New methods for calculating kinetic properties of cells in vitro using pulse labelling with bromodeoxyuridine

The transit times of Chinese hamster ovary cells through the phases of their cell cycle were measured using dual parameter flow cytometry to measure DNA content and the presence of monoclonal antibodies to bromodeoxyuridine. Up to four separate populations can be accurately measured: unlabelled cells in G2 + M; labelled cells that have not yet divided; labelled cells that have already divided; and the unlabelled cells that were originally in G1 plus the cells that were originally in G2 + M and have since divided. The fractions of cells in these populations can be easily followed in time and the usual kinetic properties can be estimated from these fractions, or combinations thereof, including the times through G1, S, G2 + M and the cycle time. We present equations for analysing this type of data and comment on which equations are most appropriate for measuring specific kinetic properties of the cells.     

New methods for calculating kinetic properties of cells in vitro using pulse labelling with bromodeoxyuridine

Abstract. The transit times of Chinese hamster ovary cells through the phases of their cell cycle were measured using dual parameter flow cytometry to measure DNA content and the presence of monoclonal antibodies to bromodeoxyuridine. Up to four separate populations can be accurately measured: unlabelled cells in G₂+ M; labelled cells that have not yet divided; labelled cells that have already divided; and the unlabelled cells that were originally in G₁ plus the cells that were originally in G₂+ M and have since divided. The fractions of cells in these populations can be easily followed in time and the usual kinetic properties can be estimated from these fractions, or combinations thereof, including the times through G₁, S, G₂+ M and the cycle time. We present equations for analysing this type of data and comment on which equations are most appropriate for measuring specific kinetic properties of the cells.     

Modelling complex populations formed by proliferating,quiescent and quasi-quiescent cells: application to plant root meristems

A proliferating population of cells may be considered complex when its proliferative or growth fraction P is lower than 1 and/or when it is formed by subpopulations with different mean cycle times. The present paper shows that in such complex populations exponential growth is consistent with a steady-state distribution of cells. Obviously, when P=1 then cell distribution is only a function of cell age. An analytical model has been developed to study complex populations including both quiescent fractions formed by cells with unreplicated genome (G(0) cells) and cells with fully duplicated chromosomes (Q(2) cells). The model also considers those quasi-quiescent cells in their last transit through G(1) and S (Q(1) and Q(s) cells) before becoming quiescent. In order to solve the difficulties of a direct analysis of the whole population, its kinetic parameters have been obtained by studying the negative exponential distribution of two subpopulations: one formed by the proliferating cells and another formed by the quasi-quiescent cells. Additionally, the model could be applied when quiescence is initiated at any other cycle phase different from G(1) and G(2), for instance, cells in the process of replicating their DNA or being at any other mitotic phases. The utility of the method was illustrated in populations which constitute the root meristems of both Allium cepa L. and Pisum sativum L. Three facts should be stressed: (1) the method seems to be rather powerful because it can be carried out from different sets of experimentally measured parameters; (2) the rate of division and, therefore, the population doubling time can be easily estimated by this method; and (3) it also allows the determination of the amount of cells that had become quiescent either before they had replicated their DNA (G(0)) or after having completed their replication (Q(2)), as well as those quasi-quiescent cells which are progressing throughout their last pre-replicative and replicative periods (thus Q(1) and Q(s), respectively).     

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.     

Mathematical Determination of Cell Population Doubling Times for Multiple Cell Lines

Cell cycle times are vital parameters in cancer research, and short cell cycle times are often related to poor survival of cancer patients. A method for experimental estimation of cell cycle times, or doubling times of cultured cancer cell populations, based on addition of paclitaxel (an inhibitor of cell division) has been proposed in literature. We use a mathematical model to investigate relationships between essential parameters of the cell division cycle following inhibition of cell division. The reduction in the number of cells engaged in DNA replication reaches a plateau as the concentration of paclitaxel is increased; this can be determined experimentally. From our model we have derived a plateau log reduction formula for proliferating cells and established that there are linear relationships between the plateau log reduction values and the reciprocal of doubling times (i.e. growth rates of the populations). We have therefore provided theoretical justification of an important experimental technique to determine cell doubling times. Furthermore, we have applied Monte Carlo experiments to justify the suggested linear relationships used to estimate doubling time from 5-day cell culture assays. We show that our results are applicable to cancer cell populations with cell loss present.     

