HIV model parameter estimates from interruption trial data including drug efficacy and reservoir dynamics

Mathematical models based on ordinary differential equations (ODE) have had significant impact on understanding HIV disease dynamics and optimizing patient treatment. A model that characterizes the essential disease dynamics can be used for prediction only if the model parameters are identifiable from clinical data. Most previous parameter identification studies for HIV have used sparsely sampled data from the decay phase following the introduction of therapy. In this paper, model parameters are identified from frequently sampled viral-load data taken from ten patients enrolled in the previously published AutoVac HAART interruption study, providing between 69 and 114 viral load measurements from 3-5 phases of viral decay and rebound for each patient. This dataset is considerably larger than those used in previously published parameter estimation studies. Furthermore, the measurements come from two separate experimental conditions, which allows for the direct estimation of drug efficacy and reservoir contribution rates, two parameters that cannot be identified from decay-phase data alone. A Markov-Chain Monte-Carlo method is used to estimate the model parameter values, with initial estimates obtained using nonlinear least-squares methods. The posterior distributions of the parameter estimates are reported and compared for all patients.     

Semiparametric functional mapping of quantitative trait loci governing long-term HIV dynamics

MOTIVATION: Functional mapping has proven to be powerful for characterizing quantitative trait loci (QTL) that control complex dynamic traits. More recently, functional mapping has been extended to identify the host QTL responsible for HIV dynamics by incorporating a parametric bi-exponential function for earlier stages of viral load trajectories. However, existing functional mapping cannot be used to map long-term HIV dynamics because no mathematical functions are available for later stages of HIV dynamic changes. RESULTS: We derived a statistical model for functional mapping of dynamic QTL through characterizing HIV load trajectories during a long-term period semiparametrically. The new model was constructed within the maximum likelihood framework and implemented with the EM-simplex algorithm. It allows for the test of differences in the genetic control of short- and long-term HIV dynamics and the characterization of the effects of viral-host genome interaction. Extensive simulation studies have been performed to test the statistical behavior of this model. The new model will provide an important tool for genetic and genomic studies of human complex diseases like HIV/AIDS and their pathological progression. AVAILABILITY: Available on request from the corresponding author.     

Assessing antiviral potency of anti-HIV therapies in vivo by comparing viral decay rates in viral dynamic models

A virologic marker, the number of HIV RNA copies or viral load, is currently used to evaluate anti-HIV therapies in AIDS clinical trials. This marker can be used to assess the antiviral potency of therapies, but is easily affected by noncompliance, drug resistance, toxicities, and other factors during the long-term treatment evaluation process. Recently it has been suggested to use viral dynamics to assess the potency of antiviral drugs and therapies, since viral decay rates in viral dynamic models have been shown to be related to the antiviral drug potency directly, and they need a shorter evaluation time. In this paper we first review the two statistical approaches for characterizing HIV dynamics and estimating viral decay rates: the individual nonlinear least squares regression (INLS) method and the population nonlinear mixed-effect model (PMEM) approach. To compare the viral decay rates between two treatment arms, parametric and nonparametric tests, based on the estimates of viral decay rates (the derived variables) from both the INLS and PMEM methods, are proposed and studied. We show, using the concept of exchangeability, that the test based on the empirical Bayes' estimates from the PMEM is valid, powerful and robust. This proposed method is very useful in most practical cases where the INLS-based tests and the general likelihood ratio test may not apply. We validate and compare various tests for finite samples using Monte Carlo simulations. Finally, we apply the proposed tests to an AIDS clinical trial to compare the antiviral potency between a 3-drug combination regimen and a 4-drug combination regimen. The proposed tests provide some significant evidence that the 4-drug regimen is more potent than the 3-drug regimen, while the naive methods fail to give a significant result.*To whom correspondence should be addressed.     

