The application of mathematical modelling to aspects of adjuvant chemotherapy scheduling

In this paper simple models for tumour growth incorporating age-structured cell cycle dynamics are considered in the presence of two non-cross-resistant S-phase specific chemotherapeutic drugs. According to the seminal work of Goldie and Coldman, if one cannot deliver two cell cycle phase non-specific, non-cross-resistant drugs simultaneously, for example due to toxicity, and both drugs are identical apart from resistance, one should alternate their delivery as rapidly as possible. However consider S-phase specific drugs. One might speculate that, for example, alternating the two drugs at intervals of T, where T is the mean cell cycle time, is better than alternating the drugs at intervals of T/2, as the latter strategy allows the possibility of a cell cycle sanctuary. Such speculation implicitly requires a sufficiently low variance of the cell cycle time, and hence it is not clear if such reasoning prevents a generalisation of the results of Goldie and Coldman. This question is addressed in this paper via a detailed modelling investigation, as motivated by suggestions for future colorectal adjuvant chemotherapy trials and developments in hepatic arterial infusion technology. It is shown that the cell cycle distribution of the resistant cell populations is strongly influenced by the chemotherapy schedule. The consequences of this can be dramatic, and can lead to chemotherapy failure at resonant chemotherapy timings, especially for a small standard deviation of the cell cycle time. The novel aspects of this observation are highlighted compared to other models in the literature exhibiting resonant behaviour in the timing of a periodic chemotherapy protocol. The above investigation also results in the principal prediction of this paper that reducing the drug alternation time to approximately a few hours, if possible, can result in substantial improvements in predicted chemotherapy outcomes. Critically, such improvements are not predicted by the Goldie Coldman model or other chemotherapy scheduling models in the literature.     

Optimal scheduling for cell synchronization by cycle-phase-specific blockers

On the basis of a general kinetic model of the cell cycle, the time schedule of administration of a blocking agent for cell synchronization was optimized. As blockers we considered agents that slow down the rate of transit through the short phase of the cycle. The Pontryagin maximum principle is used. Only stationary populations (the model of the steady state normal tissues) were considered. For such populations the exact form of optimal protocols may be simplified, without any significant loss in effectiveness, to the periodic alternation of suitably chosen intervals of maximum treatment and intervals of rest. The proper lengths of these intervals were obtained from the optimal protocols; their values for various parameters characterizing the cell cycle and the blocker action are presented. With the periodic form of protocols the synchronous movement of cells through any number of cycles may be obtained. The utilization of periodic protocols of synchronization in multiple cancer chemotherapy is discussed.     

Effect of a chalone-containing preparation from Ehrlich ascites tumor on DNA synthesis and cell division in the tumor in relation to the time of day

The mitosis inhibitory action of chalone-containing preparation of the Ehrlich ascite tumour was shown to depend on the time of its administration on round the clock, and on the circadian rhythm phase of the mitotic activity in this tumour. This allowed a conclusion that the chalone system of the tumour may be involved in the formation of the circadian rhythm of cell division. It was found that Ehrlich's ascite tumour chalone system regulated DNA synthesis influencing the cell passage from G1-phase of the mitotic cycle to S-phase, and the processes occurring during S-phase.     

Screening of five specific cell cycle inhibitors using a T Cell lymphoma cell line synchrony/release assay

To obtain different cell populations at specific cell cycle stages, we used a cell culture synchronization protocol. Effects of five different cell cycle inhibitors acting throughout the cell cycle were examined by DNA flow cytometric analysis of a synchrony/release lymphoma cell line (CEM). The screening synchronized protocol showed that staurosporine, mimosine and aphidicolin are reversible G1 phase inhibitors that act at different times. Staurosporine acted in early G1, exhibited the strongest cytotoxic effect, and induced apoptosis. Mimosine and aphidicolin acted in late G1 and at the G1/S boundary, respectively. Hydroxyurea arrested CEM cells in early S phase, but later than the aphidicolin arrest point. Nocodazole synchronized CEM cells in M phase. All the inhibitors examined in this study can be used to synchronize cells at different phases of the cell cycle and were reversible with little toxicity except for staurosporine which is highly toxic. Because the regulatory mechanism of the cell cycle is disrupted by their effects on protein synthesis, however, these drugs must be used with caution.     

Cell cycle kinetics, tissue transglutaminase and programmed cell death (apoptosis).

