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Cell-cycle research with synchronous cultures: An evaluation
Biochimie 83 (2001) 83−89 © 2001 Société française de biochimie et biologie moléculaire / Éditions scientifiques et médicales Elsevier SAS. All rights reserved. S0300908400012293/REV
Cell-cycle research with synchronous cultures: An evaluation Charles E. Helmstettera, Maureen Thorntona, N.B. Groverb* b
a Department of Biological Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA Hubert H. Humphrey Center for Experimental Medicine and Cancer Research, Hebrew University Faculty of Medicine, P.O. Box 12272, Jerusalem 91120, Israel
(Received 7 November 2000; accepted 24 November 2000) Abstract — The baby-machine system, which produces new-born Escherichia coli cells from cultures immobilized on a membrane, was developed many years ago in an attempt to attain optimal synchrony with minimal disturbance of steady-state growth. In the present article, we put forward a model to describe the behaviour of cells produced by this method, and provide quantitative evaluation of the parameters involved, at each of four different growth rates. Considering the high level of selection achievable with this technique and the natural dispersion in interdivision times, we believe that the output of the baby machine is probably close to optimal in terms of both quality and persistence of synchrony. We show that considerable information on events in the cell cycle can be obtained from populations with age distributions very much broader than those achieved with the baby machine and differing only modestly from steady state. The data presented here, together with the long and fruitful history of findings employing the baby-machine technique, suggest that minimisation of stress on cells is the single most important factor for successful cell-cycle analysis. © 2001 Société française de biochimie et biologie moléculaire / Éditions scientifiques et médicales Elsevier SAS baby machine / cell cycle / distribution of cell interdivision times / model for synchronous growth of Escherichia coli / synchronous growth parameters
1. Introduction Much of our understanding of the events in the bacterial cell cycle originates from use of the baby machine culture technique. In this procedure, described in detail by Helmstetter [1], Escherichia coli cells are grown immobilised on the surface of a membrane such that division results in the release of new-born cells into culture medium passing through the membrane. That methodology was successful for two main reasons. First and foremost, this way of producing synchronous new-born cells causes minimal disturbance to cultures in steadystate growth, enabling the physiological state of the cells to be reasonably well-defined. In addition, much of the early work involved measurements of the rate of DNA replication during the cell cycle using the technique in age classification mode. In that form of the method, cultures were pulse-labelled with radioactive thymidine prior to immobilisation, and then the level of incorporation was measured in the progeny cells released from the surface. The cells eluted during the first generation were the daughters of the successively younger cells initially deposited on the membrane, those eluted during the second generation were their granddaughters, and so on. Thus, the rates of incorporation of the labelled compound into cells * Correspondence and reprints. E-mail address: [email protected] (N.B. Grover).
of different ages in the cycle were determined by measuring the amount of label in their progeny. A major advantage of this approach is that the label was added while the cells were in undisturbed steady-state growth, the only subsequent requirement being that the cells divide in the same sequence while immobilised that they would have done in the original culture prior to immobilisation [1]. The second reason for the success of this technique is the high purity of the new-born cells released from the membrane, as judged by the ease with which periodic events in the cell cycle can be detected [2, 3]. By collecting samples of the effluent over time and growing them, one can also use the baby machine to produce highly synchronous cultures for cell-cycle analysis [1]. The similarity of findings obtained with such synchronously growing E. coli cells and those from the age classification method [4], and successful applications of this approach to different strains and species [5, 6], indicate that the additional growth of the cells does not materially disturb their physiological state. This has generally not been the case with methods that involve treatments designed to induce synchronised growth in growing cultures, such as periodic changes in temperature or in nutrient conditions. Although there have been occasional reports of very highly synchronised cell divisions over many generations with such treatments [7–9], to our knowledge these techniques have never been used to further our understanding of the division cycle. They do
84 not provide information on the undisturbed steady-state cycle because the totality of cell processes are not aligned [10] and so any apparent synchrony that is achieved would be compromised by the response to the treatment of whatever cell property is under investigation. They are also difficult to reproduce. Experiments involving the alignment of chromosome replication by shifts in temperature of temperature-sensitive, initiation-defective mutants [11], aimed at correlating biosynthetic processes with synchronised chromosome replication, may be an exception so long as it is recognised that the cells in such cultures are not synchronous in overall cell mass nor in mass synthesis. If indeed the baby machine produces a high level of selection of minimally disturbed new-born cells, the resulting synchronous growth of the cells most likely approaches the highest quality and duration of synchrony achievable with E. coli. The purpose of this paper is to provide data on the extent of synchronous cell division over multiple generations achievable with baby machinegenerated new-born cells at each of four different growth rates. Quantitative assessments of the parameters of the synchronous growth are presented using an extension of the model described previously [12]. It is further shown that considerable information on events in the cell cycle can be obtained from populations with age distributions differing only modestly from steady state, suggesting that achievement of minimal physiological disturbance is more important for cell-cycle studies than quality or persistence of synchrony. 2. Materials and methods Cultures of E. coli B/r A (ATCC 12407) were grown in minimal salts medium [2] supplemented with 0.1% glucose plus 0.2% Casamino acids (Difco, USA), 0.1% glucose, 0.1% glycerol, or 0.2% sodium succinate. The baby-machine technique was used to obtain synchronous cultures [1]. Briefly, 100 mL of minimal medium was inoculated with bacteria from a fresh stationary-phase stock, diluted approximately 1:1000, and incubated in a shaking water bath at 37 °C until the cells were in steady-state growth. When a culture reached a concentration of approximately 5 × 107 cells/mL, it was filtered onto the surface of a type GS 142 mm-diameter membrane filter (Millipore, USA) in an incubator at 37 °C. The filter was then inverted and elution with fresh medium begun. After a delay that depended on the composition of the culture medium, an aliquot was collected from the effluent in a 50-mL culture flask (Bellco, USA) and placed in a 37 °C shaking water bath. Samples were collected from the culture flask at intervals and diluted in Isoton II (Beckman-Coulter, USA); cell concentrations were determined with a model ZB electronic particle counter (Beckman-Coulter, USA).
