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.     

Inhibition of breast cancer xenografts in a mouse model and the induction of apoptosis in multiple breast cancer cell lines by lactoferricin B peptide

Breast cancer has a diverse aetiology characterized by the heterogeneous expression of hormone receptors and signalling molecules, resulting in varied sensitivity to chemotherapy. The adverse side effects of chemotherapy coupled with the development of drug resistance have prompted the exploration of natural products to combat cancer. Lactoferricin B (LfcinB) is a natural peptide derived from bovine lactoferrin that exhibits anticancer properties. LfcinB was evaluated in vitro for its inhibitory effects on cell lines representing different categories of breast cancer and in vivo for its suppressive effects on tumour xenografts in NOD-SCID mice. The different breast cancer cell lines exhibited varied levels of sensitivity to apoptosis induced by LfcinB in the order of SKBR3>MDA-MB-231>MDA-MB-468>MCF7, while the normal breast epithelial cells MCF-10A were not sensitive to LfcinB. The peptide also inhibited the invasion of the MDA-MB-231 and MDA-MB-468 cell lines. In the mouse xenograft model, intratumoural injections of LfcinB significantly reduced tumour growth rate and tumour size, as depicted by live imaging of the mice using in vivo imaging systems (IVIS). Harvested tumour volume and weight were significantly reduced by LfcinB treatment. LfcinB, therefore, is a promising and safe candidate that can be considered for the treatment of breast cancer.     

Travelling-wave analysis of a model of the immune response to cancer

In this paper we present a travelling-wave analysis of a mathematical model describing the growth of a solid tumour in the presence of an immune system response. From a modelling perspective, attention is focused upon the attack of tumour cells by tumour infiltrating cytotoxic lymphocytes (TICLs), in a small multicellular tumour, without necrosis and at some stage prior to (tumour-induced) angiogenesis. As we have shown in previous work, for a particular choice of parameters, the underlying reaction-diffusion-chemotaxis system of partial differential equations is able to simulate the well-documented phenomenon of cancer dormancy by depicting spatially heterogeneous tumour cell distributions that are characterized by a relatively small total number of tumour cells. This behaviour is consistent with several immunomorphological investigations. Moreover, the alteration of certain parameters of the model is enough to induce bifurcations into the system, which in turn result in tumour invasion in the form of a standard travelling wave. The work presented in this paper complements the bifurcation analysis undertaken by Matzavinos et al. [Math. Med. Biol. IMA 21 (2004) 1-34] and establishes the existence of travelling-wave solutions for the system under discussion by promoting the understanding of the geometry of an appropriate phase space.     

Cell cycle specificity of apoptosis during treatment of leukaemias

This review summarizes our observations on the mechanism of induction of apoptosis in vitro in leukaemic cell lines and in vivo in patients with leukaemia undergoing chemotherapy, in relation to the cell cycle. Multiparameter flow cytometric methods allowed us to identify apoptotic cells and position them with respect to their cell cycle phase. Several antitumor agents of different classes have been characterized in terms of the cell cycle phase specificity of induction of apoptosis. Three types of apoptosis could be distinguished in relation to the initial damage to the cell vis-a-vis cell cycle position: (1) homo-phase apoptosis where the cells underwent apoptosis during the same phase in which they were initially affected; (2) homo-cycle apoptosis, where the cells underwent apoptosis during the same cell cycle in which they were initially affected, i.e., prior to or during the first mitosis, and (3) post-mitotic apoptosis, where cells underwent apoptosis during the cell cycle(s) subsequent to that in which the cell was initially affected, most likely at the G1 or G2 checkpoints of these cycle(s). Four ranges of drug concentration can be distinguished in vitro for most drugs, where either: (1) no immediate effects; (2) cytostasis or post-mitotic apoptosis; (3) homo-cycle or homo-phase apoptosis; or (4) necrosis are observed. Analysis of cell death of blast cells from peripheral blood or bone marrow of over 250 leukaemia patients (AML, ALL, CML in blast crisis) treated with various drugs during routine chemotherapy reveals that in the case of DNA topoisomerase inhibitors (e.g., mitoxantrone, VP-16) apoptosis is often rapid (peaks at 1-2 days after drug administration) and has features of homo-phase apoptosis. In contrast, cell death observed after administration of paclitaxel (taxol) or cytarabine (cytosine arabinoside) occurs later and has features of post-mitotic apoptosis: the cells divide but die in G1 of the subsequent cycle(s).     

