Retention of the mitochondrial probe rhodamine 123 in normal lymphocytes and leukemic cells in relation to the cell cycle

The cationic fluorochrome rhodamine 123 (R123) is specifically taken up by mitochondria of live cells where it is retained due to the mitochondrial transmembrane potential. After pulse exposure of human normal quiescent or proliferating lymphocytes, human lymphocytic leukemic MOLT cells, and mice leukemic L1210 cells to 10 micrograms/ml of R123, the dye release was studied using flow cytometry. Two distinct phases of R123 release, each following first-order kinetics, were apparent; the half-time of retention for the rapidly and slowly released fractions of R123 was 0.8-1.1 and 2.8-4.2 h, respectively. Simultaneous supravital cell staining with R123 and Hoechst 33342 made it possible to correlate retention of R123 with cell position in the cell cycle. No significant differences were observed in the rate of R123 release from cells in G1 vs S or vs G2 + M phases of the cycle. The data rule out a possibility that the release of R123 is due to periodic depolarization of the mitochondria in the cell as may be postulated by cell cycle models that assume a transient passage of cells through resting phase following division. The observed similar rates of R123 release regardless of cell type or cell cycle phase suggest that the factors affecting the exchange are similar in normal lymphocytes vs leukemic cells and unrelated to cell proliferation rate or phase of the cell cycle. Two distinct rates of R123 release indicate the presence of two kinds of binding sites differing in affinity to the dye.     

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.     

Cell cycle dynamics inferred from the static properties of cells in balanced growth

The duration of a morphological phase of the cell cycle is reflected in the steady state distribution of the sizes of cells in that phase. Relationships presented here provide a method for estimating the timing and variability of any cell cycle phase. It is shown that the mean size of cells initiating and finishing any phase can be estimated from (1) the frequency of cells exhibiting the distinguishing morphological or autoradiographic features of the phase; (2) the mean size of cells in the phase; and (3) their coefficient of variation. The calculations are based on a submodel of the Koch-Schaechter Growth Controlled Model which assumes that (i) the distribution of division sizes is Gaussian; (ii) there is no correlation in division sizes between successive generations; and (iii) every cell division gives rise to two daughter cells of equal size. The calculations should be useful for a wider range of models, however, because the extrapolation factors are not sensitive to the chosen model. Criteria are proposed to allow the user to check the method's applicability for any experimental case. The method also provides a more efficient test of the dependence of growth on cell size than does the Collins-Richmond method. This is because the method uses the mean and coefficient of variation of the size of the total population, in conjunction with those of the cells in a final phase of the cell cycle, to test potential growth laws. For Escherichia coli populations studied by electron microscopy, an exponential growth model provided much better agreement than did a linear growth model. The computer simulations were used to generate rules for three types of cell phases: those that end at cell division, those that start at cell division, and those totally contained within a single cell cycle. For the last type, additional criteria are proposed to establish if the phase is well enough contained for the formulae and graphs to be used. The most useful rule emerging from these computer studies is that the fraction of the cell cycle time occupied by a phase is the product of the frequency of the phase and the ratio of the mean size of cells in that phase to the mean size of all cells in the population. A further advantage of the techniques presented here is that they use the 'extant' distributions that were actually measured, and not hypothesized distributions nor the special distributions needed for Collins-Richmond method that can only be calculated from the observed distributions of dividing or newborn cells on the basis of an assumed growth law.     

Cell-cycle phase-dependence of drug-induced cycle progression delay.

The effect of adriamycin on cell cycle phase progression of CHO cells synchronized into the various phases of the cell cycle by elutriation was investigated by high resolution pulse cytophotometry. Cells treated in all phases of the cell cycle showed delay in their subsequent progression. In addition to the wellknown block of cells in the G2-phase, a delay in passage of cells from G1 to S and a decreased rate of transit through the S-phase were observed. A broadening of the DNA distributions of the treated cells was observed after cell division indicating induction of chromosomal abnormalities.     