Modeling HIV persistence, the latent reservoir, and viral blips

HIV-1 eradication from infected individuals has not been achieved with the prolonged use of highly active antiretroviral therapy (HAART). The cellular reservoir for HIV-1 in resting memory CD4⁺ T cells remains a major obstacle to viral elimination. The reservoir does not decay significantly over long periods of time but is able to release replication-competent HIV-1 upon cell activation. Residual ongoing viral replication may likely occur in many patients because low levels of virus can be detected in plasma by sensitive assays and transient episodes of viremia, or HIV-1 blips, are often observed in patients even with successful viral suppression for many years. Here we review our current knowledge of the factors contributing to viral persistence, the latent reservoir, and blips, and mathematical models developed to explore them and their relationships. We show how mathematical modeling has helped improve our understanding of HIV-1 dynamics in patients on HAART and of the quantitative events underlying HIV-1 latency, reservoir stability, low-level viremic persistence, and emergence of intermittent viral blips. We also discuss treatment implications related to these studies.     

Synonymous substitution rates predict HIV disease progression as a result of underlying replication dynamics

Upon HIV transmission, some patients develop AIDS in only a few months, while others remain disease free for 20 or more years. This variation in the rate of disease progression is poorly understood and has been attributed to host genetics, host immune responses, co-infection, viral genetics, and adaptation. Here, we develop a new “relaxed-clock” phylogenetic method to estimate absolute rates of synonymous and nonsynonymous substitution through time. We identify an unexpected association between the synonymous substitution rate of HIV and disease progression parameters. Since immune activation is the major determinant of HIV disease progression, we propose that this process can also determine viral generation times, by creating favourable conditions for HIV replication. These conclusions may apply more generally to HIV evolution, since we also observed an overall low synonymous substitution rate for HIV-2, which is known to be less pathogenic than HIV-1 and capable of tempering the detrimental effects of immune activation. Humoral immune responses, on the other hand, are the major determinant of nonsynonymous rate changes through time in the envelope gene, and our relaxed-clock estimates support a decrease in selective pressure as a consequence of immune system collapse.     

An integrated modelling approach for R5–X4 mutation and HAART therapy assessment

We have modelled the within-patient evolutionary process during HIV infection using different methodologies. New viral strains arise during the course of HIV infection. These multiple strains of the virus are able to use different coreceptors, in particular the CCR5 and the CXCR4 (R5 and X4 phenotypes, respectively) influence the progression of the disease to the AIDS phase. We present a model of HIV early infection and CTLs response which describes the dynamics of R5 quasispecies, specifying the R5 to X4 switch and the effects of the immune response. We illustrate the dynamics of HIV multiple strains in the presence of multidrug HAART therapy. The HAART combined with X4 strain blocker drugs might help to reduce infectivity and lead to slower progression of the disease. On the methodology side, our model represents a paradigm of integrating formal methods and mathematical models as a general framework to study HIV multiple strains during disease progression, and it will inch towards providing help in selecting among vaccines and drug therapies. The results presented here are one of the rare cases of methodological cross comparison (stochastic and deterministic) and a novel implementation of model checking in therapy validation.     

Rapid human immunodeficiency virus decay in highly active antiretroviral therapy (HAART)-experienced children after starting mega-HAART

Increasing numbers of patients are treated with mega-highly active antiretroviral therapy (HAART), or multiple-combination antiretroviral therapy, in an attempt to overcome the viral resistance that has contributed to treatment failure. Studies of human immunodeficiency virus (HIV) viral dynamics are used to quantify the potency of a given regimen. While mega-HAART is expected to provide potent therapy, its potency among heavily experienced HIV-infected children who have failed previous treatment is untested. HIV dynamics studies performed in children have provided minimal information on viral dynamics during mega-HAART. The present study estimates first- and second-phase viral dynamics in six children on mega-HAART, following failure of combination therapy. The first phase of viral decay was rapid, relative to rates reported in previous pediatric studies (median delta = 0.778d(-1), range = 0.583 to 1.088, half-life 1 [t1(1/2)] = 0.894d), while the second phase revealed results similar to those of previous studies (median mu = 0.026d(-1), range = -0.005 to 0.206, t2(1/2) = 9.316d). This indicates that mega-HAART can provide potent therapy among heavily experienced pediatric patients.     

