Computing multiple cell kinetic properties from a single time point

New developments in experimental procedures have made it necessary to extend the theory for describing the movement of a population of cells and estimating the kinetic properties of the population. The new procedures are based on the use of fluorescent monoclonal antibodies to halogenated analogues of thymidine, which are incorporated as a label into cells during DNA synthesis. These populations may be examined by dual-parameter flow cytometry to discriminate between the labelled and unlabelled populations of cells and define their position within the DNA reproductive cycle. A particular need exists for a theory that can be used for measurements of tumors in which many cells are not actively cycling and only a single time point can be obtained. In order to develop a useful theory for evaluating the kinetic properties of the cells observed by these techniques, the standard methods of theoretical cell kinetics have been recast in a form that is amenable to the type of analysis demanded by these constraints and a novel method for the rapid analysis of the kinetic properties of the cell population is presented. The method is shown to yield a direct measurement for the population doubling time from a single time point as well as estimates for the transit times through each phase of the cell cycle. The method which is approximately linear is shown to be robust to the effects of different assumptions about the distribution of transit times as well as being insensitive to the effects of variation in the transit times of the cells. The methodology developed in this paper may also be used to examine other theoretical methods of computing kinetic properties.     

THE DISCRETE–TIME KINETIC MODEL ANALYSIS OF DNA CONTENT DISTRIBUTIONS IN EXPERIMENTAL TUMOUR CELLS

A method was developed to analyse and characterize FMF measurements of DNA content distribution, utilizing the discrete time kinetic (DTK) model for cell kinetics analysis. The DTK model determines the time sequence of the cell age distribution during the proliferation of a tumor cell population and simulates the distribution pattern of the DNA content of cells in each age compartment of the cell cycle. The cells in one age compartment are distributed and spread into several compartments of the DNA content distribution to allow for different rates of DNA synthesis and instrument dispersion effects. It is assumed that the DNA content of cells in each age compartment has a Gaussian distribution. Thus, for a given cell age distribution the DNA content distribution depends on two parameters of the cells in each age compartment: the average DNA content and its coefficient of variation. As the DTK model generates the best fit DNA content distribution to the FMF measurement data, it enables one to estimate specific values of these two parameters in each stage of the cell cycle and to determine the fraction of cells in each cycle phase. The method was utilized to fit FMF measurements of DNA content distributions and to analyse their relationship to the cell kinetic parameters, namely cell loss rate, cell cycle times and growth fraction of exponentially growing Chinese hamster ovary cells in vitro and, also, with a wide range of coefficients of variation, of the L1210 ascites tumour during the growth period.     

The discrete-time kinetic model analysis of DNA content distributions in experimental tumour cells.

A method was developed to analyse and characterize FMF measurements of DNA content distribution, utilizing the discrete time kinetic (DTK) model for cell kinetics analysis. The DTK model determines the time sequence of the cell age distribution during the proliferation of a tumor cell population and simulates the distribution pattern of the DNA content of cells in each age compartment of the cell cycle. The cells in one age compartment are distributed and spread into several compartments of the DNA content distribution to allow for different rates of DNA synthesis and instrument dispersion effects. It is assumed that the DNA content of cells in each age compartment has a Gaussian distribution. Thus, for a given cell age distribution the DNA content distribution depends on two parameters of the cells in each age compartment: the average DNA content and its coefficient of variation. As the DTK model generates the best fit DNA content distribution to the FMF measurement data, it enables one to estimate specific values of these two parameters in each stage of the cell cycle and to determine the fraction of cells in each cycle phase. The method was utilized to fit FMf measurements of DNA content distributions and to analyse their relationship tothe cell kinetic parameters, namely cell loss rate, cell cycle times and grwoth graction of exponentially growing Chinese hamster ovary cells in vitro and, also, with a wide range of coeffficients of variation, of the L1210 ascites tumour during the growth period.     

