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Raltegravir is the first publicly released HIV-1 integrase inhibitor. In clinical trials, patients on a raltegravir-based HAART regimen were observed to have 70% less viremia in the second phase-decay of viremia than patients on an efavirenz-based HAART regimen. Because of this accelerated decay of viremia, raltegravir has been speculated to have greater antiretroviral activity than efavirenz. Alternative explanations for this phenomenon are also possible. For example, the stage in the viral life cycle at which raltegravir acts may explain the distinct viral dynamics produced by this drug.
In this report, we use a mathematical model of HIV viral dynamics to explore several hypotheses for why raltegravir causes different viral dynamics than efavirenz.
Using the experimentally observed viral dynamics of raltegravir, we calculate constraints on the mechanisms possibly responsible for the unique viral dynamics produced by raltegravir. We predict that the dominant mechanism for the 70% reduction in the second phase viremia is not antiviral efficacy but the stage of the HIV viral life cycle at which raltegravir acts. Furthermore, we find that the kinetic constraints placed on the identity of the virus-producing cells of the second phase are most consistent with monocytes/macrophages.
Our model predictions have important implications for the motivation behind the use of raltegravir and our understanding of the virus-producing cells of the second phase viremia. Our results also highlight that the viral dynamics produced by different antiretroviral drugs should not be directly compared with each other.
Upon initiation of highly active antiretroviral therapy (HAART), free human immunodeficiency virus (HIV) in the plasma declines in a characteristic two-phase manner, until the viral load falls below the lower limit of detection by ultrasensitive clinical assays. The first phase reflects the decay of productively infected CD4+ T cells. The second phase is thought to reflect the decay of chronically infected cells, whose identity is currently not known. Some evidence suggests that the length of time from initiation of HAART until viremia falls below the limit of detection correlates with the efficacy of the HAART regimen [1,2]. Therefore, antiretroviral drugs that cause a faster decay of viremia are generally considered to be more effective.
Recent clinical trials of the integrase inhibitor raltegravir have been promising. A raltegravir-based HAART regimen on average caused viremia to reach the limit of detection faster than a HAART regimen based on the reverse transcriptase inhibitor efavirenz, a drug which is part of the most effective regimen [3,4]. The raltegravir-based regimen showed a 70% reduction in the magnitude of viremia during the second phase of viral decay as compared to the efavirenz-based regimen . As a result of this decreased second phase, a longer time is required for the rapidly decaying first phase to decay to the point where the second phase dominates, producing a prolonged duration of the first phase of viral decay under raltegravir . More recently, a phase I trial has shown faster suppression of viremia with a HAART regimen based on the integrase inhibitor elvitegravir (GS-9137) compared to reverse transcriptase inhibitors , but the exact viral dynamics under elvitegravir have not yet been reported.
The unique viral dynamics observed in patients on raltegravir are intriguing and have several possible explanations [3,4]. We have previously used mathematical modeling to show that the stage at which an antiretroviral drug acts in the viral life cycle affects the resulting viral dynamics . We found that the longest stage of the viral life cycle after the latest pharmacologic block determines the asymptotic decay rate of each phase and, by extension, of overall viremia.
Here we use mathematical modeling to explore whether the 70% decrease in the second-phase decay of viremia in patients taking raltegravir may be caused by enhanced activity against viral replication, by the identity of the virus-producing cells responsible for the second phase, by the stage of the viral life at which raltegravir acts, or by altered pharmacokinetics. In particular, we assess whether any of these possibilities are consistent with known kinetic properties of infected cells and with experimentally observed viral dynamics in patients taking raltegravir.
We use our previously described mathematical model of viral dynamics (see figure 1 of ), which incorporates multiple stages of the viral life cycle, to compare a HAART regimen based on a reverse transcriptase inhibitor to a regimen based on an integrase inhibitor. We consider two populations of target cells, the CD4+ T lymphoblasts (T) and the cells responsible for the second-phase decay, which we designate as M cells. Each of these cell types can be in an uninfected state (TU, MU), a pre-integration stage of infection (T1, M1), or a post-integration stage of infection (T2, M2).
The model is defined by the following system of ordinary differential equations:
Rate constants are defined in Table 1.
Because we attempt to understand the unique viral dynamics produced by raltegravir, we focus our analysis on model solutions for the virus-producing cells of the second phase (Mcells) as well as viremia during that phase. We have previously shown  that viremia originating from M cells can be well approximated as:
for M cells inhibited at reverse transcription and integration, respectively, where 2 represents the pre-HAART steady state number of M2 cells.