Helmstetter et al. 3. The model The cell populations eluted from the membrane were taken as being composed of two components. The age of the major component was assumed to be normally distributed about zero with a standard deviation σ. The minor component, of relative size q, was considered to consist of cells that had undergone only very little age selection during the elution process: the number of these random a/sfl cells was set proportional to 2 , where a is the age of the eluted cell at the time of collection (t=0) and sfl is the observed doubling time of the culture. These are bacteria released from the membrane for reasons other than division, such as weak binding. It also proved necessary to introduce a fixed background β to account for the signals recorded by the electronic particle counter that were produced not by viable, replicating cells but by the debris and electronic noise that are invariably associated with such measurements. This, together with a proportionality constant k, constituted the original form of the model [12]; it proved inadequate once we began considering more than one generation. First it became apparent that the initial doubling sometimes took place a little earlier than subsequent ones, sometimes a little later. We introduced a time shift δ to allow for the differences between collection time and sampling time that can arise in a multi-sample experiment of this type. The second addition to the original model was more fundamental. The dispersion σ of the new-born subpopulation accounted rather well for the transition period as long as we limited ourselves to a single generation time. When we began studying several generations, however, a value of σ suitable for the first transition period systematically undercorrected for the second whereas a value suitable for the second overcorrected for the first. That was because the sharpness of the transition decreases from doubling to doubling and cannot be accommodated by a fixed σ. In order to allow for such deterioration, we introduced dispersion into the interdivision times as well: τ is distributed about sfl with a coefficient of variation cv(τ). The form of this distribution, for both cellular components, was assumed to be a Pearson type III (incomplete gamma function) rather than a normal distribution because of the widespread observation that f(τ) is skewed to the right and the solid experimental studies of Powell [13].
4. Synchronous cell division at four different growth rates The model described above was fitted to the synchronous growth data obtained from the baby machine for E. coli B/r A cells growing at four different doubling times, using an unconstrained non-linear least-squares algorithm
Cell-cycle research with synchronous cultures [14]. A plot of the experimental points for a sample of new-born cells growing in glucose plus Casamino acids is presented in figure 1a together with the predicted curve. The fit was restricted to the first two generations, where its quality is rather good; extrapolation beyond that point shows a clear tendency of the data to drop further and further below the theoretical curve as time increases. It was thought that this trend may be attributed at least in part to the increased coincidence within the electronic particle counter orifice that occurs at higher cell concentrations, and so the experiment was repeated with two-fold dilutions at the times indicated (figure 1b) and the model refitted using all the data points, over four generations. Now the fit is excellent. The results are summarized in table I. The sum of squares of the residuals in both cases is less than 0.1% of the total (P < 0.001) and they are distributed randomly
Figure 1. Cell concentrations and rates of cell division during growth of baby machinegenerated E. coli B/r A cells in glucoseCasamino acids minimal medium. a. Data. A sample of the effluent containing 11 × 106 cells/mL was collected at between 18 and 19 min of elution and incubated at 37 °C in a shaking water bath; aliquots were withdrawn at indicated times and diluted a 100-fold throughout the experiment. Curve. Unconstrained nonlinear least-squares fit, to first 26 data points, of model combining three theoretical subpopulations: a major component with age normally distributed about zero (standard deviation σ), a minor component that had undergone very little age selection (of relative size q), and a fixed background (β) of non-cellular material; in addition, model assumes that the interdivision time τ follows a Pearson type III distribution (coefficient of variation cv(τ)), and it includes a time shift (δ) to allow for differences between collection time and sampling time. Parameter estimates are as indicated; standard errors and quality of fit statistics appear in table I. Axes. Left-hand ordinate: cell concentration (millions/mL, log scale); right-hand ordinate: rate of cell division (millions/min/mL), equivalent to rate of cell number increase and obtained by numerical differentiation of concentration curve and of data points. b. Data. As in (a) except that sample contained 17 × 106 cells/mL and that dilution levels were doubled at 35 min and again at 55 min and at 79 min, marked by arrows. Curve. As in (a) but model fit to all data points. Parameter estimates are as indicated; standard errors and quality of fit statistics appear in table I. Axes. As in (a).
85 (P > 0.15), as determined by a one-tail runs test. The size of the random subpopulation q is small and so is the background β; both parameters are well-defined. The time shift δ is not far from zero. What is particularly interesting, apart from the superb fit of the dilution data itself, is the fact that σ the standard deviation at t = 0 of the age of the new-born cells that comprise the synchronous subpopulation, is zero: all the dispersion in each of the four transition periods can be fully accounted for by the variation in the interdivision-time distribution cv(τ). Synchronous growth data are plotted in figure 2 together with the predicted curves based on the first 26 points (like in figure 1a), for cells cultured in glucose, glycerol, and succinate minimal medium; the results also appear in table I. All three fits are very good but as the doubling time increases, the discrepancies between the theoretical curves and the experimental points in the
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Table I. Statistics of fit of theoretical model to experimental data obtained from the baby machine for E. coli B/r A cells growing at different doubling times. Entity
Units
Figure sfl a Residualsb P (runs)c β ± sed δ ± see q ± sef σ ± seg cv(τ) ± seh
Min % – % Min % % %
Glucose-Casamino acids 1(a) 22 0.037 0.183 4.7 ± 0.8 –1.3 ± 0.1 4.8 ± 1.6 0 13.7 ± 0.4
1(b) 24 0.028 0.638 2.3 ± 0.7 0.6 ± 0.1 6.3 ± 2.3 0 12.7 ± 0.4
Glucose
Glycerol
Succinate
2(a) 41 0.078 0.286 11.3 ± 1.2 1.6 ± 0.3 10.5 ± 3.3 8.6 ± 3.0 9.4 ± 1.8
2(b) 50 0.160 0.769 9.2 ± 1.4 0 4.5 ± 3.7 0 12.3 ± 0.9
2(c) 82 0.070 0.723 12.1 ± 1.1 4.6 ± 0.4 18.7 ± 2.0 11.6 ± 1.7 4.5 ± 2.9
a
Observed doubling time of culture. Sum of squares of residuals, expressed as percentage of total variation in measured variable. Single-sided runs test: probability that signs of residuals are distributed randomly. d Relative size and standard error of fixed background of non-cellular material. e Size and standard error of time shift between collection time and sampling time. f Relative size and standard error of minor component of eluted cells that had undergone very little age selection. g Standard deviation and its standard error, expressed as percentages of sfl , of age distribution of major component of eluted cells, assumed to be normally distributed about zero. h Standard deviation and its standard error, expressed as percentages of sfl , of interdivision-time distribution of all eluted cells, assumed to follow a Pearson type III distribution. b c
extrapolated region become larger and larger; there does not, however, appear to be any deterioration in the precision with which the various parameters can be estimated. The fit in the case of glycerol is remarkably similar to that in glucose plus Casamino acids, except for the higher background, but the other two growth media produce higher proportions of the random subpopulation as well as higher backgrounds. The fit in glucose covers two full transition periods and the apportionment of the variance between σ and cv(τ) is clear and well-defined. The larger doubling time in the case of succinate means that the second transition period is not completely covered by the first 26 points of the fit, and there is not sufficient information to determine cv(τ) with any precision; thus, although it is much smaller than the other entries for this parameter, its standard error is by far the largest.