Cell cycles in cell hierarchies

In the replacing tissues of the body, namely the bone marrow, testis, and the surface epithelia with their appendages, cell replacement would appear to be achieved using an hierarchically organized proliferative compartment with relatively few ultimate stem cells producing dividing transit cells which eventually differentiate and mature into the functional cells of the tissue. The cell cycle times of the various constituents of the hierarchy differ, and the stem cells apparently have a longer cell cycle than the transit cells. There may be variations in the cell cycle as cells pass through the transit population in some cases, e.g. in the bone marrow, while in others the cycle time remains fairly constant, e.g. in the testis. The difference in the cell cycle time between stem cells and transit cells is not completely unequivocal, and there is little or no difference in cycle time in the epithelium on the dorsal surface of the tongue while in other cases the experimental evidence for long stem-cell cycles is somewhat imprecise. However, the epithelium in the small intestine and the spermatogonia in the testis have been fairly extensively studied and here the evidence clearly shows a lengthening of the cell cycle as more primitive cells are considered.     

A rapid and simple estimation of cell cycle parameters by continuous labeling with bromodeoxyuridine

The DNA synthesis time (Ts) and other related cell cycle parameters were roughly estimated in HeLa cells labeled with bromodeoxyuridine (BrdUrd) for various durations by using the flow cytometrical technique. The labeling indices increased in proportion to time after addition of BrdUrd. The Ts can be calculated from the slope of the regression line obtained by plotting the serial labeling indices against the labeling time and was equivalent to the value determined by fraction labeled cells in mid S-phase (FLSm) method. These parameters would be determined by only two samples labeled for different times. This simple method using BrdUrd provides rough but rapid estimation of Ts and other cell cycle parameters without complicated mathematical procedures, in addition to cell cycle partition of cell populations.     

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.     

Sensitivity of flow cytometric data to variations in cell cycle parameters

Abstract 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 Go status with first-order output kinetics.     

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.     

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.     

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.     

Heterogeneity in the replicating population of cultured human epidermal keratinocytes

We studied the replication of keratinocytes in stratified squamous epithelia. Other studies have revealed functional and morphological heterogeneity in the replicating population of such cells. To examine possible kinetic heterogeneity, we determined the cell-cycle lengths of replicating cells in cultures of human epidermal keratinocytes. A double-label assay was developed, which measures the time between two successive cycles of DNA synthesis. The first cycle of DNA synthesis was marked by pulse labeling cultures for a brief period with 14C-thymidine (dThd), and the second cycle was detected by labeling at a later time with bromodeoxyuridine (BrdUrd). The time taken for the 14C-labeled DNA to become doubly labeled with BrdUrd was shown to correspond to the length of the cell cycle. In subconfluent cultures in which the cell number increased at an exponential rate, the average cell-cycle time was 21.5 h. In confluent cultures in which desquamation was balanced by cell renewal, the average cell cycle was 31.5 h. However, in confluent cultures, three populations of replicating cells were evident, these having cycle times of 22, 33, and 40 h. In subconfluent cultures, there was no clear evidence for cell-cycle heterogeneity of the replicating cells, although the most rapidly cycling cells in these cultures had a cycle time (16 h) considerably less than the most rapidly cycling cells in the confluent cultures (21 h). It is possible that the rapidly cycling cells seen in the subconfluent cultures were stem cells.(ABSTRACT TRUNCATED AT 250 WORDS)     

Random transitions,size control,and inheritance in cell population dynamics

A general model of cell population dynamics is derived and analyzed. The model uses the continuous structure variables age and size, and thus distinguishes individual cells with respect to such properties as cycle length and division size. The model allows the occurrence of random transitions as cells progress through the cell cycle, the control of cell size upon cell cycle events, and the inheritance of properties from mother to daughter cells. The concepts of asynchronous exponential growth, α-curves, β-curves, mother-daughter transit time correlations, and sister-sister transit time correlations are formalized. The existence and uniqueness of solutions to the model is proved.     