AN EVALUATION OF ERYTHROPOIESIS IN THE YOUNG RAT

Estimates of the cell population kinetic parameters have been obtained for the erythroid cells of the young growing rat using the technique of labelled mitoses and these results have been analysed by a computer programme. The phases of the cell cycle for the proliferating cells have been shown to be of shorter duration than generally reported. Together with the differential cell count and initial labelling index these data have enabled estimates of the growth fraction, birthrate, flow rate, number of divisions and transit time to be determined for each compartment.     

Flow cytometric BrdUrd-pulse-chase study of heat-induced cell-cycle progression delays

The flow cytometric, bromodeoxyuridine (BrdUrd)-pulse-chase method was extended by analysing five kinetic parameters to study perturbed cell progression through the cell cycle. The method was used to analyse the cell-cycle perturbations induced by heat shock. Exponentially growing, asynchronous Chinese hamster ovary (CHO) cells were pulse labelled with BrdUrd and simultaneously heated at 43°C for 5,10 or 15 min. The cells were then incubated in a BrdUrd-free medium and, at various times thereafter, were prepared for flow cytometry. Five compartments (BrdUrd-labelled divided and undivided, and unlabelled G₁, G₁S, and G₂) were defined in the resulting dual-parameter histograms. The fraction of cells and the mean DNA content, when appropriate, were calculated for each compartment. The rates of cell-cycle progression were assessed as time-dependent changes in the fraction of cells in a given compartment and/or the relative DNA content of cells within a given compartment. Linear regression analysis of the data revealed two distinct modes of alteration in cell progression: 1 a delay in cell transit (either out of or into a given compartment), and 2 a decrease in the rate of cell transit. Hyperthermia produced a delay in the exit of cells from the G₁ compartment of ≈ 16 min per minute of heat at 43°C with no threshold. In contrast, the delay in the exit of cells from all other compartments showed a threshold of from 3 to 5 min at 43°C. Above this threshold the delay in exit of cells from the BrdUrd-labelled, undivided compartment was 25 min per minute of heat at 43°C. The more complex dose-response function of this latter compartment may reflect the fact that it includes two cell-cycle phases, S and G₂+ M. The decrease in the rate of transit out of G₂ for cells heated in G₂ was significantly larger than that for any other compartment, consistent with previous studies, which showed a G₂ accumulation following hyperthermia. These results indicate that heat exposure induces very complex alterations in cell-cycle progression and that this flow cytometric method offers a straightforward approach for observing such alterations.     

A Rapid Automated Stathmokinetic Method For Determination of In Vitro Cell Cycle Transit Times

To provide a rapid method for examining cell cycle dynamics, we utilized continuous exposure of Chinese hamster ovary cells and human colon cancer cells to colcemid to block cycling cells in metaphase, suppressing re-entry into G₁. Changes in cell cycle compartment distribution were monitored by DNA flow cytometry. Analysis of the rate of G₂+ M compartment accumulation after addition of colcemid permitted calculation of all cycle transit parameters. These compared favorably with data in the same cell lines determined by the fraction of labeled mitoses technique. Serial assessment of DNA flow cytometry after addition of colcemid permits rapid quantitation of cycle traverse rates.     

A comment on "A method to measure the duration of DNA synthesis and the potential doubling time from a single sample"

Recently a method was introduced by Begg et al. (Cytometry 6:620-626, 1985) for the calculation of the DNA synthesis time, TS using flow cytometry to monitor the progression of cells that have been pulse-labeled by bromodeoxyuridine (BrdUrd). Ideally, the method uses only a single two-parameter histogram of the progressed cells to obtain TS. The essence of the method is to be able to obtain an initial point from general principles, draw a line through it and the measured point, and extrapolate to a level of progression that would be attained when the time is equal to TS. In this comment, explicit values are derived for the initial point and the progression of cells based on kinetic arguments, and a new method is presented for estimating TS. This new method is compared to earlier methods, and the effects of a finite labeling time and variation in the transit times are considered. Finally, an equation is developed for estimating TS following multiple measurements.     

