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[Cancer Research 64, 2825-2832, April 15, 2004]
© 2004 American Association for Cancer Research


Regular Articles

Cytostatic and Cytotoxic Effects of Topotecan Decoded by a Novel Mathematical Simulation Approach

Monica Lupi, Giada Matera, Davide Branduardi, Maurizio D’Incalci and Paolo Ubezio

Biophysics Unit, Laboratory of Anticancer Pharmacology, Department of Oncology, Istituto di Ricerche Farmacologiche "Mario Negri," Milano, Italy


    ABSTRACT
 Top
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Topotecan (TPT) is a topoisomerase I inhibitor, and like the other drugs of this family, it is believed to act in a specific way on cells in S phase at the time of treatment. Exploiting a new method, coupling a particular experimental plan with computer simulation, a complete quantitative study of the time dependence and dose dependence of the activity of cell cycle controls has become feasible, and the overall scenario of events after treatment can be reconstructed in detail. We were able to demonstrate that the response of an ovarian cancer cell line to 1 h of treatment with TPT is not limited to inhibition of DNA synthesis, leading to cell death, but involves G1 and G2-M checkpoints. G1 and G2-M block, recycling, and death follow specific dose-dependent kinetics, lasting no less than 3 days after treatment. We also found that cells treated outside S phase contribute significantly to the overall activity. The utility of this analysis was demonstrated by reproducing more complex treatment schemes in which low TPT concentrations were applied for 1 h three times at 24-h intervals. In this case, the simulation clarified the origin of the auto-potentiation observed with repeated 0.2 µM treatments, in which the cytotoxicity, particularly against S-phase cells, was higher than the cytotoxicity in cells treated with 10 µM only once. We believe that this approach will help us to understand the complexity and heterogeneity of the response of a cell population to a drug challenge and could help us to establish the rationale for drug scheduling or drug combinations.


    INTRODUCTION
 Top
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
The camptothecin derivative topotecan (TPT) is an anticancer drug widely used for the treatment of human solid malignancies, including ovarian cancer (1) and small cell lung cancer (2) . The mechanism of action of camptothecins was elucidated about 20 years ago, when it was found that they caused DNA single-strand breaks by poisoning DNA-topoisomerase I (3) . Camptothecin binds noncovalently to the normally transient DNA-topoisomerase I cleavable complex and inhibits the religation step of the enzyme (4) . As a consequence, protein-linked single-strand breaks in the DNA accumulate in the cell. Thus the enzymes of the DNA synthesis machinery come up against an obstacle while processing DNA, and the collision will be a crucial event for cytotoxicity (5) .

Although this theory implies that the DNA synthesis machinery is involved in the cytotoxicity, there is still not enough solid evidence that only S-phase cells are sensitive to the topoisomerase I inhibitors.

Topoisomerase I does not only play a role in DNA replication, but is certainly implicated in the DNA repair mechanisms and in the regulation of gene transcription; both processes occur not only during S phase but also during the other phases of the cell cycle. Whether the cytotoxicity of camptothecins is selective toward S-phase cells is very important for the appropriate use of this compound and for rational combination with other anticancer drugs.

The results of previous studies using synchronized cells (6) have to be interpreted with caution because the synchronization itself could modify the metabolic behavior of the cancer cells, possibly producing artifacts (7) . Other studies, using flow cytometry, have defined the cell cycle perturbation induced by camptothecins, detecting accumulation or depletion of cells in G1, S, and G2-M (8 , 9) . These cell cycle distribution data, obtained at a given interval after drug treatment, are difficult to interpret because they result from the superimposition of the effects of cell cycle block and cell loss. In addition, the response to treatment of single cells might vary; only some (not necessarily all), presumably dependent on the treatment dose, may be blocked, whereas some repair DNA damage and recycle and others die. Thus the cytometric data cannot unequivocally discriminate among different effects. Different combinations of the underlying cytostatic and cytotoxic effects may in fact give similar %G1, %S and %G2-M values. The present study set out to make a complete analysis of the effects of TPT on a cell line, exploiting the experimental approach recently developed by our group to overcome the partial descriptions and drawbacks of the common procedures for analysis of cell cycle perturbations.

This method (10 , 11) involves deciphering the experimental data (flow cytometric percentages and absolute cell number) by a mathematical model in terms of the underlying phenomena of inhibition of DNA synthesis, G1 and G2-M block, death, or recycling, as they superimpose on the "physiological" cell cycle progression. By fitting together the time courses for several drug dosages, we obtain an overall picture of the response of a cell population to the drug challenge. We call this a "scenario," which is an ensemble of the values of the parameters of the model ("effect descriptors"): S-phase delay, probabilities of G1 and G2-M block, recycling, and death rate. Each parameter may be viewed as a quantification of the activity of a specific molecular network. The parameters are expressed in terms of probabilities so they are suitable descriptors of inter-cell heterogeneity of the response to the drug. Thus, the scenario offers an intermediate level of observation between the microscopic molecular level and the macroscopic level, in which drug effect is expressed by global figures like growth inhibition, percentage survival, or flow cytometric percentages.

