Viral kinetic analyses after initiation of antiviral treatment have provided important insights into the biology of different viral infections, such as HIV, hepatitis B and C viruses, and influenza infection [1–6][1–6][1–6][1–6][1–6][1–6]. In the case of HIV, following treatment initiation with protease and/or reverse transcriptase inhibitors , plasma HIV-1 RNA declines in a biphasic manner: a rapid initial viral decline (half-life ∼1 day) occurs within the first 2 weeks posttreatment initiation [7,8][7,8], which is then followed by a slower virus decline, with an average half-life of 14 days, typically until the virus reaches the limit of detection of conventional assays. With more sensitive assays, further slower phases of decline were identified [9–11][9–11][9–11]. Mathematical modeling of this decrease in plasma viremia attributes the first two phases of decline to the decay of two distinct populations of cells: one short lived (e.g. recently infected activated CD4+ T cells) and the other consisting of long-lived infected cells (e.g. resting T cells, macrophages) [1,7,12][1,7,12][1,7,12].
It is unclear whether this pattern of viral decay also applies to newer classes of antiretroviral agents, in particular the integrase strand transfer inhibitors (InSTIs) [13–17][13–17][13–17][13–17][13–17]. Studies have shown that treatment with raltegravir (RAL), an InSTI, leads to rapid suppression of plasma HIV-1 RNA [18–20][18–20][18–20]. Two studies, in particular, have shown that combination antiretroviral therapy (ART) including RAL leads to undetectable plasma HIV-1 RNA faster than regimens with a nonnucleoside reverse transcriptase inhibitor (RTI) [18,19][18,19]. The effects of RAL on viral decay have been analyzed using new mathematical models that separate preintegration and postintegration steps of the viral life cycle [12,21–23][12,21–23][12,21–23][12,21–23]. Results of these modeling analyses showed that the first phase of viral decay was more profound than those described with antiretroviral agents other than RAL . These findings were subsequently confirmed in the AIDS Clinical Trials Group 5248 (A5248), a prospective, single-arm study to estimate the various phases of viral decay in treatment-naive participants initiating ART with RAL along with the reverse transcriptase inhibitors tenofovir disoproxil fumarate/emtricitabine (TDF/FTC) .
Here we developed a model including the preintegration and postintegration steps of the HIV-1 lifecycle to analyze participants treated with either RAL monotherapy , or RAL combined with the reverse transcriptase inhibitors FTC and TDF (ACTG A5248) . The model we present can be solved analytically and exhibits two early phases of viral decay, called phases 1a and 1b, rather than a single early phase as seen with protease and reverse transcriptase inhibitors used alone or in combination. We use the plasma HIV-1 RNA data from those studies to estimate these slopes and the absolute effectiveness of RAL. This is in contrast to prior modeling work on the effects of protease and reverse transcriptase inhibitors wherein one could only estimate the effectiveness of one drug regimen relative to another [24,25][24,25].
In our model of early viral decline, target cells, T, are infected at rate βTV, proportional to the availability of target cells and free virus. The infection rate constant β takes into consideration both the rate at which virus meets target cells as well as the rate of reverse transcription. Cells in which reverse transcription has occurred, I1, can be lost at rate δ1, or can progress to provirus integration at rate k. We note that δ1 includes not only loss by death of the cell, but also other factors, such as degradation of the unintegrated viral DNA. Cells with integrated provirus become productively infected, I2, and are lost at rate δ2, possibly larger than δ1 because of viral cytopathic effects. In turn, virus, V, is produced by cells I2 at rate p per cell and is cleared from the circulation at rate c per virion. A schematic of this model is presented in the left panel of Fig. 1. This system can be described by the following equations:
The left panel represents the model in equation (1), including two populations of infected cells, before (Isubscript1) and after (Isubscript2) integration of HIV DNA. The right panel shows schematically the expected decay in viral load according to the model in equation (1). Note that two phases of decay are expected within the first 10 days post-treatment initiation, the approximate slopes of those phases are indicated.