cell-cycle biosynthetic event with a distribution like that of cell division could easily be detected in such baby machine-generated synchronous cultures. The question then arises as to how far the cultures can depart from perfect synchrony before the information content of the differential curves becomes unusable. Figure 3 contains predicted cell concentration curves together with the associated rates of cell division, for a series of simulated populations extending from pure synchronous (q = 0) all the way to near uniform (q = 1). The parameter values were taken from figure 2a and, in fact, the curves for q = 0.105 in the two figures are identical. There is no essential deterioration in the information obtainable between a q of zero and a q of 0.25; even with much larger values, up to and including unity, there is clear structure in the rate curves, suggesting that any cell-cycle event coupled to cell division, would also be detectable in such asynchronous cultures.
5. Information content in asynchronous cultures An underlying assumption in cell-cycle research employing synchronous cultures has been that high quality, long-lasting synchrony is crucial. This view no doubt led to the many and varied efforts to produce such cultures through induction techniques. With this in mind, we attempted to determine just what cell-cycle information might be available in cultures that ranged from highly synchronous to near steady state. We added plots of the rate of cell division, obtained by numerical differentiation of the corresponding concentration curves, to each of the panels in figures 1 and 2. From these, it is clear that any
6. Discussion The data presented here are representative of the quality and persistence of the synchrony of cell division obtainable with the baby-machine technique. This procedure was originally developed with the idea that a successful elucidation of the cell-cycle properties of bacteria in steady-state growth would require methodology that caused only minimal disturbance to normal cell physiology. Based on many years of successful cell-cycle analyses with the technique, independently verified by non-
Cell-cycle research with synchronous cultures
Figure 2. Cell concentrations and rates of cell division during growth of baby machinegenerated E. coli B/r A cells in various media. a. Data. Glucose medium. A sample of the effluent containing 14.44 × 106 cells/mL was collected at between 36 and 38 min of elution and incubated at 37 °C in a shaking water bath; aliquots were withdrawn at times indicated. First 16 aliquots, spanning initial 62 min, were diluted a 100-fold; at 62, 102, 142, 182 min, marked by arrows, dilution levels were doubled. Curve. Unconstrained non-linear least-squares fit, to first 26 data points, of model combining three theoretical subpopulations: a major component with age normally distributed about zero (standard deviation σ), a minor component that had undergone very little age selection (of relative size q), and a fixed background (β) of non-cellular material; in addition, model assumes that the interdivision time τ follows a Pearson type III distribution (coefficient of variation cv(τ)), and it includes a time shift (δ) to allow for differences between collection time and sampling time. Parameter estimates are as indicated; standard errors and quality of fit statistics appear in table I. Axes. Left-hand ordinate: cell concentration (millions/ mL, log scale); right-hand ordinate: rate of cell division (millions/min/mL), equivalent to rate of cell number increase and obtained by numerical differentiation of concentration curve and of data points. b. Data. Glycerol medium. As in (a) except that sample contained 5.28 × 106 cells/mL and that cells were collected at between 45 and 47 min of elution; aliquots were diluted a 100-fold throughout the experiment. Curve. As in (a). Parameter estimates are as indicated; standard errors and quality of fit statistics appear in table I. Axes. As in (a). c. Data. Succinate medium. As in (a) except that sample contained 9.52 × 106 cells/mL and that cells were collected at between 65 and 69 min of elution; aliquots were diluted a 100-fold throughout the experiment. Curve. As in (a). Parameter estimates are as indicated; standard errors and quality of fit statistics appear in table I. Axes. As in (a).
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Figure 3. Predicted cell concentrations and associated rates of cell division. Simulation of model combining three theoretical subpopulations: a major component with age normally distributed about zero (standard deviation σ), a minor component that had undergone very little age selection (of relative size q), and a fixed background (β) of non-cellular material; in addition, model assumes that the interdivision time τ follows a Pearson type III distribution (coefficient of variation cv(τ)), and it includes a time shift (δ) to allow for differences between collection time and sampling time. Five different levels of q are shown: 0%, 10.5%, 25%, 50%, 100%; other parameter values as in figure 2a. Left-hand ordinate: cell concentration (millions/mL, log scale); right-hand ordinate: rate of cell division (millions/min/mL), equivalent to rate of cell number increase and obtained by numerical differentiation of corresponding concentration curve.
synchrony methods [15], and the material presented here, we believe that this goal has been achieved. Since the baby machine produces cells that are in minimallydisturbed steady-state growth, and the eluted population usually consists of 90% or more pure new-born cells, the resulting synchrony is probably very close to optimal for E. coli. If, therefore, plots are published containing synchronous cell divisions with sharper steps, flatter plateaus, longer durations, we maintain that such cultures have been disturbed or that the measurements are faulty. There have been many attempts over the years to develop new methods or to modify existing ones in order to achieve a synchronised growth that was very precise and very persistent. Generally, these efforts have not yielded new information on the cell cycle because either they disturbed cell growth or they were not reproducible [10]. The one exception to this involves those techniques that employ temperature-sensitive, initiation-defective mutants to align chromosome replication. When such mutants are shifted from permissive temperature (30 °C) to non-permissive temperature (40 °C) for at least C min (the time required to replicate the chromosome – about 40 min in E. coli at 40 °C), ongoing rounds of chromosome replication are completed but new rounds cannot initiate.
