Metabolic characterization of the viable, residually dividing and nondividing cell classes of recombination-deficient strains of Escherichia coli.

The abilities of rec+, recB- recC-, recA-, and recA- recB- rec C- strains to support growth of bacteriophage T4, to take up oxygen, and to maintain cell integrity have been measured. (i) With respect to bacteriophage T4 growth, T4 phage is produced with identical lysis time in single -step growth curves with all strains tested. rec- strains show reduced phage production (fewer infected centers), but the average burst size per infected center is the same for all strains tested. Some rec- cells are unable to produce any phage, whereas the remainder of the rec-cells produce phage as rapidly and as efficiently as rec+ cells. (ii) With respect to oxygen consumption, rec- strains are deficient relative to the rec+ control to the same extent as the deficiency in phage production by theculture. The reduction in oxygen consumption is coordinate with reduction in rate of mass increase of the rec- culture. (iii) With respect to cell integrity, rec- cultures show increased lysis as measured by release of beta-galactosidase into the medium. The kinetics of release suggest that rec- nondividing cells all eventually lyse. These results are most consistent with the idea that rec- residually dividing cells and viable cells are metabolically normal according to the parameters we have measured, whereas nondividing cells are metabolically inactive.     

A Millifluidic Study of Cell-to-Cell Heterogeneity in Growth-Rate and Cell-Division Capability in Populations of Isogenic Cells of Chlamydomonas reinhardtii

To address possible cell-to-cell heterogeneity in growth dynamics of isogenic cell populations of Chlamydomonas reinhardtii, we developed a millifluidic drop-based device that not only allows the analysis of populations grown from single cells over periods of a week, but is also able to sort and collect drops of interest, containing viable and healthy cells, which can be used for further experimentation. In this study, we used isogenic algal cells that were first synchronized in mixotrophic growth conditions. We show that these synchronized cells, when placed in droplets and kept in mixotrophic growth conditions, exhibit mostly homogeneous growth statistics, but with two distinct subpopulations: a major population with a short doubling-time (fast-growers) and a significant subpopulation of slowly dividing cells (slow-growers). These observations suggest that algal cells from an isogenic population may be present in either of two states, a state of restricted division and a state of active division. When isogenic cells were allowed to propagate for about 1000 generations on solid agar plates, they displayed an increased heterogeneity in their growth dynamics. Although we could still identify the original populations of slow- and fast-growers, drops inoculated with a single progenitor cell now displayed a wider diversity of doubling-times. Moreover, populations dividing with the same growth-rate often reached different cell numbers in stationary phase, suggesting that the progenitor cells differed in the number of cell divisions they could undertake. We discuss possible explanations for these cell-to-cell heterogeneities in growth dynamics, such as mutations, differential aging or stochastic variations in metabolites and macromolecules yielding molecular switches, in the light of single-cell heterogeneities that have been reported among isogenic populations of other eu- and prokaryotes.     

Effects of the ccd function of the F plasmid on bacterial growth.

The ccd segment of the mini F plasmid containing the ccdA and ccdB genes controls the coordination between plasmid proliferation and cell physiology and fate. When the DNA replication of a thermosensitive-replication plasmid carrying the ccd segment of mini F is blocked, plasmid DNA molecules are progressively diluted through cell division until the copy number reaches 1 per cell. From this time on, there is little increase in the number of viable cells, although cells continue to divide, resulting in a mixed population of viable cells (mostly plasmid containing), nonviable but residually dividing cells, and nonviable nondividing cells. Results are presented suggesting that plasmid-containing cells are viable and continue to divide, whereas plasmid-free segregants are nonviable and form filaments after a few residual divisions, with DNA synthesis reduced or arrested in the filaments. Although the ccd functions are known to induce the SOS response when plasmid replication is blocked, the production of nonviable plasmid-free segregants is independent of the SOS cell division inhibition mechanism determined by the sfiA and sfiC genes.     