Studies were undertaken on a highly metastatic hamster fibrosarcoma cell line with a view to assessing whether cells entering into apoptosis, measured by counting the number of transglutaminase mediated detergent insoluble envelopes, has any synchrony with a particular phase of the cell cycle. A double exposure of thymidine was used to block cells in early S-phase. Flow cytometry in combination with [3H]thymidine incorporation into DNA was used to assess the degree of synchrony and progression through the different phases of cell cycle. The apoptotic index was found to be at its maximum in mid-S-phase. Measurement of transglutaminase activity in each phase of the cell cycle indicated that the specific activity was also at its greatest during mid S-phase. The level of enzyme was relatively unchanged throughout the cell cycle indicating that the regulation of transglutaminase activity occurs primarily through effects on catalytic activity rather than enzyme synthesis.     

Effect of cyclophosphamide on the proliferation of L 1210 ascites tumour cells and of jejunal crypt cells in the mouse

Cyclophosphamide (CY) does not act in a cell-cycle specific manner, i.e. exclusively on proliferating cells. It also kills non-proliferating cells, as shown by application of CY to L 1210 ascites tumour-bearing mice during plateau phase growth of the tumour. Moreover, treatment with CY of L 1210 ascites tumour cells, double-labelled with [3H] and [14C]-thymidine, suggests that CY is not cell cycle phase dependent, but kills cells out of all cycle phases. There is also an extensive cytocidal effect of CY (300 mg/kg) on the jejunal crypt cells of the mouse, which is even more pronounced than that of cisplatinum (DDP, 13 mg/kg). However, rapid regeneration of crypt cells occurs after treatment with the drugs.     

Phosphatidylcholine catabolism in the MCF-7 cell cycle.

The catabolism of phosphatidylcholine (PtdCho) appears to play a key role in regulating the net accumulation of the lipid in the cell cycle. Current protocols for measuring the degradation of PtdCho at specific cell-cycle phases require prolonged periods of incubation with radiolabelled choline. To measure the degradation of PtdCho at the S and G2 phases in the MCF-7 cell cycle, protocols were developed with radiolabelled lysophosphatidylcholine (lysoPtdCho), which reduces the labelling period and minimizes the recycling of labelled components. Although most of the incubated lysoPtdCho was hydrolyzed to glycerophosphocholine (GroPCho) in the medium, the kinetics of the incorporation of label into PtdCho suggests that the labelled GroPCho did not contribute significantly to cellular PtdCho formation. A protocol which involved exposing the cells twice to hydroxyurea, was also developed to produce highly synchronized MCF-7 cells with a profile of G1:S:G2/M of 90:5:5. An analysis of PtdCho catabolism in the synchronized cells following labelling with lysoPtdCho revealed that there was increased degradation of PtdCho in early to mid-S phase, which was attenuated in the G2/M phase. The results suggest that the net accumulation of PtdCho in MCF-7 cells may occur in the G2 phase of the cell cycle.     

Optimizing conditions for tobacco BY-2 cell cycle synchronization

Summary Tobacco BY-2 cells have become a major tool in plant cell biological research, in part due to the availability of a cell cycle synchronization protocol. This method, pioneered by Nagata and coworkers, involves sequential treatments with aphidicolin (a DNA synthesis inhibitor) and propyzamide (a microtubule inhibitor which arrests mitosis). The effects of these inhibitors are reversible, allowing the cell culture to progress into M phase synchronously. However, attempts to reproduce high levels of synchrony with published protocols have not been uniformly successful. This paper describes critical parameters for cell cycle synchronization and documents the kinetics and variation typically found in using this protocol.     

The initial accumulation of carbamoylphosphate synthetase in embryonic rat hepatocytes, and the cell cycle

The hormone-induced expression of the hepatocyte-specific enzyme carbamoylphosphate synthetase can take place in each phase of the cell cycle and is not restricted to the G1 or the G0 phase. To arrive at this conclusion, the cell cycle parameters of embryonic day 14 rat hepatocytes in vitro were determined by autoradiography after labeling with (3H)-TdR or with (3H)- and (14C)-TdR. An S-phase of approximately 14 h, a G2 + M-phase of 8 h, a G1-phase of 8-13 h and a total cell cycle of 30-35 h were measured. Freshly isolated embryonic hepatocytes have exponential growth parameter values, but shift to a steady state growth under culture conditions in the presence of hormones (glucocorticosteroids, thyroid hormones and cyclic AMP). The length of the S-phase and of the total cell cycle remain constant during the culture time. The time course of accumulation of carbamoylphosphate synthetase protein in embryonic hepatocytes is identical in all phases of the cell cycle. It is suggested that hormones, in particular glucocorticosteroids, simultaneously and independently regulate growth mode and gene expression in developing hepatocytes. The nucleotide-analogue 5-bromodeoxyuridine inhibits the hormone-induced expression of carbamoylphosphate synthetase only in cells that are exposed to the drug during early S-phase, indicating replication of the carbamoylphosphate synthetase gene in that part of the cell cycle.     