EGFR inhibition in glioma cells modulates Rho signaling to inhibit cell motility and invasion and cooperates with temozolomide to reduce cell growth

Enforced EGFR activation upon gene amplification and/or mutation is a common hallmark of malignant glioma. Small molecule EGFR tyrosine kinase inhibitors, such as erlotinib (Tarceva), have shown some activity in a subset of glioma patients in recent trials, although the reported data on the cellular basis of glioma cell responsiveness to these compounds have been contradictory. Here we have used a panel of human glioma cell lines, including cells with amplified or mutant EGFR, to further characterize the cellular effects of EGFR inhibition with erlotinib. Dose-response and cellular growth assays indicate that erlotinib reduces cell proliferation in all tested cell lines without inducing cytotoxic effects. Flow cytometric analyses confirm that EGFR inhibition does not induce apoptosis in glioma cells, leading to cell cycle arrest in G(1). Interestingly, erlotinib also prevents spontaneous multicellular tumour spheroid growth in U87MG cells and cooperates with sub-optimal doses of temozolomide (TMZ) to reduce multicellular tumour spheroid growth. This cooperation appears to be schedule-dependent, since pre-treatment with erlotinib protects against TMZ-induced cytotoxicity whereas concomitant treatment results in a cooperative effect. Cell cycle arrest in erlotinib-treated cells is associated with an inhibition of ERK and Akt signaling, resulting in cyclin D1 downregulation, an increase in p27(kip1) levels and pRB hypophosphorylation. Interestingly, EGFR inhibition also perturbs Rho GTPase signaling and cellular morphology, leading to Rho/ROCK-dependent formation of actin stress fibres and the inhibition of glioma cell motility and invasion.     

Estimation and prediction of cell cycle specific effects of anticancer drugs

A mathematical model is used to estimate the cell cycle phase specific action of a new anticancer drug, CI-921, based on results of a short term (8 hr) stathmokinetic (blocked divisions) study on Friend leukemia cells. The estimate obtained is in the form of a sequence of fractions of the cell flow blocked in successive subcompartments of the cell cycle. At specific drug concentrations, the information contained in this estimate is sufficient to correctly predict the results of long term (24 hr) continuous drug exposure. The result obtained seems to be of interest, since the ability to predict the cell cycle phase specific effects of anticancer drugs is crucial for any attempt to improve the existing chemotherapeutic treatment schedules for cancer. This study required developing new mathematical techniques, among them a nonparametric method for estimation of the distributions of cell residence times in the G₁ phase of the cell cycle (Appendix). The methods developed are general enough to be applicable, in principle, to any chemotherapeutic agent the action of which is distributed throughout the cell cycle.     

BrdU—Hoechst flow cytometry: A unique tool for quantitative cell cycle analysis

Unlike other techniques, flow cytometric analysis of BrdU-quenched 33258 Hoechst fluorescence may be used to measure cell activation and the G₁, S, and G₂/M compartment distributions in each of three successive cell cycles after growth stimulation of human peripheral blood lymphocytes. Cell cycle kinetic curves can be constructed from the BrdU—Hoechst flow data which allow the simultaneous assessment of growth fraction, lagtime, compartment exit rate, compartment duration, and compartment arrest. Applications of this new versatile technique include the evaluation of drug and growth factor effets, cell aging, and diagnosis in medicine and immunology.     

Cell cycle kinetics of insect cell cultures compared to mammalian cell cultures

Cell cycle kinetics of lepidopteran cell lines Sf9 (Spodoptera frugiperda) and IZDMb0503 (Mamestra brassicae) were investigated and compared to mammalian cell cycle distributions. The resting phase (G₀) of mammalian cells is characterized by a 2c-DNA content whereas G₀-phase of insect cell lines is characterized by a 4c-DNA content. Flow cytometric data in combination with growth curves of partially synchronized and asynchronously growing cells proved the existence of this phenomenon. Kinetics of cells labeled by the thymidine analog on 5-bromo-2′-deoxyuridine supported these results, which now render the possibility of applying cell cycle analysis in fermentation technology of insect cells.     

Flow cytometry and cell cycle kinetics in continuous and fed-batch fermentations of budding yeast.