In equation (1), we have also included the effect of reverse transcriptase inhibitors in blocking infection with effectiveness η, where η varies between 0 and 1, with 1 indicating 100% effectiveness, as well as the effect of an integrase inhibitor in blocking integration with effectiveness ω. This model is a simple extension of the basic model of viral infection  and similar models have been proposed [12,23,26][12,23,26][12,23,26]. Here, as has been done before [1,6][1,6], we assume that the plasma HIV-1 RNA is at set point before therapy, that the virus and infected cells are in quasi-steady state (i.e. V≈ p I2/c), and as we focus on the early viral kinetics, we make the standard approximation that the number of target cells remains constant. These assumptions allow us to solve the resulting linear system of equations, and we find that plasma HIV-1 RNA over time is given by
, V0 is the initial plasma HIV-1 RNA before therapy, t is the time on therapy, and we have allowed for a pharmacological delay, τ, before the effect of therapy is manifested in a change in plasma HIV-1 RNA.
An interesting property of this model is that it predicts two early phases of decay, even though we have not included long-lived infected cells, such as macrophages or resting T cells, as has been done before to study long-term decay characteristics under potent ART [1,7][1,7]. Indeed, analysis of this model indicates that there is an initial phase of viral decay, phase 1a, with slope ∼ δ2, followed by phase 1b with slope ∼ δ1+k(1–ω)η (Fig. 1, right panel). The possibility of these phases (1a and 1b) for different monotherapy regimens in a more complex model has recently been discussed .
Human participant data
In order to determine the effect of RAL monotherapy or RAL in combination with TDF/FTC, we analyzed two data sets with frequent plasma HIV-1 RNA sampling from HIV-infected participants treated with this InSTI.
The first data set was obtained from 28 HIV-infected participants treated with RAL monotherapy for 9 days, from a previously published dose-ranging study . Participants received 100, 200, 400, or 600 mg RAL twice daily, and had plasma HIV-1 RNA measured before the first dose, 6 and 12 h postdose, and on days 1, 2, 3, 4, 7, and 9. Plasma was assayed for HIV-1 RNA using the Amplicor HIV-1 Monitor Assay, version 1.5 (Roche Molecular Diagnostics, Alameda, California, USA), with a limit of quantification (LOQ) = 400 copies/ml; if the result was below that level, the UltraSensitive HIV-1 Monitor Assay (LOQ = 50 copies/ml) was used (Roche Molecular Diagnostics) . We treated plasma HIV RNA data below the limits of quantification as censored at the corresponding values.
The second set of data was obtained from 11 HIV-infected participants treated with a combination of FTC/TDF 200 mg/300 mg daily along with RAL 400 mg twice daily enrolled in an intensive viral dynamics substudy (A5249s) of ACTG protocol A5248 . Plasma HIV-1 RNA was measured immediately prior to administration of the first dose (0 h), and at 2, 4, 6, 12, 18, 24, 30, 36, 42, and 48 h and days 3, 4, 7, 10, and 14 after treatment initiation. For consistency with the first data set, only data through day 10 was used in the current analyses. Plasma was assayed for HIV-1 RNA using the Amplicor HIV-1 Monitor, version 1.5, UltraSensitive protocol (LOQ = 50 copies/mL; Roche Molecular Systems, Branchburg, New Jersey, USA).
Both clinical studies were approved by the respective Institutional Review Boards and all participants provided written informed consent [17,20][17,20].
Comparisons of variables (e.g., baseline plasma HIV-1 RNA) between the two treatment groups were performed using the Wilcoxon test. Significance was considered at the α = 0.05 level.
Participant plasma HIV RNA data was fitted using nonlinear mixed effects. In this approach, each individual parameter is written as
, wherein θ represents the mean value of the parameter in the population, and the random term ϕi, chosen from a Gaussian distribution with mean 0 and standard deviation α, accounts for the interindividual variability. The inclusion of such a random part for the parameters was tested using a likelihood ratio test. Given that antiviral effectiveness was high and very close to 1, the estimation of individual effectiveness parameters was stabilized using a logistic transformation. As is usually done, we assumed an additive independent error on the logarithm of the plasma HIV-1 RNA data with standard error σ.
