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 β-curve behavior of cell populations, it is necessary to define the parameters in terms of pairwise behavior of newborn sister cells. From the β-curve, we demonstrate that at least 50% of the cells must pass through the G₀ state. The α-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 randomexiting phase of the cell cycle, then an alternative 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.     

Effects of asymmetric division on a stochastic model of the cell division cycle

The stochastic model of cell division formulated by Alt and Tyson is generalized to the case of imprecise binary fission. Closed-form expressions are derived for the generation-time distribution, the birth-size and division-size distributions, the beta curve, and the correlation coefficient of generation times of sister cells. The theoretical results are compared to observations of cell division statistics in a culture of fission yeast.     

Kinetic analysis of cell size and DNA content distributions during tumor cell proliferation: Ehrlich ascites tumor study.

In order to study the growth dynamics of proliferating and non-proliferating cells utilizing discrete-time state equations, the cell cycle was divided into a finite number of age compartments. In analysing tumor growth, the kinetic parameters associated with a retardation in the growth rate of tumors were characterized by computer simulation in which the simulated results of the growth curve, the growth fraction, and the mean generation time were adjusted to fit the experimental data. The cell age distibution during the period of growth was obtained and by a linear transformation of the state transition matrices, was employed to specify the cell size and DNA content distributions. In an application of the model, the time-course behavior of cell cycle parameters of Ehrlich ascites tumor is illustrated, and the parameters important for the transition of cells in the proliferating compartment to the non-proliferating compartment are discussed, particularly in relation to the G1-G0 and G2-G0 transitions of non-cycling cells as revealed by the variation of cell size distribution.     

Interdependence of the cell cycles of mammalian sister cells in monolayer cultures detected through their desynchronization by UV microirradiation

The duration and variability of cell cycles in epithelial and fibroblast-like mammalian sister cells with different types of intercellular contacts were estimated using time-lapse cinemicrographic technique. To study a possible interrelation between cell cycles of the sister cells, one cell in each pair of sister cells was inactivated by selective UV microbeam irradiation at the beginning of its cell cycle. It is shown that this action may delay the cycle of the intact cell as well. Such an interrelation of sister cells was found only at the G1 phase of the cell cycle and only in epithelial cells.     

The distributions of cell size and generation time in a model of the cell cycle incorporating size control and random transitions

A deterministic/probabilistic model of the cell division cycle is analysed mathematically and compared to experimental data and to other models of the cell cycle. The model posits a random-exiting phase of the cell cycle and a minimum-size requirement for entry into the random-exiting phase. By design, the model predicts exponential "beta-curves", which are characteristic of sister cell generation times. We show that the model predicts "alpha-curves" with exponential tails and hyperbolic-sine-like shoulders, and that these curves fit observed generation-time data excellently. We also calculate correlation coefficients for sister cells and for mother-daughter pairs. These correlation coefficients are more negative than is generally observed, which is characteristic of all size-control models and is generally attributed to some unknown positive correlation in growth rates of related cells. Next we compare theoretical size distributions with observed distributions, and we calculate the dependence of average cell mass on specific growth rate and show that this dependence agrees with a well-known relation in bacteria. In the discussion we argue that unequal division is probably not the source of stochastic fluctuations in deterministic size-control models, transition-probability models with no feedback from cell size cannot account for the rapidity with which the new, stable size distribution is established after perturbation, and Kubitschek's rate-normal model is not consistent with exponential beta-curves.     

Frequency of chromosome aberrations induced in human peripheral lymphocytes by in vitro 60Co gamma quanta at doses of 1 to 5 Gr. in an analysis of the 1st-division cells at different fixation times

The quantitative analysis of chromosomal aberrations in the first division cells of 50-, 54-, 58-, 52- and 66-hour peripheral blood lymphocytes cultures of healthy donors was performed after irradiation in vitro with 60Co gamma-quantums at doses 1--5 Gy. Cells of the first division were identified by a differential staining of sister chromatid method using 5-bromdeoxyuridine. No significant differences in frequencies of aberrant cells and aberrations of chromosomal type were found between cultures fixed at different times. The distribution of dicentrics in cells did not differ from the Poisson distribution regardless of fixation times and doses. On the basis of these findings it is concluded that chromosomes of human peripheral blood lymphocytes passing the cell cycle at different rates have approximately equal radiosensitivity.     

