A Stochastic Model For Cell Populations With Circadian Rhythms

A mathematical model for cell kinetics, based on a random walk, is developed. the model allows variations with time of the rates of passage of proliferating cells through the four phases of the mitotic cycle. Circadian variations in the mitotic and labelling indices of the Syrian hamster cheek pouch epithelium have previously been observed, and the random walk model has been used to simulate this phenomenon. Assuming that all basal cells are proliferative and that these cells leave the basal layer randomly throughout the mitotic cycle to become differentiated cells, it was found that the experimentally observed circadian rhythms of the mitotic and labelling indices could be reproduced in the model by postulating a circadian rhythm in the rate of passage of cells through the G₁ and S phases only. Moreover, the growth activity of cells in both the G₁ and S phases appears to reach a peak during the dark hours of the light-dark cycle, and to fall off rapidly in the early hours of daylight. the postulate of Møller, Larsen & Faber (1974) that injection of the animals with tritiated thymidine causes a shortening of the G₂ phase duration has been qualitatively confirmed by using the random walk model to simulate the FLM and MI curves after injection with tritiated thymidine.     

Modelling the fission yeast cell cycle.

The molecular networks regulating basic physiological processes in a cell can be converted into mathematical equations (eg differential equations) and solved by a computer. The division cycle of eukaryotic cells is an important example of such a control system, and fission yeast is an excellent test organism for the computational modelling approach. The mathematical model is tested by simulating wild-type cells and many known cell cycle mutants. This paper describes an example where this approach is useful in understanding multiple rounds of DNA synthesis (endoreplication) in fission yeast cells that lack the main (B-type) mitotic cyclin, Cdc13. It is proposed that the key physiological variable driving progression through the cell cycle during balanced growth and division is the mass/DNA ratio, rather than the mass/nucleus ratio.     

Cell-cycle variation in the induction of lethality and mitotic recombination after treatment with UV and nitrous acid in the yeast, Saccharomyces cerevisiae.

Exponentially growing yeast cultures separated into discrete periods of the cell cycle by zonal rotor centrifugation show cyclic variation in both UV and nitrous acid induced cell lethality, mitotic gene conversion and mitotic crossing-over. Maximum cell survival after UV treatment was observed in the S and G2 phases of the cell cycle at a time when UV induction of both types of mitotic recombination was at a minimum. In contrast, cell inactivation by the chemical mutagen nitrous acid showed a single discrete period of sensitivity which occurred in S phase cells which are undergoing DNA synthesis. Mitotic gene conversion and mitotic crossing-over were induced by nitrous acid in cells at all stages of the cell cycle with a peak of induction of both events occurring at the time of maximum cell lethality. The lack of correlation observed between maximum cell and the maximum induction of mitotic intragenic recombination suggest that other DNA-repair mechanisms besides DNA-recombination repair are involved in the recovery of inactivated yeast cells during the cell cycle.     

The simulation of thymidine kinase enzyme kinetics in cultured cells using the computer language cellsim

Thymidine kinase is an enzyme that occurs in cells actively synthesizing DNA. In studies of synchronized cell populations, it has been shown that the enzyme activity disappears during the G1 phase of the cell cycle and reappears during the S and G2 phases. Its reappearance is consistent with the synthesis of the mRNA for this enzyme during the S and G2 phases and its immediate translation into active enzyme by the protein synthesis machinery within the cell. The disappearance of the enzyme is consistent with the cessation of mRNA synthesis by mitotic cells. We have now tested this concept by computer simulation of a growing cell population in which a specific mRNA is generated while cells are in the S and G2 phases of the cell cycle. The computer simulation was done using the simulation language Cellsim designed for modeling populations of cells. The Cellsim program which we developed allowed each cell to make about 1 mRNA molecule per min during the S and G2 phases. Every 3 min each mRNA molecule generated a protein enzyme molecule. The mRNA had a half-life of about 9 min, and the enzyme had a half-life of about 150 min. When these molecular parameters were coupled to the cell cycle parameters for Chinese hamster fibroblasts, the resulting curve of enzyme production with time closely matched the observed kinetics of enzyme activity seen in synchronized cells. The only part of the curve that did not fit was the rapid drop in enzyme activity which was seen as the population of mitotic cells was permitted to enter G1. This drop in activity was not seen in mitotic cells blocked with Colcemid where mRNA synthesis must be lacking. Earlier studies have shown that the Gl cells do not contain any inhibitor of enzyme activity. It therefore appears that the enzyme molecule is more unstable during the G1 phase than in any of the other phases of the cell cycle.     

