Increase in cell mass during the division cycle of Escherichia coli B/rA.

Increase in the mean cell mass of undivided cells was determined during the division cycle of Escherichia coli B/rA. Cell buoyant densities during the division cycle were determined after cells from an exponentially growing culture were separated by size. The buoyant densities of these cells were essentially independent of cell age, with a mean value of 1.094 g ml-1. Mean cell volume and buoyant density were also determined during synchronous growth in two different media, which provided doubling times of 40 and 25 min. Cell volume and mass increased linearly at both growth rates, as buoyant density did not vary significantly. The results are consistent with only one of the three major models of cell growth, linear growth, which specifies that the rate of increase in cell mass is constant throughout the division cycle.     

The relationship between yeast cell size and cell division in Candida albicans

The mean size and percentage of budded and unbudded cells of Candida albicans grown in batch culture over a wide range of doubling times have been measured. Cell volume decreased with increased doubling time and a nonlinear approach to an asymptotic minimum was observed. When cells were separated by age according to bud scars, each age showed a similar decrease. During each cell division cycle, size increased slowly during both budded and unbudded periods so that each generation was significantly larger than the preceding. There was no difference in size between the parent portion of budded cells and unbudded cells of the same age. Time-lapse photomicroscopy of cells growing on solid medium showed that cells divide asymmetrically with larger parents having a shorter subsequent cycle time than the smaller daughter, although the time utilized for bud formation was similar. When cells were shifted from a medium supporting a low growth rate and small size to a medium supporting a faster growth rate and larger size, both budded and unbudded cells increased significantly in size. As the doubling time increased, both the budded and unbudded portions of parental and daughter cycles increased.     

Unequal division in Saccharomyces cerevisiae and its implications for the control of cell division

The budding yeast, Saccharomyces cerevisiae, was grown exponentially at different rates in the presence of growth rate-limiting concentrations of a protein synthesis inhibitor, cycloheximide. The volumes of the parent cell and the bud were determined as were the intervals of the cell cycle devoted to the unbudded and budded periods. We found that S. cerevisiae cells divide unequally. The daughter cell (the cell produced at division by the bud of the previous cycle) is smaller and has a longer subsequent cell cycle than the parent cell which produced it. During the budded period most of the volume increase occurs in the bud and very little in the parent cell, while during the unbudded period both the daughter and the parent cell increase significantly in volume. The length of the budded interval of the cell cycle varies little as a function of population doubling time; the unbudded interval of the parent cell varies moderately; and the unbudded interval for the daughter cell varies greatly (in the latter case an increase of 100 min in population doubling time results in an increase of 124 min in the daughter cell's unbudded interval). All of the increase in the unbudded period occurs in that interval of G1 that precedes the point of cell cycle arrest by the S. cerevisiae alpha-mating factor. These results are qualitatively consistent with and support the model for the coordination of growth and division (Johnston, G. C., J. R. Pringle, and L. H. Hartwell. 1977. Exp. Cell. Res. 105:79-98.) This model states that growth and not the events of the DNA division cycle are rate limiting for cellular proliferation and that the attainment of a critical cell size is a necessary prerequisite for the "start" event in the DNA-division cycle, the event that requires the cdc 28 gene product, is inhibited by mating factor and results in duplication of the spindle pole body.     

Asymmetrical division of Saccharomyces cerevisiae.

The unequal division model proposed for budding yeast (L. H. Hartwell and M. W. Unger, J. Cell Biol. 75:422-435, 1977) was tested by bud scar analyses of steady-state exponential batch cultures of Saccharomyces cerevisiae growing at 30 degrees C at 19 different rates, which were obtained by altering the carbon source. The analyses involved counting the number of bud scars, determining the presence or absence of buds on at least 1,000 cells, and independently measuring the doubling times (gamma) by cell number increase. A number of assumptions in the model were tested and found to be in good agreement with the model. Maximum likelihood estimates of daughter cycle time (D), parent cycle time (P), and the budded phase (B) were obtained, and we concluded that asymmetrical division occurred at all growth rates tested (gamma, 75 to 250 min). D, P, and B are all linearly related to gamma, and D, P, and gamma converge to equality (symmetrical division) at gamma = 65 min. Expressions for the genealogical age distribution for asymmetrically dividing yeast cells were derived. The fraction of daughter cells in steady-state populations is e-alpha P, and the fraction of parent cells of age n (where n is the number of buds that a cell has produced) is (e-alpha P)n-1(1-e-alpha P)2, where alpha = IN2/gamma; thus, the distribution changes with growth rate. The frequency of cells with different numbers of bud scars (i.e., different genealogical ages) was determined for all growth rates, and the observed distribution changed with the growth rate in the manner predicted. In this haploid strain new buds formed adjacent to the previous buds in a regular pattern, but at slower growth rates the pattern was more irregular. The median volume of the cells and the volume at start in the cell cycle both increased at faster growth rates. The implications of these findings for the control of the cell cycle are discussed.     

