Mammalian cell cycles need two random transitions

Although a single transition in the cell cycle is both sufficient and necessary to account for the distribution of differences in the intermitotic times of sister cells, two random transitions seem necessary to account for the responses of quiescent cells to stimulation by growth factors. We propose that serum-depleted quiescent cells “rest” in an indeterminate state (Q) which they leave at random upon stimulation and initiate a lengthy process (L). Upon completion of L the cells enter another indeterminate state (A) which they also leave at random and shortly thereafter initiate S phase and subsequently divide. On leaving A they also re-enter Q, and, again at random, initiate L. This sequence, Q → L → A, is maintained in steady state proliferation, and because of the random exit from Q and A, overlaps to varying degrees with the conventional cell cycle (M-G1-S-G2-M). The hypothesis provides a qualitative account of various problematic features of the lag between stimulation and entry into S phase. It also provides a good quantitative account of the distribution of sibling differences, the correlation coefficient for sibling intermitotic times and the distribution of intermitotic times in steady state growing cultures. There are striking similarities between the hypothetical cycle and the centriole cycle.     

ANALYSIS OF THE VARIABILITY IN CLEAVAGE TIMES AND DEMONSTRATION OF A MITOTIC GRADIENT DURING THE CLEAVAGE STAGES OF NOTHOBRANCHIUS GUENTHERI

Living embryos of the annual cyprinodont fish Nothobranchius guentheri were observed under the microscope. Detailed records were made of the time of cell division, disappearance of the nucleus and of the position of each cell within the blastoderm up to and including the sixth cleavage. Combination of these data revealed the presence of a mitotic gradient, a cell division gradient and a gradient of cell cycle duration in the 8-cell, 16-cell and 32-cell stage. Comparison of the variabilities in the duration of the interphase and mitosis reveals that differences between sister cell intercleavage times in the 8-, 16- and 32-cell stage are, for the most part, due to the variability in the duration of the mitotic process. It is concluded that the DNA-division cycle is composed of at least two parallel series of events. We found the random transition model of cell cycle control, originally based on the analysis of intermitotic times of mammalian cells in tissue culture, helpful also in analysing intercleavage time variability in embryonic cells.     

Time-lapse cinematography studies of cell cycle and mitosis duration

The progenies of 44 cells (EMT6 cell line) have been studied in vitro by time-lapse cinematography for up to eight generations. It has been found that the mean mitotic and intermitotic times vary significantly with the age of the culture and that they are positively correlated. There are correlations between mother and daughter parameters and between sister cells. All these correlations are higher when the age of the culture is greater.     

Variability of the duration of the cell cycle in pig embryo kidney cells in monolayer culture and correlation of the cycle duration in sister cells

The distribution of generation time of sister cells for the exponentially proliferating monolayer SPEV culture was obtained with time lapse cinemicrographic technique. The distribution is characterized by the average generation time equal to 24.3 hour, with the variation coefficient, asymmetry coefficient and correlation coefficient for sister pair cell being, respectively, 17%, 0.2 and 0.78. The results obtained are compared with the prediction of "a random transition" in the cell cycle.     

Cell size, cell cycle and transition probability in mouse fibroblasts

This paper describes the relationship between cell size and cell division in two situations. In the first, quiescent cells were sorted on the basis of cell size using a fluorescence-activated cell sorter and returned to culture. The results of this type of experiment are compatible with the idea that once cells have completed a size-dependent lag, the rate of entry of cells into S phase is controlled by a rate-limiting random event (or transition).The second kind of experiment follows the kinetics of complete cell cycles in rapidly proliferating cells whose mothers had been sorted on the basis of cell size. The cells born of small mother cells have longer cycle times than cells derived from large mothers. The difference in the cycle time of these two classes was due to differences in the B phase of the cell cycle [containing S, G2, M and part of G1 (G1B)], transition probability being the same in both size classes. Our results show that S, G2 and M are unaffected by size, thus confining the effect of size to G1B. It seems probable that the variability of B phase in cloned cell populations is partly due to variations of cell size at division, and correlations between the cycle times of sister cells result because sibling cells are more similar in size than unrelated cells. The major factor controlling cell division in mouse fibroblasts is shown, however, to be the transition probability; size has a more minor role.     

Differences in Cell Cycle Duration of Sister Cells in Secondary Root Meristems of Cocos nucifera L.

Cell lengths of Gl/Gl pairs of sister cells and in mitotic packetsof cells were measured in secondary roots of Cocos nuciferaL. Due to symplastic growth cell length ratios of sister cells,over a cell cycle, remained constant for the dwarf, hybrid andtall varieties of C. nucifera; the mean cell length ratio, betweenthe larger and smaller cell, was between 116:1 and 1 –20:1.From the cell length ratios, mean differences in cell cycleduration for sister cells were calculated to lie between 0–22and 0–27 of the average cell cycle duration. Cumulative distributions of the cell length ratios of sistercells, when converted to differences in cell cycle durationand plotted on semi-log graph paper deviated from an exponentialdistribution. In 86 per cent of the sister cells studied, thelarger cell of a sister pair divided first, however in the remaining14 per cent, half had the smaller cell of a sister pair dividingfirst while in the other half of the sister pairs, the cellswere of equal length but one had entered mitosis ahead of itssister. These results support neither cell cycle models basedon a cell sizer control per se nor on a random transition frominactive to active parts of the cell cycle.     