Cell size distributions, obtained either as protein distribution by flow cytometry or as cell volume distribution by a Coulter counter, give relevant information about the growth conditions of populations of budding yeast Saccharomyces cerevisiae. We have previously found a good correlation between these distributions and the growth rate in continuous cultures (Ranzi et al., Biotechnol. Bioeng. 1986, 28, 185-190). We now present determinations of the protein distributions and cell volume distributions during different fed-batch fermentations performed with a simple on/off controller. Since during the fed-batch fermentation a true steady state is not obtained, the distributions continuously change with time, but nevertheless we observed a good correlation between the average of both distributions and the actual growth rate. The behavior of the cell size distributions can be interpreted on the basis of a two-threshold cell cycle model in which both the critical protein content at budding (Ps) and the critical protein content for cell division (Pm) are differently modulated by the growth rate. Additional findings will be presented showing that this model can be used to successfully explain the insurgence and the maintenance of oscillatory states in continuous cultures.     

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     

Resveratrol interference with the cell cycle protects human neuroblastoma SH-SY5Y cell from paclitaxel-induced apoptosis

In previous studies we demonstrated that resveratrol acts in an antiapoptotic manner on the paclitaxel-treated human neuroblastoma (HN) SH-SY5Y cell line inhibiting the apoptotic pathways induced by the antineoplastic drug. In the present study we evaluated the antiapoptotic effect of resveratrol, studying its activity on cell cycle progression. We determined the mitotic index of cultures exposed to resveratrol and paclitaxel alone or in combination, the cell cycle distribution by flow cytometric analysis (FACS), and the modulation of some relevant cell cycle regulatory proteins. Resveratrol is able to induce S-phase cell arrest and this interference with the cell cycle is associated with an increase of cyclin E and cyclin A, a downregulation of cyclin D1, and no alteration in cyclin B1 and cdk 1 activation. The resveratrol-induced S-phase block prevents SH-SY5Y from entering into mitosis, the phase of the cell cycle in which paclitaxel exerts its activity, explaining the antiapoptotic effect of resveratrol.     

Fluorescence kinetics in HeLa cells after treatment with cell cycle arrest inducers visualized with Fucci (fluorescent ubiquitination-based cell cycle indicator)

Fucci (fluorescent ubiquitination-based cell cycle indicator) is able to visualize dynamics of cell cycle progression in live cells; G1- and S-/G2-/M-phase cells expressing Fucci emit red and green fluorescence, respectively. This system could be applied to cell kinetic analysis of tumour cells in the field of cancer therapy; however, it is still unclear how fluorescence kinetics change after various treatments, including exposure to anticancer agents. To explore this, we arrested live HeLa cells expressing the Fucci probes at various cell cycle stages and observed the fluorescence, in conjunction with flow cytometric analysis. X-irradiation, HU (hydroxyurea) and nocodazole arrest cells at G2/M boundary, early S-phase and early M-phase, respectively. Although X-irradiation and HU treatment induced similar accumulation kinetics of green fluorescent cells, nocodazole treatment induced an abnormal red fluorescence at M phase, followed by accumulation of both red and green fluorescent cells with 4N DNA content. We conclude that certain agents that disrupt normal cell cycle regulation could cause unexpected fluorescence kinetics in the Fucci system.     

Multiparametric cell cycle analysis by automated microscopy

Cell cycle analysis using flow cytometry (FC) to measure cellular DNA content is a common procedure in drug mechanism of action studies. Although this technique lends itself readily to cell lines that grow in suspension, adherent cell cultures must be resuspended in a cumbersome and potentially invasive procedure that normally involves trypsinization and mechanical agitation of monolayer cultures. High-content analysis (HCA), an automated microscopy-based technology, is well suited to analysis of monolayer cell cultures but provides intrinsically less accurate determination of cellular DNA content than does FC and thus is not the method of choice for cell cycle analysis. Using Cellomics's ArrayScan reader, the authors have developed a 4-color multiparametric HCA approach for cell cycle analysis of adherent cells based on detection of DNA content (4,6-diamidino-2-phenylindole [DAPI] fluorescence), together with the known cell cycle markers bromo-2-deoxyuridine (BrdU) incorporation, cyclin B1 expression, and histone H3 (Ser28) phosphorylation within a single cell population. Considering all 4 markers together, a reliable and accurate quantification of cell cycle phases was possible, as compared with flow cytometric analysis. Using this assay, specific cell cycle blocks induced by treatment with thymidine, paclitaxel, or nocodazole as test drugs were easily monitored in adherent cultures of U-2 OS osteosarcoma cells.     