DNA synthesis during meiosis of eight-spored strains ofChlamydomonas reinhardi

Summary In strain 137F ofChlamydomonas reinhardi, the zygospores undergo one round of nuclear DNA replication followed by three divisions to produce octospores. The third division without replication has been interpreted by Sueoka et al. (1967, 1969) to mean that the gametes and vegetative cells have at least binemic chromosomes. We have repeated their experiments using the same strain. However, the meiotic products were inviable — unable to undergo postmeiotic vegetative growth, DNA replication or division. On the other hand, using a variant of strain 137C which also has three divisions during germination we have shown that meiosis is normal. Zygospores from this strain undergo two rounds of nuclear DNA replication prior to the formation of octospores. These meiotic products are viable and capable of postmeiotic vegetative growth, replication and division. Since the third division without DNA replication subsequent to the two meiotic divisions leads to inviable products, and the strain which has viable products after three divisions does not lack the additional replication, meiosis inChlamydomonas reinhardi provides no evidence of a bineme chromosome structure.     

The nature of cell division forces in epithelial monolayers

Epithelial cells undergo striking morphological changes during division to ensure proper segregation of genetic and cytoplasmic materials. These morphological changes occur despite dividing cells being mechanically restricted by neighboring cells, indicating the need for extracellular force generation. Beyond driving cell division itself, forces associated with division have been implicated in tissue-scale processes, including development, tissue growth, migration, and epidermal stratification. While forces generated by mitotic rounding are well understood, forces generated after rounding remain unknown. Here, we identify two distinct stages of division force generation that follow rounding: (1) Protrusive forces along the division axis that drive division elongation, and (2) outward forces that facilitate postdivision spreading. Cytokinetic ring contraction of the dividing cell, but not activity of neighboring cells, generates extracellular forces that propel division elongation and contribute to chromosome segregation. Forces from division elongation are observed in epithelia across many model organisms. Thus, division elongation forces represent a universal mechanism that powers cell division in confining epithelia.     

The relative effects of different types of growth factors on DNA replication, mitosis, and cellular enlargement

It was recently demonstrated that growth in cell size can be dissociated from DNA synthesis and mitosis. 3T3 cells starved to quiescence in low serum concentration can be stimulated to undergo DNA synthesis and one cell division without growing in size (unbalanced growth) (42-44). We report here that in cells stimulated to undergo unbalanced growth, the cell nucleus undergoes balanced growth, i.e., nearly doubles in size prior to mitosis. The reduced ability to grow in cell size under unbalanced growth conditions is thus mainly ascribable to the cytoplasm. Furthermore, the extent to which cells grow in size prior to mitosis is dependent on the serum concentration in the tissue culture medium (44). This data suggests that some macromolecular factor or factors in serum are required for growth in cell size prior to mitosis. We report in this study that epidermal growth factor (EGF) alone exerts a small but significant stimulatory influence on DNA synthesis and mitosis but does not affect cellular enlargement. In contrast, insulin added at supraphysiological concentrations does not stimulate quiescent cells to enter S phase but instead stimulates growth in cell size in the small fraction of dividing cells. Furthermore, cells stimulated to proliferate by EGF could be induced to undergo balanced growth when insulin was added concomitantly. Finally, platelet-derived growth factor (PDGF) stimulates quiescent sparse 3T3 cells to undergo DNA synthesis and mitosis. PDGF also exerts a limited but significant effect on cellular enlargement. However, PDGF alone could not induce a complete balanced growth, i.e., a doubling in cell size prior to mitosis.     

Age Distribution of Human Diploid Fibroblasts: A Stochastic Model for In Vitro Aging

Variation in the lifespan of mass cultures and clones of human diploid fibroblasts can be explained on the basis of variation in the length of the mitotic cycle. This variation is of biological significance; the intrinsic standard deviation of culture lifespan is equal to about 10% of the mean. We constructed a two-parameter stochastic model based on the following assumptions: the time between successive divisions of a given cell is of random duration; cells divide or lose the ability to divide independently of one another; the probability that a cell can undergo further division is constant up to some maximum number of divisions and zero thereafter. We determined numerically the proportion of nondividing cells and the distribution of cell generations. Samples taken by Monte Carlo means from a hypothetical in vitro population were compared with clonal survival data obtained experimentally. The fit between experimental and theoretical findings was within the range of sampling variation. If we accept our model as being applicable to human diploid cell culture, we can draw the following conclusions: the proportion of dividing cells is an inadequate index of a population's age; even in populations in which almost all cells are still capable of division, a majority of the cells have less than eight generations remaining to them. At each subcultivation the ultimate fate of a culture is determined by the disposition of a relatively small number of “young” cells.     