How the change from FLM to FACS affected our understanding of the G1-phase of the cell cycle

The frequency of labeled mitoses (FLM) method for analyzing cell-cycle phases necessitates a determination of cell-cycle interdivision times and the absolute lengths of the cell-cycle phases. The change to flow sorting (FACS) analysis, a simpler, less labor intensive, and more rapid method, eliminated determinations of absolute phase times, yielding only percents of cells exhibiting particular DMA contents. Without an interdivision time value, conversion of these fractions into absolute phase lengths is not possible. This change in methodology has led to an alteration in how the cell cycle is viewed. The FLM method allowed the conclusion that G1 phase variability resulted from constancy of S and G2 phase lengths. In contrast, with FACS analysis, slow growing cells exhibiting a large fraction of cells with a G1-phase amount of DMA appeared to be "arrested in G1 phase". The loss of absolute phase length determinations has therefore led to the proposals of G1-phase arrest, G1-phase controls, restriction points, and G0 phase. It is suggested that these G1-phase controls and phenomena require a critical reevaluation in the light of an alternative cell-cycle model that does not require or postulate such G1-phase controls.     

How the Change from FLM to FACS Affected Our Understanding of the G1-Phase of the Cell Cycle

The frequency of labeled mitoses (FLM) method for analyzing cell-cycle phases necessitates a determination of cell-cycle interdivision times and the absolute lengths of the cell-cycle phases. The change to flow sorting (FACS) analysis, a simpler, less labor intensive, and more rapid method, eliminated determinations of absolute phase times, yielding only percents of cells exhibiting particular DNA contents. Without an interdivision time value, conversion of these fractions into absolute phase lengths is not possible. This change in methodology has led to an alteration in how the cell cycle is viewed. The FLM method allowed the conclusion that G1-phase variability resulted from constancy of S and G2 phase lengths. In contrast, with FACS analysis, slow growing cells exhibiting a large fraction of cells with a G1-phase amount of DNA appeared to be “arrested in G1 phase”. The loss of absolute phase length determinations has therefore led to the proposals of G1-phase arrest, G1-phase controls, restriction points, and G0 phase. It is suggested that these G1-phase controls and phenomena require a critical reevaluation in the light of an alternative cell-cycle model that does not require or postulate such G1-phase controls.     

Synchronization in chains of pacemaker cells by phase resetting action potential effects

Interactions between pacemaker cells in a chain were calculated according to a "phase-reset" model. It is based on effects of action potentials in the cells on the cycle lengths of neighbouring cells. These effects were defined for each cell by a latency-phase curve (LPC), giving the latency time (L) until the onset of the next action potential in that cell, as a function of the phase (phi) at which a neighbour cell fired an action potential. Neighbour cells with simultaneous action potentials did not influence each others cycle length. We investigated how stable synchronization depends on the shape of the LPC's of the pacemaker cells and on chain length. Three types of interactive behaviour were distinguished. First, anti-phase synchrony, in which neighbouring cells fired with large phase differences with respect to the synchronized period Ps. Second, asynchrony, in which the periods of the cells did not become equal and constant. Third, in-phase synchrony, in which the phase differences between the neighbouring cells were zero or much smaller than the synchronized period Ps, depending on the differences between the intrinsic periods. Asynchrony and anti-phase synchrony may be seen as cardiophysiological arrhythmias, while in-phase synchrony represents the physiological type of synchrony in the heart. In-phase synchrony appeared to be strongly favoured by LPC's, which have a no-effect (refractory) part at early phases, a lengthened latency (or phase delay) part at intermediate phases and a shortened latency (or phase advance) part at late phases in the cycle. Such LPC-shapes are commonly found in preparations of cardiac pacemaker cells. When the pacemaker cells were identical, the synchronized period Ps during in-phase synchrony was equal to their intrinsic period P*i. For different intrinsic periods, Ps was equal to the intrinsic period of the fastest cell if the LPC's contained a sufficiently long initial no-effect period at early phases and a shortened latency part at late phases. When, on the other hand, such cell chains had a linear gradient in their intrinsic periods, "action potentials" started from the fast end and traveled along the chain. The propagation of an action potential wave slowed down as it reached the slower cells. When the gradient in the intrinsic periods was too steep, only the intrinsically fast end of the chain developed synchrony.(ABSTRACT TRUNCATED AT 400 WORDS)     