Upon shift back to permissive temperature, chromosome replication is synchronised. This technique has therefore proved useful in examining cell properties specifically connected to chromosome replication, such as the methylation state of newly replicated chromosomal DNA [16, 17]. There is also a partially synchronised cell division C + D min (this is the time that elapses between initiation of chromosome replication and the subsequent cell division – about 110 min in E. coli at 30 °C) after synchronised initiation of replication [18], which could be useful for studying processes coupled to cell division. It must be emphasized, however, that overall growth is not synchronized by such procedures, that the cells still possess a broad size distribution, and that substantive changes in temperature have been imposed – each of which is in itself sufficient to vitiate this approach to cell-cycle studies of unstressed bacteria in steady-state growth. Similar considerations apply to procedures that attempt to align chromosome replication by using selective inhibitors of protein or DNA synthesis. In view of what has been presented here, and the history of findings employing the baby-machine technique, we propose that minimisation of stress on cells, rather than the quality of synchrony, is the single most
Cell-cycle research with synchronous cultures important factor for successful cell-cycle analysis. Our results indicate little fundamental difference in the information obtainable from populations of pure synchronous cells and those with a random component of 25% or more. There was clear structure to the rate of cell division, suggesting that cell-cycle events coupled to cell division, such as rate of initiation of chromosome replication or rate of minichromosome plasmid replication, could be detectable. Interestingly, even in a population in which almost all ages are equally represented, the timing of such replication events within the cell cycle would be indicated by gradual but clearly discernable periodic stepwise increases in the rate of cell division. Although there are clear advantages to working with cultures displaying synchrony of very high quality, in light of the substantive dispersions inherent in the timing of cell-cycle events in E. coli, when a choice is made among techniques, preference should be given to those that cause the least disturbance to cell physiology. The best option, in our view, is the baby machine, which can achieve near-optimal synchrony without compromising the normal physiology of the cell [6, 19–21].
89 [6] Li Z., Clarke A.J., Beveridge T.J., A major autolysin of Pseudomonas aeruginosa: subcellular distribution, potential role in cell growth and division, and secretion in surface membrane vesicles, J. Bacteriol. 178 (1996) 2479–2488. [7] Lark K.G., Maaløe O., Nucleic acid synthesis and the division cycle of Salmonella typhimurium, Biochim. Biophys. Acta 21 (1956) 448–457. [8] Cutler R.G., Evans J.E., Synchronization of bacteria by a stationary-phase method, J. Bacteriol. 91 (1967) 469–476. [9] Kepes F., Kepes A., Long-lasting synchrony of the division of enteric bacteria, Biochem. Biophys. Res. Commun. 99 (1981) 761–767. [10] Cooper S., Bacterial Growth and Division, Academic Press, San Diego, CA, 1991, pp. 33–38. [11] Helmstetter C.E., Timing of synthetic activities in the cell cycle, in: Neidhardt F.C., Curtiss R.III, Ingraham J.L., Lin E.C.C., Low K.B., Magasanik B., Reznikoff W.S., Riley M., Schaechter M., Umbarger H.E. (Eds.), Escherichia coli and Salmonella: Cellular and Molecular Biology. American Society for Microbiology, 2 edn., Washington, DC, 1996, pp. 1627–1639. [12] Grover N.B., Helmstetter C.E., Characterization of cell-cyclespecific events in synchronous cultures of Escherichia coli: a theoretical evaluation, Microbiology 141 (1995) 59–62. [13] Powell E.O., Growth rate and generation time of bacteria, with special reference to continuous culture, J. Gen. Microbiol. 15 (1956) 492–511.
Acknowledgments
[14] IMSL, Math and Stat Libraries, in: Fortran PowerStation, Microsoft Corporation, Professional Edition, Redmond, WA, Version 4.0, 1995.
The authors wish to express their thanks to C. Coustère-Yakir for her capable programming. This work was supported in part by NASA grant NAG8-1582 to C.E.H.
[15] Skarstad K., Steen H.B., Boye E., Escherichia coli DNA distributions measured by flow cytometry and compared with theoretical computer simulations, J. Bacteriol. 163 (1985) 661–668.
References [1] Helmstetter C.E., Methods for studying the microbial division cycle, in: Norris J.R., Ribbons D.W. (Eds.), Methods in Microbiology, Vol. I, Academic Press, New York, NY, 1969, pp. 327–363. [2] Helmstetter C.E., Pierucci O., DNA synthesis during the division cycle of three substrains of Escherichia coli B/r, J. Mol. Biol. 102 (1976) 477–486. [3] Helmstetter C.E., Thornton M., Zhou P., Bogan J.A., Leonard A.C., Grimwade J.E., Replication and segregation of a miniF plasmid during the division cycle of Escherichia coli, J. Bacteriol. 179 (1997) 1393–1399. [4] Helmstetter C.E., Initiation of chromosome replication in Escherichia coli. I. Requirements for RNA and protein synthesis at different growth rates, J. Mol. Biol. 84 (1974) 1–19. [5] Loebner-Olesen A., Hansen F.G., Rasmussen K.V., Martin B., Kuempel P.L., The initiation cascade for chromosome replication in wild-type and Dam methyltransferase deficient Escherichia coli cells, EMBO J. 13 (1994) 1856–1862.
