How does a bacterium grow during its cell cycle?

Rod-shaped bacteria such as Escherichia coli and Bacillus subtilis appear to extend continuously in length between divisions. However, the kinetics of growth of the individual cell in the steady state is still unknown. A brief, critical account of the main approaches used to determine the pattern of surface extension is given. In general, these approaches are of three types. Firstly, attempts have been made to relate average cell size to growth rate of the culture and to determine possible stages in the cell cycle at which the rate of length extension might change. Secondly, comparisons have been made between the measured length distribution of cells and theoretical distributions, based on three primary hypotheses (linear, bilinear and exponential growth). Thirdly, the principle of Collins and Richmond, involving the calculation of growth rate from the length distributions of extant, separating and new-born cells, is described. It is emphasized that there is a strong element of variation in size at different stages of the cell cycle. This variation imposes severe limitations on models which utilize only average cellular dimensions. We conclude that the Collins-Richmond principle affords the most powerful approach to the analysis of bacterial growth kinetics. However, we propose that the method be modified to permit calculation of separate rates of growth of cells between discernible events in the cell cycle, as well as simply between birth and division.     

Predicted steady-state cell size distributions for various growth models

The question of how an individual bacterial cell grows during its life cycle remains controversial. In 1962 Collins and Richmond derived a very general expression relating the size distributions of newborn, dividing and extant cells in steady-state growth and their growth rate; it represents the most powerful framework currently available for the analysis of bacterial growth kinetics. The Collins-Richmond equation is in effect a statement of the conservation of cell numbers for populations in steady-state exponential growth. It has usually been used to calculate the growth rate from a measured cell size distribution under various assumptions regarding the dividing and newborn cell distributions, but can also be applied in reverse--to compute the theoretical cell size distribution from a specified growth law. This has the advantage that it is not limited to models in which growth rate is a deterministic function of cell size, such as in simple exponential or linear growth, but permits evaluation of far more sophisticated hypotheses. Here we employed this reverse approach to obtain theoretical cell size distributions for two exponential and six linear growth models. The former differ as to whether there exists in each cell a minimal size that does not contribute to growth, the latter as to when the presumptive doubling of the growth rate takes place: in the linear age models, it is taken to occur at a particular cell age, at a fixed time prior to division, or at division itself; in the linear size models, the growth rate is considered to double with a constant probability from cell birth, with a constant probability but only after the cell has reached a minimal size, or after the minimal size has been attained but with a probability that increases linearly with cell size. Each model contains a small number of adjustable parameters but no assumptions other than that all cells obey the same growth law. In the present article, the various growth laws are described and rigorous mathematical expressions developed to predict the size distribution of extant cells in steady-state exponential growth; in the following paper, these predictions are tested against high-quality experimental data.     

Conformation and Segregation of Nucleoids Accompanying Cell Length Extension After Completion of a Single Round of DNA Replication in Germinated and Outgrowing Bacillus subtilis Spores

When germinating spores of the temperature-sensitive DNA initiation mutant of Bacillus subtilis TsB134 are shifted to the restrictive temperature at a time such that just one or two rounds of replication are accomplished, the completed, nonreplicating nucleoids that form eventually adopt a doublet conformation. This conformation has now been observed after fixation by glutaraldehyde or osmium tetroxide, as well as by Formalin as found previously. The doublet was observed in media of different degrees of richness and under both light and electron microscopes. Electron micrographs of serial sections through the doublet were consistent with its formation by the gradual pulling apart of a single mass of DNA into two lobes. A systematic study was made of the effect of the time of shifting from the permissive to the restrictive temperature and of the restrictive temperature used on the number of nucleoids segregating within the outgrowing rod. It was established that the doublet nucleoid behaved as a single unit in replication control and segregation in both rich and poor media. Measurement of the relative position of the two segregating nucleoids within the outgrowing rod after completion of just one round of replication yielded quantitative information on the segregation and cell length extension processes. Segregation was accompanied by cell length extension at approximately equal rates on both sides of each nucleoid. Furthermore, the data were consistent with an exponential increase in such an extension with time over the early and major portion of the period studied, but it was not possible to rule out other models of length extension.     

