Heterogeneity in the mouse epidermal cell cycle analysed by computer simulations.

Different sets of cell kinetic data obtained over many years from hairless mouse epidermis have been simulated by a mathematical model including circadian variations. Simulating several independent sets of data with the same mathematical model strengthens the validity of the results obtained. The data simulated in this investigation were all obtained with the experimental system in a state of natural synchrony. The data include cell cycle phase distributions measured by DNA flow cytometry of isolated epidermal basal cells, fractions of tritiated thymidine ([3H]TdR) labelled cells within the cell cycle phases measured by cell sorting at intervals after [3H]TdR pulse labelling, bivariate bromodeoxyuridine (BrdUrd)/DNA data from epidermal basal cells isolated at intervals after pulse labelling with BrdUrd, mitotic rate and per cent labelled mitosis (PLM) data from histologic sections. The following main new findings were made from the simulations: the second PLM peak observed at about 35 h after pulse labelling is hardly influenced by circadian variations; the peak is mainly determined by persisting synchrony of a rapidly cycling population with a G1-duration (TG1) of 20 h to 30 h; and there is a highly significant population of slowly cycling G1-cells (G1 sigma). However, no significant circadian variations were found in the number of these cells.

Selection of optimal model for the DNA histogram by analysis of error of estimated parameters.

The ability of four different mathematical models of the DNA histogram to give accurate estimates for the fractions of cells in G1, S, and G2 + M has been investigated. The models studied differ in the form and number of parameters of the function used to represent cells in S-phase. Results obtained from simulated DNA histograms suggest that the standard deviations of the model parameters increase exponentially with the width of the G1 and G2 + M peaks of the histogram. Error analysis is presented as a method to select a model of optimal complexity in relation to the resolution provided by the data in a given set of DNA histograms. Introduction of additional parameters improves the agreement between model and data but may result in a less well-posed model. A model with an optimal number of parameters can therefore be found that will yield parameter estimates with the smallest possible standard deviations.

Turnover and maturation kinetics in the hairless mouse epidermis. Continuous [3H]TdR labelling and mathematical model analyses.

Hairless mice were continuously labelled with 10 microCi of tritiated thymidine ([3H]TdR) every 4 h for 8 d, and the proportions of labelled basal and differentiating cells were recorded separately. The mitotic rate was measured by the stathmokinetic method and the cell cycle distributions were measured by flow cytometry of isolated basal cells at intervals during the labelling period. The mitotic rate of the [3H]TdR-injected animals did not deviate from control values during the first 5 d. Computer simulations of the data based on various mathematical models were made, and three main conclusions were obtained: (1) a large spread in transit times through the G1 phase was found, together with a very narrow distribution in maturation time of differentiating cells; (2) about 20% of the differentiating cells were estimated to leave the basal cell layer directly after mitosis. This is consistent with results obtained from different sets of data; and (3) during continuous labelling more than 90% of the cells are labelled during each passage through the S phase.

Mathematical model analysis of mouse epidermal cell kinetics measured by bivariate DNA/anti-bromodeoxyuridine flow cytometry and continuous [3H]-thymidine labelling.

In a previous study the epidermal cell kinetics of hairless mice were investigated with bivariate DNA/anti-bromodeoxyuridine (BrdU) flow cytometry of isolated basal cells after BrdU pulse labelling. The results confirmed our previous observations of two kinetically distinct sub-populations in the G2 phase. However, the results also showed that almost all BrdU-positive cells had left S phase 6-12 h after pulse labelling, contradicting our previous assumption of a distinct, slowly cycling, major sub-population in S phase. The latter study was based on an experiment combining continuous tritiated thymidine [( 3H]TdR) labelling and cell sorting. The purpose of the present study was to use a mathematical model to analyse epidermal cell kinetics by simulating bivariate DNA/BrdU data in order to get more details about the kinetic organization and cell cycle parameter values. We also wanted to re-evaluate our assumption of slowly cycling cells in S phase. The mathematical model shows a good fit to the experimental BrdU data initiated either at 08.00 hours or 20.00 hours. Simultaneously, it was also possible to obtain a good fit to our previous continuous labelling data without including a sub-population of slowly cycling cells in S phase. This was achieved by improving the way in which the continuous [3H]TdR labelling was simulated. The presence of two distinct subpopulations in G2 phase was confirmed and a similar kinetic organization with rapidly and slowly cycling cells in G1 phase is suggested. The sizes of the slowly cycling fractions in G1 and G2 showed the same distinct circadian dependency. The model analysis indicates that a small fraction of BrdU labelled cells (3-5%) was arrested in G2 phase due to BrdU toxicity. This is insignificant compared with the total number of labelled cells and has a negligible effect on the average cell cycle data. However, it comprises 1/3 to 1/2 of the BrdU positive G2 cells after the pulse labelled cells have been distributed among the cell cycle compartments.