Modelling the regulation of telomere length: the effects of telomerase and G-quadruplex stabilising drugs

Telomeres are guanine-rich sequences at the end of chromosomes which shorten during each replication event and trigger cell cycle arrest and/or controlled death (apoptosis) when reaching a threshold length. The enzyme telomerase replenishes the ends of telomeres and thus prolongs the life span of cells, but also causes cellular immortalisation in human cancer. G-quadruplex (G4) stabilising drugs are a potential anticancer treatment which work by changing the molecular structure of telomeres to inhibit the activity of telomerase. We investigate the dynamics of telomere length in different conformational states, namely t-loops, G-quadruplex structures and those being elongated by telomerase. By formulating deterministic differential equation models we study the effects of various levels of both telomerase and concentrations of a G4-stabilising drug on the distribution of telomere lengths, and analyse how these effects evolve over large numbers of cell generations. As well as calculating numerical solutions, we use quasicontinuum methods to approximate the behaviour of the system over time, and predict the shape of the telomere length distribution. We find those telomerase and G4-concentrations where telomere length maintenance is successfully regulated. Excessively high levels of telomerase lead to continuous telomere lengthening, whereas large concentrations of the drug lead to progressive telomere erosion. Furthermore, our models predict a positively skewed distribution of telomere lengths, that is, telomeres accumulate over lengths shorter than the mean telomere length at equilibrium. Our model results for telomere length distributions of telomerase-positive cells in drug-free assays are in good agreement with the limited amount of experimental data available.     

Population study of cell cycle in a continuous culture ofCandida utilis

The mean lengths of G1, S, G2 and M phases of the cell cycle were determined on the basis of the population distribution ofCandida utilis grown in a continuous culture under steady-state conditions by using an original mathematical method. The length of the G2 phase was proportional to that of G1; the length of M was effectively independent of the growth rate. The length of S was proportional to the mean number of mitochondria in the cell.     

A Generalised Age- and Phase-Structured Model of Human Tumour Cell Populations Both Unperturbed and Exposed to a Range of Cancer Therapies

We develop a general mathematical model for a population of cells differentiated by their position within the cell division cycle. A system of partial differential equations governs the kinetics of cell densities in certain phases of the cell division cycle dependent on time t (hours) and an age-like variable τ (hours) describing the time since arrival in a particular phase of the cell division cycle. Transition rate functions control the transfer of cells between phases. We first obtain a theoretical solution on the infinite domain −∞ < t < ∞. We then assume that age distributions at time t=0 are known and write our solution in terms of these age distributions on t=0. In practice, of course, these age distributions are unknown. All is not lost, however, because a cell line before treatment usually lies in a state of asynchronous balanced growth where the proportion of cells in each phase of the cell cycle remain constant. We assume that an unperturbed cell line has four distinct phases and that the rate of transition between phases is constant within a short period of observation (‘short’ relative to the whole history of the tumour growth) and we show that under certain conditions, this is equivalent to exponential growth or decline. We can then gain expressions for the age distributions. So, in short, our approach is to assume that we have an unperturbed cell line on t ≤ 0, and then, at t=0 the cell line is exposed to cancer therapy. This corresponds to a change in the transition rate functions and perhaps incorporation of additional phases of the cell cycle. We discuss a number of these cancer therapies and applications of the model.     