Variability of cell generation times in a hepatoma cell pedigree

Time-lapse cinematographic analysis of a clone of HTC rat hepatoma cells showed variations in interdivision time within the clone. A positive correlation was found between the interdivision times of mother and daughter cells. The variability of the differences between interdivision times of cells of sister, cousin, second cousin or second-second cousin relationship was calculated. The proportion of cells with large differences in intermitotic times was found to increase with decreasing relationship. The clonal division pattern observed suggests strongly that 'inherited' factors goven the process leading to cell division but that their effects can be modified.     

Temperature compensation in the mammalian cell cycle

Random and synchronous V79 cells were shifted from 37.5 °C to temperatures between 29 ° and 41 °C. Intermitotic time determinations of random cultures showed an increase in generation time and a broadening in the distribution of generation times in cells whose cycle spanned the temperature shift, but only a slight increase in generation time after one generation at temperatures between 34 °–40 °C. At 33.5 °C and below there was a stepwise increase in generation time. When cells grown at non-standard temperatures were allowed to habituate for 48 h at the altered temperature prior to analysis, the increase in median intermitotic time was slightly less in comparison to analyses done after only one generation following the temperature step. The Q₁₀ for cell division of cells growing at temperatures from 34 ° to 40 °C was between 1.15 and 1.26, suggesting that the mammalian cell cycle is temperature compensated over a limited (6–7 °C) temperature span. Mammalian cells in culture appear to have the same capacity for temperature compensation in their cell cycle as do unicellular eukaryotes. The fact that cycle time at lower temperatures increases in a discrete manner is taken as evidence for a quantal clock.     

Analysis of the variability and of the lengthening of intercleavage times during the cleavage stages of Nothobranchius guentheri

By means of time-lapse cinematography the early development of the annual fish Nothobranchius guentheri was recorded on 16-mm film up to the tenth cleavage round. Analysis of the films showed that the mean intercleavage time is much the same up to the seventh cleavage. Thereafter, intercleavage times increase, with steps of about 30 min or a multiple of it, at each subsequent cleavage. As development proceeds, the variability in intercleavage times increases. A positive correlation of sister intercleavage times exists from the seventh generation, whereas intercleavage times of mother-daughter cells are positively correlated in the ninth generation. The results suggest that the lengthening of the cell cycle after the seventh cleavage is due to the insertion of a time period in a programmable mitotic clock. The duration of this time period differs between the different cell lines of a pedigree, probably because of a difference in cell volume. Variability in intercleavage times might also arise as a result of some random transition which the cells traverse only once per 5 min with a transition probability of 0.67/5 min.     

A rare family tree of cultured rat cells showing a change in proliferative potential

In most family trees examined by time-lapse cinemicrography of proliferative rat liver epithelial-like cells in primary culture, a clonal population first expanded, and then ceased to expand. We encountered one rare family tree in which a clonal population first expanded, stopped expanding for a while, and then began to expand again. In this family tree, we noted one particular intermitotic cell, all descendants of which divided during the period of observation when the rest of the cells had ceased division. We consider that this rare family tree showed for the first time part of the process of indefinite proliferation.     

Correlation in G1 transit time of sister cells synchronized by mitotic selection

Chinese hamster ovary (CHO) cells synchronized by mitotic selection were monitored by [³H]TdR autoradiography for entry into S phase. Consistent with the transition probability model of cell cycle control [1], the percent of cells remaining in G1 vs time (plotted on semi-log scale) appears linear after a slight initial curve. Analysis of the labeling pattern of sister cells indicates the following.

1. 1. The labeling index, determined from scoring only cells distinguishable as sister pairs, is the same as that for the total population;

2. 2. the proportion of pairs in which one sister is labeled is less than that expected if labeling is random, while the proportion of pairs in which both sisters are labeled is greater than that expected if labeling is random.

These results indicate either exit from a hypothetical A state is not random, and/or transit through G1 subsequent to exit from the A state results in significant correlation of sister cell transit time.     

Studies on the variations in generation times of rat hepatoma cells in culture

The proliferation kinetics of a cultured hepatoma cell line, HTC, was studied by time-lapse photography and autoradiography. Variability of G1 phase, S phase and intermitotic times of sister cells were compared with data on the variability of G1 phase, G2 phase, S phase and intermitotic times of unrelated cells. Evidence is presented that the variation in times spent in intermitosis by a pair of sisters is determined by the variation of G2 phase durations, while the variation in intermitotic times of unrelated cells is mainly determined by the variation of G1 phase times.     