The growth kinetics ofB. subtilis

There has been considerable discussion by Kubitschek and Cooper concerning the growth rate of cells ofE. coli throughout the cell cycle. Consequently, it is relevant to test Kubitschek's linear model against the exponential model espoused by Cooper (and many others) with another organism and another technique.Burdett et al. measured, by electron microscopy and computer analysis of the microphotographs, the distribution of lengths of a population of cells ofBacillus subtilis grown in 0.4% succinate in a minimal medium. The data were fitted to the extended Collins-Richmond method of Kirkwood & Burdett which subdivided the cell cycle into several phases. I have taken their results and compared them with the linear and exponential growth models for the entire cell cycle after applying correction to the data for the shape of completed and forming poles; i.e., to put the data on a cell-volume basis instead of a cell-length basis. Most of the correction involves no arbitrary assumptions. The conclusion is that global volume growth rate is nearly proportional to cell volume; i.e. growth ofBacillus subtilis is nearly exponential for almost every cell in the growing culture.     

Dimensional rearrangement of rod-shaped bacteria following nutritional shift-up. II. Experiments with Escherichia coliBr

The dimensions of Escherichia coli$\text{B}\text{r}$ (strain H266) in transition between two states of balanced growth, were determined from electron micrographs of fixed cells by sampling the culture at various times following nutritional shift-up from a doubling time of 72 min to one of 24 min. Mean cell length rises immediately and overshoots its final steady-state value, cell diameter increases monotonically; both approach their asymptotic levels only after several hours.The results are compared with the dimensions predicted by each of two models of cell growth and morphogenesis in rod-shaped bacteria. The first attributes cell elongation to circular zones that double in number at a particular time during the cell cycle and which act at rates proportional to the growth rate; the second is similar, except that it considers surface growth rather than length extension as the active process, length being determined passively. Two possibilities are examined, that the zonal growth rate adjusts immediately to the new growth conditions, and that it does so gradually.The experimental data appear consistent with the gradual response version of the surface growth model.     

Nucleoid partitioning and the division plane in Escherichia coli.

Escherichia coli nucleoids were visualized after the DNA of OsO4-fixed but hydrated cells was stained with the fluorochrome DAPI (4',6-diamidino-2-phenylindole dihydrochloride hydrate). In slowly growing cells, the nucleoids are rod shaped and seem to move along the major cell axis, whereas in rapidly growing, wider cells they consist of two- to four-lobed structures that often appear to advance along axes lying perpendicular or oblique to the major axis of the cell. To test the idea that the increase in cell diameter following nutritional shift-up is caused by the increased amount of DNA in the nucleoid, the cells were subjected to DNA synthesis inhibition. In the absence of DNA replication, the nucleoids continued to move in the growing filaments and were pulled apart into small domains along the length of the cell. When these cells were then transferred to a richer medium, their diameters increased, especially in the region enclosing the nucleoid. It thus appears that the nucleoid motive force does not depend on DNA synthesis and that cell diameter is determined not by the amount of DNA per chromosome but rather by the synthetic activity surrounding the nucleoid. Under the non-steady-state but balanced growth conditions induced by thymine limitation, nucleoids become separated into small lobules, often lying in asymmetric configurations along the cell periphery, and oblique and asymmetric division planes occur in more than half of the constricting cells. We suggest that such irregular DNA movement affects both the angle of the division plane and its position.     

Inhibition and restart of initiation of chromosome replication: effects on exponentially growing Escherichia coli cells.

Escherichia coli strains in which initiation of chromosome replication could be specifically blocked while other cellular processes continued uninhibited were constructed. Inhibition of replication resulted in a reduced growth rate and in inhibition of cell division after a time period roughly corresponding to the sum of the lengths of the C and D periods. The division inhibition was not mediated by the SOS regulon. The cells became elongated, and a majority contained a centrally located nucleoid with a fully replicated chromosome. The replication block was reversible, and restart of chromosome replication allowed cell division and rapid growth to resume after a time delay. After the resumption, the septum positions were nonrandomly distributed along the length axis of the cells, and a majority of the divisions resulted in at least one newborn cell of normal size and DNA content. With a transient temperature shift, a single synchronous round of chromosome replication and cell division could be induced in the population, making the constructed system useful for studies of cell cycle-specific events. The coordination between chromosome replication, nucleoid segregation, and cell division in E. coli is discussed.     