Once a scenario fitting the data has been defined, one can retrieve from the simulation any information related to the flow of cells through the cell cycle, like the number of cells blocked or dying in the different phases at any time or the history of any cohort of cells.

In this paper, we describe the scenario underlying the response of an ovarian cancer cell line to a single, short TPT treatment, building up a complete description of the time dependence and dose dependence of each cytotoxic or cytostatic effect of the drug. Then the model is challenged and validated in decoding the data from multiple TPT treatments.


    MATERIALS AND METHODS
 Top
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Cell Culture and Drug Treatment
The effects of TPT (generously provided by Glaxo SmithKline) were studied using an ovarian cancer cell line, IGROV1, growing in vitro. This line is maintained as monolayers in T-25 cm2 tissue culture flasks (Iwaki, Bibby Sterilin, Staffordshire, United Kingdom). The culture medium consisted of RPMI 1640 (Sigma, St. Louis, MO) with 10% fetal bovine serum (Euroclone, CELBIO, Milano, Italy) and 1% L-glutamine (Sigma). Culture was maintained in an incubator with 5% CO2 in air at 37°C and 96% relative humidity. Exponentially growing cells were treated for 1 h with different drug concentrations (0.05, 0.2, 1, 10, and 100 µM). After the treatment, the cells were washed twice with warm PBS and left in drug-free medium for specified times, in our case 0, 6, 24, 48, 72, and 96 h. At each time the cells were detached, using 1 ml of 0.05% trypsin-0.02% EDTA (Sigma) in PBS, counted with a Coulter Counter ZM (Coulter Electronics, Harpenden, United Kingdom), and then fixed in cold 70% ethanol.

Multiple treatments were done using the lowest drug concentrations (0.05 and 0.2 µM). We take 0 h as the time of the first treatment, so the cells were treated at 0, 24, and 48 h. Each treatment lasted 1 h, and the cells were counted and fixed every 24 h for 96 h.

Colony Assay
Chemosensitivity of the single and repeated treatments with TPT (0.2 µM, 0.2 µM triple treatment, 1 µM, 10 µM, and 100 µM) was assessed by a clonogenic assay. IGROV1 cells were seeded at a low density (about 250 cells/ml) in a 6-well plate (Iwaki) and treated with different drug concentrations at 24 h. One week after the treatment, the plates were washed with PBS, and colonies were stained for 3 min with crystal violet (1% in 20% ethanol). The colonies (>50 cells) were counted using an image analyzer (Immagini & Computer, Milano, Italy). Surviving fractions were obtained by normalizing the plating efficiencies to the respective control values (plating efficiency of untreated cells, 40%); each value is the mean of four replicates.

Flow Cytometric Analysis
DNA analysis was done on cells fixed at different times after the treatment. Short-term perturbations were investigated by bromodeoxyuridine (BrdUrd) pulse-chase analysis. BrdUrd (Sigma) replaces thymidine during DNA synthesis, catching cells that are in S phase during the pulse. The BrdUrd pulse-chase 6 h after the treatment detects the cell movement through the S phase and the outflow of unlabeled G1 and G2-M cells. BrdUrd pulse labeling 48 and 96 h after treatment involved incubating the cells with 30 µM BrdUrd for 15 min before detaching them to obtain qualitative information about the reduction of DNA synthesis.

Monoparametric Staining of DNA Content.
About 1 x 106 fixed cells were washed with cold PBS and resuspended in 1 ml of 25 µg/ml propidium iodide (Calbiochem, Darmstad, Germany) in PBS plus 25 µl of 1 mg/ml RNAse (Sigma) in H2O. The samples were measured with a FACS Calibur flow cytometer (Becton Dickinson, San Jose, CA) after about 2 h of incubation at room temperature in the dark.

Two-Parameter Flow Cytometry Analysis: DNA Content and BrdUrd Incorporation.
About 2 x 106 fixed cells were washed with PBS and resuspended in 3 N HCl for 30 min. After washing with 0.1 M Na2B4O7 (pH 8.5) to stop acid depurination, the cells were resuspended with 180 µl of 0.5% Tween 20 (Sigma) with 1% normal goat serum (Dako, Glostrup, Denmark) in PBS. After this, 20 µl of anti-BrdUrd monoclonal antibody (Becton Dickinson) were added, and the mixture was incubated for 1 h at room temperature. After washing with PBS, cells were incubated for 1 h with FITC-conjugated affinity pure F(ab')2 fragment goat antimouse IgG (Jackson, West Grove, PA) diluted 1:50 in PBS with 0.5% Tween 20 and 1% normal goat serum. After incubation with antibody, cells were centrifuged, resuspended in 2.5 µg/ml propidium iodide in PBS plus 25 µl of 1 mg/ml RNAse in H2O, incubated overnight, and analyzed.

Computer Simulation of Cell Population Growth and Drug Effects
To combine all of these experimental data quantitatively, we used a computer program to predict the cell cycle flux in a cell population, starting from the cell cycle distribution at a given time. This program has been described in detail elsewhere (10) and is freely available on request from the corresponding author. It reproduces the unperturbed growth of a cell population and its response to treatment with several drug concentrations by constructing a complete and coherent kinetic scenario based on a quantitative estimate of the time dependence and dose dependence of the probabilities of cell arrest and killing.