[16] Ogden G.B., Pratt M.J., Schaechter M., The replicative origin of the E. coli chromosome binds to cell membranes only when hemimethylated, Cell 54 (1988) 127–135. [17] Campbell J.L., Kleckner N, E. coli oriC and the dnaA gene promoter are sequestered from dam methyltransferase following passage of the chromosomal replication fork, Cell 62 (1990) 967–979. [18] Zhou P., Bogan J.A., Welch K., Pickett S.R., Wang H.J., Zaritsky A., Helmstetter C.E., Gene transcription and chromosome replication in Escherichia coli, J. Bacteriol. 179 (1997) 163–169. [19] Cooper S., Ruettinger T., Replication of deoxyribonucleic acid during the division cycle of Salmonella typhimurium, J. Bacteriol. 114 (1973) 966–973. [20] Holmes M., Rickert M., Pierucci O., Cell division cycle of Bacillus subtilis: evidence of variability in D period, J. Bacteriol. 142 (1980) 254–261. [21] Helmstetter C.E., Eenhuis C., Theisen P., Grimwade J., Leonard A.C., Improved bacterial baby machine: Application to Escherichia coli K12 with increased cell yield, J. Bacteriol. 174 (1992) 3445–3449.
Cell-cycle research with synchronous cultures: An evaluation Charles E. Helmstettera, Maureen Thorntona, N.B. Groverb* b
a Department of Biological Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA Hubert H. Humphrey Center for Experimental Medicine and Cancer Research, Hebrew University Faculty of Medicine, P.O. Box 12272, Jerusalem 91120, Israel
(Received 7 November 2000; accepted 24 November 2000) Abstract — The baby-machine system, which produces new-born Escherichia coli cells from cultures immobilized on a membrane, was developed many years ago in an attempt to attain optimal synchrony with minimal disturbance of steady-state growth. In the present article, we put forward a model to describe the behaviour of cells produced by this method, and provide quantitative evaluation of the parameters involved, at each of four different growth rates. Considering the high level of selection achievable with this technique and the natural dispersion in interdivision times, we believe that the output of the baby machine is probably close to optimal in terms of both quality and persistence of synchrony. We show that considerable information on events in the cell cycle can be obtained from populations with age distributions very much broader than those achieved with the baby machine and differing only modestly from steady state. The data presented here, together with the long and fruitful history of findings employing the baby-machine technique, suggest that minimisation of stress on cells is the single most important factor for successful cell-cycle analysis. © 2001 Société française de biochimie et biologie moléculaire / Éditions scientifiques et médicales Elsevier SAS baby machine / cell cycle / distribution of cell interdivision times / model for synchronous growth of Escherichia coli / synchronous growth parameters
1. Introduction Much of our understanding of the events in the bacterial cell cycle originates from use of the baby machine culture technique. In this procedure, described in detail by Helmstetter [1], Escherichia coli cells are grown immobilised on the surface of a membrane such that division results in the release of new-born cells into culture medium passing through the membrane. That methodology was successful for two main reasons. First and foremost, this way of producing synchronous new-born cells causes minimal disturbance to cultures in steadystate growth, enabling the physiological state of the cells to be reasonably well-defined. In addition, much of the early work involved measurements of the rate of DNA replication during the cell cycle using the technique in age classification mode. In that form of the method, cultures were pulse-labelled with radioactive thymidine prior to immobilisation, and then the level of incorporation was measured in the progeny cells released from the surface. The cells eluted during the first generation were the daughters of the successively younger cells initially deposited on the membrane, those eluted during the second generation were their granddaughters, and so on. Thus, the rates of incorporation of the labelled compound into cells * Correspondence and reprints. E-mail address: [email protected] (N.B. Grover).
of different ages in the cycle were determined by measuring the amount of label in their progeny. A major advantage of this approach is that the label was added while the cells were in undisturbed steady-state growth, the only subsequent requirement being that the cells divide in the same sequence while immobilised that they would have done in the original culture prior to immobilisation [1]. The second reason for the success of this technique is the high purity of the new-born cells released from the membrane, as judged by the ease with which periodic events in the cell cycle can be detected [2, 3]. By collecting samples of the effluent over time and growing them, one can also use the baby machine to produce highly synchronous cultures for cell-cycle analysis [1]. The similarity of findings obtained with such synchronously growing E. coli cells and those from the age classification method [4], and successful applications of this approach to different strains and species [5, 6], indicate that the additional growth of the cells does not materially disturb their physiological state. This has generally not been the case with methods that involve treatments designed to induce synchronised growth in growing cultures, such as periodic changes in temperature or in nutrient conditions. Although there have been occasional reports of very highly synchronised cell divisions over many generations with such treatments [7–9], to our knowledge these techniques have never been used to further our understanding of the division cycle. They do
84 not provide information on the undisturbed steady-state cycle because the totality of cell processes are not aligned [10] and so any apparent synchrony that is achieved would be compromised by the response to the treatment of whatever cell property is under investigation. They are also difficult to reproduce. Experiments involving the alignment of chromosome replication by shifts in temperature of temperature-sensitive, initiation-defective mutants [11], aimed at correlating biosynthetic processes with synchronised chromosome replication, may be an exception so long as it is recognised that the cells in such cultures are not synchronous in overall cell mass nor in mass synthesis. If indeed the baby machine produces a high level of selection of minimally disturbed new-born cells, the resulting synchronous growth of the cells most likely approaches the highest quality and duration of synchrony achievable with E. coli. The purpose of this paper is to provide data on the extent of synchronous cell division over multiple generations achievable with baby machinegenerated new-born cells at each of four different growth rates. Quantitative assessments of the parameters of the synchronous growth are presented using an extension of the model described previously [12]. It is further shown that considerable information on events in the cell cycle can be obtained from populations with age distributions differing only modestly from steady state, suggesting that achievement of minimal physiological disturbance is more important for cell-cycle studies than quality or persistence of synchrony. 2. Materials and methods Cultures of E. coli B/r A (ATCC 12407) were grown in minimal salts medium [2] supplemented with 0.1% glucose plus 0.2% Casamino acids (Difco, USA), 0.1% glucose, 0.1% glycerol, or 0.2% sodium succinate. The baby-machine technique was used to obtain synchronous cultures [1]. Briefly, 100 mL of minimal medium was inoculated with bacteria from a fresh stationary-phase stock, diluted approximately 1:1000, and incubated in a shaking water bath at 37 °C until the cells were in steady-state growth. When a culture reached a concentration of approximately 5 × 107 cells/mL, it was filtered onto the surface of a type GS 142 mm-diameter membrane filter (Millipore, USA) in an incubator at 37 °C. The filter was then inverted and elution with fresh medium begun. After a delay that depended on the composition of the culture medium, an aliquot was collected from the effluent in a 50-mL culture flask (Bellco, USA) and placed in a 37 °C shaking water bath. Samples were collected from the culture flask at intervals and diluted in Isoton II (Beckman-Coulter, USA); cell concentrations were determined with a model ZB electronic particle counter (Beckman-Coulter, USA).