Electron microscopic study of the division processes in cysts of the sarcosporidian, Sarcocystis, ovifelis

The metrocyte stage in the cysts of S. ovifelis has been found to divide not by endodyogeny, but by a different mode, not yet completely understood. The nucleus of the dividing metrocyte displays no nuclear envelope, the cytoplasm is full of large vacuoles. During the metrocyte division, some kind of nucleoplasm spreading occurs over the cytoplasm and between the large vacuoles, thus making any morphological limits between the cytoplasm and the nucleus invisible. The cytokinesis is accomplished due to the deep invaginations of the metrocyte pellicle. The metrocyte division first gives rise to a large multicellular (4--6) body lying in the peripheral zone of the cyst. The very impossibility of endodyogenetic division in the metrocyte stage may be due to its vaery peculiar morphofunctional organization, much different from what is characteristic of any asexual penetrative stage (= zoite) of Apicomplexa. The progeny of a metrocyte are interstitial cells which eventually, through the number of generations, evolve towards the metrozoite stage. Step by step, the interstitial cells aquire polarity due to the establishment of a conoid, rhoptries and micronnemes on the anterior pole, the pellicle becoming more rigid thus making, together with subpellicular microtubules, the cytoskeleton of the parasite. The study performed enables us to conclude that it is interstitial cells of advanced generations that divide by endodogeny. Merozoites being homologous to gamonts of other coccidia undergo no asexual division at all.     

A defect in the acetyl coenzyme A<-->acetate pathway poisons recombinational repair-deficient mutants of Escherichia coli

Recombinational repair-dependent mutants identify ways to avoid chromosomal lesions. Starting with a recBC(Ts) strain of Escherichia coli, we looked for mutants unable to grow at 42 degrees C in conditions that inactivate the RecBCD(Ts) enzyme. We isolated insertions in ackA and pta, which comprise a two-gene operon responsible for the acetate<-->acetyl coenzyme A interconversion. Using precise deletions of either ackA or pta, we showed that either mutation makes E. coli cells dependent on RecA or RecBCD enzymes at high temperature, suggesting dependence on recombinational repair rather than on the RecBCD-catalyzed linear DNA degradation. Complete inhibition of growth of pta/ackA rec mutants was observed only in the presence of nearby growing cells, indicating cross-inhibition. pta rec mutants were sensitive to products of the mixed-acid fermentation of pyruvate, yet none of these substances inhibited growth of the double mutants in low-millimolar concentrations. pta, but not ackA, mutants also depend on late recombinational repair functions RuvABC or RecG. pta/ackA recF mutants are viable, suggesting, together with the inviability of pta/ackA recBC mutants, that chromosomal lesions due to the pta/ackA defect are of the double-strand-break type. We have isolated three insertional suppressors that allow slow growth of pta recBC(Ts) cells under nonpermissive conditions; all three are in or near genes with unknown functions. Although they do not form colonies, ackA rec and pta rec mutants are not killed under the nonpermissive conditions, exemplifying a case of synthetic inhibition rather than synthetic lethality.     

An Automata-theoretical Model of Meristem Development as Applied to the Primary Root of Zea mays L.