Epidermal cell proliferation. I. Changes with time in the proportion of isolated, paired and clustered labelled cells in sheets of murine epidermis

A new technical approach to analysing labelled cells in sheets of epidermis is presented. The changes in the proportion of isolated single labelled cells, paired or clusters of 3, 4, or more than 4, labelled cells in sheets of epidermis from the back of the mouse have been analysed at various times up to 500 h after 3HTdR administration at either 03.00 h or 15.00 h. The technique is not dependent on the relative number of labelled cells (i.e. the labelling index) but on the spatial distribution of labelled cells. The data cannot be adequately explained on the basis of a simple homogeneous stem cell population in the basal layer but can be better understood on the basis of an hierarchical stem cell-dividing transit proliferative model. The data are consistent with an average cell cycle time of about 100 h but there are suggestions of considerable cell kinetic heterogeneity. The data also suggest that the amount of lateral cell movement within the basal layer is small. The results may suggest that some stem cells either loose label in a manner similar to that suggested by Cairns (1975) i.e. through a process of selective segregation of their DNA strands, or that they have an extremely short S phase duration as postulated earlier (Potten et al. 1982). The present data have been extensively mathematically modelled in an accompanying paper. The model which best fits all the data is an hierarchical scheme with three cell divisions in the transit population but some branches of the lineage may be prematurely terminated by the early production of post-mitotic cells.(ABSTRACT TRUNCATED AT 250 WORDS)     

The labelled mitosis curve for a population consisting of fast and slowly cycling cells

In studies of tumour growth, and particularly of tumour treatment with phase-specific chemotherapeutic agents, the fraction labelled mitosis technique is frequently used to estimate the kinetic properties of the cell population making up the tumour. We show here that the FLM technique is in principle very insensitive to the behaviour of slowly cycling cells, even if these constitute a large proportion of the total cell population. Furthermore, since the rate of DNA synthesis is frequently lower in slowly growing cells than in those growing rapidly, there is a higher probability of labelling error associated with the former cells. In view of these theoretical and experimental considerations, it is suggested that considerable caution be used when applying the FLM technique to heterogeneous cell populations such as those of solid tumours.     

Measuring cell cycle progression kinetics with metabolic labeling and flow cytometry

Precise control of the initiation and subsequent progression through the various phases of the cell cycle are of paramount importance in proliferating cells. Cell cycle division is an integral part of growth and reproduction and deregulation of key cell cycle components have been implicated in the precipitating events of carcinogenesis. Molecular agents in anti-cancer therapies frequently target biological pathways responsible for the regulation and coordination of cell cycle division. Although cell cycle kinetics tend to vary according to cell type, the distribution of cells amongst the four stages of the cell cycle is rather consistent within a particular cell line due to the consistent pattern of mitogen and growth factor expression. Genotoxic events and other cellular stressors can result in a temporary block of cell cycle progression, resulting in arrest or a temporary pause in a particular cell cycle phase to allow for instigation of the appropriate response mechanism. The ability to experimentally observe the behavior of a cell population with reference to their cell cycle progression stage is an important advance in cell biology. Common procedures such as mitotic shake off, differential centrifugation or flow cytometry-based sorting are used to isolate cells at specific stages of the cell cycle. These fractionated, cell cycle phase-enriched populations are then subjected to experimental treatments. Yield, purity and viability of the separated fractions can often be compromised using these physical separation methods. As well, the time lapse between separation of the cell populations and the start of experimental treatment, whereby the fractionated cells can progress from the selected cell cycle stage, can pose significant challenges in the successful implementation and interpretation of these experiments. Other approaches to study cell cycle stages include the use of chemicals to synchronize cells. Treatment of cells with chemical inhibitors of key metabolic processes for each cell cycle stage are useful in blocking the progression of the cell cycle to the next stage. For example, the ribonucleotide reductase inhibitor hydroxyurea halts cells at the G1/S juncture by limiting the supply of deoxynucleotides, the building blocks of DNA. Other notable chemicals include treatment with aphidicolin, a polymerase alpha inhibitor for G1 arrest, treatment with colchicine and nocodazole, both of which interfere with mitotic spindle formation to halt cells in M phase and finally, treatment with the DNA chain terminator 5-fluorodeoxyridine to initiate S phase arrest. Treatment with these chemicals is an effective means of synchronizing an entire population of cells at a particular phase. With removal of the chemical, cells rejoin the cell cycle in unison. Treatment of the test agent following release from the cell cycle blocking chemical ensures that the drug response elicited is from a uniform, cell cycle stage-specific population. However, since many of the chemical synchronizers are known genotoxic compounds, teasing apart the participation of various response pathways (to the synchronizers vs. the test agents) is challenging. Here we describe a metabolic labeling method for following a subpopulation of actively cycling cells through their progression from the DNA replication phase, through to the division and separation of their daughter cells. Coupled with flow cytometry quantification, this protocol enables for measurement of kinetic progression of the cell cycle in the absence of either mechanically- or chemically- induced cellular stresses commonly associated with other cell cycle synchronization methodologies. In the following sections we will discuss the methodology, as well as some of its applications in biomedical research.     