Axial filament formation in Bacillus subtilis: induction of nucleoids of increasing length after addition of chloramphenicol to exponential-phase cultures approaching stationary phase.

When chloramphenicol was added to a culture of Bacillus subtilis in early exponential growth, microscopic observation of cells stained by 4',6-diamidino-2-phenylindole showed nucleoids that had changed in appearance from irregular spheres and dumbbells to large, brightly stained spheres and ovals. In contrast, the addition of chloramphenicol to cultures in mid- and late exponential growth showed cells with elongated nucleoids whose frequency and length increased as the culture approached stationary phase. The kinetics of nucleoid elongation after the addition of chloramphenicol to exponential-phase cultures was complex. Immediately after treatment, the rate of nucleoid elongation was very rapid. The nucleoid then elongated steadily for about 4 min, after which the rate of elongation decreased considerably. Nucleoids of cells treated with 6-(p-hydroxyphenylazo)-uracil (an inhibitor of DNA synthesis) exhibited the immediate rapid elongation upon chloramphenicol treatment but not the subsequent changes. These observations suggest that axial filament formation during stationary phase (stage I of sporulation) in the absence of chloramphenicol results from changes in nucleoid structure that are initiated earlier, during exponential growth.     

Control of cell length in Bacillus subtilis.

During inhibition of deoxyribonucleic acid synthesis in Bacillus subtilis 168 Thy-minus Tryp-minus, the rate of length extension is constant. A nutritional shift-up during thymine starvation causes an acceleration in the linear rate of length extension. During a nutritional shift-up in the presence of thymine, the rate of length extension gradually increases, reaching a new steady state at about 50 min before the new steady-state rate of cell division is reached. The steady-state rates of nuclear division and length extension are reached at approximately the same time. The ratio of average cell length to numbers of nuclei per cell in exponential cultures is constant over a fourfold range of growth rates. These observations are consistent with: (i) surface growth zones which operate at a constant rate of length extension under any one growth condition, but which operate at an absolute rate proportional to the growth rate of the culture, (ii) a doubling in number of growth zones at nuclear segregation, and (iii) a requirement for deoxyribonucleic acid replication for the doubling in a number of sites.     

FtsZ ring formation without subsequent cell division after replication runout in Escherichia coli

In this report, we have investigated cell division after inhibition of initiation of chromosome replication in Escherichia coli. In a culture grown to the stationary phase, cells containing more than one chromosome were able to divide some time after restart of growth, under conditions not allowing initiation of chromosome replication. This shows that there is no requirement for cell division to take place within a certain time after initiation of chromosome replication. Continued growth without initiation of replication resulted in filamented cells that generally did not have any constrictions. Interestingly, FtsZ rings were formed in a majority of these cells as they reached a certain cell length. These rings appeared and were maintained for some time at the cell quarter positions on both sides of the centrally localized nucleoid. These results confirm previous findings that cell division sites are formed independently of chromosome replication and indicate that FtsZ ring assembly is dependent on cell size rather than on the capacity of the cell to divide. Disruption of the mukB gene caused a significant increase in the region occupied by DNA after the replication runout, consistent with a role of MukB in chromosome condensation. The aberrant nucleoid structure was accompanied by a shift in FtsZ ring positioning, indicating an effect of the nucleoid on the positioning of the FtsZ ring. A narrow cell length interval was found, under and over which primarily central and non-central FtsZ rings, respectively, were observed. This finding correlates well with the previously observed oscillatory movement of MinC and MinD in short and long cells.     

Early development of the granule cell in the cerebellum of the chick embryo

The sequence of differentiation of the cerebellar granule cell in chick embryos from the eighth to the 15th days of incubation has been studied in Golgi-stained celloidin sections. In the germinal-cell phase, the presumptive granule cell sends out one or two horizontal processes which may originate either in the body of the cell or in the extension which attaches it to the pial surface. Thus the germinal cell may be converted into either a monopolar or a bipolar presumptive granular cell. Bipolar cells may have two processes of the same length (symmetrical cells) or of unequal length (asymmetrical cells). In the symmetrical as well as asymmetrical bipolar cells the leading process is formed, by means of which the perikaryon emigrates until it situates itself definitely in the internal granular layer. Thus, symmetrical and asymmetrical bipolar cells give rise to a granule cell with parallel fibers of equal or different lengths. The monopolar element may originate a second process or may remain in the monopolar phase until it reaches the internal granular layer. Once there, it completes the formation of the parallel fibers.     

