## Abstract

Previous studies in our laboratory have described increased and preferential radiosensitization of mismatch repair-deficient (MMR^{−}) HCT116 colon cancer cells with 5-iododeoxyuridine (IUdR). Indeed, our studies showed that MMR is involved in the repair (removal) of IUdR-DNA, principally the G:IU mispair. Consequently, we have shown that MMR^{−} cells incorporate 25% to 42% more IUdR than MMR^{+} cells, and that IUdR and ionizing radiation (IR) interact to produce up to 3-fold greater cytotoxicity in MMR^{−} cells. The present study uses the integration of probabilistic mathematical models and experimental data on MMR^{−} versus MMR^{+} cells to describe the effects of IUdR incorporation upon the cell cycle for the purpose of increasing IUdR-mediated radiosensitivity in MMR^{−} cells. Two computational models have been developed. The first is a stochastic model of the progression of cell cycle states, which is applied to experimental data for two synchronized isogenic MMR^{+} and MMR^{−} colon cancer cell lines treated with and without IUdR. The second model defines the relation between the percentage of cells in the different cell cycle states and the corresponding IUdR-DNA incorporation at a particular time point. These models can be combined to predict IUdR-DNA incorporation at any time in the cell cycle. These mathematical models will be modified and used to maximize therapeutic gain in MMR^{−} tumors versus MMR^{+} normal tissues by predicting the optimal dose of IUdR and optimal timing for IR treatment to increase the synergistic action using xenograft models and, later, in clinical trials. [Cancer Res 2007;67(22):10993–11000]

## Introduction

Over the last 15 years, DNA mismatch repair (MMR) has been well characterized with respect to its effect on determining the predisposition toward hereditary nonpolyposis colorectal cancer (HNPCC). Heterozygous germ line mutations in the genes coding for components of MutSα (MSH2 and MSH6) and MutLα (MLH1 and PMS2) have been recognized as major causes of this syndrome (1). Deletion (loss of heterozygosity), mutation, and methylation-induced gene promoter silencing of *MSH2* and *MLH1* have been reported as probable reasons for somatic inactivation of a *MSH2* or *MLH1* wild-type allele, leading to sporadic tumor development in multiple tissues, including gastrointestinal, gynecologic, and genitourinary (2–5). Mutation rates in tumor cells with MMR deficiency are 100- to 1,000-fold higher than normal (MMR^{+}) cells (1). These mutations can affect the expression of important growth-regulating genes, especially those having repetitive sequences including *TGFβRII, BAX*, and *TCF4* genes (5, 6). The association of mutations with nonfunctional MMR is considered to be the basis of the genomic instability hypothesis (7, 8), explaining the link of MMR gene mutations and the development of HNPCC and other sporadic cancers.

The role of MMR in determining the cytotoxicity to certain classes of chemotherapeutic agents has underscored the clinical relevance of studying the response of this mechanism to such drugs. There are two distinct hypotheses explaining the higher sensitivity of MMR-proficient (MMR^{+}) tumors toward specific chemotherapeutic agents (9). Repeated repair of the DNA mismatch damage on the template strand leading to cytotoxic double strand breaks (DSB) is the foundation for the “futile cycle” theory. Another model suggests a different function of MMR proteins as a general DNA damage–sensing and relay machinery, leading to activation of cell cycle checkpoints. The link between the independent activation of DNA damage checkpoints by MMR proteins and cell death is not yet fully understood. On the other hand, the resistance of mismatch-deficient (MMR^{−}) tumors toward alkylating/methylating drugs, nucleoside analogues, some platinum analogues, and topoisomerase inhibitors has opened up avenues to selectively target these tumors (9).