Genetic characterization of rebounding human immunodeficiency virus type 1 in plasma during multiple interruptions of highly active antiretroviral therapy

Various strategies of interrupting highly active antiretroviral therapy (HAART) are being investigated for the treatment of human immunodeficiency virus (HIV) infection. Interruptions of greater than 2 weeks frequently result in rebound of plasma HIV RNA. In order to discern changes in the viral population that might occur during cycles of treatment interruption, we evaluated the homology of HIV-1 envelope gene sequences over time in 12 patients who received four to seven cycles of 4 weeks off HAART followed by 8 weeks on HAART by using the heteroduplex tracking assay and novel statistical tools. HIV populations in 9 of 12 patients diverged from those found in the first cycle in at least one subsequent cycle. The substantial genetic changes noted in HIV env did not correlate with increased or decreased log changes in levels of plasma HIV RNA (P > 0.5). Thus, genetic changes in HIV env itself did not contribute in a systematic way to changes in levels of plasma viremia from cycle to cycle of treatment interruption. In addition, the data suggest that there may be multiple compartments contributing to the rebound of plasma viremia and to viral diversity from cycle to cycle of intermittent therapy.     

The amplitudes of viral blips in HIV-1 infected patients treated with antiretroviral therapy are power-law distributed

We previously reported that in patients treated with highly active antiretroviral therapy (HAART) who achieve viral load (VL) suppression, low fluctuations of viral load over the threshold of detection (viral blips) more than 4 weeks apart occur at random, with a frequency that does not change with longer times of observation. The etiology of viral blips is currently unknown, but viral blip frequency inversely correlates with the decay of the latent reservoir, whose stability has been proposed as the major hurdle to HIV eradication. We show here that the distribution of viral blip amplitudes observed in a group of 272 patients successfully treated with highly active antiretroviral therapy appears to be power-law distributed. Such a distribution can be theoretically generated by randomly sampling the arrival of asynchronous and overlapping elementary pulses of viremia, with asymptotic exponential decay of kinetics, thus suggesting that the low fluctuations of viremia observed in patients during HAART treatment is, in part, a discrete phenomenon consistent with random activation of latently infected cells or release of virus and infected cells into the blood compartment from unknown sites of active viral replication.     

The gut mucosal viral reservoir in HIV-infected patients is not the major source of rebound plasma viremia following interruption of highly active antiretroviral therapy

Interruption of suppressive highly active antiretroviral therapy (HAART) in HIV-infected patients leads to increased HIV replication and viral rebound in peripheral blood. Effects of therapy interruption on gut-associated lymphoid tissue (GALT) have not been well investigated. We evaluated longitudinal changes in viral replication and emergence of viral variants in the context of T cell homeostasis and gene expression in GALT of three HIV-positive patients who initiated HAART during primary HIV infection but opted to interrupt therapy thereafter. Longitudinal viral sequence analysis revealed that a stable proviral reservoir was established in GALT during primary HIV infection that persisted through early HAART and post-therapy interruption. Proviral variants in GALT and peripheral blood mononuclear cells (PBMCs) displayed low levels of genomic diversity at all times. A rapid increase in viral loads with a modest decline of CD4(+) T cells in peripheral blood was observed, while gut mucosal CD4(+) T cell loss was severe following HAART interruption. This was accompanied by increased mucosal gene expression regulating interferon (IFN)-mediated antiviral responses and immune activation, a profile similar to those found in HAART-naive HIV-infected patients. Sequence analysis of rebound virus suggested that GALT was not the major contributor to the postinterruption plasma viremia nor were GALT HIV reservoirs rapidly replaced by HIV rebound variants. Our data suggest an early establishment and persistence of viral reservoirs in GALT with minimal diversity. Early detection of and therapy for HIV infection may be beneficial in controlling viral evolution and limiting establishment of diverse viral reservoirs in the mucosal compartment.     

Intracellular Dynamics of HIV Infection

Early studies of HIV infection dynamics suggested that virus-producing HIV-infected cells had an average half-life of approximately 1 day. However, whether this average behavior is reflective of the dynamics of individual infected cells is unclear. Here, we use HIV-enhanced green fluorescent protein (EGFP) constructs and flow cytometry sorting to explore the dynamics of cell infection, viral protein production, and cell death in vitro. By following the numbers of productively infected cells expressing EGFP over time, we show that infected cell death slows down over time. Although infected cell death in vivo could be very different, our results suggest that the constant decay of cell numbers observed in vivo during antiretroviral treatment could reflect a balance of cell death and delayed viral protein production. We observe no correlation between viral protein production and death rate of productively infected cells, showing that viral protein production is not likely to be the sole determinant of the death of HIV-infected cells. Finally, we show that all observed features can be reproduced by a simple model in which infected cells have broad distributions of productive life spans, times to start viral protein production, and viral protein production rates. This broad spectrum of the level and timing of viral protein production provides new insights into the behavior and characteristics of HIV-infected cells.     