We choose parameters consistent with previously reported values. Parameters regarding the kinetics (e.g. rates of decay and integration) and numbers of productively infected CD4+ T cells (T1 and T2) are taken from previous studies [7–10] which have characterized these values (Table 1). Our model also includes the cells that produce virus during the second phase of decay, M cells. We do not a priori assume an identity for M cells. Instead, we gain insight into their properties by determining parameter choices (e.g. δM1 = 0.0069 day−1, δM2 = 0.077 day−1, kM = 0.1 day−1) compatible with the experimental observation that their corresponding viremia decays with a half-life between approximately one to four weeks .
We also explore the possibility that the second phase of viremia decay arises from pre-integration latently infected resting CD4+ T cells (PLIC). In this scenario, M1 represent PLIC and M2 represent post-integration productively infected CD4+ T cells (similar to T2), because the integration of the HIV provirus does not occur without an activation event. While the decay rate of productively infected CD4+ T cells is dominated by cell death, the decay rate of PLIC (δM1) is dominated by the decay of the preintegration complex (PIC). This decay occurs with a half-life of two to three days [11,12], much more rapid than the death rate of resting CD4+ T cells. Because δM1 equals the sum of the PLIC death rate and the PIC decay rate, δM1 is dominated by the decay rate of the PIC and can be approximated as 0.3 day−1 [11,12]. Additionally, in this scenario M2 represents the same cell type as T2, and thus has the same kinetic characteristics: the parameter δM2 is equal to δT2 and can be approximated to be at least 0.7 day−1 [8,13].
The integration rate of HIV provirus, while very rapid in activated CD4+ T cells, is slow in PLIC because it is dependent on a T-cell activation event, which is infrequent. Consequently, the parameter kM, reflecting the rate at which PLIC are activated with subsequent integration of HIV DNA, is limited by the long time to activation of PLIC—not the rapid process of integration that occurs in the activated CD4+ T cells—and the numerical value of kM largely reflects the activation rate of resting CD4+ T cells. We and others have previously shown that the activation rate of resting CD4+ T cells is constrained to be quite slow, since this kinetic parameter is a major determinant of the decay rate for the resting CD4+ T cell latent reservoir [10,14] with stably integrated HIV. Based on this evidence, we estimate that kM is less than or on the order of 0.01 day−1.
We previously derived expressions for virus production when there is pharmacologic block before the pre-integration infected cell, i.e. at β, or at the transition from pre-integration to post-integration infected cells, i.e. at k. We initially consider the case of complete inhibition (i.e. either β = 0, k = 0, or both). 
Because raltegravir acts at the integration step, it can cause the experimentally observed reduction in the second phase of viremia without change in the second phase decay rate  if the viral life cycle in M cells satisfies the constraint δM1 + kM > δM2 (see equation 8) [4,6]. If this constraint is violated, the second-phase decay rate is different in the setting of raltegravir compared to efavirenz, in disagreement with the reported data. The magnitude of this effect can be determined by dividing equation 8 with kM = 0 by equation 8 with βM = 0 and taking the limit of time going to infinity. Thus, our model predicts that, asymptotically, the second phase of viremia under raltegravir is suppressed compared to the viremia under efavirenz by a factor of
This reduction is due only to the stage of the life cycle at which these drugs act. With parameter choices (e.g. δM1 = 0.0069 day−1, δM2 = 0.077 day−1, kM = 0.1 day−1) consistent with previously observed viral dynamics of the second phase decay [8,15], our model predicts an asymptotic reduction in the second phase by 60 to 70% (Figure 1).
When resting CD4+ T cells are infected by HIV, the viral life cycle proceeds to reverse transcription of the genome, producing a full length, unintegrated DNA copy of the HIV genome. This DNA copy in combination with additional viral proteins comprises the pre-integration complex (PIC). Resting CD4+ T cells containing unintegrated HIV DNA may be activated to undergo blast transformation. At this point, integration of the HIV genome and subsequent viral replication occurs . Thus resting CD4+ T cells containing unintegrated HIV DNA represent a form of latency called pre-integration latency. In the setting of conventional HAART regimens without raltegravir, these preintegration latently infected cells (PLIC) would serve as a reservoir for virus production—decaying through either death of the cell, degradation of the PIC, or activation to a productively infected cell. Addition of an integrase inhibitor to a HAART regimen should decrease or eliminate virus production from this reservoir. Recent work has proposed that the decreased second-phase with raltegravir is due to the unique effect of raltegravir on the PLIC reservoir .