Measuring cell proliferation by relative movement. I. Introduction and in vitro studies

This paper presents two new ways of analysing data which may be obtained from pulse labelling a population of cells with bromodeoxyuridine and analysing that population as a function of time with bivariate flow cytometry. The progression of cells is measured by the change in position in the cell cycle, as shown by a change in the mean DNA content of the labelled and unlabelled cells. The particular measures of the mean DNA content used are extensions of the relative movement of the labelled undivided cells, RMlu(t), which was introduced by Begg and co-workers to measure the DNA synthesis time, TS. In general, the relative movement is defined as the mean DNA fluorescence of a population of cells less the DNA fluorescence of the cells in G1 and divided by the difference in DNA fluorescence of the cells in G2 + M and G1. In this paper we examine the relative movements of all the labelled cells and all of the unlabelled cells, denoted RML(t) and RMU(t) respectively. It is found that RML(t) and RMU(t) exhibit clear cyclic behaviour and distinguishable characteristics which depend directly on the transit times (T) of the cell cycle phases, i.e. TG1, TS and TG2 + M. Furthermore, the peak heights of the RMU(t) curve are shown to depend strongly on the growth fraction of the population under consideration. A theoretical treatment of the curves so obtained is presented, and is shown to yield values in close agreement with those from other methods for measuring these transit times and a lower limit to values for the growth fraction of Chinese hamster ovary cells grown in vitro.     

RATE AND TIME OF DNA SYNTHESIS OF INDIVIDUAL CHINESE HAMSTER CELLS

The duration of DNA synthesis of a diploid cell line of Chinese hamster fibroblasts was determined in a comparative study by the FLM technique, and also by a new technique for measuring the rate of DNA synthesis of individual cells. These methods produced comparable results when applied during exponential growth of the cells. The rate of DNA synthesis was measured by means of quantitative autoradiography following a short-term incubation of the cells with 5 × 10^-6 M FUdR and 10^-5 M ¹⁴C-TdR. The choice of the medium for this purpose did not seem to be critical. The autoradiographic silver grains over cells and ¹⁴C-standard sources are counted by microphotometry using incident light bright-field. The direct measurements of DNA synthesis rate are ‘compartment’ statistics which have been converted into ‘flux’ parameters for comparison with the FLM method and applicability in cell-kinetic calculations. Frequency distributions of the rate of DNA synthesis of individual cells thus obtained may resemble normal distributions quite closely. They result from several factors: differences in the rate of synthesis in different parts of the S-phase, the density distribution of cells within the S-phase, the variation in the time of DNA synthesis among individual cells, and the experimental error. In the case of a pronounced partial synchronization as probably has been present in one experiment performed in the lag phase, an incorrect time of DNA synthesis may result from the rate values. Due to the variation in DNA synthesis rate in different parts of the S-phase it is not possible to determine the duration of DNA synthesis of an individual cell. However, the mean values of DNA synthesis time are reliable. The new method will be preferentially applied for determining the duration of DNA synthesis of human cells in as far as difficulties are encountered with the classical methods. In addition, it may be used to advantage for studying cells which make up low percentages in mixed populations. It finally permits a safer morphological classification of the cells under study than is possible with the classical methods.     

