping with time) determined without vortexing. The time lapse between sample withdrawal and the first [O_{2}] data point was recorded and used to back-calculate the [O_{2}] at the time of sampling. These same samples were then vortexed ca. 15 sec and [O_{2}] measured again as a function of time. The rate of O_{2} consumption was calculated from the slope of cell density-normalized [O_{2}] (TAPC plating was performed simultaneously on LB) as a function of time (apparent K_{m} ~ 15 ± 6 μM) [18].
96-well Microplate Protocol
In order to avoid water condensation which might interfere with absorbance readings, the interior surface of microplate covers were rinsed with a solution of 0.05% Triton X-100 in 20% ethanol [12] and dried in a microbiological hood under UV light. About 270 μL of each bacterial cell concentration was pipetted into every well. Each initial concentration (C_{I}) is equal to C_{0} Φ_{I} where C_{0} is the cell density from liquid culture (either log or stationary phase). When C_{0} ≤ 10^{8} CFU mL^{-1}, the cells were sampled from an early-to mid-log phase culture. When C_{0} ≥ 10^{9} CFU mL^{-1}, the cells were sampled from a stationary phase culture. Typically, each 96-well microplate contained 2 replicates each of the 8 least dilute samples (Φ = 3×10^{-3} to 5×10^{-6}; 16 wells), 4 replicates of the next 4 highest dilutions (Φ = 2×10^{-6} to 5×10^{-7}; 16 wells), 8 replicates each of the following 2 dilutions (Φ = 2×10^{-7} or 1×10^{-7}; 16 wells), and, lastly, 24 replicates of the 2 most dilute samples (Φ = 6×10^{-8} or 3×10^{-8}; 48 wells). The 96-well plate was then covered with the Triton-treated top, placed in a temperature-equilibrated Perkin-Elmer HTS 7000+ 96-well microplate reader, and monitored for optical density (OD) under the following conditions: λ = 590 nm; the time between points (Δt) = 10-25 min; total points = 50-110; temperature = 37°C; 5 sec of moderate shaking before each reading (see Results section). These dilutions, listed above, produced at least some negative (no growth) readings mainly associated with the 4 most dilute sets of wells. This lack of growth in wells associated with these dilutions is evidence for single CFU-based growth occurrences at these low C_{I}. Thus, these low C_{I} have been diluted to such a degree that at least an occasional random sampling of 270 μL should contain no cells at all. Generally speaking, the most probable number (single dilution MPN) calculation for these dilutions agreed with the plate count estimate. The variability of growth parameters at such low concentrations (~ 1 CFU/well) has generated much recent interest [4, 6–8].
Calculations
While Eq. 1 is an empirical equation, it does rely on a first order rate constant (k) therefore the doubling time can be extracted as τ = k^{-1} Ln [2]. All curve-fitting was performed using a Gauss-Newton algorithm on an Excel spreadsheet [20]. In Eq. 1, OD_{I} is the estimated initial optical density (0.05-0.1), OD_{F} is the calculated final OD (0.5-0.7), k is the first-order rate constant, and t_{m} is the time to OD_{F} ÷ 2. The Boltzmann relationship appears to be generally useful with optically-based growth results since excellent fits were achieved (21°C growth in LB, τ = 3.26 ± 0.0292 hrs) when Eq. 1 was utilized to fit previously published [21] bacterial growth data from a microchemostat.
As demonstrated previously [12], t_{m} can be used (for high C_{I}) as a method for estimating cell density. The inset plot in Fig. 8 shows both OD and first derivative (ΔOD/Δt) versus time data sets that were typically observed when growing our native E. coli isolate in MM. In order to achieve the best fit in the region which provides the most information (i.e., the exponential increase in OD), we have truncated these data and used only 2-10 points beyond the apparent t_{m} to fit to Eq. 1. Such data abbreviation had only minor effects on the growth parameters: e.g., if the OD[t] data points in the main plot of Fig. 8 were truncated to only 3 points past the calculated t_{m}, τ would change only from ~ 19.2 to 19.8 min and t_{m} only by 0.7 min. All values of τ and t_{m} reported herein are derived from such curve-fitting. Of course, t_{m} can also be estimated from the x-axis value where the center of symmetry in ΔOD/Δt occurs (Fig. 8). We have tested two other microplate readers (Bio-Tek EL 312e and Tecan Safire II) in order to determine the variability in τ (from OD[t] data; C_{I} > 1000 CFU mL^{-1}) due to the devices themselves. The Perkin-Elmer instrument consistently gave the lowest τ values (τ = 18 ± 0.99 min) followed by the Bio-Tek (τ = 19 ± 1.0 min) and Tecan (τ = 21 ± 1.2 min); {Error Mean Square ÷ n} ^{1/2}. = 0.42. It seems likely that the observed plate reader-associated differences in τ are due to instrument-based disparities in temperature.
and a plot of t_{m} with Log_{2} [CI] is linear (Excel τ = ABS (LINEST(t_{m,1}:t_{m,n}, LOG(C_{I,1}:C_{I,n},2)))) with a slope equal to -τ and an intercept of (T + Log_{2} [C_{F}/2]).
Eq. 6 implies that the time in lag phase (T) can be obtained knowing τ, C_{F}, and the intercept from a plot of t_{m} as a function of Log_{2} [C_{I}]. When numerous values of t_{m} are plotted against C_{I} (semi-log plot shown in Fig. 3) by diluting either log or stationary phase cells in LB one sees a significant perturbation in T (offsets in the intercept) of the semi-log plots (10^{2} < C_{I} < 10^{7} CFU mL^{-1} region only). T calculations (Eq. 6) from the growth of stationary phase-diluted cells (T = 41 ± 8.4 min; average of 10 experiments; C_{I} > 10^{2} CFU mL^{-1}) indicate that T was similar to lag times calculated from TAPC experiments (63 ± 9 min; average of 7 experiments). However, T values calculated in a similar fashion from log phase-diluted cells produced near-zero values (T = -11 ± 15 min; average of 8 experiments; C_{I} > 100 CFU mL^{-1}). Thus, the total offset between log and stationary phase-derived cells shown in Fig. 3 was about 52 min and implies that stationary phase cells require about an hour to revert to log-phase. However, because of the variability in the intercept and C_{F}, we believe that the value of T using Eq. 6 has only a relative meaning. In other words, Eqs. 5 & 6 show that variability in t_{m} can be due to either variability in T, τ or both.
In Eq. 7, α is the fraction of the population associated with mean μ_{τ1} and standard deviation σ_{τ1}; a second Gaussian is characterized by β (= 1 - α), μ_{τ2}, and σ_{τ2}.
Regarding other statistical methods used in this work: analysis of variance tables were generated using Microsoft Excel and standard statistical formulae for a randomized complete block design. Values for F were taken from a college-level statistics table of F-values.
Declarations
Acknowledgements
All funding was from ARS base funds associated with Current Research Information System (CRIS) Project Number 1935-42000-058-00 D (Integrated Biosensor-Based Processes for Multipathogenic Analyte Detection).
Authors’ Affiliations
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