We explored this possibility using our model and parameter values (δM1 = 0.3 day−1, δM1 = 0.7 day−1, and kM = 0.01 day−1) consistent with the experimentally determined kinetic properties of PLIC [8,10–14]. Our model predicts that the decay rate of the second phase viremia is determined by the smaller of the quantities δM2 and δM1 + kM. Based on the experimentally derived values of δM1, δM2, and kM for PLIC, the second phase decay predicted by our model would be much faster than what has been experimentally observed [8,15]. Moreover, given these experimentally observed parameter estimates, we have δM1 + kM = 0.3 + 0.001 < 0.7 ≤ δM2, in violation of the kinetic constraint δM1 + kM > δM2. This kinetic characteristic of PLIC is supported by the experimental observation that first-phase and second-phase decay rates are distinct [8,15]. Moreover, if PLIC obeyed the kinetic constraint that δM1 + kM > δM2, the second phase decay rate in the setting of a reverse transcriptase inhibitor-based or integrase inhibitor-based would be δM2, which is equal to the first phase decay rate δT2, and therefore inconsistent with the reported data [8,15]. Our model predicts that inhibition at integration (kM) compared to reverse transcription (β) would cause a change in the second phase decay rate (Figure 2). This qualitative result remains unchanged under physiologically relevant variations in drug potency or other pharmacologic properties. Therefore, we conclude PLIC do not possess the kinetic properties required of M cells to be consistent with the viral dynamics under raltegravir.
Could a decreased second phase arise from raltegravir’s unique ability to penetrate a sanctuary site? Assume the presence of such a site containing a steady number of post-integration infected cells inaccessible to all drugs except raltegravir. During steady-state infection, the contribution of this sanctuary to total viremia is approximately where c reflects the clearance rate of free virus, NT reflects the virus production rate of T cells, and NM reflects the virus production rate of M cells. We assume that raltegravir is able to penetrate this sanctuary site to completely stop the viral replication therein, while all other clinically tested antiretroviral drugs are unable to affect viral replication within the sanctuary. Under the same assumptions used to derive equation 8, in the presence of a sanctuary site a raltegravir-based HAART regimen causes viremia to decay with an approximate time course of
while an RT inhibitor-based HAART regimen would cause viremia to decay with approximate time course of
In this scenario, the second-phase decays for the two drugs look initially identical but later diverge. Because of constant virus production in the reservoir, under the efavirenz-based regimen the second phase approaches a low-level steady-state viremia (Figure 3). This divergence of viral dynamics results in a time-dependent decrease in viremia (i.e. with increasing time on the HAART regimen, patients on raltegravir would demonstrate a greater decrease in viremia). This prediction is not consistent with the reported clinical-trial data [3,4].
The size of the sanctuary affects the predicted viral dynamics. The smaller the drug sanctuary, the longer the time scale on which the viral dynamics of raltegravir-based and efavirenz-based regimens would be identical before diverging. The size of a realistic sanctuary is likely small enough that such a divergence in viral-load decays would occur after the viral load has dropped to below the limit of detection—otherwise the viral-load decay curves of previous HAART regimens would have demonstrated a clinically observable divergence from exponential decay. This reasoning is consistent with the most likely locations of sanctuary sites for HIV replication in the central nervous system and testes, where target cells for HIV replication are much less plentiful than in the lymphoid tissues. In either case, the qualitative results of the sanctuary-site model are not consistent with the reported data [3,4].
The decreased second phase produced by raltegravir may be due to superior suppression of viral replication by raltegravir. To explore this possibility, we consider the case where raltegravir causes complete suppression of viral replication (i.e. kT = kM = 0) while a competing HAART regimen consisting of efavirenz in combination with other reverse transcriptase or protease inhibitors leads to incomplete suppression of viremia (i.e. βT > 0 and βM > 0). We do assume, however, that the efavirenz-based HAART regimen is sufficiently suppressive to cause viremia to decay towards zero [10,16]. For physiologically realistic inhibition of viral replication by an efavirenz-based HAART regimen, our model does not predict a significant deviation in the second phase decay compared to an efavirenz-based HAART regimen that completely suppresses viral replication (i.e. βT = βM = 0) (Figure 4A). Our model predicts that low antiviral activity would contribute to the difference in second-phase viremia only if the efavirenz-based regimen exhibited non-physiologically low inhibition of viral replication (≤90% inhibition). This prediction is inconsistent with the clinically observed efficacy of efavirenz-based HAART regimens [17,18] and in vitro measurements demonstrating many orders of magnitude inhibition of viral replication by efavirenz alone . Moreover, at such low levels of inhibition, the first-phase decay rate would also be affected (Figure 4A), which is inconsistent with data from the raltegravir clinical trials.
