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It was shown recently that retroviral infection induces integrase-dependent apoptosis (programmed cell death) in DNA-dependent protein kinase (DNA-PK)-deficient scid pre-B cell lines, and it has been proposed that retroviral DNA integration is perceived as DNA damage that is repairable by the DNA-PK-dependent nonhomologous end-joining pathway (R. Daniel, R. A. Katz, and A. M. Skalka, Science 284:644–647, 1999). Very few infectious virions seem to be necessary to induce scid cell death. In this study, we used a modeling approach to estimate the number of integration events necessary to induce cell death of DNA-PK-deficient scid cells. Several models for integration-mediated cell killing were considered. Our analyses indicate that a single hit (integration event) is sufficient to kill a scid cell. Moreover, the closest fit between the experimental data and our computational simulations was achieved with a model in which the infected scid cell must pass through S phase to trigger apoptosis. This model is consistent with the findings that a single double-strand DNA break is sufficient to kill a cell deficient in DNA repair and illustrates the potential of a modeling approach to address quantitative aspects of virus-cell interactions.
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-PKCS), 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. Fig.1).1).
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 Table1).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.
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 ude.cccf@niwtil_s.
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.
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.
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, τ, of target cells.
Delay d1 includes the time required for viral entry into the cell (after cell contact), reverse transcription, nuclear import of the preintegration complex containing viral DNA and bound integrase, and the processing and joining reactions mediated by the retroviral integrase (8, 13, 25). After infection with MoMLV, it takes 6 to 8 h for viral DNA integration to be detected. This includes the time necessary for the virus to adsorb to a target cell (35). Experiments with ASV infection of avian cells (A. M. Skalka, unpublished observations) suggest that the time necessary for ASV-based vectors to integrate into host DNA following infection is probably between 4 and 8 h. Therefore, intervals ranging from 4 to 8 h were considered.
The interval d2 appears to depend on the apoptosis-inducing agent. For example, dexamethasone-induced killing has been detected 1.5 h after addition of the drug (17). We do not know the interval needed for integrase-mediated killing. However, it has been shown that radiation treatment kills Ku-deficient cells as early as 2 h posttreatment (31). Thus, we have incorporated a second, adjustable, variable time interval into our model, covering this period. (See Fig. Fig.33 legend for parameter ranges.)
Detection of scid cell death may be influenced by the generation time of the cells. In the scid cell line used for these studies (S33), the doubling time was close to 20 h under optimal growth conditions. However, this number differs somewhat from experiment to experiment, depending on the stage of the culture. In addition, the virus-containing medium added at the time of infection can slow the growth of S33 cells by as much as 20 to 30% (data not shown). Generation time was thus included as another parameter.
where a is cell age and τ is generation time, here approximately 1 day. Units of a and τ 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 τ (Fig. (Fig.2,2, top). Our simulation model is based on an array of initial cells (n = 1,000). Times of birth of these cells start at −τ 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. Fig.2,2, 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, ... , −tn 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 kV 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, kV, is determined by
where RC is the cell radius and D is the viral diffusion constant given by
where Rg is the gas constant, T is the absolute temperature, N is Avogadro's number, η is the viscosity of the medium, and RV 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: RC = 0.5066 × 10−5m; RV = 0.573 × 10−7m; N = 6.0228 × 1023 molecules/mol; Rg = 8.315 × 107 ergs/mol K; T = 310 K; and η = 0.01005 P.
Between cell divisions, while cell concentration C is constant, V(t) = V(0)e−kVCt, where t = 0 marks the start of such an interval. V(t)/V(0) is the fraction of free viruses at the start of the interval that remain free at time t. We identify this fraction with the chance that a randomly chosen virus free at t = 0 remains free at time t. If T is the adsorption time of this virus then p(T > t) = e−kVCt. If there are nV free viruses, then the time, Tmin, until one of these is adsorbed, diminishing their number to nV − 1, has exponential distribution
Following the results of Andreadis et al. (1), we account for the half-life of the amphotropic viral vector while in solution as 6.5 h, which we used throughout our simulations. When a virus was scheduled to infect a cell, we generated a deviate from the exponential having this half-life. If the deviate was smaller than the elapsed time of the experiment at that point, the virus was declared to be inactivated. Otherwise it successfully infected the cell.
Time epochs are defined by intervals between cell births and between viral adsorption events. New cell birth times are predetermined by the original birth order. A succession of random viral adsorption times is generated, according to the above distribution, where each virus adsorbed is assigned to a random cell. The cell stores the exact time of each viral adsorption and may be infected by several (up to six) viruses in the model. The sum of the time intervals between viral adsorptions is tallied and added to the time of the most recent cell division. When this tally exceeds the time of birth of the next cell, the last adsorption time is discarded and computation is resumed after the two new daughter cells are added, the parent cell is removed, and C is adjusted accordingly. This exploits the “forgetting” property of the exponential distribution. The simulation continues until the next cell birth would occur beyond our intended time horizon, here 36 simulated hours.
Five models for cell killing by virus were considered initially in fitting our experimental data (Table (Table1).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.”
In model 1, cell cycle phase is not a critical parameter. The damage occurs and apoptosis is signaled d1 h after the virus contacts the cell, and cell death is detectable d2 h thereafter. If the interval d1 is completed prior to the end of the cell cycle (see Fig. Fig.2A),2A), then cell death is detectable d2 h later and the infected cell does not replicate. If cell division is completed before interval d1, then the two daughter cells randomly inherit all infecting viruses. In that case the damage takes place in a daughter cell d1 h after the virus infected the parental cell, and the daughter cell dies d2 h later.