Commitment point during G0-->G1 that controls entry into the cell cycle

Initiation of T-lymphocyte-mediated immune responses involves two cellular processes: entry into the cell cycle (G(0)-->G(1)) for clonal proliferation and coordinated changes in surface and secreted molecules that mediate effector functions. However, a point during G(0)-->G(1) beyond which T cells are committed to enter the cell cycle has not been defined. We define here a G(0)-->G(1) commitment point that occurs 3 to 5 h after CD3 and CD28 stimulation of human CD4 or CD8 T cells. Transition through this point requires cdk6/4-cyclin D, since inhibition with TAT-p16(INK4A) during the first 3 to 5 h prevents cell cycle entry and maintains both naive and memory T cells in G(0). Transition through the G(0)-->G(1) commitment point is also necessary for T cells to increase in size, i.e., to enter the cellular growth cycle. However, transition through this point is not required for the induction of effector functions. These can be initiated while cells are maintained in G(0) with TAT-p16(INK4A). We have termed this quiescent, activated state G(0(A)). Our data provide proof of the principle that entry of T cells into the cell cycle and cellular growth cycles are coupled at the G(0)-->G(1) commitment point but that these processes can be uncoupled from the early expression of molecules of effector functions.     

Family tree analysis of a transformed cell line and the transition probability model for the cell cycle

Variation in intermitotic time between individual cells in culture can be ascribed to the occurrence of random transitions in the cell cycle. We have analysed a family tree of mouse neuroblastoma cells, and observed that variation in difference in intermitotic time between sister cells is smaller than between cousin cells, and this difference is again smaller than between second-cousin and unrelated cells. This observation is incompatible with all transition probability models presented so far. We propose a model for the cell cycle with a single random transition, but with the additional assumption that the (two) system parameters may show variability within the population such that the closer cells are in their relation to each other, the closer their values of the system parameters will be. This model describes correctly the behaviour of the family tree of the cell line and in addition is able to explain why differences in intermitotic time between sister cells are exponentially distributed, while intermitotic times themselves are more or less normally distributed. Methods have been described to quantify the various system parameters.     

Caffeine induces sister-chromatid exchanges during the whole S-phase of the cell cycle

The capacity of caffeine to induce sister chromatid exchanges (SCEs) in different cell cycle stages and the proliferation kinetics were studied. Continuous treatment with this xanthine during the whole second cycle significantly increased the baseline SCE frequency. Pulse-treatment experiments showed that the induction of SCEs by caffeine, which was dose-dependent, was restricted to the S-phase of the cell cycle without effect on G1 or G2 cells. Moreover, unlike other SCE-inducing agents, such as DNA-synthesis inhibitors and DNA-damaging agents, caffeine produced similar SCE increases in cells treated at different times throughout the S-phase. In the light of Painter's model for SCE formation and the known effects of caffeine on the DNA replication pattern, the most likely mechanism of SCE induction by caffeine is an increase in the number of DNA-replication sites.     

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.     

Mouse epidermal stem cells proceed through the cell cycle

The epidermis is a continuously renewing tissue maintained by undifferentiated stem cells. For decades it has been assumed that epidermal stem cells (ESCs) were held in the G0 phase of the cell cycle and that they only entered the cell cycle when needed. Previously, we showed that ESCs retained nuclear label for long periods, indicating that these cells did not proceed through the cell cycle at the same rate as the other proliferative basal cells. However, their exact cell-cycle profile has not been determined because a pure population of ESCs has not been available. In this study, we sorted stem and transient amplifying (TA) cells from murine neonatal back skin, and adult ear, footpad, and back skin, using our recently developed method. We found that neonatal back skin had two times the number of ESCs as the adult tissues. Despite the age and anatomical difference, these ESC populations exhibited similar cell cycle profiles with approximately 96% in G0/G1 and 4% in S-G2/M. The cell cycle profiles of the TA cells from neonatal back skin and adult footpad also showed a profile similar to each other (85% in G1 and 15% in S-G2/M). Examination of genes on a cell cycle chip showed that proliferation associated genes and only p57 were upregulated in the TA cell and ESC population, respectively. We found BrdU positive and cyclin B1 positive cells in all groups, confirming that both ESCs and TA cells were cycling. These data demonstrate that there are more TA cells dividing than ESCs, that the cell cycle profile of adult TA cells is related to the proliferative state of the tissue in which they reside, and that ESC proceed through the cell cycle.     