Cell cycle phase expansion in nitrogen-limited cultures of Saccharomyces cerevisiae

The time and coordination of cell cycle events were examined in the budding yeast Saccharomyces cerevisiae. Whole-cell autoradiographic techniques and time-lapse photography were used to measure the duration of the S, G1, and G2 phases, and the cell cycle positions of "start" and bud emergence, in cells whose growth rates were determined by the source of nitrogen. It was observed that the G1, S, and G2 phases underwent a proportional expansion with increasing cell cycle length, with the S phase occupying the middle half of the cell cycle. In each growth condition, start appeared to correspond to the G1 phase/S phase boundary. Bud emergence did not occur until mid S phase. These results show that the rate of transit through all phases of the cell cycle can vary considerably when cell cycle length changes. When cells growing at different rates were arrested in G1, the following synchronous S phase were of the duration expected from the length of S in each asynchronous population. Cells transferred from a poor nitrogen source to a good one after arrest in G1 went through the subsequent S phase at a rate characteristic of the better medium, indicating that cells are not committed in G1 to an S phase of a particular duration.     

PAR proteins direct asymmetry of the cell cycle regulators Polo-like kinase and Cdc25

Cell cycle lengths vary widely among different cells within an animal, yet mechanisms of cell cycle length regulation are poorly understood. In the Caenorhabditis elegans embryo, the first cell division produces two cells with different cell cycle lengths, which are dependent on the conserved partitioning-defective (PAR) polarity proteins. We show that two key cell cycle regulators, the Polo-like kinase PLK-1 and the cyclin-dependent kinase phosphatase CDC-25.1, are asymmetrically distributed in early embryos. PLK-1 shows anterior cytoplasmic enrichment and CDC-25.1 shows PLK-1-dependent enrichment in the anterior nucleus. Both proteins are required for normal mitotic progression. Furthermore, these asymmetries are controlled by PAR proteins and the muscle excess (MEX) proteins MEX-5/MEX-6, and the latter is linked to protein degradation. Our results support a model whereby the PAR and MEX-5/MEX-6 proteins asymmetrically control PLK-1 levels, which asymmetrically regulates CDC-25.1 to promote differences in cell cycle lengths. We suggest that control of Plk1 and Cdc25 may be relevant to regulation of cell cycle length in other developmental contexts.     

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.     

Cell elongation and division probability during the Escherichia coli growth cycle.

A new method is presented for determining the growth rate and the probability of cell division (separation) during the cell cycle, using size distributions of cell populations grown under steady-state conditions. The method utilizes the cell life-length distribution, i.e., the probability that a cell will have any specific size during its life history. This method was used to analyze cell length distributions of six cultures of Escherichia coli, for which doubling times varied from 19 to 125 min. The results for each culture are in good agreement with a single model of growth and division kinetics: exponential elongation of cells during growth phase of the cycle, and normal distributions of length at birth and at division. The average value of the coefficient of variation was 13.5% for all strains and growth rates. These results, based upon 5,955 observations, support and extend earlier proposals that growth and division patterns of E. coli are similar at all growth rates and, in addition, identify the general growth pattern of these cells to be exponential.     

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.     

Influence of the existence of a resting state on the probability of cell division in culture

A cell cycle model developed by Smith and Martin is generalized to allow for the possibility that the duration of the B phase is not fixed. The B phase is the equivalent of the traditional S, G₂, and M phases of the cell cycle. The duration of the B phase is represented by a Gaussian probability distribution; the duration of the resting or A state which replaces the traditional G₁ phase is represented by a decaying exponential distribution. A doubling time distribution, termed the CEG distribution, is obtained by convolution of the A state and B phase distributions. Like the reciprocal normal, rate normal, and log normal distributions, it is a rounded unimodal peak that is skewed to the right. None of the three former distributions is associated with a cell cycle model that includes a resting state. However the CEG distribution, which is so associated, bears little resemblance to the delayed exponential distribution which results when the duration of the B phase is fixed and the duration of the A state is random. Consequently, it would be difficult to use the doubling time distribution to determine whether or not a resting state exists in a particular cell population.     

