INTRODUCTION

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All cells are subject to DNA damage, and unrepaired DNA damage can induce cell death. The extreme sensitivity of some cells, such as those derived from the severe combined immune-deficient (scid) mouse, led to the discovery of genes and proteins that are required for DNA repair (41, 45). DNA-damaging agents induce a variety of lesions. For example, ionizing radiation induces both single- and double-strand (ds) DNA breaks (32). In contrast, UV radiation induces primarily pyrimidine dimers (38, 44). The several types of DNA-damaging agents differ in their potential to induce cell death (32). The most lethal type of DNA damage appears to be an unrepaired ds DNA break (32, 43). Analysis of the kinetics of killing by DNA-damaging drugs or ionizing radiation indicates that a single unrepaired ds break is lethal to both mammalian (32) and yeast cells (3, 4, 20).

scid cells carry a mutation in the gene for the catalytic subunit of the DNA-dependent protein kinase (DNA-PK_CS), which is a critical component of the nonhomologous end-joining (NHEJ) DNA repair pathway in mammalian cells (6, 40). As a consequence of this mutation, scid cells are hypersensitive to DNA damage (5, 15). It was shown recently that retroviral infection induces apoptotic cell death in scid lymphocytic cell lines (10). The vectors used for those studies do not express viral genes and are replication defective in mammalian cells (avian sarcoma virus-derived) or have all viral coding sequences deleted (human immunodeficiency virus type 1 derived). Thus, contrary to a recent suggestion (7), viral gene expression cannot account for this phenomenon. The scid cell killing is, however, dependent on the presence of active, retroviral integrase, the enzyme that catalyzes retroviral DNA integration (8, 13, 25).

The integrase-catalyzed DNA integration reaction proceeds in two distinct steps. In the first step (processing), two nucleotides are removed from the 3' ends of the linear viral DNA, and in the second step (joining), these new 3' ends are joined to staggered phosphates in both strands of host-cell DNA (8, 13, 25). The resulting integration intermediate leaves single-strand gaps in the flanking host DNA and unjoined 5' ends of viral DNA which must be repaired to create a stably integrated "provirus." It has been proposed that apoptosis is induced in scid cells because the integration event or some other integrase-mediated activity is perceived as DNA damage that cannot be repaired (10; Fig. 1).

View larger version (27K): [in this window] [in a new window]   FIG. 1.   Model for integrase-dependent scid cell killing. scid pre-B cells die by apoptosis when infected with an integration-competent retrovirus (10). (IN)n, retroviral integrase multimer.

In those experiments, scid cells were infected at a multiplicity of approximately two infectious virions per cell (10). Despite this low virus-to-cell ratio, approximately 50% of scid cells died by apoptosis following retroviral infection (10; Table 1). The computational modeling approach described in this report addresses the question of how many integration events are necessary to kill a scid cell.

The models that were tested included variables relating to cell cycle, because of its possible influence on both retroviral DNA integration and induction of apoptosis. For example, it has been reported that passage through mitosis is necessary for Moloney murine leukemia virus (MoMLV) to enter the nucleus (36) and it is known that MoMLV can replicate only in dividing cells. In contrast, the avian sarcoma virus (ASV), which can also replicate only in dividing cells, does not seem to require passage through mitosis to integrate its DNA in target cells (22). However, it has been proposed that ASV may need cellular DNA replication and, thus, a passage through S phase for integration (21, 42). Therefore, although virus replication is neither possible nor demanded in our experimental system, cell cycle status may still be relevant to integrase-mediated killing by the ASV-based retroviral vector used. In addition, in the absence of DNA repair, passage through S phase and the attendant DNA replication might cause single-strand gaps introduced during retroviral DNA integration to be converted into highly lethal ds breaks (32, 43). Finally, expression of cellular proteins critical to integrase-mediated killing may be limited to a specific phase of the cell cycle. Thus, the cell cycle status of target cells was included in our models.