Evidence for control of protein synthesis in HeLa cells via the elongation rate

The effects of fresh medium and serum on protein synthesis in suspension-cultured HeLa cells after growth to high cell density (>5 × 10⁵ cells/ml) were studied. Cells which were resuspended in fresh medium plus serum and grown for 24 hours (control) were compared with cells grown for 2 hours after resuspension (stimulated). The spectrum of proteins being synthesized by control and stimulated cells does not appear to be grossly different; that is, the weight and number average molecular weights of newly synthesized whole-cell protein are about the same in both cultures. Also, no significant differences were observed in the number of ribosomes per polysome or in the fraction of total ribosomes in polysomes. However, the transit times (combined elongation and termination times) were found to differ significantly; the average transit time for control cells was 2.24 minutes, while the average transit time for stimulated cells was 1.26 minutes. (An appendex evaluating the methodology involved in measuring the transit time is included.) In agreement with the difference in transit time, the absolute rate of protein synthesis in stimulated cells was approximately 1.8 times the rate measured in control cells. These data are taken as evidence that under certain conditions, the rate of elongtion and/or termination of polypeptide chains limits the overall rate of translation, and that cells can respond to growth conditions by changing the elongation and/or termination rate of protein synthesis.     

Reversible alterations in the mitotic cycle of chick embryo cells in various states of growth regulation

Chick embryo cells which have been kept overnight at pH 6.8 in the absence of serum multiply very slowly. Only a small fraction of cells is in the S period at any given time, and the rate of uptake of 2-deoxy-D-glucose is very low. Upon raising the pH to 7.4 and adding serum (“turn-on”) the uptake of 2-deoxy-D-glucose increases immediately; the rate of DNA synthesis increases after a lag of about 4 hours, and represents an increase in the fraction of cells synthesizing DNA. The uptake of 2-deoxy-D-glucose is rapidly returned to its original low rate at any time by again lowering the pH and removing serum (“turn-off”). The synthesis of DNA in the culture remains constant or continues to rise at a markedly reduced rate following the same treatment. Lowering pH or removing serum independently of each other is less efficient at inhibiting the increase in DNA synthesis than the combined treatment but each accomplishes a similar result. Cultures which have been “turnedoff” during the early stages of the rapid increase in DNA synthesis, resume their prior rate of increase immediately if “turned-on” again within 2.5 hours. If the cultures have been “turned-off” for 5.5 hours before restoring the “turn-on,” there is a 2 hour delay before they resume an increased rate of DNA synthesis. The results indicate that chick embryo cells do not become committed to the initiation of DNA synthesis until shortly before, or at the time of the onset of the S period. Up to 96% of the cells in post-confluent cultures growing in conventional medium become labeled upon continuous, prolonged exposure to ³H-thymidine. Seventy-eight percent of the cells in serum-deprived cultures growing at a very low rate become labeled. These and other considerations suggest that the inhibition of cell multiplication by high population density or serum deprivation is caused by a lengthening of the time cells remain in the prereplicative G₁ period rather than by shifting cells into a qualitatively distinct G₀ period. There may, however, be a period common to all cells regardless of growth rate, in which cells are not progressing toward the S period. The length of this variable period would then determine the growth rate of a population of cells.     

Two-color flow-cytometric analysis of the growth cycle of Plasmodium falciparum in vitro: identification of cell cycle compartments

A previous study (Hare JD, Bahler DW: J Histochem Cytochem 34:215, 1986) has shown that the flow cytometric analysis of acridine-orange-stained Plasmodium falciparum growing in vitro generates a complex two-color display, regions of which correlate with the major morphological stages. In this report, four cell cycle compartments (A-D) are defined by characteristic ratios of red and green fluorescence of cells distributed throughout the erythrocytic cycle as well as by the differential effects of several metabolic inhibitors. The primary characteristic of cells in compartment A is the significant increase in red fluorescence. Inhibition of DNA synthesis by either aphidicolin or hydroxyurea causes the accumulation of cells at the interface between compartments A and B, whereas n-butyrate prevents cells in compartment A from reaching the A-B interface. Cells in compartment A display a small increase in green fluorescence which is independent of DNA synthesis but is enhanced by n-butyrate treatment. Cells in compartment B display a continued increase in red fluorescence coupled with a significant increase in green fluorescence, reflecting the onset of DNA synthesis in compartment B. The transition to compartment C is more abrupt and is associated with a marked increase in green fluorescence and little increase in red fluorescence. Compartment D is characterized by an increase in red fluorescence and a continued rise in green fluorescence. It is postulated that these discontinuities in the two-color display reflect not only changes in the rates of RNA and DNA synthesis but also decondensation of parasite chromatin in compartment A as the organism prepares for DNA synthesis, and re-condensation in compartment D as the newly replicated chromatin prepares for segregation into merozoites. The method described promises to provide a sensitive and rapid technique to study the effects of various factors on the growth cycle of the parasite.     