Unperturbed Growth.
The following inputs are needed to describe the baseline unperturbed growth of control IGROV1 cells: mean transit times in the cell cycle phases TG1, TS, and TG2M; the intercellular spread of G1, S, and G2-M transit times, measured by the respective coefficients of variation CVG1, CVS, and CVG2M; and initial cell distribution through the cycle phases.

A detailed BrdUrd study of the growth of IGROV1 cells (not shown) led us to adopt the following values: TG1 = 6.1 h; CVG1 = 50%; TS = 8.6 h; CVS = 10%; TG2M = 3.1 h; CVG2M = 10%. Because cells were treated while in exponential growth, asynchronous initial cell distribution was chosen (i.e., cell percentages in every phase are constant over time).

Drug Effects.
To simulate all possible cell cycle perturbations, a set of additional parameters ("effect descriptors") was devised, all associated with cell cycle perturbations with a true biological significance.

Delay Rate.
The delay rate is the proportion of cells whose progression inside S phase is inhibited at each step, resulting in a longer mean transit time for this phase. The value of the parameter is equivalent to the fractional reduction of the DNA synthesis rate. The extreme situation (delay rate = 1) indicates complete cell "freezing" within S phase.

Blocking Activity.
The blocking activity is the proportion of cells entering a block in G1 or G2-M phase instead of proceeding to the next phase. In other words, "it" represents the probability of being intercepted by a checkpoint and blocked there. Blocked cells may subsequently either re-enter the cycle or die in the block, depending on the next two parameters.

Recycling Rate.
The recycling rate is the proportion of blocked cells re-entering the cycle at each time step. It is indicative of recovery in cells blocked at a checkpoint.

Death Rate.
The death rate is the proportion of cells removed from a group at each time step. Independent rates can be applied to cycling, blocked, or delayed cells in a phase.

The death and recycling rates are expressed in terms of the corresponding percentage of cells that would die or recycle in a group of blocked cells in the interval of interest.

Output Data.
Giving as input a set of values of the parameters describing drug effects (the "scenario" under evaluation), as output the simulation program then gives the time course of several measurable quantities consequent to this scenario. These values are compared directly with the experimental data: total number of cells, reproducing the growth curve; percentages of cells in the G1, S, and G2-M phases; and output of BrdUrd experiments [percentages of G1, S, G2-M BrdUrd unlabeled cells; percentages of "undivided" and "divided" BrdUrd-positive cells (i.e., BrdUrd-labeled cells still in the S and G2-M phases of their first simulated cycle and in the G1 phase of their second simulated cycle); and total percentage of BrdUrd-positive cells].

Optimization.
During the simulation, hundreds of sets of input parameters are tested by a trial-and-error procedure, starting from the simplest scenario and looking for the best fitting of the experimental data with the fewest parameters. Because the experimental precision of flow cytometric percentages is about 3% and of cell counts is 20%, the fitting was considered satisfactory when all experimental data were reproduced with the same precision.

The parameters were taken as constant in the intervals between successive experimental data. The resulting values for "block," "recycling," and "death" should be considered as descriptions of average effects in those intervals.

Sensitivity.
To study the sensitivity of each parameter in our model, we took into account every nonzero parameter in the best scenario reproducing the experimental data and changed them, one by one, in a wide range. By comparing the experimental data and the results of the simulation, we could assign a penalty score, measuring the closeness of the simulation to the data. If the experimental data were reproduced with a precision of about 3% for flow cytometric percentages and 20% for cell counts, we associated a score of 0; if the experimental data were reproduced with a precision between 3 and 6% for flow cytometric percentages and between 20 and 40% for cell count, we gave a score of 1 and so on.

The final score for simulation of a time course was calculated by summing the scores for the differences between each finding and the corresponding simulation. This meant we could determine a range of values for each parameter that produced the minimum score and thus were compatible with the data.


    RESULTS
 Top
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Exponentially growing IGROV1 cells were treated for 1 h with 0.05, 0.2, 1, 10, and 100 µM TPT. We measured the following quantities related to the cell kinetics after treatment: overall (absolute) cell number; flow cytometric DNA histograms; and biparametric DNA-BrdUrd flow cytometric histograms using two protocols (pulse-chase and pulse labeling).

Fig. 1Citation shows the growth curves after treatment, from 0.05 µM, with almost no difference from controls, to 10 µM, in which cell number was stable up to 48 h and then increased, and 100 µM, in which no regrowth was observed up to the end of observation (96 h). One µM would represent the IC50 on a 72-h growth inhibition test. Controls and 0.05 µM TPT-treated cells reached sub-confluence at 72 h, whereas 0.2 µM TPT-treated cells continued to grow up to 96 h. The 72–96-h interval was included in the subsequent analyses only for 0.2 µM and higher TPT concentrations.