A Computer Model of Spermatogenesis In the Rat; Correlation With Flow Cytometric Data Based On Autoradiographic Cell-Cycle Properties

Abstract. A computer model of rat spermatogenesis was created, based on autoradiographic studies of durations of the phases of the cell cycle (G₁, S, G₂ and mitotic phases) of each germ-cell type. With this model it is possible to predict and to gain insight into the changes of the DNA content occurring during the normal process of spermatogenesis. the relative proportions of haploid, diploid, S phase and tetraploid germ cells with increasing age of the rats were calculated. Calculated and actual experimental flow cytometry data were compared to test the accuracy of the model, and these show good agreement. the present work demonstrates that single-parameter DNA analysis of testicular cells is primarily a reflection of germ cells in the spermatocyte and spermatid stages of development, and of non-germ cells. the FCM single-parameter DNA analysis of testicular cells is relatively insensitive to changes in the stem cell and spermatogonial stages of germ-cell development.     

A computer model of spermatogenesis in the rat; correlation with flow cytometric data based on autoradiographic cell-cycle properties

A computer model of rat spermatogenesis was created, based on autoradiographic studies of durations of the phases of the cell cycle (G1, S, G2 and mitotic phases) of each germ-cell type. With this model it is possible to predict and to gain insight into the changes of the DNA content occurring during the normal process of spermatogenesis. The relative proportions of haploid, diploid, S phase and tetraploid germ cells with increasing age of the rats were calculated. Calculated and actual experimental flow cytometry data were compared to test the accuracy of the model, and these show good agreement. The present work demonstrates that single-parameter DNA analysis of testicular cells is primarily a reflection of germ cells in the spermatocyte and spermatid stages of development, and of non-germ cells. The FCM single-parameter DNA analysis of testicular cells is relatively insensitive to changes in the stem cell and spermatogonial stages of germ-cell development.     

Cyclin levels during TNF-alpha-induced apoptosis in HIV-infected cells.

Cyclins are cell cycle regulatory proteins. We compared the concurrent kinetics of apoptosis and cyclin expression between HIV-infected cells (J1.1), and uninfected Jurkat cells. Cells were cultured with TNF-alpha and harvested at 24, 48 and 72 hr to examine cyclin expression and DNA content. We found a decline in the levels of the mitotic B cyclin in Jurkat cells (16 to 2%, 48 hr), while in J1.1 cells it was observed in cyclin E (60 to 37%, 72 hr). Because cyclin B is mitotic, results suggest that Jurkat cells undergo apoptosis at G2, while J1.1 cells enter mitosis and then die by apoptosis, as no changes in cyclin B or DNA content at G2M were observed. G1 cyclin E decline in J1.1 cells also suggests that they die after entering mitosis. Based on differences in the cyclins involved, it seems that HIV-1 manipulates the cell cycle to protect J1.1 cells from apoptosis induction at G2, a critical cell cycle phase for HIV replication. Thus, cyclins are useful to characterize points in the cell cycle at which apoptosis is induced, and could become excellent tools to evaluate mechanisms of action of antiretroviral drugs in the cell cycle of HIV-infected cells.     

Heat shock-induced arrests in different cell cycle phases of rat C6-glioma cells are attenuated in heat shock-primed thermotolerant cells

The response kinetics of rat C6 glioma cells to heat shock was investigated by means of flow cytometric DNA measurements and western blot analysis of HSP levels. The results showed that the effects on cell cycle progression are dependent on the cell cycle phase at which heat shock is applied, leading to either G1 or G2/M arrest in randomly proliferating cells. When synchronous cultures were stressed during G0 they were arrested with G1 DNA content and showed prolongation of S and G2 phases after release from the block. In proliferating cells, HSC70 and HSP68 were induced during the recovery and reached maximum levels just before cells were released from the cell cycle blocks. Hyperthermic pretreatment induced thermotolerance both in asynchronous and synchronous cultures as evidenced by the reduced arrest of cell cycle progression after the second heat shock. Thermotolerance development was independent of the cell cycle phase. Pre-treated cells already had high HSP levels and did not further increase the amount of HSP after the second treatment. However, as in unprimed cells, HSP reduction coincided with the release from the cell cycle blocks. These results imply that the cell cycle machinery can be rendered thermotolerant by heat shock pretreatment and supports the assumption that HSP70 family members might be involved in thermotolerance development.     