	MATERIALS AND METHODS

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Computation. All models were programmed in Fortran 77 and run on a UNIX work station (DEC alpha). Model output was graphed using Splus software. The Fortran source code can be obtained from S. Litwin at s_litwin{at}fccc.edu.

Infection protocols. In the viability assays, pre-B S33 cells were infected as previously described (10). Log phase cells were distributed in 24-well plates at 5 × 10⁵ cells per ml per well. DEAE dextran at a final concentration of 5 µg/ml and the ASV viral vector (IN⁺; 10) at a multiplicity of infection (MOI) of two infectious virions/cell were added to each well. The final volume was 2 ml per well. The number of infectious virions was determined by the ability of the vector to transduce a drug resistance marker after infection of normal (DNA-PK-proficient) cells (10). Cell viability was measured by trypan blue dye exclusion. At each time point indicated, aliquots were removed from the individual wells and the number of stained and unstained cells was determined (in samples of approximately 100) to estimate the percentage remaining viable. For infection at a higher MOI (i.e., 5.4), 6 × 10⁶ cells were pelleted and then resuspended directly in the virus-containing medium, in the presence of 5 µg of DEAE dextran/ml. The mixture was then distributed into separate wells so that each contained 1 × 10⁶ cells and the final volume was again 2 ml. Viability was measured as described above.

	RESULTS

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Experimental design. One goal of this study was to determine the number of integration events required to kill a DNA-PK-deficient cell. First, a series of infections was carried out using a known titer of the ASV-derived viral vector, and cell viability was monitored at given times thereafter. As the ASV vector cannot replicate in the mammalian cells, the experiments measure the effects of only a single cycle of integration, that of the infecting vector. The observed pattern of cell killing was then compared to patterns predicted from mathematical models that take into account a number of critical parameters described below.

Parameters included in the computational analyses. All of the models developed for our analyses use the same method of determining viral adsorption time. However, the models differ in the way cell cycle status affects apoptosis timing after viral adsorption. Three parameters are used to control this timing: (i) the delay time, d₁, between virus adsorption and integrase-mediated joining of viral to host-cell DNA; (ii) the delay time d₂, the minimum time between the initiation of apoptosis and detectable cell death; and (iii) the generation time, , of target cells.

Structure of the model of infection of scid cells by the retrovirus. scid cells were suspended in growth medium while in log phase. If we assume that scid cell generation times are homogenous (29, 33, 34), then the distribution of cell ages under these conditions is
where a is cell age and  is generation time, here approximately 1 day. Units of a and  are hours. The age distribution has the property that there are always twice as many cells of age near zero as cells of age just short of  (Fig. 2, top). Our simulation model is based on an array of initial cells (n = 1,000). Times of birth of these cells start at and end at 0. The set of birth times is distributed in a nonlinear way so as to closely approximate the above age distribution (see Fig. 2, top). To this end we set the time of birth of the most recently born cell at 0 (t₁ = 0). Successive earlier birth times t₂, t₃, ... , t_n are defined by
Approximately two infectious virions per cell were added to the log phase cell culture at time zero. We model virus adsorption as taking place upon contact. All cells, alive or dead, may adsorb viruses in our model. Let V be the concentration of free virus in solution, C the concentration of cells, and k_V the rate constant determining the rate of viral adsorption by cells (28). Then
describes the concentration of free virus over time. The adsorption rate constant, k_V, is determined by
where R_C is the cell radius and D is the viral diffusion constant given by
where R_g is the gas constant, T is the absolute temperature, N is Avogadro's number,  is the viscosity of the medium, and R_V is the viral radius. The virus and cell radii were determined independently using electron microscopy and represent the average of five and six measurements, respectively. Both are assumed to be spherical in our calculations. Parameters used were as follows: R_C = 0.5066 × 10⁵ m; R_V = 0.573 × 10⁷ m; N = 6.0228 × 10²³ molecules/mol; R_g = 8.315 × 10⁷ ergs/mol K; T = 310 K; and  = 0.01005 P. 