Morphological analysis of the division cycle of two Escherichia coli substrains during slow growth.

Morphological parameters of the cell division cycle have been examined in Escherichia coli B/r A and K. Whereas the shape factor (length of newborn cell/width) of the two strains was the same at rapid growth (doubling time, tau, less than 60 min), with decreasing growth rate the dimensions of the two strains did change so that B/r A cells became more rounded and B/r K cells became more elongated. The process of visible cell constriction (T period) lasted longer in B/r A than in B/r K during slow growth, reaching at tau = 200 min values of 40 and 17 min, respectively. The time between termination of chromosome replication and cell division (D period) was found to be longer in B/r A than in B/r K. As a result, in either strain completion of chromosome replication seemed always to occur before initiation of cell constriction. Nucleoplasmic separation did not coincide with termination as during rapid growth but occurred in both strains within the T period, about 10 min before cell division.     

Cell Growth and Division: IV. Determination of Volume Growth Rate and Division Probability

Volume growth rate and division probability functions for mammalian cells have been determined as functions of cell volume with good reproducibility and statistical precision using Coulter volume spectrometry and the equations of the Bell model. Results are compared with independent measurements on synchronous cultures. The slow rate of volume dispersion requires that the growth rate F(tau, V) be closely proportional to volume for cells of a given age. However, when F(tau, V) is averaged over the age distribution of a population in balanced exponential growth to give the growth rate function f(V), the latter may rise more steeply than V.     

Length growth of two Escherichia coli B/r substrains.

Length growth of synchronized Escherichia coli B/r substrain A (ATCC 12407) and B/r substrain F26 (Thy his) was followed with an electron microscope. Cells were grown with doubling times (tau) of 60 min (B/rA) and of 82 and 165 min (B/rF26). Different length growth patterns were found for the two substrains. In B/rF, the length growth rate increased about midway in the cell cycle. For tau = 165 min, the rate increase was preceded by a short period of slow growth. For B/r A (r = 60 min), this period seemed to occur at the beginning of the cell cycle. The possibility is raised that the different length growth patterns are related to different deoxyribonucleic acid replication patterns of the respective strains.     

Cell elongation and division probability during the Escherichia coli growth cycle.

A new method is presented for determining the growth rate and the probability of cell division (separation) during the cell cycle, using size distributions of cell populations grown under steady-state conditions. The method utilizes the cell life-length distribution, i.e., the probability that a cell will have any specific size during its life history. This method was used to analyze cell length distributions of six cultures of Escherichia coli, for which doubling times varied from 19 to 125 min. The results for each culture are in good agreement with a single model of growth and division kinetics: exponential elongation of cells during growth phase of the cycle, and normal distributions of length at birth and at division. The average value of the coefficient of variation was 13.5% for all strains and growth rates. These results, based upon 5,955 observations, support and extend earlier proposals that growth and division patterns of E. coli are similar at all growth rates and, in addition, identify the general growth pattern of these cells to be exponential.     

A bimolecular mechanism for the cell size control of the cell cycle

A molecular model for the control of cell size has been developed. It is based on two molecules, one (I) acts as an inhibitor of the entrance into S phase, and it is synthetised just after cell separation in a fixed amount per nucleus. The other (A) is an activator of the S phase, and it is synthetised at a ratio proportional to the overall protein accumulation. The activator reacts stoichiometrically with (I), and after all the (I) molecules have been titrated, (A) begins to accumulate. When it reaches a threshold value, it triggers the onset of DNA replication. This model was tested by simulation and when applied to the case of unequal division explains a number of features of an exponentially growing yeast cell population: (a) the lengths of TP (cycle time of parent cells) and TD (cycle time of daughter cells) verify the condition exp(- KTP ) + exp(- KTD ) = 1; (b) the changes of the average cell size of populations at different growth rates; (c) the frequency of parents and daughters at various growth rates; (d) the increase of cell size at bud initiation for cells of increasing genealogical age; (e) the existence of a TP - TB period (difference between the cycle time of parents and the length of budded phase) that depends linearly upon the doubling time of the population.     

Morphological analysis of nuclear separation and cell division during the life cycle of Escherichia coli.