Helmstetter et al. 3. The model The cell populations eluted from the membrane were taken as being composed of two components. The age of the major component was assumed to be normally distributed about zero with a standard deviation σ. The minor component, of relative size q, was considered to consist of cells that had undergone only very little age selection during the elution process: the number of these random a/sfl cells was set proportional to 2 , where a is the age of the eluted cell at the time of collection (t=0) and sfl is the observed doubling time of the culture. These are bacteria released from the membrane for reasons other than division, such as weak binding. It also proved necessary to introduce a fixed background β to account for the signals recorded by the electronic particle counter that were produced not by viable, replicating cells but by the debris and electronic noise that are invariably associated with such measurements. This, together with a proportionality constant k, constituted the original form of the model [12]; it proved inadequate once we began considering more than one generation. First it became apparent that the initial doubling sometimes took place a little earlier than subsequent ones, sometimes a little later. We introduced a time shift δ to allow for the differences between collection time and sampling time that can arise in a multi-sample experiment of this type. The second addition to the original model was more fundamental. The dispersion σ of the new-born subpopulation accounted rather well for the transition period as long as we limited ourselves to a single generation time. When we began studying several generations, however, a value of σ suitable for the first transition period systematically undercorrected for the second whereas a value suitable for the second overcorrected for the first. That was because the sharpness of the transition decreases from doubling to doubling and cannot be accommodated by a fixed σ. In order to allow for such deterioration, we introduced dispersion into the interdivision times as well: τ is distributed about sfl with a coefficient of variation cv(τ). The form of this distribution, for both cellular components, was assumed to be a Pearson type III (incomplete gamma function) rather than a normal distribution because of the widespread observation that f(τ) is skewed to the right and the solid experimental studies of Powell [13].
4. Synchronous cell division at four different growth rates The model described above was fitted to the synchronous growth data obtained from the baby machine for E. coli B/r A cells growing at four different doubling times, using an unconstrained non-linear least-squares algorithm
Cell-cycle research with synchronous cultures [14]. A plot of the experimental points for a sample of new-born cells growing in glucose plus Casamino acids is presented in figure 1a together with the predicted curve. The fit was restricted to the first two generations, where its quality is rather good; extrapolation beyond that point shows a clear tendency of the data to drop further and further below the theoretical curve as time increases. It was thought that this trend may be attributed at least in part to the increased coincidence within the electronic particle counter orifice that occurs at higher cell concentrations, and so the experiment was repeated with two-fold dilutions at the times indicated (figure 1b) and the model refitted using all the data points, over four generations. Now the fit is excellent. The results are summarized in table I. The sum of squares of the residuals in both cases is less than 0.1% of the total (P < 0.001) and they are distributed randomly
Figure 1. Cell concentrations and rates of cell division during growth of baby machinegenerated E. coli B/r A cells in glucoseCasamino acids minimal medium. a. Data. A sample of the effluent containing 11 × 106 cells/mL was collected at between 18 and 19 min of elution and incubated at 37 °C in a shaking water bath; aliquots were withdrawn at indicated times and diluted a 100-fold throughout the experiment. Curve. Unconstrained nonlinear least-squares fit, to first 26 data points, of model combining three theoretical subpopulations: a major component with age normally distributed about zero (standard deviation σ), a minor component that had undergone very little age selection (of relative size q), and a fixed background (β) of non-cellular material; in addition, model assumes that the interdivision time τ follows a Pearson type III distribution (coefficient of variation cv(τ)), and it includes a time shift (δ) to allow for differences between collection time and sampling time. Parameter estimates are as indicated; standard errors and quality of fit statistics appear in table I. Axes. Left-hand ordinate: cell concentration (millions/mL, log scale); right-hand ordinate: rate of cell division (millions/min/mL), equivalent to rate of cell number increase and obtained by numerical differentiation of concentration curve and of data points. b. Data. As in (a) except that sample contained 17 × 106 cells/mL and that dilution levels were doubled at 35 min and again at 55 min and at 79 min, marked by arrows. Curve. As in (a) but model fit to all data points. Parameter estimates are as indicated; standard errors and quality of fit statistics appear in table I. Axes. As in (a).