Decreased Sensitivity to Hydroxyurea and to [3H]Thymidine Suicide In the Middle of the S Phase

Pluripotent haemopoietic stem cells (CFUs) move synchronously through the cell cycle in hydroxyurea-treated mice in a cohort 1–2 hr broad. Ten to fifteen hours after hydroxyurea they pass through S phase. DNA synthesis appears to be depressed 5–10 times when the cells are in the middle part of the S phase but does not seem to be completely interrupted. High concentrations of [³H]thymidine must be used for ‘suicide’ in order to achieve lethality for the cells with depressed DNA synthesis. At the time when DNA synthesis is depressed, the sensitivity of the cells to hydroxyurea also decreases. This may lead to a significant underestimation of the S phase fraction by the hydroxyurea method, because CFUs with low DNA synthesis rate are resistant to hydroxyurea although being in S phase.     

Mathematical models of hierarchically structured cell populations under equilibrium with application to the epidermis

Abstract. There are three categories of keratinocytes in the germinative compartment of the epidermis – stem, transit-amplifying and post-mitotic. Their population structure is hierarchical. This means that stem cells differentiate into transit-amplifying cells which, after a few rounds of division, become post-mitotic cells. The cell processes of birth, differentiation, death and migration affect the composition and proliferation rate of the germinative compartment. These phenomena are quantified by various cell kinetic parameters. In this paper we derive equations that relate these parameters for different models of hierarchically structured cell populations in equilibrium. We include in the models asymmetric and symmetric division, variations in cell-cycle times, apoptosis and variation in the number of transit generations. We conclude that variation in cell-cycle times need only be considered if apoptosis is not negligible. If it is negligible, then only average cell-cycle times are needed. Unfortunately, it is impossible to predict the importance of apoptosis from the available experimental data. However, the strength of its effect is determined by the other parameters, especially the fraction of cycling stem cells. We show that variation in the number of transit generations can have a potentially large effect on cell birth rate. We also show that cell birth rate does not directly depend on the mean transit-amplifying cell-cycle time, only on the mean stem cell-cycle time. We argue that 'homogeneous cell population' equations should not be used to study hierarchical cell populations as has been done in the past. Finally we argue that stem cell parameters and transit-amplifying cell parameters should not be lumped together.     

Rearrangements of chromatin structure in newly repaired regions of deoxyribonucleic acid in human cells treated with sodium butyrate or hydroxyurea

The rate and extent of redistribution of repair-incorporated nucleotides within chromatin during very early times (10-45 min) after ultraviolet irradiation were examined in normal human fibroblasts treated with 20 mM sodium butyrate, or 2-10 mM hydroxyurea, and compared to results for untreated cells. Under these conditions, DNA replicative synthesis is reduced to very low levels in each case. However, DNA repair synthesis is stimulated by sodium butyrate and partially inhibited by hydroxyurea. Furthermore, in the sodium butyrate treated cells, the core histones are maximally hyperacetylated. Using methods previously described by us, it was found that treatment with sodium butyrate had little or no effect on either the rate or the extent of redistribution of repair-incorporated nucleotides during this early time interval. On the other hand, there was a 1.7-2.5-fold decrease in the rate of redistribution of these nucleotides in cells treated with hydroxyurea; the extent of redistribution was unchanged in these cells. Since hydroxyurea has been shown to decrease the rate of completion of "repair patches" in mammalian cells, these results indicate that nucleosome rearrangement in newly repaired regions of DNA does not occur until after the final stages of the excision repair process are completed. Furthermore, hyperacetylation of the core histones in a large fraction of the total chromatin prior to DNA damage and repair synthesis does not appear to alter the rate or extent of nucleosome core formation in newly repaired regions of DNA.     