Earlier studies in our lab have successfully used halogenated thymidine analogues, iododeoxyuridine (IUdR) and bromodeoxyuridine (BrdUrd), for selective radiosensitization of MMR^{−} cells with mutated *MLH1* (10) and *MSH2* genes (11). These base analogues need to be incorporated in the DNA to affect their role as radiosensitizers. It was shown that these thymidine analogues are present in significantly higher levels in the DNA of MMR^{−} cells and, thus, provided better radiosensitization when there was no such gain observed in MMR^{+} cells. This differential radiosensitization carries immense potential for selectively targeting MMR^{−} tumors while sparing MMR^{+} normal tissues. The incorporated bases (thymidine analogues) are perceived as DNA mispairs probably due to the formation of some structurally distorted conformation (i.e., G:IU mispairs), which are recognized by the MMR complex. The functionally active state of the MMR machinery may also be linked to apparent changes in cell cycle regulation of certain cell lines (12). Recently, there have been mathematical modeling efforts implicating these cell cycle perturbations to nucleoside analogue drug treatment (13).

Mathematical modeling of the effects of drugs on the cell cycle may provide insights that can help identify and develop effective drug targets and multiple drug targeting strategies (14). These model-building exercises have been found to be useful in providing quantitative hypotheses that can be experimentally tested (15). The current ordinary differential equation (ODE) models of the cell cycle are based on a bottom-up mechanistic approach, i.e., they are based on biochemical modeling of protein dynamics involved in the cell cycle (16, 17). The models for G_{1}-S and G_{2}-M transitions and restriction points have been recently reviewed by Clyde et al. (14). Although there are successful bottom-up models of the cell cycle, there are still several important problems to be overcome for this type of modeling, which include the lack of sufficient quantitative data on molecular concentrations and kinetic parameters (14, 15, 18). In contrast, McAdams and Shapiro (18) suggest that a top-down modeling paradigm could be a potentially useful approach toward modeling the cell cycle, and this is the approach taken in this work.

In this report, we develop a probabilistic model that captures the cell cycle dynamics using a top-down modeling approach to develop the correlation between cell cycle progression and the functional relevance of MMR as operative on IUdR-generated mispairs. Differences in temporal patterns of the cell cycle dynamics for genetically matched MMR^{+} and MMR^{−} cell lines that were observed are accentuated in the presence of external DNA mismatch damage conferred due to treatment by IUdR. This is the first report of a comprehensive mathematical modeling and computational study that links the effects of a nucleoside analogue in determining cell cycle kinetics to the functional status of MMR.

## Materials and Methods

**Cell lines and culture conditions.** The isogenic human colon cancer cells, HCT116 (MLH1^{−}) vector control and HCT116 MLH1^{+} transfected cell lines, were generously provided by Dr. Francoise Praz (Institut Gustav Roussy, France; ref. 19). HCT116 parental cells are defective in mismatch repair due to a hemizygous nonsense mutation in the *MLH1* gene located on chromosome 3. Cells were grown in DMEM supplemented with 10% fetal bovine serum (FBS), 2 mmol/L glutamine, and 100 μmol/L nonessential amino acids (complete medium) in a 10% CO_{2} incubator at 37°C. Cell doubling times for HCT116 vector (MMR^{−}) and HCT116 MLH1-transfected (MMR^{+}) cells are 16 and 18 h, respectively.

**Clonogenic survival.** Subconfluent cell cultures were trypsinized, counted, and plated onto 60-mm plates and then allowed to adhere for 16 h before treatments with 0, 2, 5, 10 and 30 μmol/L IUdR in DMEM supplemented with 10% dialyzed FBS for 24 h. Drug-containing medium was removed after the 24-h exposure and was replaced with DMEM/10% defined FBS complete medium. Cells were allowed to grow for 10 to 12 days before fixing and staining with 0.5% crystal violet in 3:1 methanol/acetic acid. Colonies consisting of 50 cells or more were counted, and total cell survival was corrected for plating efficiency of nontreated (0 μmol/L IUdR) cells.