View larger version (14K): [in this window] [in a new window]   FIG. 2.   Models for the age distribution of log phase cells, and the relevance of cell cycle phase to retroviral DNA integration and apoptosis in scid cells. (Top) The age distribution of cells growing in log phase culture is a truncated exponential with twice as many cells just born as there are about to be born (see text). The simulation program starts with an inoculum of 1,000 cells whose birth times are determined to closely adhere to this age distribution. Illustrated is the process for a set of 50 cells. Each tick mark is a cell age at the start of the simulation: the oldest cell is 24 h of age and the youngest is 0 h. (A) Time line showing birth and phases of the cell cycle and times of their occurrence. tb, time of birth; s1 and s2, start and end of S phase; , generation time. The percentage of cells in S phase was determined by flow cytometry analysis of propidium iodine-stained cells. We determined s1 = 0.43, s2 = 0.886. The figures are not to scale. (B) Position of replication fork at time t for tb + s1 < t < tb + s2. a, fraction of genome replicated at time t; b, fraction not yet replicated; a + b = 1. When t = tb + s1, a = 0, and when t = tb + s2, a = 1. (C) If retroviral DNA integration occurs prior to tb + s1, then the integration site is chosen at random (uniformly) from the entire genome. Apoptosis will be signaled when the replication fork intercepts the unrepaired integration site. Even if integration occurs in S phase but the integration site is (randomly) chosen beyond the replication fork, as illustrated, then, again, apoptosis is signaled when the fork reaches the unrepaired integration point. The chance of this event is b/(2 a + b) where b is the fraction of the genome still unreplicated at the moment of retroviral DNA integration. If t is the time of integration then a = [t (tb + s1)]/(s2  s1) and b = 1a. Cell death is detected via trypan blue exclusion after delay d2. (D) If viral integration occurs in S phase but the site is selected from a branch of the already replicated genome, then (absent other viruses) one daughter cell escapes apoptosis while the daughter containing the unrepaired integrated site will signal apoptosis when its replication fork reaches this site. The chance of this type of integration is 2a/(2a + b). However, the infected daughter cell will signal apoptosis at a time in her S phase that reflects the earlier integration event. For example, if the integration takes place at t = tb + s1 + (s2  s1)/2, i.e., half-way through the genome, then the chance that it lands on one of the already replicated branches is 2/3. Its position in the daughter cell genome is then randomly selected between 0 and 1/2. Thus, the time of this daughter cell's apoptosis will be uniformly distributed between tb +  + s1 and tb +  + s1 + (s2  s1)/2, rather than uniformly over the whole of S phase.

k_V^Ct

k_V^Ct

Alternative models of scid cell killing by the retrovirus. Five models for cell killing by virus were considered initially in fitting our experimental data (Table 1). Each assumes that the trigger for apoptosis is retroviral DNA integration or some other integrase-mediated event that takes place at a single locus. In what follows, the triggering event will be referred to as "damage."

A single hit in model 4 provides the best fit to the experimental data. The left panels of Fig. 3 show one- and two-hit least squares best fits with the data in Table 1 for the five models described above. For model 1, the fit at 12 h is achieved by delaying cell death approximately 12 h from viral adsorption. Even so, the fits at 16, 20, and 24 h for one hit are poor, as are the fits at 9, 24, and 36 h for two hits. For model 2, both one- and two-hit fits at 24 h are poor and the fit at 9 h for one hit and at 20 and 36 h for the two-hit option are also poor. For model 3 the fit for one hit at 24 h misses the data. This lack of fit is not sufficient, however, to reject the model (see Discussion). However, the values for d₂ (0.0 h) are implausible, and the fits at 12, 16, 20, 24, and 36 h are poor for two hits with this model. For model 4, the one-hit fit is good and the parameters dictated are close to the predicted ranges. In contrast, the two-hit fit is poor at 12, 16, 20, 24, and 36 h and the time interval for d₂ is not plausible. Finally, with model 5 both one- and two-hit fits are poor at 12, 16, 20, and 24 h with implausible values for d₂. In addition, the fit at 36 h is poor for the two-hit option with this model.