Cell cycle phases of two human lung tumor cell lines derived from squamous cell carcinoma and pulmonary metastasis of a rhabdomyosarcoma (HS 24 and HS 57) and N-acetylalanine aminopeptidase activity

The cell cycle phase distribution of two human lung cancer cell lines (HS 24 and HS 57) grown both to half-confluency and confluency was determined. Both cell lines were then synchronized by applying a thymidine block forcing them to stay in the S-phase. After removal of the thymidine block, which allows the cells to go then through their cell cycle phases, N-acylamino acylpeptide hydrolase (EC 3.4.19.1) activity was measured using N-acetylalanine-p-nitroanilide as substrate (N-acetylalanine aminopeptidase). At the same times that the enzymatic activity was measured, the cell cycle phase distribution was analyzed, in order to determine the cell cycle phase of N-acetylalanine aminopeptidase synthesis. However, the cell cycle phase of N-acetylalanine aminopeptidase synthesis could not be determined. This result was caused by the fact that the cells remained synchronous only for a short period of time.     

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.     

The proliferative state of clonogenic cells in the Lewis lung tumour after treatment with cytotoxic agents

The proportion of clonogenic cells from the Lewis lung carcinoma which are in S-phase of the cell cycle has been measured as the fraction killed by a short exposure to hydroxyurea in vitro. Estimates of the proportions of S-phase cells before and 30 min after doses of gamma-radiation of 1000--2000 rad suggest no alternation in the cell cycle age distribution due to these doses of radiation. As the survivors of these high doses of radiation are predominantly hypoxic, the results imply that hypoxic cells have the same cell cycle age distribution as oxygenated cells in Lewis lung tumours. After treatment with cyclophosphamide or CCNU, the proportion of S-phase cells among the survivors exceeds the faction of S-phase cells in untreated populations. This increase is consistent with a relative resistance of S-phase cells to alkylating agents and nitrosoureas.     

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.     

Two Molecularly Distinct G2/M Checkpoints Are Induced by Ionizing Irradiation

Cell cycle checkpoints are among the multiple mechanisms that eukaryotic cells possess to maintain genomic integrity and minimize tumorigenesis. Ionizing irradiation (IR) induces measurable arrests in the G(1), S, and G(2) phases of the mammalian cell cycle, and the ATM (ataxia telangiectasia mutated) protein plays a role in initiating checkpoint pathways in all three of these cell cycle phases. However, cells lacking ATM function exhibit both a defective G(2) checkpoint and a prolonged G(2) arrest after IR, suggesting the existence of different types of G(2) arrest. Two molecularly distinct G(2)/M checkpoints were identified, and the critical importance of the choice of G(2)/M checkpoint assay was demonstrated. The first of these G(2)/M checkpoints occurs early after IR, is very transient, is ATM dependent and dose independent (between 1 and 10 Gy), and represents the failure of cells which had been in G(2) at the time of irradiation to progress into mitosis. Cell cycle assays that can distinguish mitotic cells from G(2) cells must be used to assess this arrest. In contrast, G(2)/M accumulation, typically assessed by propidium iodide staining, begins to be measurable only several hours after IR, is ATM independent, is dose dependent, and represents the accumulation of cells that had been in earlier phases of the cell cycle at the time of exposure to radiation. G(2)/M accumulation after IR is not affected by the early G(2)/M checkpoint and is enhanced in cells lacking the IR-induced S-phase checkpoint, such as those lacking Nbs1 or Brca1 function, because of a prolonged G(2) arrest of cells that had been in S phase at the time of irradiation. Finally, neither the S-phase checkpoint nor the G(2) checkpoints appear to affect survival following irradiation. Thus, two different G(2) arrest mechanisms are present in mammalian cells, and the type of cell cycle checkpoint assay to be used in experimental investigation must be thoughtfully selected.     