By contrast, our model can reproduce a decreased second phase of viremia if we assume a lower potency of raltegravir, constrained at 85% to 90% inhibition or less, and if post-integration infected M cells (M2 cells) exhibit the kinetics of productively infected cells (δM2 = δT2) but with δM1 + kM ≈ 0.0495 (reflecting a 14 day half-life) (Figure 4B). Although in this scenario the second-phase decay rates are not exactly the same for the raltegravir-based and efavirenz-based HAART regimens, on times scales similar to those used in the raltegravir clinical trials the second phase viremia as well as decay rates are comparable. While an intriguing possibility, the parameter choices required for this scenario are not consistent with any known cell type. This scenario requires that M cells be some kind of CD4+ T cells based on the constraint that δM2 = δT2. However, the kinetic constraint that δM1 + kM ≈ 0.0495 day−1 (reflecting the 14 day average half-life of the second phase decay) cannot accommodate in vitro and in vivo data showing the decay rate of unintegrated HIV in the PLIC to be approximately δM1 ≈ 0.3 day−1—significantly greater than the required 0.0495 day−1. Additionally, it is unlikely that raltegravir would inhibit only 85 to 90% of viral replication on average. Thus there is no evidence for a cell type that is consistent with the kinetic constraints imposed by this scenario nor is there sufficient evidence to suggest that raltegravir would consistently have low enough in vivo potency. New experimental evidence to the contrary would require us to reconsider this scenario.
We use our model to consider whether the decreased second phase viremia with raltegravir is a consequence of more rapid onset of action compared to standard RT or protease inhibitors. For simplicity, we assume that raltegravir takes action immediately while the effect of RT inhibitors is delayed and begins at time τ. We calculate the ratio of second-phase viral decays in the setting of raltegravir and of RT inhibitors, let time go to infinity, and find that the second-phase viremia under raltegravir is asymptotically reduced by a factor of . For values of τ << 1/(δM1 + kM) ≈ 9 days the asymptotic reduction in the second-phase viremia is similar to our original case with no delay at all (equation 9). Given physiologically realistic parameters and delays of 0.5 to 2 days , a pharmacologic delay is unlikely to be the dominant mechanism for the decreased second-phase viremia with raltegravir but may nevertheless contribute to it (figure 5).
Upon initiation of HAART, HIV viremia decays with a classic two-phase decay to below the limit of detection [8,15]. Previous mathematical models have predicted that the rate of decay correlates to first approximation with the drug potency [1,2,21,22]. Efavirenz is a potent non-nucleoside reverse transcriptase inhibitor (nnRTI) and a mainstay of standard HAART regimens [23,24]. However, in recent clinical trials, treatment-naïve HIV+ patients receiving a HAART regimen based on the integrase inhibitor raltegravir exhibited faster decay of viremia to below the limit of detection than patients receiving an efavirenz-based HAART regimen [3,4]. Quantitative studies of HIV viral dynamics under raltegravir treatment revealed a second phase of viral decay that had comparable decay rate but 70% less viremia than observed with an efavirenz-based HAART regimen. The mechanism for this finding remains unknown [4,25,26].
Here, we explored for various mechanisms whether they could cause the viral dynamics observed under raltegravir and what their contribution to the decreased second-phase viremia would be. We considered the possibilities that the differences in viral dynamics between raltegravir-based and efavirenz-based HAART regimens are due to enhanced activity against viral replication, the identity of the virus-producing cells responsible for the second phase, or different pharmacokinetics.