Diversity of cell lengths in terminal portions of roots: implications to cell proliferation

Terminal meristems are responsible for all primary growth of roots. It has been asserted that all cells of root meristems are actively dividing (no cells cycle slowly or arrest in the cycle) and stem cell populations expand exponentially. Because cells do not slide relative to each other in roots, relative cell lengths may be used to determine relative cell cycle durations and/or proportions of cells actively dividing in root tissues. If all cells are cycling, no interphase cells should be longer than critical length (length of longest mitotic cell in the meristem) and cells should exhibit an exponential cell-age distribution. Lengths of all cells were obtained radially across entire median longitudinal root sections at 0.5, 1.0, 1.5, 2.0, 2.5 and 3.0 mm from the founder cell/root cap boundary for five plant species to estimate percentages of cells longer than critical length. For example, up to 15 and 90% of all interphase cells were longer than critical length in 0.5 and 2.0 mm tissues, respectively, indicating that slow-cycling and/or non-proliferative cells are present in such tissues. In order to determine if the distribution of cell lengths in 0.5 mm segments approximated an exponential cell-age distribution, lengths of interphase cells less than critical length were determined. Such interphase cells were placed into ten groups according to cell length and percentages of cells in each group were compared with percentages of cells in groups calculated from an exponential cell-age distribution. Percentages of cells were significantly different from predicted percentages of between 6 and 9 out of ten groups - cell lengths were not distributed exponentially. Because there are significant numbers of interphase cells longer than critical length and since lengths of interphase cells shorter than critical length do not resemble an exponential cell-age distribution, it must be concluded that not all cells in root segments from 0.5 to 3.0 mm root segments are actively dividing. Heretofore, no databases of cell lengths have been used to test these assertions.     

Cell cycle phases in the unequal mother/daughter cell cycles of Saccharomyces cerevisiae.

During cell division in the yeast Saccharomyces cerevisiae mother cells produce buds (daughter cells) which are smaller and have longer cell cycles. We performed experiments to compare the lengths of cell cycle phases in mothers and daughters. As anticipated from earlier indirect observations, the longer cell cycle time of daughter cells is accounted for by a longer G1 interval. The S-phase and the G2-phase are of the same duration in mother and daughter cells. An analysis of five isogenic strains shows that cell cycle phase lengths are independent of cell ploidy and mating type.     

Cell Cycle Kinetics of Aerated, Hypoxic and Re-Aerated Cells In Vitro Using Flow Cytometric Determination of Cellular Dna and Incorporated Bromodeoxyuridine

Abstract. The effects of extreme hypoxia on cell cycle progression were studied by simultaneous determination of DNA and bromodeoxyuridine (BrdU) contents of individual cells. V79-379A cells were pulse-labelled with BrdU (1 μM, 20 min, 37°C) and then incubated for up to 12 hr in BrdU-free medium under either aerated or extremely hypoxic conditions. After the incubation interval (0-12 hr), the cells were trypsinized and fixed in 50% EtOH. Propidium iodide and a fluorescein-labelled monoclonal antibody to BrdU were then used to quantify DNA content and incorporated BrdU, respectively. Measurements in individual cells were made by simultaneous detection of green and red fluorescence upon excitation at 488 nm using flow cytometry. Bivariate analysis revealed progression of BrdU-labelled cells in aerated cultures out of S phase, into G₂ and cell division, with halving of mean fluorescence, and back into S phase by approximately 9 hr after the BrdU pulse. Hypoxia immediately arrested cells in all phases of the cell cycle. Both the DNA distribution and the bivariate profile of cells that were fixed from 2 to 12 hr after induction of hypoxia were identical to the 0 hr controls. the percent of cells with green fluorescence in a mid-S phase window remained 100% and the mean fluorescence of these cells remained at control (0 hr) levels. This indicates that, under hypoxic conditions, cells were moving neither into nor out of S phase. Cultures that had been hypoxic for 12 hr exhibited an increasing rate of BrdU uptake with time after re-aeration. Re-aerated cells were able to complete or initiate DNA synthesis, but their rates of progression through the cell cycle were markedly reduced. A large fraction of cells appeared unable to divide up to 12 hr following release from hypoxia.