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Fig. 1. Growth curves of IGROV1 cells after 0.05, 0.2, 1, 10, and 100 µM TPT for 1 h, measured by Coulter counter. Each point is an average of at least three replicate flasks.

 
Flow cytometric DNA histograms of control and treated samples are shown in Fig. 2Citation . Simple visual inspection of the histograms shows departures from the steady-state distribution of controls with 1–10 µM (increased percentage of cells within S at 6 h and within G2-M at 24 h) and 100 µM (debris and high S-late+G2 peak at 24–48 h, high G2 peak at 96 h).



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Fig. 2. Time course of DNA histograms after 0.05, 0.2, 1, 10, and 100 µM TPT for 1 h. DNA corresponding to G1 and G2-M cells is indicated. Persistent accumulation in the G2-M peak is particularly evident in the 100 µM histograms. PI, propidium iodide.

 
Short-term effects of TPT were evaluated by a pulse-chase experiment. Cells were exposed to BrdUrd in the last 15 min of treatment, allowing DNA-synthesizing cells to incorporate BrdUrd and become "BrdUrd positive," and collected 6 h later. The resulting biparametric DNA-BrdUrd plots are shown in Fig. 3Citation . They indicate the movement of the cells in the cell cycle in the first 6 h after treatment. In untreated samples, BrdUrd-positive cells that occupied S phase at 0 h were distributed within late-S, G2-M, and G1 phases at 6 h. A dose-dependent delay was observed in treated samples. The cloud of BrdUrd-positive cells covered the middle-S to G2-M part of the cell cycle (with no detectable cells in G1, after mitosis) with 0.2 µM and remained almost in the starting position (covering all of S phase) with 10 and 100 µM. The similarity of the 10 and 100 µM plots at 6 h with controls at 0 h indicates the complete freezing of the cell cycle, although DNA synthesis was not yet inhibited at 0 h, meaning that at the end of the 1-h treatment, BrdUrd was incorporated even by 100 µM-treated cells.



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Fig. 3. Biparametric propidium iodide (PI) fluorescence (DNA content) and FITC-fluorescence (BrdUrd content) plots. Cells incorporated BrdUrd 15 min before the end of the 1-h treatment and were harvested 6 h after the treatment (BrdUrd pulse-chase). Cells were considered BrdUrd positive (in the S phase at the time of treatment, 0 h) when detected above the straight line. BrdUrd-positive cells with G1 DNA content (G1+) at 6 h were born from mitosis of cells in S phase at the time of treatment. G1 BrdUrd-positive cells are present only in the control and in samples treated with the lowest concentration of TPT. BrdUrd-negative cells did not flow from G1 to S in samples treated with 1 µM or higher TPT concentrations (cells were detected in the "S-" region at 6 h only in controls and samples treated with 0.05 and 0.2 µM).

 
A mathematical model of the cell cycle is essential to combine all of these experimental data and to interpret them in terms of the underlying cell cycle effects (blocking activity in G1 and G2-M, death rate and recycling of blocked cells, reduction of DNA synthesis rate, and death rate of S-phase cells), looking for scenarios in which all data are coherently explained in terms of effect descriptors (see "Materials and Methods"). During the simulation, we tested hundreds of sets of values of blocking activity, death rate, and recycling rate, looking for those that enabled us to reproduce the observation within the experimental precision.

The suggestion that TPT had an effect only on cells in S phase during treatment (BrdUrd-positive) was proven false by the simulation (not shown), especially because it was in contradiction with the behavior of cells treated in G1. As shown in Fig. 3Citation , BrdUrd-negative cells in G1 at the time of treatment were unable to go through S phase, at least in the first 6 h and with 1 µM or higher TPT concentrations.

However, the experimental data available at this point were too few to clarify whether the effects in BrdUrd-positive and BrdUrd-negative cells were different, because concurrent scenarios, with and without those effects, simulated the data within the range of the experimental error (not shown). Thus, additional experiments were run using two different BrdUrd methods.

The "BrdUrd labeling" experiment (Fig. 4A)Citation , based on exposure to BrdUrd at a given time after treatment immediately followed by cell harvesting and fixation, serves to qualitatively monitor the DNA synthesis rate of S-phase cells. At 48 h, BrdUrd incorporation was similar to controls up to 1 µM, but was strongly reduced at 10 µM. Almost all S-phase cells incorporated no BrdUrd after 100 µM. DNA synthesis was completely restored at 96 h after 10 µM but was still inhibited in 100 µM-treated cells.



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Fig. 4. Additional BrdUrd labeling (A) and pulse-chase (B) experiments. A (BrdUrd labeling), 48 and 96 h after treatment, cells were labeled with BrdUrd and immediately harvested and fixed (BrdUrd-labeling), and the DNA synthesis rate of S phase cells was qualitatively monitored. At 48 h, BrdUrd incorporation was similar to controls up to 1 µM but was strongly reduced at 10 µM. The samples treated with 10 µM TPT had restored their DNA synthesis activity by 96 h, but BrdUrd incorporation was still reduced in 100 µM-treated cells. B (pulse-chase), cells incorporated BrdUrd 15 min before the end of the 1-h treatment and were harvested 72 h after the treatment. BrdUrd-positive cells amounted to <15% even in the samples treated with 0.2 µM TPT.