Vaccinia virus infection of HeLa cells. I. Synthesis of vaccinia DNA in host cell nuclei.

The replication of vaccinia virus is thought to take place exclusively in the cytoplasm of host cells. However, using DNA-DNA hybridization techniques, it can be shown that a significant fraction of the synthesis of vaccinia DNA takes place in the nucleus as well as the cytoplasm. The (3H) thymiding pulse-labeled vaccinia DNA synthesized in the nucleus reaches a maximum at about 3 h after infection, corresponding to the time of maximal DNA synthesis in infected cells. At this time host DNA synthesis drops to about 25% of the rate of the uninfected cells. Even with short labeling times (2 min) the nucleus is found to contain 60% of the incorporated (3H)thymidine, much of which is in vaccinia DNA. Prior inhibition of host nuclear DNA synthesis with mitomycin C, followed by removal of the antibiotic causes a subsequent inhibition of vaccinia DNA synthesis and complete suppression of mature virus. Purified nuclei, isolated from vaccinia-infected cells, also synthesize vaccinia DNA in vitro. Over 90% of the DNA synthesized in vitro by isolated nuclei contain vaccinia-specific sequences.     

Rate and time of DNA synthesis of individual Chinese hamster cells.

The duration of DNA synthesis of a diploid cell line of Chinese hamster fibroblasts was determined in a comparative study by the FLM technique, and also by a new technique for measuring the rate of DNA synthesis of individual cells. These methods produced comparable results when applied during exponential growth of the cells. The rate of DNA synthesis was measured by means of quantitative autoradiography following a short-term incubation of the cells with 5 X 10(-6) M FUdR and 10(-5) M 14C-TdR. The choice of the medium for this purpose did not seem to be critical. The autoradiographic silver grains over cells and 14C-standard sources are counted by microphotometry using incident light bright-field. The direct measurements of DNA synthesis rate are 'compartment' statistics which have been converted into 'flux' parameters for comparison with the FLM method and applicability in cell-kinetic calculations. Frequency distributions of the rate of DNA synthesis of individual cells thus obtained may resemble normal distributions quite closely. They result from several factors: differences in the rate of synthesis in different parts of the S-phase, the density distribution of cells within the S-phase, the variation in the time of DNA synthesis among individual cells, and the experimental error. In the case of a pronounced partial synchronization as probably has been present in one experiment performed in the lag phase, an incorrect time of DNA synthesis may result from the rate values. Due to the variation in DNA synthesis rate in different parts of the S-phase it is not possible to determine the duration of DNA synthesis of an individual cell. However, the mean values of DNA synthesis time are reliable. The new method will be preferentially applied for determining the duration of DNA synthesis of human cells in as far as difficulties are encountered with the classical methods. In addition, it may be used to advantage for studying cells which make up low percentages in mixed populations. It finally permits a safer morphological classification of the cells under study than is possible with the classical methods.     

Mechanism of mitotic synchronization induced by 5-aminouracil.

The mechanism of mitotic synchronization induced by 5-aminouracil (5-AU) in onion root meristems has been investigated. We studied the effect of the chemical upon asynchronous meristematic cells, as well as upon a synchronous fraction of them the position of which in the cell cycle was known. The kinetic studies have shown a fairly linear relationship between the treatment time and the induced mitotic wave. Therefore, cell accumulation in a particular zone of interphase appears to be the cause of mitotic synchronization. This zone seems to be located at the end of S period. 5-AU induces maximal mitotic delay on the cells located in the accumulation zone and severely depresses the S-G2 transit while the passage through G 2 remains relatively unaffected. The possibility that preferential inhibition affects the late replicating DNA synthesis is discussed.