ANALYSIS OF THE PROLIFERATION KINETICS OF BURKITT'S LYMPHOMA CELLS

The in vitro proliferation kinetics of a cell line derived from a patient with American Burkitt's lymphoma were investigated at three different growth phases: lag (day 1), exponential (day 3) and plateau (day 5). The growth curve, labeling and mitotic indices, percentage labeled mitosis (PLM) curves and DNA content distributions were determined. The data obtained have been analysed by the previously developed discrete-time kinetic (DTK) model by which a time course of DNA distributions during a 10-day growth period was characterized in terms of other cell kinetic parameters. The mean cell cycle times, initially estimated from PLM curves on days 1, 3 and 5, were further analysed by the DTK model of DNA distributions and subsequently the mean cell cycle times with respect to DNA distributions during the entire growth period were determined. The doubling times were 39·6, 31·2 and 67·2 hr, respectively, at days 1, 3 and 5. The mean cell cycle time increased from 23·0 to 37·7 hr from day 3 to day 5 mainly due to an elongation of the G₁ and G₂ phases. A slight increase in the cell loss rate from 0·0077 to 0·0081 fraction/hr was accompanied by a decrease in the cell production rate from 0·0299 to 0·0184 fraction/hr. This calculated cell loss rate correlated significantly with the number of dead cells determined by trypan blue exclusion. Analysis of the number of dead cells in relation to the cell cycle stage revealed that a majority of cell death occurred in G₁ (r= 0·908; P < 0·0001). There was a good correlation between the in vitro proliferation kinetics at plateau phase of this Burkitt's lymphoma derived cell line and the in vivo proliferation kinetics of African Burkitt's lymphoma (Iversen et al., 1974), suggesting the potential utility of information obtained by in vitro kinetic studies.     

Effect of separase depletion on ionizing radiation-induced cell cycle checkpoints and survival in human lung cancer cell lines

Abstract.   Objectives : This study is to evaluate the effect of separase depletion on cell cycle progression of irradiated and non-irradiated cells through the G₂/M phases and consecutive cell survival. Materials and methods : Separase was depleted with siRNA in two human non-small cell lung carcinoma (NSCLC) cell lines. Cell cycle progression, mitotic fraction, DNA repair, apoptotic and clonogenic cell death were determined. Results : By depletion of endogenous separase with siRNA in NSCLCs, we showed that separase affects progression through the G₂ phase. In non-irradiated exponentially growing cells, separase depletion led to an increased G₂ accumulation from 17.2% to 29.1% in H460 and from 15.7% to 30.9% in A549 cells and a decrease in mitotic cells. Depletion of separase significantly ( P <  0.01) increased the fraction of radiation-induced G₂ arrested cells 30–56 h after irradiation and led to decrease in the mitotic fraction. This was associated with increased double-strand break repair as measured by γ-H2AX foci kinetics in H460 cells and to a lesser extent in A549 cells. In addition, a decrease in the expression of mitotic linked cell death after irradiation was found. Conclusions : These results indicate that separase has additional targets involved in regulation of G₂ to M progression after DNA damage. Prolonged G₂ phase arrest in the absence of separase has consequences on repair of damaged DNA and cell death.     

Modelling cell death in human tumour cell lines exposed to the anticancer drug paclitaxel

Most anti-cancer drugs in use today exert their effects by inducing a programmed cell death mechanism. This process, termed apoptosis, is accompanied by degradation of the DNA and produces cells with a range of DNA contents. We have previously developed a phase transition mathematical model to describe the mammalian cell division cycle in terms of cell cycle phases and the transition rates between these phases. We now extend this model here to incorporate a transition to a programmed cell death phase whereby cellular DNA is progressively degraded with time. We have utilised the technique of flow cytometry to analyse the behaviour of a melanoma cell line (NZM13) that was exposed to paclitaxel, a drug used frequently in the treatment of cancer. The flow cytometry profiles included a complex mixture of living cells whose DNA content was increasing with time and dying cells whose DNA content was decreasing with time. Application of the mathematical model enabled estimation of the rate constant for entry of mitotic cells into apoptosis (0.035 per hour) and the duration of the period of DNA degradation (51 hours). These results provide a dynamic model of the action of an anticancer drug that can be extended to improve the clinical outcome in individual cancer patients.Revised version: 9 October 2003     