 
In the BrdUrd pulse-chase experiment (Fig. 4B)Citation , samples were labeled with BrdUrd at the time of treatment and harvested at 72 h. BrdUrd-positive cells were <15% even in the samples treated with a low TPT concentration (0.2 µM).

This additional information enabled us to draw a single scenario of the time course of events occurring in G1, S, and G2-M consistent with all of the data for each TPT concentration. The different panels of Fig. 5Citation detail this scenario, whose main characteristics are the following.



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Fig. 5. Characteristics of the response scenario for a complete reproduction of the experimental data. The blocking activity is represented as the percentage of cells that remain blocked among those traversing G1 or G2-M in the time interval indicated. The death rate and recycling rate are expressed in terms of the percentages of cells that die/recycle in each time interval, within the compartment of G1 (or G2-M)-blocked cells. In the 0–6-h interval, the death rate in G1 or G2-M is applied to both blocked and proliferating cells, because they cannot be distinguished. Parameters whose values are irrelevant are defined nondetectable (ND). The S-delay (Delay) rate is equivalent to the percentage reduction of the average DNA synthesis rate.

 
Events Occurring in G1 Phase (Fig. 5A)Citation .
The controls of G1 phase act during and immediately after treatment on BrdUrd-negative cells, whereas BrdUrd-positive cells cross G1 checkpoint only after their first division, which may occur several hours after treatment. BrdUrd-negative cells remained blocked in this phase immediately after treatment. One µM TPT was the lowest concentration required to intercept almost all (80–100%) cells in transit from G1 to S in the interval of 0–6 h (Fig. 5ACitation , top right panel). With lower TPT concentrations, less than 20% of those cells remained blocked. No more BrdUrd-negative cells were blocked after 6 h.

The cytotoxic response is characterized by a substantial loss of cells in G1 immediately after treatment (0–6 h; Fig. 5ACitation , middle right panel). G1-blocked BrdUrd-negative cells that had survived the 0–6-h loss re-entered the cycle before 24 h (up to 10 µM), or continued to die, recycling after 48 h (100 µM; Fig. 5ACitation , bottom right panel). BrdUrd-positive cells that could divide and reach G1 phase were very strongly blocked for 72 h even with 0.2 µM TPT (Fig. 5ACitation , top left panel). G1 block was initially not detectable in BrdUrd-positive cells, simply because no BrdUrd-positive cells were expected to come out G1 before 24 h, and for the same reason, the block again became undetectable between 72 and 96 h. There was no evidence of recycling within G1-blocked BrdUrd-positive cells (Fig. 5ACitation , bottom left panel), meaning that the cells that were able to reach G1 phase remained blocked there. However, they were few, and it was uncertain whether they remained blocked or eventually died.

Events Occurring in S Phase (Fig. 5B)Citation .
At low concentrations (<1 µM), there was a reduction in the DNA synthesis rate for BrdUrd-positive cells (Fig. 5BCitation , top left panel). Even though this effect was lower than 40%, it was still well detectable for the samples treated with 0.05 µM TPT, and it peaked in the 6–24-h interval, in which 0.2 µM was enough to almost completely inhibit DNA synthesis. Then the intensity declined at the low concentrations, but it remained strong at least up to 48 h with the highest concentrations. Cell death was limited to BrdUrd-positive cells treated with the highest concentrations of TPT up to 24 h (10 µM) or 48 h (100 µM; Fig. 5BCitation , bottom left panel). BrdUrd-negative cells were not delayed when entering S phase (Fig. 5BCitation , top right panel). Cells treated outside S phase were able to traverse it like controls.

Events Occurring in G2-M Phase (Fig. 5C)Citation .
The effects of TPT in G2-M phase were stronger for cells that were in S phase at the time of treatment (Fig. 5CCitation , left panels) than for cells initially in G1 or in G2-M (Fig. 5CCitation , right panels). Of the BrdUrd-positive cells expected to divide in the 0–6-h interval, 80–100% remained blocked in G2-M when treated even with a concentration as low as 0.2 µM, and roughly one-half of them remained blocked in G2-M when treated with 0.05 µM. The duration of that block was dose dependent, and cells arriving in G2-M continued to be blocked up to 24 h (0.2 µM), 48 h (1–10 µM), and at least 72 h with the very high 100 µM treatment (Fig. 5CCitation , top left panel). Once blocked, cells were unable to recycle (not shown), and some of them eventually died (Fig. 5CCitation , bottom left panel). The pattern of the effects in G2-M of BrdUrd-negative cells was similar but with lower intensity and shorter duration (Fig. 5CCitation , right panels).

This detailed picture of the response to a single, short TPT treatment can be used as a starting point for interpreting the response to more complex treatment schemes. We investigated the effects of repeated 1-h TPT treatments with 0.05 or 0.2 µM TPT on three consecutive days, comparing them with single treatments.