Quantitative electron microscope observations were performed on Escherichia coli B/r after balanced growth with doubling times (tau) of 32 and 60 min. The experimental approach allowed the timing of morphological events during the cell cycle by classifying serially sectioned cells according to length. Visible separation of the nucleoplasm was found to coincide with the time of termination of chromosome replication as predicted by the Cooper-Helmstetter model. The duration of the process of constrictive cell division (10 min) appeared to be independent of the growth rate for tau equals 60 min or less but to increase with increase doubling time in more slowly growing cells. Physiological division, i.e., compartmentalization prior to physical separation of the cells, was only observed to occur in the last minute of the cell cycle. The morphological results indicate that cell elongation continues during the division process in cells with tau equals 32 min, but fails to continue in cells with tau equals 60 min.     

Control of cell division in the yeast Saccharomyces cerevisiae cultured at different growth rates

Saccharomyces cerevisiae has been grown with different generation times by alterations in media richness and by altering the flow rate of the limiting nutrient, glucose in a chemostat. Within the generation time range 2.89-approx. 8.0 h the time from the initiation of DNA synthesis to cell division was independent of generation time and was approx. 2 h. Thus the cell cycle of yeast can be divided into an expandable phase from cell division to the initiation of DNA synthesis, the length of which is dependent on growth rate and a constant phase from the initiation of DNA synthesis to cell division which takes a constant time independent of generation time. In cells growing with generation times longer than 8.6 h this constant phase expands somewhat in time. These results are reminiscent of the observation that in the bacterium Escherichia coliB/R the time from initiation of DNA synthesis to cell division is constant except at very slow growth rates.     

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.     

Cell volume increase in Escherichia coli after shifts to richer media.

Synchronous cultures of Escherichia coli 15-THU and WP2s, which were selected by velocity sedimentation from exponential-phase cultures growing in an acetate-minimal salts medium, were shifted to richer media at various times during the cell cycle by the addition of glucose or nutrient broth. Cell numbers and mean cell volumes were measured electronically. The duration of the division cycle of the shifted generation was not altered significantly by the addition of either nutrient. Growth rates, measured as rates of cell volume increase, were constant throughout the cycle in unshifted acetate control cultures. When glucose was added, growth rates also remained unchanged during the remainder of the cell cycle and then increased abruptly at or after cell division. When nutrient broth was added, growth rates remained unchanged from periods of 0.2 to 0.4 generations and then increased abruptly to their final values. In all cases, the cell volume increase was linear both before and after the growth rate transition. The strongest support for a linear cell volume increase during the cell cycle of E. coli in slowly growing acetate cultures, however, was obtained in unshifted cultures, in complete agreement with earlier observations of cell volumes at much more rapid growth rates. Although cell growth and division are under the control of the synthesizing machinery in the cell responsible for RNA and protein synthesis, the results indicate that growth is also regulated by membrane-associated transport systems.     

Yeast-phase cell cycle of the polymorphic fungus Wangiella dermatitidis.

The yeast-phase cell cycle of Wangiella dermatitidis was studied using flow microfluorimetry and the deoxyribonucleic acid (DNA) synthesis inhibitor hydroxyurea (HU). Exposure of exponential-phase yeastlike cells to 0.1 M HU for 3 to 6 h resulted in the arrest of the cells in DNA synthesis and produced a nearly homogeneous population of unbudded cells. Treatment of the yeast-phase cells with HU for 9 h or longer resulted in the accumulation of the cells predominantly as budded forms having either a single nucleus in the mother cell or a single nucleus arrested in the isthmus between the mother cell and the daughter bud. Exposure of unbudded stationary-phase cells to 0.1 M HU resulted in the accumulation of the cells in the same phenotypes. Analysis by flow microfluorimetry and cell counts of HU-inhibited mithramycin-stained cells indicated that the eventual progress of HU-inhibited cells from unbudded to the two budded forms was due to the limited continuation of the growth sequence of the cell cycle even in the absence of DNA synthesis, nuclear division, and in some cases nuclear migration. On the basis of these observations and the results of flow microfluorimetric analysis of exponential-phase cells, a map of the yeast-phase cell cycle was constructed. The cycle appears to consist of two independent sequences of events, a budding growth sequence and a DNA division sequence. The nuclear division cycle of yeast-phase cells growing exponentially with a 4.5-h generation time is composed of a G1 interval of 148 min, as S phase of 16 min, and a G2 plus M interval of 107 min.     

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.     