Observations were made of the sequence of division within thecellular packets (groups of cells of common descent) which comprisethe cell files that run the length of the central cortex ofthe primary root meristem ofZea mays. These sequences, and alsothe relative lengths of the cells within the packets recordedat various times during root growth, indicate that cell-filedevelopment can be expressed using one, or a limited number,of deterministic ‘bootstrap’ L-systems which assigndifferent lifespans to sister cells of successive cell generations.The outcome is a regular pattern of divisions from which daughtercells emerge usually with unequal, but definite, lengths. Inthe immediately post-germination stage of root growth, one divisionpathway is especially common in the cortex and generates sequencesof unequal daughters having a particular basi-apical orientation.Later in root growth, the cellular pattern in the cortex indicatesthat this pathway is replaced by another where unequal divisionsare not so marked, but which nevertheless continues to maintaina regular arrangement of differently sized cells. This latterpathway is characteristic of a zone close to the initial cellsof the cortex. It is present at all stages of root growth andspreads along the length of the cortex as the descendants ofthese initials proliferate. The development of the whole corticalcell file can be simulated from knowledge of the growth functionsof the bootstrap systems. The files so generated contain allthe observed cell patterns. The growth functions also predictthe sequence in which cells cease dividing near the proximalmargin of the meristem, but for this it is necessary to incorporatea counter for the number of divisions that will be accomplishedin the cell file. Cytological requirements for the propagationof unequal divisions, together with a consideration of the natureof the division counter, as well as the significance of theswitch in division pathways encountered during early root growth,are discussed in the context of this deterministic model ofcell division. Cell division; root meristem; L-systems; Zea mays     

Coordination of the initiation of recombination and the reductional division in meiosis in Saccharomyces cerevisiae

Early exchange (EE) genes are required for the initiation of meiotic recombination in Saccharomyces cerevisiae. Cells with mutations in several EE genes undergo an earlier reductional division (MI), which suggests that the initiation of meiotic recombination is involved in determining proper timing of the division. The different effects of null mutations on the timing of reductional division allow EE genes to be assorted into three classes: mutations in RAD50 or REC102 that confer a very early reductional division; mutations in REC104 or REC114 that confer a division earlier than that of wild-type (WT) cells, but later than that of mutants of the first class; and mutations in MEI4 that do not significantly alter the timing of MI. The very early mutations are epistatic to mutations in the other two classes. We propose a model that accounts for the epistatic relationships and the communication between recombination initiation and the first division. Data in this article indicate that double-strand breaks (DSBs) are not the signal for the normal delay of reductional division; these experiments also confirm that MEI4 is required for the formation of meiotic DSBs. Finally, if a DSB is provided by the HO endonuclease, recombination can occur in the absence of MEI4 and REC104.     

Growth kinetics of cells following freezing in liquid nitrogen

The growth kinetics of cells frozen to ?196 °C were monitored after thawing by various techniques. Progression through the cell cycle in the exposed generation was observed by monitoring cell growth either via multiplicity counts or by electronic cell counts of trypsinized suspensions. Subsequent generations were followed by time-lapse microcinematography.The division delay in the exposed generation of exponential-phase cells was dependent on cell age at the time of freezing and varied from 4 to 8 hr. The time of the first generation was still prolonged significantly but subsequent generations revealed cell cycle times that are comparable to unfrozen cells. In the case of plateau-phase cells, mitosis was delayed 7 hr in the exposed generation. This is 50% longer than the delay seen for pre-DNA synthetic g₁ cells in exponentially growing cultures.A rather important observation in this study was that frozen-thawed cells which divide once will probably continue dividing whereas eventual nonsurvivors are not likely to divide at all. The latter, however, remain active for more than 35 hr as observed microscopically, hence possibly indicating residual metabolic activity.     

Regulation of interstitial cell differentiation in Hydra attenuata. I. Homeostatic control of interstitial cell population size.

Mechanisms regulating the population size of the multipotent interstitial cell (i-cell) in Hydra attenuata were investigated. Treatment of animals with 3 cycles of a regime of 24 h in 10-2 M hydroxyurea (HU) alternated with 12 h in culture medium selectively killed 95-99% of the i-cells, but had little effect on the epithelial cells. The i-cell population recovered to the normal i-cell:epithelial cell ratio of I:I within 35 days. Continuous labelling experiments with [3H]thymidine indicate that the recovery of the i-cell population is not due to a change in the length of the cell cycle of either the epithelial cells or the interstitial cells. In control animals 60% of the i-cell population undergo division daily while 40% undergo differentiation. Quantification of the cell types of HU-treated animals indicates that a greater fraction of the i-cells were dividing and fewer differentiating into nematocytes during the first 2 weeks of the recovery after HU treatment. Therefore, the mechanism for recovery involves a shift of the 60:40 division:differentiation ratio of i-cells towards a higher fraction in division until the normal population size of the i-cells is regained. This homeostatic mechanism represents one of the influences affecting i-cell differentiation.     