The data for the samples treated with 0.05 and 0.2 µM TPT only once in this new experiment were correctly simulated with minor modifications of the values of the parameters of the scenario described in Fig. 5Citation , confirming the previous results (not shown). As a starting working hypothesis to simulate the repeated treatments, we repeatedly applied the parameters of the single-treatment simulation between 0–6 and 6–24 h. As shown in Fig. 6Citation , this led to a correct simulation of the 0.05 µM repeated three times treatment (Fig. 6A)Citation , but not of 0.2 µM repeated three times (Fig. 6B)Citation , failing to reproduce the cell cycle percentages at 72 h and especially the cell number at 96 h. Correct simulation of the 0.2 µM repeated three times treatment (Fig. 6C)Citation was obtained using the modified response scenario that differed from a simple repetition of the single treatment effect in two aspects. (a) Cell loss in S phase was present after 24 h (i.e., after the second treatment), whereas this was completely absent in the samples treated only once at concentrations lower than 10 µM. This kind of loss occurred mainly in the subset of BrdUrd-negative cells. (b) BrdUrd-positive cells remained blocked for a long time in G2-M, and part of them were lost after 72 h; whereas for the samples treated only once, a weaker cell loss in G2-M was present after 24 h of recovery.



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Fig. 6. Data and simulation of repeated treatments. To reproduce the pattern of the experimental data (DNA analysis and cell count) from the samples treated three times with 0.05 µM TPT, we applied three times the scenario describing a single treatment between 0–6 and 6–24 h. This led to a correct simulation of the 0.05 µM three times treatment (A), but not 0.2 µM three times (B). The correct simulation of the 0.2 µM three times treatment (C) was obtained using a modified response scenario including some cell loss in S phase.

 
Once the scenario was defined, the simulation gave additional information on the behavior and heterogeneity of the cell population that was not directly measurable from the experimental data. In particular, we retrieved the percentage of cells blocked in G1 or in G2-M at each time (Fig. 7)Citation and the total amount of cells that died in 96 h (Fig. 8)Citation . These quantities measure the impact of a specific block and killing on the growth of the whole cell population. Instead, the values of the parameters in Fig. 5Citation indicate the strength of the blocking or killing activity independent of the absolute number of cells that reached that phase. Fig. 7ACitation reports the time course of the percentages of blocked cells in G1 and G2-M in the single-treatment experiment. The proportion of cells blocked in G1 was not negligible compared with the percentage of G2-M blocked. For instance, with 100 µM, about 20% of the whole cell population was blocked in G1 at 48 h, despite a decrease in %G1. In the repeated-treatment experiment (Fig. 7B)Citation , the percentage of G1-blocked cells remained low, whereas the percentage of G2-M-blocked cells increased, reaching a peak of 30% of the whole population after the third 0.2 µM treatment.



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Fig. 7. Dose dependence and time dependence of the percentage of total (full height of the bars) and blocked (height of the filled area of the bars) cells in G1 and in G2-M. This serves to evaluate the impact of the blocking effect on the cell population after treatment with 0.05, 0.2, 1, 10, and 100 µM TPT (A) and after repeated treatments (B). The error bars in the histograms indicate of the range in which different simulations give predictions fitting the data within the experimental error.

 


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Fig. 8. Total percentage of dead cells in 96 h obtained from the simulation (A) and the survival fraction measured by a colony assay (B). For this test, every percentage is the average of four replicates; the error bars of the histogram in A were calculated as reported in Fig. 7Citation . Both the simulation and the colony assay confirmed that 0.2 µM three times was more "cytotoxic" than single treatment with 10 µM TPT.

 
The percentage of lost cells in 96 h (Fig. 8A)Citation indicates that 0.2 µM repeated three times was more "cytotoxic" than a single treatment with 10 µM TPT. This was confirmed by a colony assay (Fig. 8B)Citation .


    DISCUSSION
 Top
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
In the present study we quantified the response of human ovarian cancer cells to a short TPT treatment, unraveling the complex dose dependence and time dependence of the block, delay, "recycling from block," and death effects. We used a mathematical model reproducing cell growth in normal conditions or after treatment with an anticancer agent (10 , 11) . This method presents several advantages over the classical techniques used to evaluate cell cycle effects of anticancer agents. We treat cells in physiological conditions and in exponential growth. Previous synchronization becomes unnecessary to obtain information about the specific perturbation of each cell cycle phase. At the same time, we are able to select a cohort of cells at time 0 h (for instance cells in S at that time) and follow them through the cycle. This was done by simulating in parallel the cell cycles of BrdUrd-positive cells (treated while in S phase) and BrdUrd-negative cells (treated while in G1 or G2-M phases). Although exogenous BrdUrd was added to the culture, a low concentration of it was used and for a short period (15 min). In this way, we were able to minimize possible BrdUrd perturbations, reported in the literature with higher or longer BrdUrd exposures (12) . In the cell line adopted in this study, no differences were observed in DNA profiles in TPT-treated cells with and without BrdUrd (not shown).