**Cell synchronization in G _{0}.** Cells for the correlative synchronized cell cycle and IUdR-DNA incorporation studies were grown to confluence and subsequently arrested in G

_{0}by serum starvation with 0.1% defined FBS/DMEM for 60 h. After serum starvation, cells were released into either 10% dialyzed FBS/DMEM alone or with 2, 5, or 10 μmol/L IUdR and then seeded into 100-mm plates with 3 × 10

^{6}cells per plate. Samples were taken for cell cycle analysis immediately post-release (time 0) to confirm synchronization in G

_{0}. Time points for IUdR incorporation and for cell cycle analysis were taken simultaneously every hour after cells started moving into S phase, typically around 10 h following release. Samples for cell cycle analysis were washed with PBS and then fixed with 10% Tris-saline buffer [10 mmol/L Tris base, 150 mmol/L sodium chloride (pH, 7.0)]/90% ethanol and stored at 4°C. Samples for DNA incorporation studies were washed with PBS and then stored as dry pellets at −80°C.

**IUdR-DNA incorporation studies.** Frozen cell pellets were processed for IUdR-DNA incorporation studies using high-performance liquid chromatography (HPLC) as previously described (10). HPLC analysis was done on a Waters 1525 solvent delivery system (Waters Corporation). Nucleosides were detected at 290 nm on a Waters Model 2487 absorbance detector, and standard curves were generated using authentic thymidine (TdR) and IUdR standards (Sigma-Aldrich Chemicals). Waters Breeze GPC Chromatography Manager software (Waters Corporation) was used for analysis of peaks and data quantitation.

**Flow cytometry.** Fixed cell pellets were washed once with phosphate citric acid buffer and resuspended in propidium iodide stain [33 μg/mL propidium iodide, 1 mg/mL RNase A, 0.2% IGEPAL CA-630, and 1 mmol/L EDTA (pH 8.0); all from Sigma-Aldrich Chemicals] for 30 min before running samples on the flow cytometer. Samples were run on an EPICS-XL MCL flow cytometer (Coulter Corporation). Data were analyzed by Modfit LT software (Verity Software House).

**Statistical methodology.** ANOVA was conducted using GraphPad's InStat Biostatistics Program (version 3.0). A *P* value of <0.05 is considered to be statistically significant.

**Model development.** Two types of computational models were developed using our experimental data. The first model is a stochastic model of the progression of cell cycle states, and the output of this model gives the cell cycle distribution at any given time. This model is used to estimate the cell cycle distributions over time for the two cell lines with and without IUdR treatment. The second model gives the relationship between the percentage of cells in the different cell cycle states at any given time and the corresponding levels of IUdR-DNA incorporation for the different time points. Combining these two models using the distributions obtained from the first model as inputs into the second model, the incorporation of IUdR at any given time can be estimated for the different types of cells.

The probabilistic cell cycle distribution (first) model is a finite-state automaton that represents the states of a cell cycle on a per-cell basis. The jumps between states are modeled using continuous probability distribution functions to account for the time spent in each cell cycle state. The population behavior is modeled as the aggregation of the simulation of the individual cell models. The model is shown in Fig. 1, together with an example of the probability density function used in the development of the model. Here, *f _{X-Y}* (

*t*|

_{j}*t*) represents the probability density function of a jump from state

_{i}*X*to state

*Y*at time

*t*given that the jump to state

_{j}*X*occurred at time

*t*. The parameters of this density function are the mean (

_{i}*m*) and the variance (

*v*). Three probability density functions are defined in the model for the state changes from G

_{1}to S, from S to G

_{2}, and from G

_{2}to G

_{1}. The data for G

_{2}and M are aggregated in the experiments, and these two states are combined in the model. Each of the three density functions has two parameters (

*m*and

*v*) that need to be adjusted using the experimental data. The triangular density functions are chosen because they are defined by two parameters and have compact support, and the piecewise linear characteristics simplify the computations.

The wet lab experiments were done with synchronized cells as described above, and all cells start in the state G_{0} following release into complete media. In the computational experiments, it is also assumed that all cells start in G_{0}. Then, the probability of being in G_{1} at a given time *T* is calculated from the formula:

for the first cell cycle after the cells are released from the initial state G_{0}. Here, *f*_{1}(*t*_{1} − *t*_{0}) is the probability density function of a jump from state G_{1} to state S at time *t*_{1}, assuming that the jump to state G_{1} occurred at *t*_{0}. In this first cell cycle, the probability that the cell is in S phase at time *t*_{1} and then is in state G_{2} at time *T* is given by the following equations:

The probabilities for the second cell cycle are calculated using the following equations:

The experimental data provided information on two cell cycles, so the distribution of the cells in the different cell cycle states is calculated for these two cycles in the model. The model also takes into account the effect of cell doubling as time progresses. The total number of cells (*N*) in each cell cycle state is calculated as the sum of the number of cells in these states for the first and second cell cycles as follows:

Here, *n* is the total number of cells at the start of the first cell cycle. The total number of cells is doubled in the second cell cycle in Eq. (G). It is assumed that all the cells survive and continue to the second cell cycle.