In model 2, cell cycle phase is a critical factor. As ASV may require S phase for integration (22), this model stipulates that damage can occur only after the start of S phase. If delay d1 terminates before S phase, then integration and apoptosis commence at the start of S phase. If d1 terminates during or after S phase, then integration occurs at that moment and this triggers apoptosis. When delay d1 terminates after the cell cycle is completed, viral hits are shared randomly by the daughter cells. Daughters inheriting the virus also require the start of S phase to enter apoptosis.
In model 3, damage can occur only at the end of the cell cycle (during M phase) and death always occurs d2 h later if interval d1 is completed before the end of the cell cycle. During early stages of mitosis, the nuclear envelope is dissolved, which, as already noted, is generally assumed to be required for MoMLV DNA and its integrase to gain access to host cell DNA (36). Otherwise, damage is inherited as in models 1 and 2.
In model 4, apoptosis is signaled only when a cellular DNA replication fork intercepts the damage during S phase (Fig. (Fig.2A2A to D). In these cases the damage is modeled to have taken place randomly over whatever nuclear material is present. Cell death is detectable d2 h after apoptosis is signaled. The amount of nuclear material varies continuously from one to two genomes. If the cell's only damage occurs after S phase, this damage is inherited randomly by daughter cells (Fig. (Fig.2D).2D). Such daughters, again, signal apoptosis only during their S phases. In this case, as with model 1, one daughter will be damage free if only one infecting virus entered the parental cell or if all infecting viruses damage the DNA of the same daughter.
A model in which integration is allowed only after the start of S phase (as in model 2) but initiates apoptosis when the replication fork intercepts the damage (as in model 4) was also considered. The behavior of such a model is indistinguishable from that of model 4.
In model 5, as in model 3, damage can occur only in M phase but apoptosis can only be triggered in S phase. The initially infected cell does not enter apoptosis, and damage is randomized to the daughter genomes. The interception of a replication fork with the damage in an affected daughter cell is required to trigger apoptosis. The daughters whose DNA has been damaged fail to replicate, and cell death is detectable d2 h after apoptosis signaling.
Dead cells are also viral targets in all models and do not disintegrate during the simulated experiment (36 h). Cells may die from nonviral causes. In the growing virus-free culture, a constant fraction (approximately 7%) of dead cells is observed. In our models similar results are obtained by setting a 6% death rate for all cells at their moments of replication. Two-hit options are approximated from the one-hit models in all cases by programming the models to ignore the first hit. Either the earliest infecting virus (models 1, 2, 3) or the one causing DNA damage closest to but ahead of the replication fork (models 4 and 5) determines the time of cell death. Other viruses infecting the same cell have no effect other than to reduce the number of free viruses in solution.
The left panels of Fig. Fig.33 show one- and two-hit least squares best fits with the data in Table Table11 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.
We then examined the fit of all five models under conditions of fixed delays d1 and d2. Delay d1 was set at 4, 6, or 8 h, which brackets the range observed in vivo (35; Skalka, unpublished observation). Delay d2 was set at either 1 (Fig. (Fig.3,3, right panels) or 2 h (data not shown), which is consistent with apoptosis induced by either drugs or irradiation (17, 31). Generation time was set at the average 22 h, which is a commonly observed doubling time for our log phase S33 cultures. We observed a good fit for the one-hit option of model 4 when d1 was 4 h and d2 was 1 h. The fit was not as good with model 3 and poor for the one-hit options of models 1, 2, and 5, regardless of the length of d1 or d2. None of the models fit even remotely to the data when two-hit options were considered. We also examined the fits of models 3 and 4 when cells were infected at a higher MOI, from the data set provided in Table Table2.2. Delays d1 and d2 and generation time τ for fitting model 4 to the high MOI (5.4) data set were taken from the least squares values determined from the low MOI (2.0) data set. Figure Figure4A4A shows that model 4 fits the high MOI data set without a change of these parameters. For model 3, however, delays d1 and d2 and generation time τ were fit by least squares directly to the high MOI data set. Even so, the resulting fit is poor and, moreover, requires the unrealistic value of d2 = 0.
Finally, we considered a different scenario (model 6) in which integrase molecules are released from an infecting virion and the nuclease activity of such molecules is capable of introducing damage at multiple locations in the host cell DNA. As each virion contains approximately 100 molecules of integrase (8) and the active enzyme is a multimer (minimally a dimer), we chose 50 as a reasonable minimal number of potential damage sites in model 6. In this model the integrase molecules are released d1 h after cell contact. As in model 4, apoptosis is signaled only in S phase when the replication fork encounters the unrepaired damage. If the release of integrase occurs prior to S phase, then apoptosis is signaled very near the start of S phase. Apoptosis is signaled very soon after integrase release if it occurs in S phase. Release of integrase after S phase causes both daughters to inherit hits and both to signal apoptosis at the start of their S phases. If the delay d1 is completed after cell division, parental viral hits are randomly distributed between daughter cells. The results (Fig. (Fig.4B)4B) show a poor least squares fit of our data with model 6 with either the one- or the two-hit option.
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. Fig.33 and and44 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 = 2−5 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, τ) 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. (Fig.4B).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-PKCS 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.
We thank T. Gales and M. Jarnik of the FCCC Electron Microscope Facility for virus and cell measurements, R. Perry, T. London, and Eugene Toll for critical reviews, and M. Estes for preparation of the manuscript.
This work was supported by U.S. Public Health Service grant 2P30, by National Institutes of Health grants AI40385, CA71515, and CA06927, and also by an appropriation from the Commonwealth of Pennsylvania.
R. Daniel and S. Litwin contributed equally to this work.