Stochastic nucleoid segregation dynamics as a source of the phenotypic variability in E. coli

Segregation of the replicating chromosome from a single to two nucleoid bodies is one of the major processes in growing bacterial cells. The segregation dynamics is tuned by intricate interactions with other cellular processes such as growth and division, ensuring flexibility in a changing environment. We hypothesize that the internal stochasticity of the segregation process may be the source of cell-to-cell phenotypic variability, in addition to the well-established gene expression noise and uneven partitioning of low copy number components. We compare dividing cell lineages with filamentous cells, where the lack of the diffusion barriers is expected to reduce the impact of other factors on the variability of nucleoid segregation dynamics. The nucleoid segregation was monitored using time-lapse microscopy in live E. coli cells grown in linear grooves. The main characteristics of the segregation process, namely, the synchrony of partitioning, rates of separation, and final positions, as well as the variability of these characteristics, were determined for dividing and filamentous lineages growing under the same conditions. Indeed, the gene expression noise was considerably homogenized along filaments as determined from the distribution of CFP and YFP stochastically expressed from the chromosome. We find that 1) the synchrony of nucleoid partitioning is progressively decreasing during consecutive cell cycles, but to a significantly lesser degree in filamentous than in dividing cells; 2) the mean partitioning rate of nucleoids is essentially the same in dividing and filamentous cells, displaying a substantial variability in both; and 3) nucleoids segregate to the same distances in dividing and filamentous cells. Variability in distances is increasing during successive cell cycles, but to a much lesser extent in filamentous cells. Our findings indicate that the variability of the chromosome segregation dynamics is reduced upon removal of boundaries between nucleoids, whereas the remaining variability is essentially inherent to the nucleoid itself.     

Changes in Cell Size and DNA Content in Sulfolobus Cultures during Dilution and Temperature Shift Experiments

Stationary-phase cultures of different hyperthermophilic species of the archaeal genus Sulfolobus were diluted into fresh growth medium and analyzed by flow cytometry and phase-fluorescence microscopy. After dilution, cellular growth started rapidly but no nucleoid partition, cell division, or chromosome replication took place until the cells had been increasing in size for several hours. Initiation of chromosome replication required that the cells first go through partition and cell division, revealing a strong interdependence between these key cell cycle events. The time points at which nucleoid partition, division, and replication occurred after the dilution were used to estimate the relative lengths of the cell cycle periods. When exponentially growing cultures were diluted into fresh growth medium, there was an unexpected transient inhibition of growth and cell division, showing that the cultures did not maintain balanced growth. Furthermore, when cultures growing at 79 degrees C were shifted to room temperature or to ice-water baths, the cells were found to "freeze" in mid-growth. After a shift back to 79 degrees C, growth, replication, and division rapidly resumed and the mode and kinetics of the resumption differed depending upon the nature and length of the shifts. Dilution of stationary-phase cultures provides a simple protocol for the generation of partially synchronized populations that may be used to study cell cycle-specific events.     

Elongation and surface extension of individual cells of Escherichia coli B/r: comparison of theoretical and experimental size distributions

