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Antivir Ther. Author manuscript; available in PMC 2010 November 13.

Published in final edited form as:

Antivir Ther. 2009; 14(2): 263–271.

PMCID: PMC2980788

NIHMSID: NIHMS246009

See other articles in PMC that cite the published article.

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 [4]. 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 [4]. 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 [5], 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 [6]. 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 [6]), 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 (*T _{U}*,

Log_{10} change in viremia from the pre-HAART steady state predicted by our model (equations 1–7) in the presence of an integrase inhibitor (red), assuming complete inhibition of viral replication (i.e. *k*_{T} = *k*_{M} = 0), and in the presence of a reverse **...**

The model is defined by the following system of ordinary differential equations:

$$\frac{{\mathit{\text{dT}}}_{U}}{\mathit{\text{dt}}}={\lambda}_{T}-{\delta}_{{T}_{U}}{T}_{U}-{\beta}_{T}{T}_{U}V,$$

(1)

$$\frac{{\mathit{\text{dT}}}_{1}}{\mathit{\text{dt}}}={\beta}_{T}{T}_{U}V-({\delta}_{{T}_{1}}+{k}_{T}){T}_{1},$$

(2)

$$\frac{{\mathit{\text{dT}}}_{2}}{\mathit{\text{dt}}}={k}_{T}{T}_{1}-{\delta}_{{T}_{2}}{T}_{2},$$

(3)

$$\frac{{\mathit{\text{dM}}}_{U}}{\mathit{\text{dt}}}={\lambda}_{M}-{\delta}_{{M}_{U}}{M}_{U}-{\beta}_{M}{M}_{U}V,$$

(4)

$$\frac{{\mathit{\text{dM}}}_{1}}{\mathit{\text{dt}}}={\beta}_{M}{M}_{U}V-({\delta}_{{M}_{1}}+{k}_{M}){M}_{1},$$

(5)

$$\frac{{\mathit{\text{dM}}}_{2}}{\mathit{\text{dt}}}={k}_{M}{M}_{1}-{\delta}_{{M}_{2}}{M}_{2},$$

(6)

$$\frac{\mathit{\text{dV}}}{\mathit{\text{dt}}}={N}_{T}{T}_{2}+{N}_{M}{M}_{2}-\mathit{\text{cV}}.$$

(7)

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 (*M*cells) as well as viremia during that phase. We have previously shown [6] that viremia originating from *M* cells can be well approximated as:

$$\begin{array}{c}V(t)=\frac{{N}_{M}}{c}\left[\frac{{\delta}_{{M}_{2}}}{{\delta}_{{M}_{2}}-{\delta}_{{M}_{1}}-{k}_{M}}{\overline{M}}_{2}{e}^{-({\delta}_{{M}_{1}}+{k}_{M})t}-\frac{{\delta}_{{M}_{1}}+{k}_{M}}{{\delta}_{{M}_{2}}-{\delta}_{{M}_{1}}-{k}_{M}}{\overline{M}}_{2}{e}^{-{\delta}_{{M}_{2}}t}\right]\phantom{\rule{thinmathspace}{0ex}}\text{and}\hfill \\ V(t)=\frac{{N}_{M}{\overline{M}}_{2}{e}^{-{\delta}_{{M}_{2}}t}}{c},\hfill \end{array}$$

(8)

for *M* cells inhibited at reverse transcription and integration, respectively, where _{2} represents the pre-HAART steady state number of *M _{2}* 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 (*T _{1}* and

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, *M _{1}* represent PLIC and

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 *k _{M}*, 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

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). [6]

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 [4] if the viral life cycle in *M* cells satisfies the constraint δ_{M1} + *k _{M}* > δ

$${\delta}_{{M}_{2}}/({\delta}_{{M}_{1}}+{k}_{M}).$$

(9)

This reduction is due only to the stage of the life cycle at which these drugs act. With parameter choices (e.g. δ_{M1} = 0.0069 day^{−1}, δ_{M2} = 0.077 day^{−1}, *k _{M}* = 0.1 day

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 [9]. 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 [4].