Equation (2) was fitted to the data to estimate the parameters using an extension of the Stochastic Approximation Expectation-Maximization algorithm to handle data below the LOQ, [27,28][27,28], implemented in the software MONOLIX 4.2.2 (http://www.lixoft.eu).
We examined the influence of RAL monotherapy vs. combination therapy on the parameters. For each model parameter separately, we compared participant-specific estimates between the two treatment groups using the Wilcoxon test. All the parameters for which the treatment group (monotherapy vs. combination therapy) had a P value less than 0.1 during the individual screening were tested in the mixed-effects model. The effect of treatment in each parameter was successively introduced from the one having the lowest P value (the most significant) to the one having the largest P value (the least significant). Each model covariate was tested separately using a likelihood ratio test and was kept in the final model if the P value was less than 0.05. For RAL monotherapy, we repeated this procedure to test dose as a covariate.
Random-effect covariance structure selection
After the covariate model was selected, the correlation between the empirical Bayes estimates of the parameters was tested using partial Spearman correlation. All correlations associated with a P value less than 0.1 were included in the model and were tested using a likelihood ratio test. However, none of these correlations were significant in the final model.
The two groups of HIV-infected participants had similar baseline plasma HIV-1 RNA values [median 4.8 (range 3.59–5.59) and 4.74 (range 4.42 to 5.79) log10 copies/ml, for monotherapy and combination therapy, respectively; P = 0.82]. At approximately 10 days (9–11 days), the plasma HIV-1 RNA was still similar between the two groups (2.60 vs. 2.47 log10 copies/ml, P = 0.60), and the relative decay from baseline was not significantly different (P = 0.77).
We next analyzed if the treatment data with RAL monotherapy showed evidence of two phases of viral decay, by comparing fits of a simple heuristic double exponential function with a single exponential function. The double exponential fitted the data much better (P < 0.00005 using a likelihood ratio test). We then fit the analytical solution of our model, equation (2), to the monotherapy data alone. The absence of reverse transcriptase inhibitors implies η = 0 and leads to a simpler equation with fewer parameters. These fits (Figure S1 in Supplementary Information, http://links.lww.com/QAD/A765) confirmed that there were two phases of viral decay, 1a and 1b, early on (before day 10) and provided estimates of the loss rates of cells preintegration, that is, δ1 ≈ 0.1/day and postintegration, that is, δ2 ≈ 1.0/day. The use of a mixed-effects model also allowed us to rigorously test the effect of dose on the viral decay and the effectiveness of RAL in blocking integration, ω. We found that dose was not a significant covariate for effectiveness (P = 0.11). This may be the case because, in this trial, trough concentrations of RAL were above the IC95 (inhibitory concentration for 95% of infections in 50% human serum) at all doses .
We next fitted the two data sets together. Analysis of the model shows that the predicted plasma HIV-1 RNA is largely insensitive to variations in the effectiveness of RTIs, η, for η > 0.9; and there is a trade-off between estimates of k, the transition rate from reverse transcription to integration of proviral HIV DNA, and the RAL effectiveness, ω. These identifiability limitations were taken into account by fixing η, at η = 0.95 for the combination therapy and η = 0 for monotherapy, and trying different fixed values for k, based on previous work in the literature. Mohammadi et al. performed a detailed in-vitro study of the lifecycle of a cell infected with HIV. In that study (see the first figure and supplementary material of ref. ), the authors showed that the median time of transition from reverse transcription to proviral integration is approximately 9 h. Murray et al. analyzed the durations of phases of the HIV lifecycle based on the delays observed in plasma HIV-1 RNA decline during monotherapy with drugs from different classes, which inhibit distinct steps of the lifecycle. They estimated that it took approximately 5 h from reverse transcription to integration. From these times (Δt), we can calculate k = ln(2)/Δt, obtaining that this rate varies between 1.8  and 3.3/day [23,26][23,26].