Alterations in the cell cycle characteristics of granulosa cells during the periovulatory period: evidence of ovarian and oviductal influences

Granulosa cells at different stages of differentiation were collected from ovarian follicles and oviducts during the periovulatory period, and their nuclear DNA content was monitored by flow cytometry to establish their cell cycle characteristics (G0 + G1, S, G2 + M). The proportion of cells in the three phases of the cell cycle varied in characteristics patterns depending upon the time they were collected, before or following ovulation. Granulosa (cumulus) cells recovered from ovulated oocytes were mitotically inactive as shown by the large proportion of cells with a 2C amount of DNA and the absence of cells in S phase. The proportion of granulosa cells in G2 + M decreased when recovery from the oviducts was delayed. In contrast, granulosa (cumulus and/or mural) cells recovered from preovulatory follicles prior to luteinizing hormone (LH) exposure contained a considerable population of cells undergoing DNA synthesis, and a decreased proportion of cells with a 2C DNA content. Our findings indicate that granulosa cells undergo dynamic and characteristics changes in all cell cycle phases during the periovulatory period, within follicular and oviductal environments. Intrafollicular events appear to play a major role in controlling DNA synthesis, proliferation, and related cell cycle events in the granulosa cells. Flow cytometric techniques provide objective and detailed information on the cell cycle characteristics of granulosa cell populations at different stages of differentiation. Elucidation of the mechanisms regulating cell cycle parameters of granulosa cells and their physiological significance thus seems feasible.     

Regulation of Polo-like kinase 1 by DNA damage in mitosis. Inhibition of mitotic PLK-1 by protein phosphatase 2A

DNA damage triggers multiple checkpoint pathways to arrest cell cycle progression. Polo-like kinase 1 (Plk1) is an important regulator of several events during mitosis. In addition to Plk1 functions in cell cycle, Plk1 is involved in DNA damage check-point in G2 phase. Normally, ataxia telangiectasia-mutated kinase (ATM) is a key enzyme involved in G2 phase cell cycle arrest following DNA damage, and inhibition of Plk1 by DNA damage during G2 occurs in a ATM/ATR-dependent manner. However, it is still unclear how Plk1 is regulated in response to DNA damage in mitosis in which Plk1 is already activated. Here, we show that treatment of mitotic cells with doxorubicin and gamma-irradiation inhibits Plk1 activity through dephosphorylation of Plk1, and cells were arrested in G2 phase. Treatments of the phosphatase inhibitors and siRNA experiments suggested that PP2A pathway might be involved in regulating mitotic Plk1 activity in mitotic DNA damage. Finally, we propose a novel pathway, which is connected between ATM/ATR/Chk and protein phosphatase-Plk1 in DNA damage response in mitosis.     

Epidermal cell kinetics in the nude mouse

The epidermal cell kinetics in nude mice is investigated by determining the mitotic rate and the mitotic count, the H3Tdr labelling index, and the proportion of basal cells in the different cell cycle phases by flow cytometry. The mitotic duration was calculated. The parameter values of the epidermal cell kinetics of the nude mouse are largely similar to those of the hairless mouse.     