Variation in cell-substratum adhesion in relation to cell cycle phases

The quantification of focal adhesion sites offers an assessable method of measuring cell-substrate adhesion. Such measurement can be hindered by intra-sample variation that may be cell cycle derived. A combination of autoradiography and immunolabelling techniques, for scanning electron microscopy (SEM), were utilised simultaneously to identify both S-phase cells and their focal adhesion sites. Electron-energy 'sectioning' of the sample, by varying the accelerating voltage of the electron beam, combined with backscattered electron (BSE) imaging, allowed for S-phase cell identification in one energy 'plane' image and quantitation of immunogold label in another. As a result, it was possible simultaneously to identify S-phase cells and their immunogold-labelled focal adhesions sites on the same cell. The focal adhesion densities were calculated both for identified S-phase cells and the remaining non-S-phase cells present. The results indicated that the cell cycle phase was a significant factor in determining the density of focal adhesions, with non-S-phase cells showing a larger adhesion density than S-phase cells. Focal adhesion morphology was also seen to correspond to cell cycle phase; with 'dot' adhesions being more prevalent on smaller non-S-phase and the mature 'dash' type on larger S-phase cells. This study demonstrated that when quantitation of focal adhesion sites is required, it is necessary to consider the influence of cell cycle phases on any data collected.     

Hdm2- and proteasome-dependent turnover limits p21 accumulation during S phase

Double-strand DNA breaks detected in different phases of the cell cycle induce molecularly distinct checkpoints downstream of the ATM kinase. p53 is known to induce arrest of cells in G₁ and occasionally G₂ phase but not S phase following ionizing radiation, a time at which the MRN complex and cdc25-dependent mechanisms induce arrest. Our understanding of how cell cycle phase modulates pathway choice and the reasons certain pathways might be favored at different times is limited. In this report, we examined how cell cycle phase affects the activation of the p53 checkpoint and its ability to induce accumulation of the cdk2 inhibitor p21. Using flow cytometric tools and centrifugal elutriation, we found that the p53 response to ionizing radiation is largely intact in all phases of the cell cycle; however, the accumulation of p21 protein is limited to the G₁ and G₂ phase of the cell cycle because of the activity of a proteasome-dependent p21 turnover pathway in S-phase cells. We found that the turnover of p21 was independent of the SCF^skp2 E3 ligase but could be inhibited, at least in part, by reducing hdm2, although this depended on the cell type studied. Our results suggest that there are several redundant pathways active in S-phase cells that can prevent the accumulation of p21.     

Considerations in the design of possible cell cycle effective drugs

Antineoplastic agents are known to induce differential cytotoxic and cytostatic effects throughout the cell cycle. Many drugs have greater toxicity for cycling cells and act selectively at one or more phases of the cycle and may cause partial synchrony of surviving cells. However, these observations have been generally carried out on in vitro systems only and present a variety of complexities and pitfalls. Furthermore, human tumours are often characterized by a relatively low fraction of proliferating cells and present a large cellular heterogeneity as far as their cytogenetic, cytokinetic, and clonogenic features and their responses to drugs are concerned. Therefore, resistance to chemotherapy is due to various factors characterizing, in some instances, each individual tumour. In spite of the advent of technological advances such as flow cytometry, it is still difficult to design kinetic-orientated therapies especially for the treatment of solid tumours. Consequently, it is also difficult to design protocols based on cell cycle effective drugs. The possibility remains, at least for the moment, to stratify tumours according to their cellular heterogeneity. Different protocols could then be assigned to classes of tumours. Such an approach could be completed by further advances in the cellular monitoring of individual tumours.     

The Proliferative State of Clonogenic Cells In the Lewis Lung Tumour After Treatment With Cytotoxic Agents

The proportion of clonogenic cells from the Lewis lung carcinoma which are in S-phase of the cell cycle has been measured as the fraction killed by a short exposure to hydroxyurea in vitro. Estimates of the proportions of Sphase cells before and 30 min after doses of γ-radiation of 1000–2000 rad suggest no alternation in the cell cycle age distribution due to these doses of radiation. As the survivors of these high doses of radiation are predominantly hypoxic, the results imply that hypoxic cells have the same cell cycle age distribution as oxygenated cells in Lewis lung tumours. After treatment with cyclophosphamide or CCNU, the proportion of S-phase cells among the survivors exceeds the faction of S-phase cells in untreated populations. This increase is consistent with a relative resistance of S-phase cells to alkylating agents and nitrosoureas.     

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.