In Fig. 2, we show the median predicted decays for the two studies. Some representative individual fits are shown in Fig. 3 (all fits are shown in Supplementary Information, http://links.lww.com/QAD/A765). The fits confirm that there is a double decay (phases 1a and 1b) in early infection (before day 10) in both monotherapy and combination therapy. We then tested the effect of monotherapy vs. combination therapy as a covariate for ω, τ, δ1, and δ2. The effect of treatment group was highly significant when we allowed for a different value of RAL effectiveness, ω, for the monotherapy and the combination therapy studies, with the former being systematically larger than the latter (P < 0.00005). For example, in Table 1, when we fix k = 2.6/day, we found τ = 11 h, δ1 = 0.15/day, δ2 = 0.89/day, ω = 0.997 (monotherapy), and ω = 0.940 (combination therapy), with the difference in effectiveness being significant, P < 0.00005. If we fix k at 1.8/day or 3.3/day, our estimates vary less than 2% for δ2. The estimates of ω also show minor variations (Table 1). When k = 1.8/day, ω for monotherapy and combination therapy are 0.995 and 0.910, respectively, and for k = 3.3/day, the estimates are 0.997 and 0.939, respectively, which are essentially unchanged from the estimates with k = 2.6/day. However, for k = 1.8/day, we estimate δ1 = 0.19/day, whereas for k = 3.3/day, we estimate δ1 = 0.12/day.
We have analyzed in detail the early dynamics of plasma HIV-1 RNA decay with RAL monotherapy and in combination with RTIs. From a biological point of view, the virus assayed in the periphery is mostly being produced in lymphoid tissues by populations of newly infected activated CD4+ T cells, recently activated latently infected CD4+ T cells, and long-lived productively infected cells (such as macrophages). The latter two populations will not be affected by the InSTI or RTI therapy studied here, as these drugs block de-novo infection. In the model, we assume that these latter populations contribute relatively little to the early decay observed, as we only analyze the first 10 days. Thus, the first phase of viral decay mostly represents the loss of newly infected cells by the blunting of productive infection and/or cell death. This assumption is borne out because the model that we propose fits the early viral loss decay data quite well across all patients (fits in Supplementary Information, http://links.lww.com/QAD/A765). We found a two-phase decay (phases 1a and 1b) during the first ∼10 days of treatment. This profile is different from that predicted by early models used to analyze protease and RTI inhibitor-based therapy in HIV infection [1,6,7][1,6,7][1,6,7]. In our model, phase 1a is due to a rapid loss of productively infected cells that contained integrated provirus at the start of treatment. On the contrary, phase 1b is driven by continuous slow decay of cells that complete reverse transcription and integration (i.e. it is due to ω < 1) (Fig. 1, right panel).
Interestingly, ART using a combination of four reverse transcriptase and protease inhibitors may also lead to a two-phase decay early on, as seen in Fig. 1 of Markowitz et al.. However, in that study, this was not explored and the second-phase of decay was simply attributed to the loss of long-lived infected cells . In our model of the effects of RAL-based therapy, the inclusion of long-lived infected cells would give rise to an additional phase of decay as long as the loss rate of these long-lived infected cells was noticeably less than the loss rate of cells with an integrated provirus (i.e., I2 cells). It seems unlikely that monotherapy with RAL would lead to the same mechanistic explanation for the two-phase decay, but we cannot exclude it completely and we are conducting further analyses of this point that will be reported elsewhere.