Analysis of the effect descriptors allows us to focus on a certain phase and see what happens when the cells pass through it. This analysis gave a pattern of time dependence and dose dependence of the cellular response to TPT much more complex than cell cycle analyses reported in the literature. Indeed, early reports of the cell cycle perturbations induced by camptothecin and its derivatives stressed S-phase cytotoxicity (6) but in particular dose ranges and using synchronization techniques in which S-phase cells are just released from an artificial block. In these studies, G2-enriched fractions appeared much less sensitive than S-phase cells, despite the presence of considerable S-phase contaminants. In our opinion, factors other than phase specificity, like the time from release of the synchronizing block, may play a role in the outcome of this kind of experiments.

The effects of single concentrations of TPT were studied by flow cytometry by McDonald et al. (8) and Taron et al. (9) , evidencing transient S and more lasting G2-M accumulation of cells and suggesting the possibility of a G1 block.

Feeney et al. (13) investigated cell cycle effects of TPT by time-lapse microscopy. They suggested that cells treated with TPT while in G1 and S phase were unable to duplicate in 48 h, whereas part of G2-M cells could divide. The proliferation of S-phase cells, unlike G1 and G2-M cells, was inhibited even at a low TPT concentration.

Our results are not in contradiction with these observations, but they introduce a much deeper level of understanding, making a clear distinction between cytotoxic and cytostatic effects and analyzing their dose dependence. First, even though TPT is supposed to be S-phase-specific, it was impossible to account for our experimental data assuming cytotoxic and cytostatic effects only on BrdUrd-positive cells. As shown in the final scenario (Fig. 5)Citation , both BrdUrd-positive and BrdUrd-negative cells contributed to the overall effects, interacting with all cell cycle controls while traversing each phase.

The challenge of a short TPT treatment caused prompt activation of the G1 block, in which the cells processed the damage rapidly, committing some cells to death or succeeding in repairing others that were able to recycle in the 6–24-h interval. Roughly one-half the G2-M-treated cells remained blocked there, but the fate of the other half is less clear, because after division, they mixed with the much more numerous subpopulation of G1 cells. Cells treated while traversing S phase follow a quite different path, and their outcome was decided over a very long time. Most of them were delayed in their progression of S phase, experienced a G2-M block, and died at a low rate over a long period, up to 72 h. Even with a concentration as low as 0.2 µM, less than 15% of the population present at the end of the observation (96 h) were cells treated in S phase or their descendants, but this is due more to the prolonged inhibition of proliferation, while surviving BrdUrd-negative cells multiplied by subsequent divisions, than to selective cell loss.

It is important to note that the events in G1 phase for BrdUrd-positive and BrdUrd-negative cells are quite different. The cells exposed to the drug while in G1 (most of them) or in G2-M remained blocked in G1 immediately after treatment, preventing them from starting S phase but only for a short period (<=6 h). The block was weak with low concentrations, and blocked cells were able to recycle in the 6–24-h interval. At higher concentrations (1–10 µM), the block was almost complete, and there was some lethality within 6 h. With 100 µM, cell loss was more extensive, longer-lasting, and residual; blocked cells were able to recycle only after 48 h. Few BrdUrd-positive cells could divide and reach G1 with concentrations >=1 µM, but they were unable to progress further to S, suggesting that although damaged by TPT, they had bypassed the previous G2-M checkpoint. Thus the G1 checkpoint was stricter or more sensitive to intercept and block damaged cells.

Our data were not sensitive enough to clarify at which point of G1 these events occur, and the model arbitrarily sets the G1 block at the end of the phase. The observation that almost no cells entered S phase in the first 6 h suggests that the block is at the G1-S border (i.e., just before the onset of DNA synthesis) or throughout the phase. At least at the higher concentration, block and cell loss probably occur throughout the phase, because the whole cell cycle progression is frozen and the amount of cells lost is incompatible with the (few) cells expected to reach the G1-S border in that interval.

Simulation also allows us to evaluate the time course of the overall cell loss, irrespective of the phase in which cells were actually lost, but still separately within the subpopulation of BrdUrd-positive and BrdUrd-negative cells. BrdUrd-negative cells are lost mainly in G1, immediately after treatment (from 1 µM), whereas BrdUrd-positive cells are lost mainly in G2-M, over a longer period, from 0–72 h at the highest dose, 6–72 h with 10 µM, 24–72 h with 1 µM, and 24–48 h with the 0.2 µM.

In the whole 0–96-h interval, although more BrdUrd-positive cells were lost, the short-term loss of BrdUrd-negative cells was not negligible at 1 µM and above. For instance, the simulation of 1 µM treatment suggested that 20% of the cells treated in G1 (or G2-M) were killed in the 0–6-h interval, against 30% of cells treated in S phase, mainly in the 24–72-h interval.

These findings on cell cycle perturbations can be linked to published data at the molecular level. The primary topoisomerase I-mediated DNA lesions are single-strand breaks, but a time-dependent formation of DNA double-strand breaks is expected as a consequence of collisions between the replication fork and topoisomerase I-DNA cleavage complex (14) . As a consequence of DNA double-strand breaks, Chk2 phosphorylation occurs in an ATM-dependent manner (15) . This should be in agreement with the theory that ATM activates a pathway of inhibition of DNA synthesis after double-strand breakage (16) and is also a possible explanation of the slowing down of the BrdUrd-positive cells in S phase that we quantify in our simulation.