85 (P > 0.15), as determined by a one-tail runs test. The size of the random subpopulation q is small and so is the background β; both parameters are well-defined. The time shift δ is not far from zero. What is particularly interesting, apart from the superb fit of the dilution data itself, is the fact that σ the standard deviation at t = 0 of the age of the new-born cells that comprise the synchronous subpopulation, is zero: all the dispersion in each of the four transition periods can be fully accounted for by the variation in the interdivision-time distribution cv(τ). Synchronous growth data are plotted in figure 2 together with the predicted curves based on the first 26 points (like in figure 1a), for cells cultured in glucose, glycerol, and succinate minimal medium; the results also appear in table I. All three fits are very good but as the doubling time increases, the discrepancies between the theoretical curves and the experimental points in the
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Table I. Statistics of fit of theoretical model to experimental data obtained from the baby machine for E. coli B/r A cells growing at different doubling times. Entity
Units
Figure sfl a Residualsb P (runs)c β ± sed δ ± see q ± sef σ ± seg cv(τ) ± seh
Min % – % Min % % %
Glucose-Casamino acids 1(a) 22 0.037 0.183 4.7 ± 0.8 –1.3 ± 0.1 4.8 ± 1.6 0 13.7 ± 0.4
1(b) 24 0.028 0.638 2.3 ± 0.7 0.6 ± 0.1 6.3 ± 2.3 0 12.7 ± 0.4
Glucose
Glycerol
Succinate
2(a) 41 0.078 0.286 11.3 ± 1.2 1.6 ± 0.3 10.5 ± 3.3 8.6 ± 3.0 9.4 ± 1.8
2(b) 50 0.160 0.769 9.2 ± 1.4 0 4.5 ± 3.7 0 12.3 ± 0.9
2(c) 82 0.070 0.723 12.1 ± 1.1 4.6 ± 0.4 18.7 ± 2.0 11.6 ± 1.7 4.5 ± 2.9
a
Observed doubling time of culture. Sum of squares of residuals, expressed as percentage of total variation in measured variable. Single-sided runs test: probability that signs of residuals are distributed randomly. d Relative size and standard error of fixed background of non-cellular material. e Size and standard error of time shift between collection time and sampling time. f Relative size and standard error of minor component of eluted cells that had undergone very little age selection. g Standard deviation and its standard error, expressed as percentages of sfl , of age distribution of major component of eluted cells, assumed to be normally distributed about zero. h Standard deviation and its standard error, expressed as percentages of sfl , of interdivision-time distribution of all eluted cells, assumed to follow a Pearson type III distribution. b c
extrapolated region become larger and larger; there does not, however, appear to be any deterioration in the precision with which the various parameters can be estimated. The fit in the case of glycerol is remarkably similar to that in glucose plus Casamino acids, except for the higher background, but the other two growth media produce higher proportions of the random subpopulation as well as higher backgrounds. The fit in glucose covers two full transition periods and the apportionment of the variance between σ and cv(τ) is clear and well-defined. The larger doubling time in the case of succinate means that the second transition period is not completely covered by the first 26 points of the fit, and there is not sufficient information to determine cv(τ) with any precision; thus, although it is much smaller than the other entries for this parameter, its standard error is by far the largest.
cell-cycle biosynthetic event with a distribution like that of cell division could easily be detected in such baby machine-generated synchronous cultures. The question then arises as to how far the cultures can depart from perfect synchrony before the information content of the differential curves becomes unusable. Figure 3 contains predicted cell concentration curves together with the associated rates of cell division, for a series of simulated populations extending from pure synchronous (q = 0) all the way to near uniform (q = 1). The parameter values were taken from figure 2a and, in fact, the curves for q = 0.105 in the two figures are identical. There is no essential deterioration in the information obtainable between a q of zero and a q of 0.25; even with much larger values, up to and including unity, there is clear structure in the rate curves, suggesting that any cell-cycle event coupled to cell division, would also be detectable in such asynchronous cultures.
5. Information content in asynchronous cultures An underlying assumption in cell-cycle research employing synchronous cultures has been that high quality, long-lasting synchrony is crucial. This view no doubt led to the many and varied efforts to produce such cultures through induction techniques. With this in mind, we attempted to determine just what cell-cycle information might be available in cultures that ranged from highly synchronous to near steady state. We added plots of the rate of cell division, obtained by numerical differentiation of the corresponding concentration curves, to each of the panels in figures 1 and 2. From these, it is clear that any
6. Discussion The data presented here are representative of the quality and persistence of the synchrony of cell division obtainable with the baby-machine technique. This procedure was originally developed with the idea that a successful elucidation of the cell-cycle properties of bacteria in steady-state growth would require methodology that caused only minimal disturbance to normal cell physiology. Based on many years of successful cell-cycle analyses with the technique, independently verified by non-
Cell-cycle research with synchronous cultures
Figure 2. Cell concentrations and rates of cell division during growth of baby machinegenerated E. coli B/r A cells in various media. a. Data. Glucose medium. A sample of the effluent containing 14.44 × 106 cells/mL was collected at between 36 and 38 min of elution and incubated at 37 °C in a shaking water bath; aliquots were withdrawn at times indicated. First 16 aliquots, spanning initial 62 min, were diluted a 100-fold; at 62, 102, 142, 182 min, marked by arrows, dilution levels were doubled. Curve. Unconstrained non-linear least-squares fit, to first 26 data points, of model combining three theoretical subpopulations: a major component with age normally distributed about zero (standard deviation σ), a minor component that had undergone very little age selection (of relative size q), and a fixed background (β) of non-cellular material; in addition, model assumes that the interdivision time τ follows a Pearson type III distribution (coefficient of variation cv(τ)), and it includes a time shift (δ) to allow for differences between collection time and sampling time. Parameter estimates are as indicated; standard errors and quality of fit statistics appear in table I. Axes. Left-hand ordinate: cell concentration (millions/ mL, log scale); right-hand ordinate: rate of cell division (millions/min/mL), equivalent to rate of cell number increase and obtained by numerical differentiation of concentration curve and of data points. b. Data. Glycerol medium. As in (a) except that sample contained 5.28 × 106 cells/mL and that cells were collected at between 45 and 47 min of elution; aliquots were diluted a 100-fold throughout the experiment. Curve. As in (a). Parameter estimates are as indicated; standard errors and quality of fit statistics appear in table I. Axes. As in (a). c. Data. Succinate medium. As in (a) except that sample contained 9.52 × 106 cells/mL and that cells were collected at between 65 and 69 min of elution; aliquots were diluted a 100-fold throughout the experiment. Curve. As in (a). Parameter estimates are as indicated; standard errors and quality of fit statistics appear in table I. Axes. As in (a).
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Figure 3. Predicted cell concentrations and associated rates of cell division. Simulation of model combining three theoretical subpopulations: a major component with age normally distributed about zero (standard deviation σ), a minor component that had undergone very little age selection (of relative size q), and a fixed background (β) of non-cellular material; in addition, model assumes that the interdivision time τ follows a Pearson type III distribution (coefficient of variation cv(τ)), and it includes a time shift (δ) to allow for differences between collection time and sampling time. Five different levels of q are shown: 0%, 10.5%, 25%, 50%, 100%; other parameter values as in figure 2a. Left-hand ordinate: cell concentration (millions/mL, log scale); right-hand ordinate: rate of cell division (millions/min/mL), equivalent to rate of cell number increase and obtained by numerical differentiation of corresponding concentration curve.
synchrony methods [15], and the material presented here, we believe that this goal has been achieved. Since the baby machine produces cells that are in minimallydisturbed steady-state growth, and the eluted population usually consists of 90% or more pure new-born cells, the resulting synchrony is probably very close to optimal for E. coli. If, therefore, plots are published containing synchronous cell divisions with sharper steps, flatter plateaus, longer durations, we maintain that such cultures have been disturbed or that the measurements are faulty. There have been many attempts over the years to develop new methods or to modify existing ones in order to achieve a synchronised growth that was very precise and very persistent. Generally, these efforts have not yielded new information on the cell cycle because either they disturbed cell growth or they were not reproducible [10]. The one exception to this involves those techniques that employ temperature-sensitive, initiation-defective mutants to align chromosome replication. When such mutants are shifted from permissive temperature (30 °C) to non-permissive temperature (40 °C) for at least C min (the time required to replicate the chromosome – about 40 min in E. coli at 40 °C), ongoing rounds of chromosome replication are completed but new rounds cannot initiate.