Exploring intracellular space: function of the Min system in round-shaped Escherichia coli

The MinCDE proteins help to select cell division sites in normal cylindrical Escherichia coli by oscillating along the long axis, preventing unwanted polar divisions. To determine how the Min system might function in cells with multiple potential division planes, we investigated its role in a round-cell rodA mutant. Round cells lacking MinCDE were viable, but growth, morphology and positioning of cell division sites were abnormal relative to Min+ cells. In round cells with a long axis, such as those undergoing cell division, green fluorescent protein (GFP) fusions to MinD almost always oscillated parallel to the long axis. However, perfect spheres or irregularly shaped cells exhibited MinD movement to and from multiple sites on the cell surface. A MinE-GFP fusion exhibited similar behavior. These results indicate that the Min proteins can potentially localize anywhere in the cell but tend to move a certain maximum distance from their previous assembly site, thus favoring movement along the cell's long axis. A new model for the spatial control of division planes by the Min system in round cells is proposed.     

Oxidative Damages and Repair in Euglena gracilis Exposed to Ozone. I. SH Groups and Lipids

Malondialdehyde, a product of lipid oxidation, increased graduallywhen Euglena gracilis cells were bubbled with 240 µ1.liter^–1ozone (delivery rate of 1µmolO₃.min^–1) for 120 min.Simultaneously, the sulfhydryl group content decreased by 36%during the treatment, which was mainly due to oxidation of proteinsulfhydryl groups. The molar amount of SH groups oxidized was3 times higher than that of fatty acid oxidized, indicatingthat sulfhydryl groups were more accessible or more easily oxidizedby O₃ than fatty acids. When Euglena cells were allowed to recoverunder autotrophic growth conditions following O₃ treatment,viable cells were incapable of dividing during the first 5 hof the recovery period but regenerated SH groups nearly to thecontrol level. The increase of SH content during this periodpreceded the resumption of cell division and the restorationof normal growth. These results suggest that the regenerationof SH groups by Euglena cells is a part of a mechanism involvedin the repair of oxidative damage caused by ozone and is anessential step for the initiation of cell division. (Received July 20, 1987; Accepted December 14, 1987)     

Freeze Preservation of Cultured Plant Cells. III. The Pregrowth Phase

There is an inverse relationship between cell size and capacity to survive the freeze-preservation protocol. Pregrowth of cell suspensions in media rendered more negative in water potential by addition of mannitol enhances the survival capacity of Acer pseudoplatanus and Capsicum annuum cells but this effect can only partially be explained in terms of the associated reduction in mean cell size. Studies with cell suspensions of Daucus carota indicate the importance for successful freeze-preservation of the stage in the growth cycle of suspensions propagated in batch culture; highest survival was recorded for cells taken at lag phase or early exponential phase. Regrowth of recovered cells depends upon the establishment of an appropriate inoculum density of cells which have retained the capacity to divide. The dividing cells only achieve a growth rate equal to that of untreated cells after a number of cell generations. A proportion of the recovered cells giving an initial positive fluorescein diacetate reaction lose this capacity rapidly (within 24 h), others lose the capacity more slowly and others, in which the positive reaction persists, are incapable of division. These observations indicate that different levels of injury are inflicted by the freeze-preservation protocol and that only in a proportion of the cells is the injury reparable or compatible with growth by cell division.     