<Emphasis Type="Italic">Chlamydomonas reinhardtii:</Emphasis> duration of its cell cycle and phases at growth rates affected by light intensity

In the cultures of the alga Chlamydomonas reinhardtii, division rhythms of any length from 12 to 75 h were found at a range of different growth rates that were set by the intensity of light as the sole source of energy. The responses to light intensity differed in terms of altered duration of the phase from the beginning of the cell cycle to the commitment to divide, and of the phase after commitment to cell division. The duration of the pre-commitment phase was determined by the time required to attain critical cell size and sufficient energy reserves (starch), and thus was inversely proportional to growth rate. If growth was stopped by interposing a period of darkness, the pre-commitment phase was prolonged corresponding to the duration of the dark interval. The duration of the post-commitment phase, during which the processes leading to cell division occurred, was constant and independent of growth rate (light intensity) in the cells of the same division number, or prolonged with increasing division number. It appeared that different regulatory mechanisms operated through these two phases, both of which were inconsistent with gating of cell division at any constant time interval. No evidence was found to support any hypothetical timer, suggested to be triggered at the time of daughter cell release.     

The relationship between cell size and cell division in the yeast Saccharomyces cerevisiae.

Cell numbers in synchronous cultures of yeast cultured at fast growth rates increase from N to 2N after the first division and from 2N to 4N after the second division. At these fast growth rates, there are equal numbers of parents and daughters. In contrast, at slow growth rates the cell number increases from N to 2N after one division and from 2N to 3N rather than 4N after the second division. Moreover, the percentage of daughters increases with decreasing growth rate. Thus, slowly growing cultures actually consist of two sub-populations having different cell cycle transit times. These observations are predicted if a yeast cell requires a critical size before a particular cell cycle event can be completed and that after completion of this event cell division occurs following a period of time independent of growth rate.     

The interrelationship of cell growth and division in haploid and diploid cells of Saccharomyces cerevisiae

The coordination of cell growth and division has been examined in isogenic haploid and diploid strains of Saccharomyces cerevisiae. The average cell volume of the haploid and diploid cells was unaffected by a range of environmental conditions and generation times. For most environments and generation times the mean cell volume of diploid cells was between 1.52 and 1.83 of the haploid cell volume. Both haploid and diploid cell volumes were reduced drastically when the cells were grown in the chemostat with glucose as the limiting substrate. In this environment diploid cells have the same mean cell volume as haploid cells. Diploid cells are more elongated than haploid cells, and the characteristic shape (eccentricity) of the cells is unaffected by all environmental conditions and generation times tested. Mother cell volume increased during the cell cycle, although the pattern of this increase was affected by the environmental conditions. Under most growth conditions detectable mother cell volume increase occurred only during the budding phase, whereas under conditions of carbon limitation detectable increase only occurred during the unbudded phase. A consequence of this result is that the mean cell volume of haploids at bud initiation is relatively constant in all environments, including carbon limitation. This suggests that there is a critical size for bud initiation for haploids which is constant and independent of environmental conditions. The results for diploids are more complex. Coordination of growth and division in haploid cells can be explained by a simple model initially developed for prokaryotes by Donachie. A modification of this model is proposed to account for the results with diploids.     

Linear Cell Growth in Escherichia coli

Growth was studied in synchronous cultures of Escherichia coli, using three strains and several rates of cell division. Synchrony was obtained by the Mitchison-Vincent technique. Controls gave no discernible perturbation in growth or rate of cell division. In all cases, mean cell volumes increased linearly (rather than exponentially) during the cycle except possibly for a small period near the end of the cycle. Linear volume growth occurred in synchronous cultures established from cells of different sizes, and also for the first volume doubling of cells prevented from division by a shift up to a more rapid growth rate. As a model for linear kinetics, it is suggested that linear growth represents constant uptake of all major nutrient factors during the cycle, and that constant uptake in turn is established by the presence of a constant number of functional binding or accumulation sites for each growth factor during linear growth of the cell.     

Cellular autolytic activity in synchronized populations of Streptococcus faecium.

The autolytic capacity of Streptococcus faecium (S. faecalis ATCC 9790) varied during synchronous cell division. This phenomenon was initially observed in rapidly dividing populations (TD=30 to 33 min) synchronized by a combination of induction and size selection techniques. To minimize the problems inherent in studies of cells containing overlapping chromosome cycles and possible artifacts generated by induction techniques, the autolytic capacities of slowly dividing populations (TD=60 to 110 min) synchronized by selection only were examined. Although the overall level of cellular autolytic capacity was observed to decline with decreasing growth rate, sharp, periodic fluctuations in cellular autolytic capacity were seen during synchronous growth at all growth rates examined. On the basis of similar patterns of cyclic fluctuations in autolytic capacity of cultures synchronized by (i) selection, (ii) amino acid starvation followed by size selection, and (iii) amino acid starvation followed by inhibition of DNA synthesis, a link of such fluctuations with the cell division cycle has been postulated.