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.     

Exponential 3T3 cells escape in mid-G1 from their high serum requirement.

A simple, new method for determining the temporal location of arrests induced within the cell cycle is described. This method has the advantage that the initial, exponential cell population is unperturbed. It requires neither cell synchronization nor prior arrest of cells by starvation. The method involves partitioning cells located before and after the arrest point into classes of different DNA content. The magnitude of these classes, determined by flow microfluorimetry, is used to calculate the time of arrest within the cell cycle. The calculation utilizes an age distribution function which incorporates variability in cell-cycle durations. The method is used to derive the median time in the cell cycle when low serum arrests exponential Swiss 3T3 cells. The median durations of G1, S, G2 and M in these cells were: 5.4, 8.5, 3.0, and 0.7 h, respectively. Proliferating G1 cells with a median age of up to 3.2 h were blocked from entering S by reducing the exogenous serum concentration. G1 cells closer than approx. 2 h to S, S, G2 and M cells continued to transit the cell cycle. Preincubation of the cells in higher initial serum concentrations failed to alter this median age, indicating that adherence of serum factors to the cells does not influence the time determined. The data indicate that the G1 serum-sensitive events which finally direct cells toward either S or G0 are completed after approx. 2 h before S. Exposure to high serum apparently does not turn on DNA synthesis directly, but initiates an approx. 2 h sequence of required, late G1 events leading to S phase.     

Kinetic heterogeneity of an experimental tumour revealed by BrdUrd incorporation and mathematical modelling

In the present paper we propose a method of analysis of the cell kinetic characteristics of in vivo experimental tumours, that uses DNA-BrdUrd flow cytometry data at various times after the bromodeoxyuridine (BrdUrd) injection and mathematical modelling. The model of the cell population takes into account the cell-cell heterogeneity of the progression rate across cell cycle phases within the tumour, and assumes a strict correlation between the durations of S and G2M phases. The model also allows for a nonconstant DNA synthesis rate across S phase. In addition, the measurement process is modelled, considering the possibility of nonimpulsive labelling and providing a representation of the time course of the bivariate DNA-BrdUrd fluorescence distribution. Sequential DNA-BrdUrd distributions were obtained in vivo from a human ovarian carcinoma transplanted in mice and, for comparison, in vitro from a cell line of the same origin. From these data, that included the fractional density and the mean BrdUrd-fluorescence of BrdUrd-positive cells as a function of the DNA-fluorescence, kinetic parameters such as the potential doubling time (T _pot) and the mean and variance of the transit times in S and G2M phases, were estimated. This study revealed the presence of a substantial heterogeneity in S and G2M phases within the in vivo cell population and of a lower heterogeneity in the in vitro population. Moreover, our analysis suggests a nonnegligible effect of the BrdUrd pharmacokinetics in the in vivo cell labelling.