Limits on replenishment of the resting CD4+ T cell reservoir for HIV in patients on HAART

Whereas cells productively infected with human immunodeficiency virus type 1 (HIV-1) decay rapidly in the setting of highly active antiretroviral therapy (HAART), latently infected resting CD4(+) T cells decay very slowly, persisting for the lifetime of the patient and thus forming a stable reservoir for HIV-1. It has been suggested that the stability of the latent reservoir is due to low-level viral replication that continuously replenishes the reservoir despite HAART. Here, we offer the first quantitative study to our knowledge of inflow of newly infected cells into the latent reservoir due to viral replication in the setting of HAART. We make use of a previous observation that in some patients on HAART, the residual viremia is dominated by a predominant plasma clone (PPC) of HIV-1 not found in the latent reservoir. The unique sequence of the PPC serves as a functional label for new entries into the reservoir. We employ a simple mathematical model for the dynamics of the latent reservoir to constrain the inflow rate to between 0 and as few as 70 cells per day. The magnitude of the maximum daily inflow rate is small compared to the size of the latent reservoir, and therefore any inflow that occurs in patients on HAART is unlikely to significantly influence the decay rate of the reservoir. These results suggest that the stability of the latent reservoir is unlikely to arise from ongoing replication during HAART. Thus, intensification of standard HAART regimens should have minimal effects on the decay of the latent reservoir.     

Biotic Interactions and Sunlight Affect Persistence of Fecal Indicator Bacteria and Microbial Source Tracking Genetic Markers in the Upper Mississippi River

The sanitary quality of recreational waters that may be impacted by sewage is assessed by enumerating fecal indicator bacteria (FIB) (Escherichia coli and enterococci); these organisms are found in the gastrointestinal tracts of humans and many other animals, and hence their presence provides no information about the pollution source. Microbial source tracking (MST) methods can discriminate between different pollution sources, providing critical information to water quality managers, but relatively little is known about factors influencing the decay of FIB and MST genetic markers following release into aquatic environments. An in situ mesocosm was deployed at a temperate recreational beach in the Mississippi River to evaluate the effects of ambient sunlight and biotic interactions (predation, competition, and viral lysis) on the decay of culture-based FIB, as well as molecularly based FIB (Entero1a and GenBac3) and human-associated MST genetic markers (HF183 and HumM2) measured by quantitative real-time PCR (qPCR). In general, culturable FIB decayed the fastest, while molecularly based FIB and human-associated genetic markers decayed more slowly. There was a strong correlation between the decay of molecularly based FIB and that of human-associated genetic markers (r², 0.96 to 0.98; P < 0.0001) but not between culturable FIB and any qPCR measurement. Overall, exposure to ambient sunlight may be an important factor in the early-stage decay dynamics but generally was not after continued exposure (i.e., after 120 h), when biotic interactions tended to be the only/major influential determinant of persistence.     

High Heritability Is Compatible with the Broad Distribution of Set Point Viral Load in HIV Carriers

Set point viral load in HIV patients ranges over several orders of magnitude and is a key determinant of disease progression in HIV. A number of recent studies have reported high heritability of set point viral load implying that viral genetic factors contribute substantially to the overall variation in viral load. The high heritability is surprising given the diversity of host factors associated with controlling viral infection. Here we develop an analytical model that describes the temporal changes of the distribution of set point viral load as a function of heritability. This model shows that high heritability is the most parsimonious explanation for the observed variance of set point viral load. Our results thus not only reinforce the credibility of previous estimates of heritability but also shed new light onto mechanisms of viral pathogenesis.     