Upon shift back to permissive temperature, chromosome replication is synchronised. This technique has therefore proved useful in examining cell properties specifically connected to chromosome replication, such as the methylation state of newly replicated chromosomal DNA [16, 17]. There is also a partially synchronised cell division C + D min (this is the time that elapses between initiation of chromosome replication and the subsequent cell division – about 110 min in E. coli at 30 °C) after synchronised initiation of replication [18], which could be useful for studying processes coupled to cell division. It must be emphasized, however, that overall growth is not synchronized by such procedures, that the cells still possess a broad size distribution, and that substantive changes in temperature have been imposed – each of which is in itself sufficient to vitiate this approach to cell-cycle studies of unstressed bacteria in steady-state growth. Similar considerations apply to procedures that attempt to align chromosome replication by using selective inhibitors of protein or DNA synthesis. In view of what has been presented here, and the history of findings employing the baby-machine technique, we propose that minimisation of stress on cells, rather than the quality of synchrony, is the single most
Cell-cycle research with synchronous cultures important factor for successful cell-cycle analysis. Our results indicate little fundamental difference in the information obtainable from populations of pure synchronous cells and those with a random component of 25% or more. There was clear structure to the rate of cell division, suggesting that cell-cycle events coupled to cell division, such as rate of initiation of chromosome replication or rate of minichromosome plasmid replication, could be detectable. Interestingly, even in a population in which almost all ages are equally represented, the timing of such replication events within the cell cycle would be indicated by gradual but clearly discernable periodic stepwise increases in the rate of cell division. Although there are clear advantages to working with cultures displaying synchrony of very high quality, in light of the substantive dispersions inherent in the timing of cell-cycle events in E. coli, when a choice is made among techniques, preference should be given to those that cause the least disturbance to cell physiology. The best option, in our view, is the baby machine, which can achieve near-optimal synchrony without compromising the normal physiology of the cell [6, 19–21].
89 [6] Li Z., Clarke A.J., Beveridge T.J., A major autolysin of Pseudomonas aeruginosa: subcellular distribution, potential role in cell growth and division, and secretion in surface membrane vesicles, J. Bacteriol. 178 (1996) 2479–2488. [7] Lark K.G., Maaløe O., Nucleic acid synthesis and the division cycle of Salmonella typhimurium, Biochim. Biophys. Acta 21 (1956) 448–457. [8] Cutler R.G., Evans J.E., Synchronization of bacteria by a stationary-phase method, J. Bacteriol. 91 (1967) 469–476. [9] Kepes F., Kepes A., Long-lasting synchrony of the division of enteric bacteria, Biochem. Biophys. Res. Commun. 99 (1981) 761–767. [10] Cooper S., Bacterial Growth and Division, Academic Press, San Diego, CA, 1991, pp. 33–38. [11] Helmstetter C.E., Timing of synthetic activities in the cell cycle, in: Neidhardt F.C., Curtiss R.III, Ingraham J.L., Lin E.C.C., Low K.B., Magasanik B., Reznikoff W.S., Riley M., Schaechter M., Umbarger H.E. (Eds.), Escherichia coli and Salmonella: Cellular and Molecular Biology. American Society for Microbiology, 2 edn., Washington, DC, 1996, pp. 1627–1639. [12] Grover N.B., Helmstetter C.E., Characterization of cell-cyclespecific events in synchronous cultures of Escherichia coli: a theoretical evaluation, Microbiology 141 (1995) 59–62. [13] Powell E.O., Growth rate and generation time of bacteria, with special reference to continuous culture, J. Gen. Microbiol. 15 (1956) 492–511.
Acknowledgments
[14] IMSL, Math and Stat Libraries, in: Fortran PowerStation, Microsoft Corporation, Professional Edition, Redmond, WA, Version 4.0, 1995.
The authors wish to express their thanks to C. Coustère-Yakir for her capable programming. This work was supported in part by NASA grant NAG8-1582 to C.E.H.
[15] Skarstad K., Steen H.B., Boye E., Escherichia coli DNA distributions measured by flow cytometry and compared with theoretical computer simulations, J. Bacteriol. 163 (1985) 661–668.
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[16] Ogden G.B., Pratt M.J., Schaechter M., The replicative origin of the E. coli chromosome binds to cell membranes only when hemimethylated, Cell 54 (1988) 127–135. [17] Campbell J.L., Kleckner N, E. coli oriC and the dnaA gene promoter are sequestered from dam methyltransferase following passage of the chromosomal replication fork, Cell 62 (1990) 967–979. [18] Zhou P., Bogan J.A., Welch K., Pickett S.R., Wang H.J., Zaritsky A., Helmstetter C.E., Gene transcription and chromosome replication in Escherichia coli, J. Bacteriol. 179 (1997) 163–169. [19] Cooper S., Ruettinger T., Replication of deoxyribonucleic acid during the division cycle of Salmonella typhimurium, J. Bacteriol. 114 (1973) 966–973. [20] Holmes M., Rickert M., Pierucci O., Cell division cycle of Bacillus subtilis: evidence of variability in D period, J. Bacteriol. 142 (1980) 254–261. [21] Helmstetter C.E., Eenhuis C., Theisen P., Grimwade J., Leonard A.C., Improved bacterial baby machine: Application to Escherichia coli K12 with increased cell yield, J. Bacteriol. 174 (1992) 3445–3449.