Cells regulate their proliferation through alterations in transition probability

The proliferation of 3T3, 3T6 and SV3T3 cells was examined by time lapse cinephotography under a number of different growth conditions. It was found that the frequency distributions of intermitotic times of cells with widely different proliferation rates are qualitatively and quantitatively explained by the transition probability model of the cell cycle (Smith and Martin, '73). The behaviour of quiescent cells was characterized by very low values of the transition probability. No "out of cycle" or GO compartment of cells was detectable. From a consideration of these results and those in the literature it appears that the rate of cell proliferation is determined by the value of the "transition probability" (P), and that it is the biochemical manifestation of this parameter that regulates cell growth in vitro and in vivo.     

The cell cycle,cell death,and cell morphology during retinoic acid-induced differentiation of embryonal carcinoma cells

Time-lapse films were made of PC13 embryonal carcinoma cells, synchronized by mitotic shake off, in the absence and presence of retinoic acid. Using a method based on the transition probability model, cell cycle parameters were determined during the first five generations following synchronization. In undifferentiated cells, cell cycle parameters remained identical for the first four generations, the generation time being 11–12 hr. In differentiating cells, with retinoic acid added at the beginning of the first cycle, the first two generations were the same as controls. The duration of the third generation, however, was increased to 15.7 hr while the fourth and fifth generation were approximately 20 hr, the same as in exponentially growing, fully differentiated cells. The increase in generation time of dividing cells was principally due to an increase in the length of S phase. Cell death induced by retinoic acid also occurred principally in the third and subsequent generations. Cell population growth was then significantly less than that expected from the generation time derived from cycle analysis of dividing cells. Cells lysed frequently as sister pairs suggesting susceptibility to retinoic acid toxicity determined in a generation prior to death. Morphological differentiation, as estimated by the area of substrate occupied by cells, was shown to begin in the second cell cycle after retinoic acid addition. These results demonstrate that as in the early mammalian embryo, differentiation of embryonal carcinoma cells to an endoderm-like cell is also accompanied by a decrease in growth rate but that this is preceded by acquisition of the morphology characteristic of the differentiated progeny.     

Comparison of sister chromatid exchanges from three successive cell cycles in Wallabia bicolor chromosomes

An autoradiographic analysis of tritiated thymidine labeled chromosomes of Wallabia bicolor at the second and third metaphases after label incorporations has shown that sister chromatid exchanges (SCE's) from the first and second cell cycles are less than as frequent as SCE's from the third cell cycle after label. Exchange levels per cell cycle estimated at the seconf division are under-estimated due to coincident exchanges. In both methaphases exchanges were largely distributed at random along Wallabia chromosomes with frequencies proportional to chromosome length. The ratio of twin: single SCE's in spontaneoulsy occuring tetraploid cells indicated the first cycle exchanges were marginally more frequent than second cycle exchanges.These data are compatible with exchange probabilities being equal and independent over divisions, but a component of exchanges reducing as tritium content in chromosomes decreases cannot be excluded. This findings that SCE's are primarily independent of tritium cannot be attributed to a saturation of sites for exchange and it is therefore probable that sister exchanges are, in part at least, spontaneous events in Wallabia chromosomes.     

Evidence for an intraclonal random shift between two types of cell cycle times in an embryonal carcinoma cell line

In a recent paper we reported the discovery of an intraclonal bimodal-like cell cycle time variation within the multipotent embryonal carcinoma (EC) PCC3 N/1 line growing in the exponential phase in the undifferentiated state. The variability was found to be localized in the G1 period. Furthermore, an inverse relation between cell size and cell generation time was found in the cell system analysed. It was suggested that the bimodal-like intraclonal time variability previously reported was attributable to an intraclonal shift between two types of cell-growth-rate cycles and that the cell-growth cycle has a supramitotic character, being dissociated from the DNA-division cycle. The growth rate heterogeneity in the cell population was found to need three cell cycles to reach full dispersion in time. This was assumed to be due to a decreased inheritance from sister cell pairs to second cousin cell pairs. Thus, the interesting feature is that in one and the same multipotent cell line there was evidence for an intraclonal instability with a random shift between two types of cell cycle differing in the duration of their G1 period.     

Investigation into the experimental kinetic support of the two-state model of the cell cycle

Five previously published cell generation-time distribution functions have been examined in an effort to elucidate the parameters of the two-state model of the cell cycle. These parameters are the fractional number of cells that bypass the G0 state, the probability of exit from G0, and the distribution of traversal times through the active state. To explain observed beta-curve behavior of cell populations, it is necessary to define the parameters in terms of pairwise behavior of newborn sister cells. From the beta-curve, we demonstrate that at least 50% of the cells must pass through the G0 state. The alpha-curve is consistent with any positive fraction of newborn cells passing through the G0 state, and provides no further information. We explore a possible method for resolving the remaining indeterminacy regarding the number of cells bypassing the G0 state, namely, examination of the generation-time distribution functions of fast sister cells only. Such an approach, although theoretically attractive, presents formidable experimental difficulties, however. If it should turn out that indeed only 50% of the cells are apparently passing through a random-exiting phase of the cell cycle, then an alterative plausible biological mechanism for the observed variability in generation times is supplied by Prescott's hypothesis: variability is a consequence of the inequality in the metabolic content of sister cells at birth.