We have found that the decreased second phase of viremia produced in the setting of raltegravir is unlikely to arise because of raltegravir’s higher potency or better penetration of drug sanctuaries. Our model predicts that neither of these two scenarios would result in viral dynamics that are consistent with the observed effect of raltegravir to reduce the second phase. This prediction is consistent with observations that raltegravir does not have a significantly different impact on CD4 count in treatment-naïve patients than other potent antiretroviral drugs . We have also found that the kinetic constraints placed by clinically observed viral dynamics on M cells  are not compatible with PLIC, which die very quickly once activated. Instead, our model predicts that the stage of viral life cycle at which raltegravir acts can largely explain the 70% decrease in the second phase viremia. Our model also predicts that the time delay until drug action can modulate the decreased second phase but that the magnitude of this effect should be small.
These predictions by our model are different from those previously made by Murray and colleagues. These authors used mathematical modeling to reach the conclusion that the 70% decrease in second phase viremia with raltegravir is most consistent with a unique effect of raltegravir on pre-integration latently infected cells (PLIC) . This prediction requires poor (82.5% in their simulations) inhibition of replication by raltegravir as well as the assumptions that the PLIC are activated with a half-life of 14 days and do not inherently decay but only convert to productively infected T cells. These assumptions are non-physiologic and inconsistent with reported data: such a fast activation rate of PLIC would correspond to an equally fast reactivation and therefore decay of the latent reservoir in the setting of HAART. Moreover, we and others have previously shown that the preintegration complex decays with a half-life of 2–3 days in PLIC [11,12]. If these physiologic constraints had been considered, then Murray et al. would not have predicted PLIC as the source of the second phase and therefore would not have considered this scenario as a viable explanation for the dominant effect of raltegravir on viral decay.
We have previously used mathematical modeling to demonstrate that the stage of the viral life cycle at which an antiretroviral drug acts can have a significant effect on the consequent viral dynamics —we refer to this finding as the “stage effect”. Our model predicts that a decreased second phase is an expected consequence of the inhibition of HIV integration by raltegravir . The identity of the virus producing cells during the second phase of decay remains unknown. Here, we have explicitly calculated the extent to which we expect viremia in the second phase to decrease as a consequence of the stage effect and have found that with model parameters most compatible with cell types such as monocytes or macrophages, which are highly resistant to the cytopathic effects of HIV replication , the stage effect can explain the dominant effect of raltegravir. However, our model predicts a lower value for kM than perhaps intuitively expected for macrophages. This prediction may suggest a role for monocytes as M1 cells and is consistent with the recently reported 5-to-6-day lag in vitro between reverse transcription and integration of HIV in monocytes , which may occur in vivo prior to macrophage differentiation. A slow kM may alternatively reflect the necessity of monocyte differentiation into macrophages prior to HIV integration in vivo [28,29]. Nonetheless, we also do not rule out some other cell type with these kinetic properties as the source of viremia during the second phase. Additionally, while we present here a simple model of viral dynamics meant to capture the dominant mechanisms for viral dynamics with raltegravir treatment, a more complex model may conceivably reveal a role for other phenomena in the decreased second phase viremia.
Our model predictions are based on the results of Murray et al., who found a 70% decrease in the magnitude of second phase viremia without a change in the first and second phase decay rates with raltegravir treatment . These results of Murray et al. represent the only published quantitative analysis of the viral load decay in patients on an integrase inhibitor (raltegravir)-based HAART regimen. They are based on only 2 viral load measurements within the first approximately five weeks after initiation of HAART. Because early and extensive viral load sampling while most viral load measurements remain above the limit of detection produce the most accurate viral dynamics , we temper the predictions of our or other studies based solely on these results. We look forward to the results of additional clinical trials with more extensive early viral-load measurements for raltegravir and newer integrase inhibitors , such as elvitegravir. Such measurements will ultimately help to refine our quantitative constraints and verify or refute the predictions we make.
Our results have important clinical implications. Our previous work has demonstrated the general significance of the stage effect when unusual viral dynamics are observed for drugs with novel targets. In this current work, we demonstrated that the stage effect is likely the dominant mechanism causing decreased second-phase viremia under raltegravir. Furthermore, our analysis of this effect has allowed us to gain additional insights into the identity of M cells . While ultimately the motivation for clinical use of integrase inhibitors will be resolved with clinical use and observations regarding drug resistance and patient outcomes, we hope that our work will provide useful information to be considered in the clinical decision for use of integrase inhibitors.
ARS was supported by the medical scientist training program. COW was supported by NIH grant R01 AI065960 and by a Reeder Centennial Fellowship in Systematic and Evolutionary Biology at the University of Texas (UT).
Conflicts of interest
The authors declare that they have no conflicting financial interests.