The way individual cells grow and divide uniquely determines the (time-invariant) cell size distribution of populations in steady-state exponential growth. In the preceding article, theoretical distributions were derived for two exponential and six linear models containing a small number of adjustable parameters but no assumptions other than that all cells obey the same growth law. The linear models differ from each other with respect to the timing of the presumptive doubling in their growth rate, the exponential models--according to whether there is or is not a part of the cell that does not contribute to the growth rate. Here we compared the size distributions predicted by each of these models with those of cell length and surface area measured by electron microscopy; the quality of the fit, as determined by the mean-square successive-differences test and the chi 2 goodness-of-fit test, was taken as a measure of the adequacy of the model. The actual data came from two slow-growing E. coli B/r cultures, an A strain (pi = 125 min) and a K strain (pi = 106 min), and a correction was introduced in each to account for the distortion caused by the finite size of the picture frame. The parameter estimates produced by the various models are quite reliable (cv less than 0.1%); we discuss them briefly and compare their values in the two strains. All the length extension models were rejected outright whereas most of the surface growth versions were not. When the same models were tested on A-strain data from a faster growing culture (tau = 21 min), those models that provided an adequate fit to the cell surface area data proved equally satisfactory in the case of cell length. These findings are evaluated and shown to be consistent with cell surface area rather than cell length being the dimension under active control. Three surface area models, all linear, are rejected--those in which doubling of the growth rate occurs with a constant probability from cell birth, at a particular cell age, and precisely at cell division. The evidence in the literature that appears to contradict this last result, rejection of the simple linear surface growth model, is shown to be faulty. The 16 original models are here reduced to five, two involving exponential surface growth and three linear, and possible reasons are presented for our inability to discriminate further at this stage.     

Cell cycle dynamics inferred from the static properties of cells in balanced growth

The duration of a morphological phase of the cell cycle is reflected in the steady state distribution of the sizes of cells in that phase. Relationships presented here provide a method for estimating the timing and variability of any cell cycle phase. It is shown that the mean size of cells initiating and finishing any phase can be estimated from (1) the frequency of cells exhibiting the distinguishing morphological or autoradiographic features of the phase; (2) the mean size of cells in the phase; and (3) their coefficient of variation. The calculations are based on a submodel of the Koch-Schaechter Growth Controlled Model which assumes that (i) the distribution of division sizes is Gaussian; (ii) there is no correlation in division sizes between successive generations; and (iii) every cell division gives rise to two daughter cells of equal size. The calculations should be useful for a wider range of models, however, because the extrapolation factors are not sensitive to the chosen model. Criteria are proposed to allow the user to check the method's applicability for any experimental case. The method also provides a more efficient test of the dependence of growth on cell size than does the Collins-Richmond method. This is because the method uses the mean and coefficient of variation of the size of the total population, in conjunction with those of the cells in a final phase of the cell cycle, to test potential growth laws. For Escherichia coli populations studied by electron microscopy, an exponential growth model provided much better agreement than did a linear growth model. The computer simulations were used to generate rules for three types of cell phases: those that end at cell division, those that start at cell division, and those totally contained within a single cell cycle. For the last type, additional criteria are proposed to establish if the phase is well enough contained for the formulae and graphs to be used. The most useful rule emerging from these computer studies is that the fraction of the cell cycle time occupied by a phase is the product of the frequency of the phase and the ratio of the mean size of cells in that phase to the mean size of all cells in the population. A further advantage of the techniques presented here is that they use the 'extant' distributions that were actually measured, and not hypothesized distributions nor the special distributions needed for Collins-Richmond method that can only be calculated from the observed distributions of dividing or newborn cells on the basis of an assumed growth law.     

Division Cycle of Myxococcus xanthus III. Kinetics of Cell Growth and Protein Synthesis

The kinetics of cell growth and protein synthesis during the division cycle of Myxococcus xanthus was determined. The distribution of cell size for both septated and nonseptated bacteria was obtained by direct measurement of the lengths of 8,000 cells. The Collins-Richmond equation was modified to consider bacterial growth in two phases: growth and division. From the derived equation, the growth rate of individual cells was computed as a function of size. Nondividing cells (growth phase) comprised 91% of the population and took up 87% of the time of the division cycle. The absolute and specific growth rates of nondividing cells were observed to increase continually throughout the growth phase; the growth rate of dividing cells could not be determined accurately by this technique because of changes in the geometry of cells between the time of septation and physical separation. The rate of protein synthesis during the division cycle was measured by pulselabeling an exponential-phase culture with radio-active valine or arginine and then preparing the cells for quantitative autoradiography. By measuring the size of individual cells as well as the number of grains, the rate of protein synthesis as a function of cell size was obtained. Nondividing cells showed an increase in both the absolute and specific rates of protein synthesis throughout the growth phase; the specific rate of protein synthesis for dividing cells was low when compared to growthphase cells. Cell growth and protein synthesis are compared to the previously reported kinetics of deoxyribonucleic acid and ribonucleic acid synthesis during the division cycle.     