The estimation of the loss rate, δ1, of infected cells before integration of HIV, I1, was somewhat unstable, because it depended on our choice of the integration rate, k. However, it was always larger than 0.1/day, corresponding to a half-life shorter than 7 days, and for our highest estimate of δ1, the half-life of I1 is 4 days. Both of these estimates are substantially shorter than the expected half-life of uninfected CD4+ T cells [30–33][30–33][30–33][30–33] and long-lived infected cells . It is interesting to speculate as to whether the higher loss rate may be mediated by an immune response recognizing infected cells before they are productively infected [34–38][34–38][34–38][34–38][34–38]. In this context, we should note that the in-vitro results by Spivak et al. indicate that the integration time is only ∼3.4 h, which would correspond to k = 5.0/day. Using this value of k, our estimate of δ1 would be even lower. Another important aspect is that these estimates of k are valid for cells that will ultimately become productively infected, as opposed to cells in which integration may be aborted.
One limitation of our analyses is that the monotherapy and combination therapy data sets were obtained from different studies. This means that some of the protocols used were different, as detailed in the ‘Methods’ section. However, it is unlikely that there will be further trials using RAL monotherapy. To be able to use this unique data set and mitigate issues with different protocols, we applied a mixed-effects fitting approach, which allows for systematic differences in the model parameters for the two studies. Interestingly, we did not find any differences between the parameters, except for the efficacy of RAL.
Previous quantitative analyses of RAL therapy over 8 weeks or more suggested that the first-phase of viral decay was longer than in efavirenz-based regimens [17,21][17,21]. One study using the same participants as the combination therapy trial discussed here found that the first-phase decay was longer and slower in RAL-based vs. efavirenz-based combination therapy . Our study extends that previous work, because that analysis did not use a mechanistic model of viral dynamics. Thus, we now report that what was previously described as a slower first-phase corresponds to two phases. Other modeling analyses of RAL therapy considered that the effectiveness of drug was 100% (i.e. ω = 1) [12,23][12,23], which in our model would imply a single first phase of decay. We note that Gilmore et al., also using ω = 1, suggested the possibility of a multislope first-phase based on a different model, wherein their slopes would correspond to different processes in the viral life cycle.
Potent treatment, in the absence of protease inhibitors, allowed us to directly estimate the effectiveness of RAL in blocking proviral integration, estimated as 94 and 99.7% in combination therapy and monotherapy, respectively. This is in contrast to other viral dynamics studies of HIV treatment, which only allow estimation of relative efficacies , and more similar to the situation in HCV infection, in which estimation of the absolute effectiveness of different treatment regimens is possible . Here, we estimated very high effectiveness for RAL, especially in the monotherapy trial, which is likely due to the concentrations of the drug achieved in the plasma being well above the IC95 . In the combination therapy study, the effectiveness estimated for RAL in blocking the integration step (ω = 0.94) was still high, but lower than for RAL monotherapy (ω = 0.997). This is somewhat contradictory to in-vitro data that shows that this treatment combination acts in synergy to boost the overall effect of treatment . We note, however, that here we are estimating the per cell effectiveness of drug in blocking a given step of the HIV-1 life cycle. Overall, the dynamics of the model are quite different in the two groups (combination ART with RAL vs. RAL monotherapy) (Fig. 2). We predict that from ∼15 days onward after the start of treatment, the plasma HIV-1 RNA demonstrates a greater decrease from baseline in the combination treatment (not shown). This is consistent with the overall effect of therapy being more potent with the combination of antiretroviral agents.
In conclusion, we have shown that HIV-1 RNA therapy with an InSTI leads to a pattern of viral decay unlike what has been seen before with treatment regimens including protease inhibitors, in that the first phase of decay is composed of two subphases. This allowed us to estimate the absolute effectiveness of RAL and the decay rate of infected cells before proviral integration.
The authors gratefully acknowledge Merck Sharp & Dohme for providing part of the data analyzed in this work.
This work was funded by the National Institutes of Health grants R01-AI104373, R01-AI028433, and R01-OD011095, as well as NIH grants to the AIDS Clinical Trials Group (UM1 AI068636, UM1 AI068634). Portions of this work were performed under the auspices of the US Department of Energy under contract DE-AC52–06NA25396.
The content of this manuscript is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health or of Merck Sharp & Dohme.
Conflicts of interest
There are no conflicts of interest.
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