Sensitivity of flow cytometric data to variations in cell cycle parameters

We investigated to what extent flow cytometric DNA histograms are informative of cell cycle parameters. We created a computer program to simulate cell cycle progression in a generic and flexible way. Various scenarios, characterized by different models and distributions of cell cycle phase transit times, have been analysed in order to obtain the percentages of cells in the different cell cycle phases during exponential growth and their time course after mitotic block. Cell percentages during exponential growth were insensitive to intercell variability in phase transit times and thus can be employed to estimate the relative mean phase transit times, even in the presence of non-cycling cells. However, this information is ambiguous if re-entry of such cells into the cycling status is permitted. The stathmokinetic outline gives the mean phase transit times, but also provides information about the spread, but not the form, of the phase transit time distributions, being particularly sensitive to the spread of G1 phase duration. The stathmokinetic outline also helps distinguish between scenarios considering only cycling cells, those forecasting a fraction of definitively non-cycling cells and those admitting a G0 status with first-order output kinetics.     

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.     

Reactivation of stationary Tetrahymena : A contribution to the question of G0 state

Stationary cells of Tetrahymena were reactivated to exponential growth phase by transfer to fresh medium. The sequence of resuming cell cycle events was analysed by scoring the division index, the labelling index for macro- and micronuclei and the increase in cell number. By long-term labelling it was found that all cells replicate in stationary phase cultures. They also divide eventually. Upon transfer to fresh medium a small fraction of cells (about 3%) divide immediately, whereas the rest divide 3 h later after having replicated their macronuclear DNA. The kinetics of entry into the S phase indicates that these cells have a lag period of about 2 h before they resume progress through the cell cycle. It takes more than 1 h until all cells have begun replication. These data show that in stationary cultures all cells proceed through the events of the cell cycle. The cell cycle phases are extended differentially, G1 taking the largest part. During G2 cells pass very slowly through a certain stage close to division. Under the present conditions there is no indication for cells being in a resting state that is not part of the cell cycle, from which they can be restimulated and which has been called the G0 state. The criteria to demonstrate a resting state of this nature are discussed.     

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.     

KINETIC ANALYSIS OF CELL SIZE AND DNA CONTENT DISTRIBUTIONS DURING TUMOR CELL PROLIFERATION: EHRLICH ASCITES TUMOR STUDY

In order to study the growth dynamics of proliferating and non-proliferating cells utilizing discrete-time state equations, the cell cycle was divided into a finite number of age compartments. In analysing tumor growth, the kinetic parameters associated with a retardation in the growth rate of tumors were characterized by computer simulation in which the simulated results of the growth curve, the growth fraction, and the mean generation time were adjusted to fit the experimental data. The cell age distribution during the period of growth was obtained and by a linear transformation of the state transition matrices, was employed to specify the cell size and DNA content distributions. In an application of the model, the time-course behavior of cell cycle parameters of Ehrlich ascites tumor is illustrated, and the parameters important for the transition of cells in the proliferating compartment to the non-proliferating compartment are discussed, particularly in relation to the G₁-G₀ and G₂-G₀ transitions of non-cycling cells as revealed by the variation of cell size distribution.     

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.     

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.     

The pattern of dihydrofolate reductase expression through the cell cycle in rodent and human cultured cells

We have examined the pattern of dihydrofolate reductase (DHFR) enzyme and mRNA levels in cell cycle stage-specific populations obtained by centrifugal elutriation in Chinese hamster ovary cells and in a derivative line in which the dihydrofolate reductase gene is amplified approximately 50-fold. On a per cell basis, we observed a 2-fold increase in DHFR activity as cells progressed from G1 to G2/M with a concomitant 2-fold increase in the rate of protein synthesis and steady state level of mRNA. Analysis of DHFR mRNA levels in cell cycle stage-specific mouse 3T6 and human 143 tk- cells gave a similar pattern. We also demonstrate that simple alterations in growth conditions prior to elutriations can dramatically increase the levels of DHFR mRNA in all cell cycle states, thereby indicating that growth response associated with the DHFR gene functions independent of the cell cycle. We conclude that during periods of exponential growth the increases in dihydrofolate reductase activity, rate of protein synthesis, and steady state levels of mRNA parallel the general increases in cell volume and protein content associated with normal progression through the cell cycle, and therefore DHFR cannot be considered a cell cycle-regulated enzyme.