We explored this possibility using our model and parameter values (δ_{M1} = 0.3 day^{−1}, δ_{M1} = 0.7 day^{−1}, and *k _{M}* = 0.01 day

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 $({\overline{T}}_{2}^{*},{\overline{M}}_{2}^{*})$ inaccessible to all drugs except raltegravir. During steady-state infection, the contribution of this sanctuary to total viremia is approximately $\frac{1}{c}({N}_{T}{\overline{T}}_{2}^{*}+{N}_{M}{\overline{M}}_{2}^{*})$ where *c* reflects the clearance rate of free virus, *N _{T}* reflects the virus production rate of

$$V(t)=\frac{{N}_{T}({\overline{T}}_{2}+{\overline{T}}_{2}^{*}){e}^{-{\delta}_{{T}_{2}}t}}{c}+\frac{{N}_{M}({\overline{M}}_{2}+{\overline{M}}_{2}^{*}){e}^{-{\delta}_{{M}_{2}}t}}{c},$$

(10)

while an RT inhibitor-based HAART regimen would cause viremia to decay with approximate time course of

$$V(t)=\frac{{N}_{T}}{c}\left[{\overline{T}}_{2}^{*}+\frac{{\delta}_{{T}_{2}}}{{\delta}_{{T}_{2}}-{\delta}_{{T}_{1}}-{k}_{T}}{\overline{T}}_{2}{e}^{-({\delta}_{{T}_{1}}+{k}_{T})t}-\frac{{\delta}_{{T}_{1}}+{k}_{T}}{{\delta}_{{T}_{2}}-{\delta}_{{T}_{1}}-{k}_{T}}{\overline{T}}_{2}{e}^{-{\delta}_{{T}_{2}}t}\right]+\frac{{N}_{M}}{c}\left[{\overline{M}}_{2}^{*}+\frac{{\delta}_{{M}_{2}}}{{\delta}_{{M}_{2}}-{\delta}_{{M}_{1}}-{k}_{M}}{\overline{M}}_{2}{e}^{-({\delta}_{{M}_{1}}+{k}_{M})t}-\frac{{\delta}_{{M}_{1}}+{k}_{M}}{{\delta}_{{M}_{2}}-{\delta}_{{M}_{1}}-{k}_{M}}{\overline{M}}_{2}{e}^{-{\delta}_{{M}_{2}}t}\right].$$

(11)

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].

Log_{10} change in viremia from the pre-HAART steady state in the presence of an integrase inhibitor (red), assuming complete inhibition of viral replication (i.e. *k*_{T} = *k*_{M} = 0), and in the presence of a reverse transcriptase inhibitor (blue), assuming complete **...**

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. *k _{T}* =

Log_{10} change in viremia from the pre-HAART steady state for (A) complete inhibition by raltegravir (red), complete inhibition by reverse transcriptase inhibitor (solid blue), 90% inhibition by reverse transcriptase inhibitor (dotted blue), 80% inhibition **...**

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 (*M _{2}* cells) exhibit the kinetics of productively infected cells (δ

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 $\frac{{\delta}_{{M}_{2}}+({\delta}_{{M}_{1}}+{k}_{M})({\delta}_{{M}_{2}}\tau )}{{\delta}_{{M}_{1}}+{k}_{M}+({\delta}_{{M}_{1}}+{k}_{M})({\delta}_{{M}_{2}}\tau )}$. For values of τ << 1/(δ_{M1} + *k _{M}*) ≈ 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 [20], 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 [4]. We have also found that the kinetic constraints placed by clinically observed viral dynamics on *M* cells [27] 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) [4]. 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 [6]—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 [6]. 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 [27], the stage effect can explain the dominant effect of raltegravir. However, our model predicts a lower value for *k _{M}* than perhaps intuitively expected for macrophages. This prediction may suggest a role for monocytes as

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 [4]. 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 [7], 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 [30], 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 [30]. 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.

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