Demethylating agent 5-aza-2-deoxycytidine enhances susceptibility of breast cancer cells to anticancer agents

DNA methylation plays an important role in regulation of gene expression and is increasingly being recognized as a determinant of chemosensitivity of human cancers. With the aim of improving the chemotherapeutic efficacy of breast carcinoma, the effect of DNA methyltransferase inhibitor, 5-Aza-2′-deoxycytidine (5-aza-CdR), on the chemosensitivity of anticancer drugs was investigated. The cytotoxicity of paclitaxel (PTX), adriamycin (ADR), and 5-fluorouracil (5-FU) was analyzed against human breast cancer cell lines, MDA MB 231 and MCF 7 cell lines using the MTT assay, and the synergy of 5-aza-CdR and these agents was determined by Drewinko’s fraction method. The effects of each single agent or the combined treatment on cell cycle arrest were analyzed by flow cytometric analysis. We also investigated the effect of each single agent or the combined treatment of anticancer drugs with 5-aza-CdR on the methylation status of the selected genes by methylation specific PCR. In MDA MB 231 cells, a synergistic antiproliferative effect was observed with a combination of 10 μM 5-aza-CdR and these three anticancer drugs, while in MCF 7 cells, a semiadditive effect was observed. Treatment with 5-aza-CdR and anticancer drug resulted in partial demethylation of a panel of genes including RARβ2, Slit2, GSTP1, and MGMT. Based on these findings, we propose that 5-aza-CdR enhances the chemosensitivity of anticancer drugs in breast cancer cells and may be a promising approach for increasing the chemotherapeutic potential of these anticancer agents for more effective management of breast carcinomas.     

Rapid assay for cell age response to radiation by electronic volume flow cell sorting

A new technique is described for measuring cell survival as a function of cell cycle position using flow cytometric cell sorting on the basis of electronic volume signals. The sorting of cells into different cell age compartments is demonstrated for three different cell lines commonly used in radiobiological research. Using flow cytometric DNA content analysis and [3H]thymidine autoradiography of the sorted cell populations, we demonstrate that the resolution of the age compartment separation is as good as or better than that reported for other cell synchronizing techniques. The variation in cell survival as a function of position in the cell cycle after a single dose of radiation as measured by volume cell sorting is similar to that determined by other cell synchrony techniques. This new method has several advantages, including: no treatment of the cells is required, thus, this method is noncytotoxic; no cell cycle progression is needed to obtain different cell age compartments; the cell population can be held in complete growth medium at any desired temperature during sorting; and a complete radiation age-response assay can be plated in 2 h. The application of this method to problems in radiobiology and chemotherapy is discussed, along with some of the technical limitations.     

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.     

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.     

Cell sorting analysis of cell cycle-dependent X-ray sensitivity in end joining-deficient human cells

Non-homologous end joining (NHEJ) plays a major role in the repair of ionizing radiation-induced DNA double-strand breaks (DSBs), especially during the G1-phase of the cell cycle. Using a flow cytometric cell sorter, we fractionated G1- and S/G2-phase cells based on size to assess the DSB-repair activity in NHEJ factor-deficient DT40 and Nalm-6 cell lines. Colony formation assays revealed that the X-ray sensitivities of the G1-enriched populations correctly reflected the DSB-repair activities of both the DT40 and Nalm-6 cell lines. Furthermore, as assessed by γ-H2AX foci formation, the sorted cells exhibited less DNA damage than chemically synchronized cells. Given that it does not use fluorescent labeling or chemical agents, this method of cell sorting is simpler and less toxic than other methods, making it applicable to a variety of cell lines, including those that cannot be synchronized by standard chemical treatments.     

Yew (Taxus x media Rehd.) cell suspension cultures as a source of taxanes

Natural resources of paclitaxel, an effective anticancer compound, were threatened with extinction soon after the discovery of this valuable substance. Cell suspension cultures derived from different Taxus species have rapidly become an alternative source of paclitaxel and other taxanes. In this paper we provide some insight into cell growth characteristics in cell suspension culture of Taxus x media cv. Hicksii, with emphasis on the effects of jasmonic acid (JA) on taxane production in cell lines with different initial taxane content. Additionally cell growth characteristics of two cell lines was followed during cultivation of cell suspension culture of Taxus x media cv. Hicksii. Packed cell volume (PCV) was shown to be a reliable and efficient alternative for measuring cell growth instead of fresh and dry weight. The initial total taxane content was screened in a number of cell lines, followed by observing the effect of JA on cell mass and total taxane production of selected lines. We showed a great variability in initial taxane content in different cell lines, which decreased during cell suspension maintenance. JA was shown to inhibit cell growth and increase total taxane production (14 to 106 fold).