The distribution of cells in the cell cycle given as percentages are then calculated using the formulas:

The model parameters are iteratively adjusted using the experimental cell cycle distribution time course data for both MMR^{+} and MMR^{−} cells with and without IUdR treatment. There are six model parameters for the probability density functions of the three cell cycle states. The cost function used for model fitting is defined as:

where *d*_{1}, *d*_{2}, and *d*_{3} are the experimental data for the percentages of cells in states G_{1}, S, and G_{2} of the cell cycle, respectively, and *m*_{1}, *m*_{2} and *m*_{3} are the corresponding model outputs for these states. The parameter optimization is done using the “fmincon” function of Matlab (The MathWorks, Inc.). The constraints defined on the parameters of the probability density functions are such that the density functions have zero value for negative values of time.

The second model is used to define the relationship between the cell cycle distribution and IUdR-DNA incorporation data. A linear regression model of the form: *y* = *Xβ* + *ε*, where *y* is the % IUdR incorporation, *X* is a vector that contains the distribution of cells in each cell cycle state, *β* is the vector of model parameters, and *ε* is a vector of random disturbances of appropriate dimension. The goodness of the linear fit is tested statistically using “regstats” function available in Matlab.

## Results

**MMR status determines cytotoxicity and IUdR-DNA incorporation levels of human colon cancer cells.** Asynchronous MMR^{−} cells show a marked sensitivity compared with MMR^{+} cells to the 24-h IUdR treatment using a clonogenic survival assay (Fig. 2A), which correlates with the higher levels of IUdR-DNA incorporation seen in MMR^{−} cells (Fig. 2B). Treatments starting with the clinically relevant dose of 2 μmol/L as well as 5 and 10 μmol/L IUdR result in greater cytotoxicity of approximately 2-fold, 3-fold, and almost 10-fold, respectively, in MMR^{−} cells. HCT116 MMR^{−} and MMR^{+} asynchronous cells treated for 24 h with IUdR also show distinct differences in IUdR-DNA incorporation at the time of drug removal and throughout a 24-h washout. Treatment with the increasingly higher doses of IUdR results in higher levels of incorporation in MMR^{−} cells, specifically 24% for 2 μmol/L and 32% for 5 and 10 μmol/L at 0 h, the time at which the drug is removed. The differences in IUdR incorporation levels between MMR^{+} and MMR^{−} cell lines represent the increase in non-repaired IUdR mispairs in MMR-deficient cells as previously published by our group (10, 11).

IUdR impact on overall cell growth was also determined by treating cells with IUdR for 24 h and taking samples for cell counts immediately after drug removal and for 24 h post-washout (Fig. 2C). HCT116 MMR^{+} cells treated with IUdR show a significantly greater growth delay compared with MMR^{−} cells after 24 h treatment with IUdR (at 0 h; *P* = 0.01). Following 24 h of washout (drug removal), MMR^{−} cells showed more growth delay. However, no difference was found between the two cell lines at time 24 h (*P* = 0.17). At both times (0 and 24 h following drug removal), cell growth in both cell lines were IUdR dose dependent (*P* < 0.01).