Loss of capacity for acid-induced wall loosening as the principal cause of the cessation of cell enlargement in light-grown bean leaves

Cell enlargement in primary leaves of bean (Phaseolus vulgaris L.) can be induced, free of cell divisions, by exposure of 10-d-old, red-light-grown seedlings to white light. The absolute rate of leaf expansion increases until day 12, then decreases until the leaves reached mature size on day 18. The cause of the reduction in growth rate following day 12 has been investigated. Turgor calculated from measurements of leaf water and osmotic potential fell from 6.5 to 3.5 bar before day 12, but remained constant thereafter. The decline of growth after day 12 is not caused by a decrease in turgor. On the other hand, Instron-measured cell-wall extensibility decreased in parallel with growth rate after day 12. Two parameters influencing extensibility were examined. Light-induced acidification of cell walls, which has been shown to initiate wall extension, remained constant over the growth period (days 10–18). Furthermore, cells of any age could be stimulated to excrete H⁺ by fusicoccin. However, older tissue was not able to grow in response to fusicoccin or light. Measurements of acid-induced extension on preparations of isolated cell walls showed that as cells matured, the cell walls became less able to extend when acidified. These data indicate that it is a decline in the capacity for acid-induced wall loosening that reduces wall extensibility and thus cell enlargement in maturing leaves.Abbreviations and symbols FC fusicoccin - P turgor pressure - RL red light - WEx wall extensibility - WL white light - P _w leaf water potential - P _s osmotic potential     

Effect of the Rht3 dwarfing gene on dynamics of cell extension in wheat leaves, and its modification by gibberellic acid and paclobutrazol

The second leaf of wheat was used as a model system to examinethe effects of the Rht3 dwarfing gene on leaf growth. Comparedto the rht3 wild type, the Rht3allele decreased final leaf length,surface area and dry mass by reducing the maximum growth rates,but without affecting growth duration. Gibberellic acid (GA₃)increased final leaf length and maximum growth rate in the rht3wild type, but was without effect on the Rht3 mutant, whichis generally regarded as being non-responsive to gibberellin(GA). Paclobutrazol, an inhibitor of GA biosynthesis, decreasedfinal leaf length and maximum growth rate in the rht3 wild typeto values similar to those in the untreated Rht3 mutant. NeitherGA₃ nor paclobutrazol affected the duration of leaf growth.The decrease in leaf length was produced by reduction of celllength rather than cell number. The maximum relative elementalgrowth rate (REGR) for cell extension was essentially the samein all treatments, as was the time between the cells leavingthe meristem and achieving maximum extension rate. The differencesbetween the genotypes and treatments were all almost entirelydue to differences in the time taken from the attainment ofmaximum REGR of cell extension to the cessation of extension.This was reflected in the length of the extension zone, whichwas approximately 6–8 per cent of final leaf length. Theeffects of the Rht3 allele, GA₃ and paclobutrazol all appearto be on the processes which promote the cessation of cell elongation. Key words: Cell extension, gibberellin, leaf growth, Rht3 gene, Triticum, wheat     

On-line study of growth kinetics of single hyphae of Aspergillus oryzae in a flow-through cell

Using image analysis the growth kinetics of the single hyphae of the filamentous fungus Aspergillus oryzae has been determined on-line in a flow-through cell at different glucose concentrations in the range from 26 mg L-1 to 20 g L-1. The tip extension rate of the individual hyphae can be described with saturation type kinetics with respect to the length of the hyphae. The maximum tip extension rate is constant for all hyphae measured at the same glucose concentration, whereas the saturation constant for the hyphae varies significantly between the hyphae even within the same hyphal element. When apical branching occurs, it is observed that the tip extension rate decreases temporarily. The number of branches formed on a hypha is proportional to the length of the hypha that exceeds a certain minimum length required to support the growth of a new branch. The observed kinetics has been used to simulate the outgrowth of a hyphal element from a single spore using a Monte Carlo simulation technique. The simulations shows that the observed kinetics for the individual hyphae result in an experimentally verified growth pattern with exponential growth in both total hyphal length and number of tips.