The block in G2-M was associated with impaired activation of cdc2-cyclin B complexes (17) . This is probably caused by ATR-induced phosphorylation of Chk1, which may play an important role in the cell cycle responses and survival after treatment with topoisomerase I poisons (18) .

The molecular origin of the G1 block of camptotechins has not been investigated, to our knowledge. We found two kinds of G1 block: one was strong but temporary, rapidly leading to cell death or recovery (in BrdUrd-negative cells); the other was lasting (in BrdUrd-positive cells). These findings fit with the general view of two successive waves of cell cycle checkpoint responses at G1. The first is p53 independent and exploits a pathway in which Cdc25A phosphorylation and degradation play a key role. In line with the observation that DNA single-stranded breaks are rapidly reversed 1 h after drug removal (14) and that the cleavable complexes are rapidly eliminated when TPT is removed from the external medium (13) , we assume that in BrdUrd-negative cells, only a single-stranded break occurs, leading to the short-term response driven by the p53-independent pathway.

The second response is p53 dependent and might well be activated in our IGROV1 cells, which possess wild-type p53. The p53-dependent response is expected to be sustainable for a long time (19) . Agents in this pathway might also be engaged outside G1, with a role in cell cycle delays or cell death in S and G2-M phases; these are the effects experienced by many BrdUrd-positive cells, which never had a chance to reach G1. Feeney et al. (13) found that after TPT treatment, p53 expression increased more in S and G2-M cells than in G1 cells, and the high level lasted a long time. There is also evidence of activation of p53-dependent responses outside G1 (20) .

Thus the G2-M effects in BrdUrd-positive cells may originate from the activation of p53-dependent pathways, and the fact that they also led to a late G1 block is merely a consequence of the cell kinetics (these cells reached G1 only after several hours) and not of delayed activation of the pathway.

After studying the response to a single short treatment we tested a more complicated schedule, i.e., daily repeated 0.05 or 0.2 µM TPT. These drug concentrations were similar to the plasma concentrations in patients undergoing typical TPT treatments, and the schedule is closer to the clinical condition (i.e., 30 min i.v. infusion of 1.5 mg/m2 on days 1–5 of a 21-day cycle; Ref. 21 ). Cell cycle effects of a single dose of 0.05 µM TPT (Fig. 5)Citation vanished after 24 h, so we can forecast the response to repeated treatment on the basis of simple 24-h cycles of the values of the effect descriptors measured with a single treatment. In fact, with the 0.05 µM repeated three times schedule, the data were consistent with a simple repetition of the effect of the single dose. However to fit the data with 0.2 µM repeated three times, we needed to introduce a loss rate for S-phase cells after the second treatment, particularly within BrdUrd-negative cells, which was absent in the cells treated once with this concentration. Instead, BrdUrd-positive cells died after remaining blocked for a long time in G2-M. As a result, the total percentage of cells lost in 96 h indicates that 0.2 µM repeated three times is more lethal than a single dose of 10 µM TPT (Fig. 8A)Citation . This was confirmed by a clonogenic assay, even though the survival figures with the two methods do not coincide numerically because of the different experimental conditions. Schoemaker et al. (22) suggested that topoisomerase I increases after repeated administration, and this might explain the auto-potentiation at the molecular level.

In conclusion, our approach for analysis of cell cycle perturbations in vitro was to consider all of the data from different tests and to interpret them through a mathematical formulation of the problem. Applying the procedure after in vitro treatment with TPT, we found complex but biologically consistent patterns of time dependence and dose dependence for each cell cycle effect descriptor, opening the way to a link to the parallel changes in the molecular pathways regulating the specific function described.

In earlier studies (10 , 11) , the simulation model was always used to evaluate the cell response to a "pulse-like" treatment. This is a necessary step before trying to build up the effect of prolonged or more complex schedules. With the analysis of repeated TPT treatments, we demonstrated that the model can be used to explain more complex treatment schedules. In this case, the simulation clarified the origin of the auto-potentiation observed with one of these schemes. This approach should help us understand the complexity of the response of a cell population to a drug challenge and provide the rationale for new drug schedules or drug combinations.


    FOOTNOTES
 
Grant support: Ministero dell’Istruzione, dell’Università e della Ricerca (Rome, Italy) and Consiglio Nazionale delle Ricerche—Progetto Strategico MIUR "Oncologia"–SP/4–legge 449/97 project nr. 0200063.ST97. Partially supported by Fondazione Nerina e Mario Mattoli.

The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Requests for reprints: Paolo Ubezio, Istituto di Ricerche Farmacologiche "Mario Negri," Via Eritrea 62, 20157, Milano, Italy. Phone: 39-02-39014438; Fax: 39-02-3546277; E-mail: ubezio{at}marionegri.it

Received 12/ 5/03. Revised 1/19/04. Accepted 2/11/04.


    REFERENCES
 Top
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 

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