**Synchronized, nontreated MMR ^{+} and MMR^{−} colon cancer cells show different cell cycle profiles.** To conduct studies of the impact of IUdR incorporation upon the cell cycle, it was necessary to obtain a profile of the cell cycle progression without IUdR treatment in experiments with synchronized MMR

^{+}and MMR

^{−}cell lines (Fig. 3A). Significant differences (

*P*≪ 0.01) in cell cycle entry and progression were observed. MMR

^{−}cells moved into S phase faster by 2 to 3 h and showed a lower percentage of cells in S and G

_{2}phase, with only half as many MMR

^{−}cells in G

_{2}, compared with the MMR

^{+}cells. In addition, the duration of the G

_{2}phase for MMR

^{−}cells was shorter by ∼2 h. Thus, it seems that the MMR status impacts the cell cycle profiles even in the absence of the drug.

**Incorporation of IUdR produces differing cell cycle effects in colon cancer cell lines depending on mismatch repair status.** To define the impact of IUdR incorporation upon cell cycle progression, HCT116 MMR^{−} and HCT116 MMR^{+} cells were synchronized and released into 10% dialyzed FBS medium with or without 10 μmol/L of IUdR. MMR^{−} cells treated with 10 μmol/L IUdR showed slightly lessened S and G_{1} phases at about 20 h (due to more cells in G_{2}; Fig. 3B). IUdR-treated MMR^{−} cells also had an earlier and higher G_{2} arrest (10%) at 20 to 21 h compared with nontreated cells. Additionally, these MMR^{−} cells maintained a higher G_{1} arrest (18%) at the beginning of the next cycle as compared with nontreated cells. MMR^{+} cells initially moved out of G_{1} more slowly, with IUdR-treated cells showing a greater delay in G_{1} than nontreated cells. MMR^{+} S-phase profiles were similar, with IUdR treatment producing an increase of about 10% in S phase after 19 h, presumably due to the recognition by the mismatch repair complex of additional mispairs created by IUdR. MMR^{+} cells seemed to have very similar levels of G_{2} phase with or without IUdR treatment. This prolonged G_{2} arrest allows sufficient time for the continuing repair of mispairs in DNA to take place before mitotic division proceeds, thus providing a significant survival advantage to MMR^{+} cells (Fig. 2A).

With the observation that MMR^{−} cells enter into and progress through S phase faster than MMR^{+} cells, the question of whether the difference in IUdR incorporation in synchronized cells might actually be due to differences in S-phase progression instead of mismatch repair status arose. To address this question, synchronized MMR^{+} and MMR^{−} cells were released into 10 μmol/L IUdR and subsequently treated with 50 nmol/L nocodazole at 16 h post-release to prevent exit from M phase (Fig. 3C). Time points taken 24 to 26 h post-release show that distinct differences (*P* < 0.01) in IUdR-DNA incorporation persist, indicating that mismatch repair status accounts, at least in part, for the difference in IUdR levels between MMR^{+} and MMR^{−} cells.

**Models successfully capture the dynamics of the cell cycle and IUdR incorporation.** There are four models developed to capture the dynamics of the cell cycle progression for the isogenic MMR^{−} and MMR^{+} cells, with or without IUdR treatment. The probabilistic cell cycle model parameters are iteratively adjusted using a computational algorithm, and the experimental data and the parameters are summarized in Table 1. A comparison of the model outputs and the experimental data are shown in Fig. 4A. The model outputs are a good match to the temporal dynamics of the MMR^{−} and MMR^{+} experimental cell cycle systems. The sensitivity of the model to the selection of the probability density function is also analyzed by replacing each triangular density function with the density function for the gamma distribution. The outputs of the model with the gamma density functions are very similar to the outputs of the model with triangular density functions. For example, the root-mean-square errors calculated for the MMR^{−} cells without IUdR treatment are 0.0322 for the model with triangular density functions and 0.0312 for the model with gamma density functions. These results show that the model is not sensitive to the selection of the probability density function.