CYTOKINETIC ANALYSIS OF THE JB-1 ASCITES TUMOUR AT DIFFERENT STAGES OF GROWTH

The cell kinetics of the murine JB-1 ascites tumour have been investigated on days 4, 7 and 10 after transplantation of 2·5 × 10⁶ cells. The experimental data, growth curve, percentage of labelled mitoses curves, continuous labelling curves and cytophotometric determination of single-cell DNA content have been analysed by means of a mathematical model for the cell kinetics. The important result was the existence of 8% non-cycling cells with G₂ DNA content in the 10-day tumour, while only 0·2 and 0% were observed in the 7- and 4-day tumours, respectively. The doubling times determined from the growth curve were 22·8, 70 and 240 hr, respectively, in the 4-, 7- and 10-day tumours. Growth fractions of 76, 67 and 44% were calculated for the same tumour ages. The mean cell cycle time increased from 14 to 44 hr from day 4 to 7 due to a proportional increase in the mean transit time of all phases in the cell cycle. In the 10-day tumour, the mean cell cycle changed to 41 hr and T _G1 decreased to 0·5 hr. The cell production rate was 4·3%/hr in the 4-day tumour, 1·2%/hr in the 7-day tumour and 1·0%/hr in the 10-day tumour. The cell loss rates in the same tumours were 1·3, 0·2 and 0·7%/hr, respectively. The analysis made it probable that the mode of cell loss was an age-specific elimination of non-cycling cells with postmitotic DNA content.     

Simian Virus 40-Host Cell Interaction During Lytic Infection

Both exponentially growing and serum-arrested subcloned CV-1 cell cultures were infected with simian virus 40 (SV40). By 24 h after infection 96% of the nuclei of these permissive cells contained SV40 T-antigen. Analysis of the average DNA content per cell at various times after infection indicated that by 24 h most of the cells contained amounts of DNA similar to those normally found in G(2) cells. Analysis of cell cycle distributions indicated that a G(2) DNA complement was maintained by over 90% of the cells in the infected populations 24 to 48 h postinfection. Cells continued to synthesize SV40 DNA during the first 50 h after infection, and cytopathic effect was first observed 60 h after inoculation. After infection the number of mitotic cells that could be recovered by selective detachment decreased precipitously and was drastically reduced by 24 h. A study of the kinetics of decline in the number of mitotic cells suggests that this decline is related to an event during the cell cycle at or near the G(1)-S-phase border upon which commencement of SV40 DNA replication apparently depends. It was concluded that after SV40 infection, stationary cells are induced to cycle, and cycling cells complete one round of cellular DNA synthesis but do not divide. Although the infected cells continue to synthesize viral DNA, they do not appear able to reinitiate cellular DNA replication units. These results imply that the abundance of T-antigen (produced independently of cell cycle phase) in the presence of the enzymes required for continued DNA synthesis is not sufficient for reinitiation of cellular DNA synthesis.     

The Nuclear Endoreduplication Cycle in Metaxylem Cells of Primary Roots of Zea mays L.

The nuclear DNA content of metaxylem cells in roots of Zea mayscv. Golden Bantam reaches 16C or 32C by successive rounds ofDNA endoreduplication. Each phase of endoreduplication (endo-S)is separated by a non-DNA synthetic phase (endo-G). These phasesseem to occur in zones at fixed distances from the root tip.The duration of the phases in two of the endoreduplication cycles(4C–8C, 8C–16C) has been estimated in two ways.The first makes use of the rate of movement of cells throughthe positions along the root where the different phases of thecycle are occurring, the second uses labelling with methyl-[³H]thymidineand autoradiography. Both methods indicate that the endo-S phaseswhich cause the nuclear DNA content to rise from 4C to 8C andfrom 8C to 16C last 8–10 h, and that the intervening endo-Gphase lasts 8–12 h. DNA endoreduplication keeps pace withthe increase of nuclear volume; cell volume increases at a morerapid rate, however. Comparison of the endoreduplication cyclein the metaxylem with the mitotic cycle in the adjoining filesof parenchyma cells shows that the mitotic cells complete theircycle more slowly. DNA synthesis, endoreduplication cycle, mitotic cycle, root apex, Zea mays     

A mathematical model for analysis of the cell cycle in cell lines derived from human tumors

The growth of human cancers is characterised by long and variable cell cycle times that are controlled by stochastic events prior to DNA replication and cell division. Treatment with radiotherapy or chemotherapy induces a complex chain of events involving reversible cell cycle arrest and cell death. In this paper we have developed a mathematical model that has the potential to describe the growth of human tumour cells and their responses to therapy. We have used the model to predict the response of cells to mitotic arrest, and have compared the results to experimental data using a human melanoma cell line exposed to the anticancer drug paclitaxel. Cells were analysed for DNA content at multiple time points by flow cytometry. An excellent correspondence was obtained between predicted and experimental data. We discuss possible extensions to the model to describe the behaviour of cell populations in vivo.