Cytoplasmic Volume Condensation Is an Integral Part of Mitosis

Cell growth and osmotic volume regulation are undoubtedly linked to the progression of the cell cycle as with each division, a newly generated cell must compensate for loss of half of its volume to its sister cell. The extent to which size influences cell cycle decisions, however, is controversial in mammalian cells. Further, a mechanism by which cells can monitor and therefore regulate their size has not been fully elucidated. Despite an ongoing debate, there have been few studies which directly address the question in single cell real-time experiments. In this study we used fluorescent time-lapse imaging to quantitatively assess volume in individual spontaneously dividing cells throughout the cell cycle. Together with biophysical studies, these establish that the efflux of salt and water brings about a condensation of cytoplasmic volume as glioma cells progress through mitosis. As cells undergo this pre-mitotic condensation (PMC) they approach a preferred cell volume preceding each division. This is functionally linked to chromatin condensation, suggesting that PMC plays an integral role in mitosis.     

Nuclear non-histone proteins from rat ventral prostate cell under going hypertrophy of hyperplasia.

The distribution of nuclear non-histone proteins and their labelling with [¹⁴C]amino acids or [³²P]O₄ in rat ventral prostate cells undergoing hypertrophy (cell growth) or hyperplasia (cell division) were compared by SDS polyacrylamide gel electrophoresis. Marked quantitative changes in these proteins accompanied castration and replacement of hormone, but no absolute qualitative differences in their staining patterns were established. Preparations from cells undergoing hyperplasia were augmented in high molecular weight proteins and contained fewer proteins of <20000 D. The increased amounts of nuclear non-histone proteins from hormone-treated castrated rats were highly labelled by [¹⁴C]amino acids, but the molecular weights of radioactive proteins from cells undergoing hypertrophy were less diverse than those from replicating cells, Phosphorylation of nuclear non-histone proteins from short-term and long-term castrates, treated with testosterone propionate, was 170 and 60% greater than their controls. Proteins from 20–45 × 10³ D were actively phosphorylated. Nuclear extracts from dividing cells contained additional radioactive high molecular weight proteins and fewer phosphorylated lower molecular weight components. The distribution of phosphorylated proteins and newly synthesized proteins was dissimilar. Quantitative and possible qualitative differences in staining of nuclear proteins isolated in N-ethylmalleamideurea-phosphate buffer from normal or hormone-treated castrated rats were accentuated when they were separated by charge at pH 2.8. In replicating cells, a more generalized synthesis of acidic nuclear proteins from all molecular weight classes occurred, which were not as highly phosphorylated as less heterogeneous nuclear proteins from cells undergoing hypertrophy. Examination of the immediate and the subsequent events following androgen-induced cellular hypertrophy or hyperplasia in the ventral prostate permits their comparison in the same tissue.     

Diel Division Cycle and Growth Rates of Synechococcus in Lakes Huron and Michigan1

A clone of Synechococcus isolated from Lake Huron and natural populations of Synechococcus from lakes Huron and Michigan were studied in 1989 to examine the diel division cycle and to provide estimates of the in situ growth rate based on the frequency of dividing cells (FDC) method. Cultured populations of Synechococcus exhibited a consistent diel division pattern with a midday/afternoon (1100–1800 h) peak in the percent of dividing cells. The maximum percent of dividing cells varied among cultures (8-27%) and was related to the growth rate. A small fraction of dividing cells (3-5%) remained throughout the dark period, suggesting that some cells were arrested in the doublet stage prior to division. The duration of division (t_d) ranged from 2.6-4.9 h, with a 3.7 h mean for cultures with growth rates ≥0.34 d⁻¹ but increased to 8 h at a lower growth rate of 0.20 d⁻¹. The diel division pattern for natural populations was very similar to the laboratory clone; an afternoon peak (1400-2100 h) in dividing cells and a small fraction of dividing cells (2-5%) remained during the dark period. The maximum percent of dividing cells for natural populations ranged from 6-10%. In situ growth rates, determined from the FDC and assuming a constant t_d of 3.7 h, ranged from 0.30-0.42 d⁻¹. The FDC method may provide accurate estimates of in situ growth, particularly in environments where the growth rate is >0.34 d⁻¹, but in lakes Huron and Michigan where growth rates can be lower and t_d values may increase, FDC-growth rates must be viewed with caution.     

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.