**Table 1.**

. | . | MMR^{−} no treatment
. | MMR^{−} with IUDR
. | MMR^{+} no treatment
. | MMR^{+} with IUDR
. |
---|---|---|---|---|---|

G_{1} | m_{1} | 13.15 | 13.09 | 15.41 | 15.57 |

v_{1} | 7.33 | 6.08 | 6.96 | 6.24 | |

S | m_{2} | 9.58 | 8.28 | 8.30 | 7.74 |

v_{2} | 8.78 | 6.99 | 0.1 | 0.1 | |

G_{2} | m_{3} | 4.58 | 5.09 | 4.79 | 5.89 |

v_{3} | 1.29 | 5.09 | 1.86 | 5.89 |

. | . | MMR^{−} no treatment
. | MMR^{−} with IUDR
. | MMR^{+} no treatment
. | MMR^{+} with IUDR
. |
---|---|---|---|---|---|

G_{1} | m_{1} | 13.15 | 13.09 | 15.41 | 15.57 |

v_{1} | 7.33 | 6.08 | 6.96 | 6.24 | |

S | m_{2} | 9.58 | 8.28 | 8.30 | 7.74 |

v_{2} | 8.78 | 6.99 | 0.1 | 0.1 | |

G_{2} | m_{3} | 4.58 | 5.09 | 4.79 | 5.89 |

v_{3} | 1.29 | 5.09 | 1.86 | 5.89 |

Abbreviations: *m*, means (measured in hours); *v*, variances of the density functions (hours).

The model can be used to study the effects of different chemotherapeutic agents on the cell cycle dynamics for different cancer cells. The model parameters need to be estimated for the cell line of interest. Once the models are tuned for data from a given type of cancer cell line with or without treatment, the models can be used to estimate the cell cycle distribution of that cell line for any given point of time. The outputs of these models are then used as inputs to a statistical model that estimates the time course of drug incorporation into the DNA based on the cell cycle distribution. These two models, taken together, provide an estimate of the amount of drug that has been incorporated into the DNA for the different cancer cells at any given point of time.

The model for the MMR^{+} cells is given by IUdR incorporation = −2,766.51 + 27.72 × G_{1} + 27.84 × S + 27.94 × G_{2}, where G_{1}, S and G_{2} are the percentages of cells in these cell cycle states at a given instant of time. The *P* value for this model is found to be 8.77 × 10^{−7} (<0.05), showing that the linear regression model is a good fit to the experimental cell cycle and incorporation data. In the case of the MMR^{−} cells, the incorporation model is given by −16,575.21 + 165.87 × G_{1} + 165.96 × S + 166.16 × G_{2}, and the *P* value is 5.25 × 10^{−7} (<0.05). The results from the incorporation models, together with the experimental data, are shown in Fig. 4B.

## Discussion

Cell cycle transitions are closely monitored by a series of checkpoints to ensure the fidelity of DNA replication and cell division (20, 21). MMR can detect and repair certain types of intrinsic replication errors by DNA polymerase during S phase, including base-base mispairs and small insertion-deletion loops, as well as specific types of exogenous chemical DNA damage caused by several types of chemotherapy drugs (9, 22, 23). Typically, MMR^{+} cells undergo a prolonged G_{2}-M cell cycle transition arrest, usually occurring at one or more cell cycles after drug treatment, followed by successful mismatch repair or cell death through apoptosis and possibly autophagy (24–27). However, the exact mechanisms linking a MMR-dependent G_{2} arrest following drug treatment and subsequent cell death are not clearly understood (9).

Indeed, the relationship of overall cell cycle regulation and MMR processing of endogenous base-base mispairs and exogenous chemotherapy-induced mispairs has not been previously characterized. In this study, we measured cell cycle transitions in an isogenic pair of MMR^{+} and MMR^{−} human colorectal cancer cell (HCT116) lines using standard cell synchronization and flow cytometry techniques. Additionally, we measured the effect of additional exogenous chemical mispairs on cell cycle transitions of these MMR^{+} and MMR^{−} tumor cells using treatment for one cell cycle with IUdR. We have previously shown that MMR is involved in the processing of IUdR-DNA incorporation (damage), principally by removal (repair) of G:IU mispairs (28). In this study, we use IUdR treatment to increase the amount (extent) of mispairs that need to be processed by MMR during S phase. We have reported that exposure to low concentrations of IUdR (≤2 μmol/L) results in modest cytotoxicity without a significant G_{2} arrest in MMR^{+} cells, whereas higher concentrations (>10 μmol/L) are associated with a G_{2} arrest mediated via ATR/Chk1 signaling and more significant cytotoxicity (29). In contrast, MMR^{−} cells do not recognize/repair certain IUdR mispairs during S phase, which results in higher levels of IUdR-DNA incorporation following initial cell division and which persist during subsequent cell divisions (10, 11). Additionally, we have shown that MMR^{−} cells and MMR^{−} human tumor xenografts can be targeted for IUdR-mediated radiosensitization because the extent (level) of IUdR-DNA incorporation is directly correlated with the extent (level) of IUdR-mediated radiosensitization (10, 11, 30). Thus, patients with MMR^{−} cancers that are drug tolerant (resistant) to many clinically active chemotherapy drugs can be targeted for tumor radiosensitization with sparing of MMR^{+} normal tissues from IUdR cytotoxicity (31).