View larger version (29K): [in this window] [in a new window]   FIG. 3.   Five models for ASV integrase-mediated scid cell killing. Each model is described in the text. Points represent the experimental data in Table 1. (Left panels) Parameters , d1, and d2 were determined to give least squares fits for all five models. Parameter searches, however, were restricted as follows: 20    40; 4  d1  8; 0  d2  6 h. Solid lines represent one-hit options; dotted lines represent two-hit options. (Right panels) Five models at fixed delays d1 and d2 with one- or two-hit options. In all cases delay d1 is set at 4 h (lower curve), 6 h (middle curve), or 8 h (upper curve); d2 is 1 h and  = 22 h. Options are represented as in left panels.

View larger version (16K): [in this window] [in a new window]   FIG. 4.   Further tests of models 3, 4, and a variant, model 6. (A) Model 4 at a high MOI (solid curve), using parameters derived from the low MOI data set. Data points are from Table 2. Model 3 (dashed curve) is a least squares fit. This best fit, nevertheless, fails at the 12- and 36-h data points. (B) Least squares fit of model 6, a variant of model 4. Each infecting virion releases integrase molecules presumed to damage the host genome at multiple sites ( 50). Data points are from Table 1. One-virion option, solid line; two-virion option, dotted line.

	DISCUSSION

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We have used mathematical modeling to analyze the kinetics of ASV-mediated scid cell killing and to evaluate the importance of cell phase without the use of chemical or other blocks that can introduce additional confounding variables. Our purpose was to test several reasonable hypotheses of how viral infection leads to cell death. In all models tested, two-hit versions are unequivocally refuted by the experimental data. All but one of our one-hit models (model 4) also fail to explain the data. The parameters in each model were adjusted to provide the best fit possible (least squares) for that model. Excepting models 3 or 4, no possible adjustment brings them into conformity with the data. These failures are illustrated in Fig. 3 and 4 where model best fits widely skirt observations. Six independent viability measurements were made at each sampling time. In three of the four models there were two or three sampling times at which all six viability values obtained were either above or below model predictions. The chance of this event is p = 2⁵ at each sampling time. Model curves were forced to fit the initial sample, at t = 0, hence only model fits at the seven additional sampling times were sensitive to parameter adjustment. The chance that two or more sampling times exhibit this extreme asymmetry is given by the binomial probability
As a result each of the above models is rejected at this level of significance, even though the number of sampling times is fairly small. This is noteworthy given the latitude in adjusting model parameters and the considerable data scatter at most sampling times. Model 3 cannot be rejected by our low MOI data; however, it cannot be made to fit the high MOI data. Model 4, on the other hand, fits the high MOI data using the same parameters (d₁, d₂, ) determined from the low MOI experiment.

Model 4 fits all of the existing data very smoothly, passing centrally through the scattered viability measurements at each sampling time. It does so using reasonable parameter values. There may be other models that could be made to fit the experimental data equally well, but we have not been able to find other alternatives that make biological sense. All five unsuccessful models can now be set aside, having been rejected by our limited data set. However, we claim only that our phase-dependent model 4 is consistent with the data, not that it is valid. Experiments of a different sort will be needed to refine or reject this one remaining model.

The results of our modeling indicate that infection by a single integration-competent virus is sufficient to induce scid cell death. This interpretation is consistent with our hypothesis that a single integration event can kill a scid cell. An alternative model in which active integrase molecules are released from the infecting virion, causing damage at multiple sites with resulting scid cell death, provides a poor fit to our experimental data (Fig. 4B). In addition, our preliminary experiments suggest that retrovirus-induced scid cell killing can be inhibited by the reverse transcriptase inhibitor zidovudine (AZT) (unpublished results), implying that retroviral DNA, in addition to the active integrase, is needed to induce scid cell death. Therefore, the proposal that a single integration event is sufficient to kill a scid pre-B cell seems to be the most plausible. This explanation is also consistent with the extreme sensitivity of such cells to DNA damage (18).