Evidence of rapid and slow progression of cells through G2 phase in mouse epidermis: a comparison between phase durations measured by different methods.

Percentage labelled mitosis (PLM) measurements were initiated at four different times during a 24-hr period and continued for 24 hr in hairless mouse epidermis. Estimates of G2 and S phase durations (mean TG2 and mean TS) were calculated. A significant number of labelled mitoses (10--20%) was seen after 30 min in all four PLM measurements and the estimated mean TG2 varied from 1.4 to 2.5 hr and was in agreement with values from PLM measurements in other epithelial tissues. These mean TG2 values were much shorter than expected from [3H]TdR double labelling experiments and from a multiparameter cell kinetic study in hairless mouse epidermis and did not reflect the circadian variations seen in these studies. The differences in estimates of phase durations can be explained by postulating two G2 cell populations; one with a rapid and another with a slow rate of cell cycle progression. The cells with the higher rate are mainly registered by the PLM method, whereas those with the lower rate largely escape detection by this method. TG2 estimates from PLM measurements in mouse epidermis therefore do not reflect the phase duration of the entire G2 population. It is also concluded that circadian variations in TS can not be accurately registered by the PLM method.

The stathmokinetic method in vivo. Time-response with special reference to circadian variations in epidermal cell proliferation in the hairless mouse.

Groups of hairless mice were injected i.p. with a stathmokinetic dose of 0.15 mg colcemid at seven different times of the day and animals killed 0, 15 and 30 min, 1, 2, 3 and 4 hr after the injection. The proportion of cells in metaphase and ana/telophase was determined in histological sections. The results showed a transient accumulation of metaphases about 30 min after the injection, followed by an increase in metaphases from 1 to 4 hr. Therefore, no value before 1 hr after the colcemid injection should be used in calculations of the mitotic rate. The presence of circadian rhythms with high mitotic activity in the morning and low activity in the evening was confirmed. It is shown by regression analyses that the accumulation period of 4 hr is sufficiently short to reflect circadian variations in epidermal cell proliferation and that the 4-hr accumulation value alone is sufficient to estimate the mitotic rate.

Subpopulations of slowly cycling cells in S and G2 phase in mouse epidermis.

Evidence has been presented supporting the existence of heterogeneity in cell-cycle progression in mouse epidermis, The present study was undertaken to characterize this heterogeneity in more detail. Hairless mice were continuously labelled with tritiated thymidine every 4 hr for 4 days. Basal cell suspensions were prepared from slices of mouse skin at intervals during the experiment and subjected to DNA flow cytometry. Cell-cycle analysis was combined with sorting of cells from windows in G1, S and G2 phase, and the proportion of labelled cells within each window was determined in autoradiographs. Reanalysis and resorting to control the purity of of sorted fractions were performed. Computer simulations of the data were made using a mathematical model assuming different S and G2 phase characteristics. A good fit to the data was only obtained when heterogeneity in mouse epidermal cell-cycle progression was assumed, indicating the existence of slowly traversing, distinct subpopulations of cells in G2 and S phase. These cells are assumed to contribute to about 40% of all cells in S phase and to about 70% of all in G2 phase. The estimated residence times in the resting states were 38 and 32 hr in S and G2 phase, respectively. Two-parameter sorting based on DNA and light scatter indicated that slowly cycling cells were larger than the average. There is no evidence of significant subpopulations of permanently non-proliferating keratinocytes in any of the cell-cycle phases.

Estimation of circadian variations in cell cycle phase durations in murine epidermal basal cells.

Circadian variations in the proliferative activity of squamous epithelia are well known. However, circadian variations in the duration of the various cell cycle phases (S, G2 and mitosis) have been disputed. The percent labelled mitoses method, which is traditionally used to obtain duration of cell cycle phases, is poorly suited for identification of circadian variations. Therefore methods combining changes in compartment size (cell cycle phase) and cellular flux through the compartments have been used. Three different methods using such data are presented. These incorporate various simplifying assumptions that cause methodological errors. Limits for use of the different methods are indicated. The use of all three methods gives comparable and pronounced circadian variations in the duration of S and G2 phase. These results are also compatible with circadian variations in the mitotic duration, but they may also represent artefacts due to sensitivity to model errors.