One important observation gained from the synchronized cell cycle studies was that the MMR^{−} cells have a shortened G_{2} phase, even without IUdR treatment, compared with the MMR^{+} cells. The additional damage response to IUdR treatment occurs during the late S and early G_{2} phases in MMR^{−} cells as well, indicating that IUdR mispairs that are not repaired by MMR are being recognized by another repair system, possibly base excision repair (BER; ref. 32). Irradiating MMR^{−} cells in late S phase or early G_{2} would improve the chances of creating lethal DSBs from cluster damage, possibly resulting from the action of BER on the IUdR mispairs (32) as well as from oxidative damage caused by ionizing radiation (IR) (33). The lessened and shortened G_{2} arrest that MMR^{−} cells display gives them less time to accurately repair these IR-induced DSBs by homologous recombination repair, the DSB repair system that predominates in G_{2} (34). MMR^{+} cells have a significant survival advantage not only due to the fact that MMR has repaired many IUdR mispairs during S phase, but also due to the fact that there are many more cells that are in G_{2} (3-fold more cells are in G_{2} compared with MMR^{−} cells) at 22 h. This prolonged G_{2} phase is also observed in untreated cells, perhaps due to MMR recognition of endogenous mispairs. This G_{2} arrest lasts about 2 h longer in MMR^{+} cells, allowing any DNA single strand breaks (SSB) or other intermediates resulting from alternative DNA repair processes to be completely resolved.

An increased G_{2} arrest has been reported in MMR^{+} cells in response to certain alkylating drug and nucleoside analogue treatment due to MMR recognition of mispairs that result from incorrect bases being inserted opposite a methylated base on the parental strand (35, 36). Futile cycling by MMR attempts to remove the base on the daughter strand has been cited as a possible mechanism of cell killing with methylating agents and 6-thioguanine (9). The results from our study also suggest that the differences in MMR status involve not only differing DNA repair capacity, but also differing cell cycle arrest profiles. In this instance, however, the MMR machinery effectively removes IUdR mismatches and allows adequate time for complete repair of DNA damage during G_{2} phase. The G_{2} response of MMR^{−} cells to IUdR treatment is an interesting observation made from these studies because it implicates other DNA repair processes that may contribute to the preferential IUdR and IR cytotoxicity in these cells by leaving unresolved repair intermediates, such as SSBs and DSBs, present at mitosis. Thus, MMR seems to be an important link between DNA repair and cell cycle control in response to IUdR-induced DNA damage. The mathematical modeling of IUdR incorporation and its impact on the cell cycle is an important first step in developing methods for predicting the optimal time for irradiating MMR^{−} tumors. Ongoing *in vitro* studies will determine if the first or second round of replication is most important in IUdR-DNA cytotoxicity processing by MMR.

We realize that the integration of such mathematical modeling approaches and *in vivo* experimental data from MMR^{−} versus MMR^{+} human tumor xenografts to optimize IUdR and radiation therapy scheduling will require additional modifications. We recently showed an improved therapeutic gain for IUdR-mediated radiosensitization using a novel prodrug of IUdR, 5-iodo-2-pyrimidinone-2′-deoxyribose (IPdR), in HCT116 MMR^{−} s.c. xenografts compared with HCT116 MMR^{+} s.c. xenografts (30). In this *in vivo* study, we found higher % IUdR-DNA cellular incorporation in MMR^{−} tumors compared with MMR^{+} tumors and normal (MMR^{+}) proliferating tissues such as bone marrow and bowel epithelium (30). Additionally, an improved tumor response in MMR^{−} tumor xenografts was found using a tumor regrowth assay delay (30). These experimental data are currently being integrated into our mathematical model.