Despite this sensitivity to retrovirus-induced killing, we have shown that some (10 to 20%) residual integration does occur in scid cells (10), likely via an alternative, ATM-dependent DNA repair pathway (11). In fact, the scid lines used in our studies were derived by infection of bone marrow cells with Abelson murine leukemia virus (A-MuLV) (39). The report that Fulop et al. (14) were able to isolate approximately equal numbers of v-abl transformed colonies after infection of scid and normal bone marrow cells with A-MuLV seems inconsistent with our observations (7). However, we note that the end point of these experiments, cellular transformation, is quite different from the cell viability and colony formation monitored in our experiments. Furthermore, scid mice are known to develop lymphoid tumors at a high frequency (9) and deficiencies in other components of the NHEJ pathway also lead to increased tumorigenesis in mice (12, 16, 19, 30, 37). Indeed, DNA-PK_CS has been classified as a tumor suppressor protein (23). Thus, one possible explanation for the discrepancy with our results is that scid bone marrow cells are more susceptible than normal bone marrow cells to transformation by the v-abl oncogene. If so, sensitivity to retrovirus-induced killing may be obscured by increased efficiency of transformation of the surviving infected scid cells.

How may retroviral DNA integration kill a scid cell? DNA damage readily kills DNA repair-deficient cells (5, 15, 31, 40, 41, 43). The most lethal damage is a ds break (32, 43). According to our current understanding of the biochemistry of the retroviral integrase reaction, only the 3' ends of viral DNA are joined to the host DNA, and single-strand gaps in the host DNA flank the viral DNA (8, 13, 25). Host repair proteins may respond to such gaps or other discontinuities present in the viral DNA (8, 25). In the absence of such a response, these unrepaired regions might trigger cell death. In the integration intermediate, single-strand gaps may be in close proximity (8, 13, 25). Therefore, it is also possible that the infected cell may "read" the integration intermediate as a ds break. Alternatively, unrepaired gaps may become ds breaks as a result of DNA replication. The latter explanation is consistent with our best-fitting model's mechanism for apoptosis induction: passage through S phase and interception of a replication fork with unrepaired damage at the integration site. Lack of fit or less good fits with models that required passage through mitosis for integration is consistent with results previously reported for ASV (22) and distinguishes this retrovirus from MuLV (36).

The assimilation of viral DNA into the host chromatin is likely to require chromatin remodeling. As there is evidence that DNA-PK may play a role in this process (2, 26), it is also possible that faulty remodeling following retroviral DNA integration triggers or contributes to scid cell death. In addition, DNA-PK activity fluctuates during the cell cycle, with two peaks observed during G₁/early S phase and then G₂ phase (27). Thus, the differential expression or activity of this or other critical cellular proteins in specific phases of the cell cycle may also contribute to cell cycle effects on scid cell killing. Repair of the integration intermediate and/or chromatin remodeling may then be restricted to certain cell cycle phases and, conversely, apoptosis may be initiated at these same times when the repair does not occur.

Our results are consistent with the hypotheses that a single retroviral DNA integration event can trigger death in cells that lack a critical component of the NHEJ repair pathway and that the triggering event occurs during S phase. We have recently obtained evidence that the product of the ATM gene can respond to integration-induced damage in such cells (11). This is in agreement with a recent report that the ATM protein can recognize ds DNA breaks that arise during DNA replication and direct repair machinery to such loci (24). The basis of this extraordinary sensitivity to DNA damage and its relevance to cellular physiology and the cell cycle can be investigated further using retroviral genes and proteins as convenient probes.