Clearly, one advantage to the *in vivo* or clinical use of IUdR (or IPdR) to target MMR^{−} tumors for radiosensitization is that this halogenated thymidine analogue can also be used to measure *in vivo* tumor kinetics. We have previously measured *in vivo* tumor cell kinetics in HCT116 MMR^{−} s.c. xenografts using continuous infusions of clinically relevant IUdR concentrations (2 μmol/L; ref. 37). By measuring both the % IUdR-DNA incorporation in HCT116 MMR^{−} tumor cells and the number of MMR^{−} tumor cells labeled by IUdR [i.e., labeling index (LI)], we determined the potential tumor doubling time (*T*_{pot}) to be 25 ± 2 h, whereas the tumor volume doubling time of HCT116 MMR^{−} s.c. xenografts was 5 ± 1 days (37).

The *T*_{pot} is defined as the cell cycle time (*T*_{c}) divided by the growth fraction. The median values of *T*_{pot} determined before treatment from various human solid tumors including gastrointestinal, cervical, and head and neck cancers as well as high-grade gliomas are 5 to 8 days (38). Clinically, the *T*_{pot} can be readily calculated from a single tumor biopsy taken 2 to 6 h following an i.v. bolus injection of a noncytotoxic dose (100–200 mg) of IUdR (38), from which the LI and the duration of S phase (*T*_{s}) are measured by flow cytometry using the formula:

where *λ* varies from 0.8 to 1.0.

In the HCT116 MMR^{−} s.c. xenograft model using a 5-day exposure (≈5 × *T*_{pot}) to continuous infusion IUdR (2 μmol/L), we found that the % IUdR-DNA incorporation in tumor cells was 2.0 ± 0.2%, and the fraction of tumor cells labeled (LI) was 94 ± 1% (37). More recently, we found that once-daily exposures to p.o. IPdR using 1,000 mg/kg/day × 14 days resulted in a higher (3.5%) % IUdR-DNA incorporation in the HCT116 MMR^{−} tumor cells with a 99% LI of the tumor (30). Based on these *in vivo* data (30, 37), we would predict a ≥2.5-fold enhancement in radiation-induced cytotoxicity using prolonged exposures to p.o. IPdR (or continuous infusion IUdR) for ≥5 × *T*_{pot} (≈25–40 days for the common human cancers mentioned above; ref. 38).

As we previously proposed (39), a major limiting factor for human tumor radiosensitization by IUdR (or IPdR; called the sensitizer enhancement ratio, SER) is given by a simple formula:

where *K* is the percentage of unlabeled tumor cells, and *N* is the total number of viable cells.

Based on this formula, a clinical strategy for the use of IUdR (or IPdR) as a radiosensitizer involves maximizing the extent of IUdR-DNA incorporation in MMR^{−} tumor cells in >95% to 99% of tumor cells. Noting that tumor cell kinetics can be altered by treatment with radiation therapy, often resulting in a decrease in the *T*_{pot} within several weeks of starting radiation therapy (38), we will repeatedly monitor *T*_{pot} in future *in vivo* experiments during treatment with IUdR (or IPdR) alone, radiation therapy alone, and combined IUdR (or IPdR) and radiation therapy in athymic mice with both HCT116 MMR^{−} and HCT116 MMR^{+} s.c. xenografts. Such laboratory measurements of *in vivo* tumor cell kinetics and % IUdR-DNA tumor cell incorporation will be integrated into our mathematical modeling approaches to optimize IUdR-mediated radiosensitization in MMR^{−} tumors.

## Acknowledgments

**Grant support:** NIH grants CA50595 and U56CA112963 (T.J. Kinsella).

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.

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*in vivo*.