HIV-1 dynamics at different time scales under antiretroviral therapy

We exploit a model that considers three compartments: blood plasma (BP), lymphoid tissue-interstitial spaces (LT-IS), and follicular dendritic cells (FDC), for the HIV-1 dynamics under the application of highly active antiretroviral therapy (HAART) which allowed us to unravel distinct viral dynamics occurring in short- (2 days), middle- (21 days), and long-term (183 days) time scales. The different time scales are determined by the viral clearance rate, the ratio of productively infected CD4⁺ T cells to chronically infected cells, and the dissociation rate of HIV-1 complexes from FDC. This generates a scenario in which, after an initial transient stage, the viral BP dynamics decouples and becomes governed by the lymphoid tissue (LT) dynamics; in a later stage, a new decoupling occurs in which the LT-IS dynamics is slaved to that of the FDC dynamics. We observed an initial increase in the viremia after HAART in a patient who did not receive protease inhibitors (PI). By means of the above-mentioned model we were able to highlight the relevant parameters which need to be estimated at three different time scales after HAART.     

vFitness: a web-based computing tool for improving estimation of <Emphasis Type="Italic">in vitro</Emphasis> HIV-1 fitness experiments

Background  

The replication rate (or fitness) between viral variants has been investigated in vivo and in vitro for human immunodeficiency virus (HIV). HIV fitness plays an important role in the development and persistence of drug resistance. The accurate estimation of viral fitness relies on complicated computations based on statistical methods. This calls for tools that are easy to access and intuitive to use for various experiments of viral fitness.     

T cell selection and differentiation in AIDS disease: the model of HIV-discordant monozygotic twins

The model of monozygotic twins has been repeatedly studied to control the genetic and age-specific effects on HIV disease. Focusing on this natural model, the expression of CD27/CD45RA differentiation markers and the distribution of the Vbeta TCR repertoire was analyzed on CD4+ and CD8+ T cells. In our HIV-discordant monozygotic twins, a significant reduction of naive T cells and a parallel accumulation of effector/memory T cells was induced by HIV infection, as well as a skewing of T cell repertoire evidenced by VbetaTCR analysis. The block of HIV replication by highly active antiretroviral therapy (HAART) restored most of the T cell maturation and selection process, with some exception among CTL differentiation and repertoire. Altogether, the model of HIV-discordant monozygotic twins is a valuable tool showing that HAART is not able to completely restore the CTL profile.     

Greater adherence to highly active antiretroviral therapy (HAART) between pregnant versus non-pregnant women living with HIV.

One of the most remarkable advances in the control of the HIV/AIDS pandemic has been the introduction of highly active antiretroviral therapy (HAART). The use of HAART has been associated to reductions in AIDS-related mortality in most countries where HAART is available. Unfortunately, the adherence required to keep good control of viral replication is higher than what is required in other medical conditions. Several studies have shown a relationship between adherence and viral suppression ranging between 90-95% required for complete suppression. Multiple factors have been related to adherence among which are: gender, racial/ethnic distribution, age, personality traits, education, alcohol use and others. For women living with HIV there might be additional difficulties to handle in order to be adherent (i.e. multiple family responsibilities). A group of 165 women living with HIV attending a multidisciplinary clinic were interviewed with a 3-day adherence questionnaire. Correlation with clinical information was obtained from the Clinic Data Base. A total of 37 pregnant and 128 non-pregnant women were included in this analysis, 96% of which were on HAART. Complete adherence (100%) was reported by 91% of the pregnant and 70% of the non-pregnant women. (Fisher's exact test 0.009). The majority, 99% knew the names of their medications. There were no differences among groups in scholarity, history or actual cigarette smoking, history or actual drug use, CD4 lymphocyte counts (median or proportion below 350 cells/mm3), mean HIV RNA viral load or the proportion of patients with HIV RNA < 1,000 copies/ml. The transmission rate for the sample of pregnant women was zero. The reported adherence rates to HAART for women living with HIV were highest among the pregnant women. This difference was statistically significant (Chi Sq 0.05). The great majority (93%) reported knowing the names of the medications. In spite of reported barriers to adherence, pregnant women attending a multidisciplinary clinic for HIV care and research, reported good rates of adherence to HAART. This is also reflected in the good perinatal outcomes. Non-pregnant women with lower adherence rates might need additional interventions to improve adherence.     

CCL3L1-CCR5 genotype influences durability of immune recovery during antiretroviral therapy of HIV-1-infected individuals

The basis for the extensive variability seen in the reconstitution of CD4(+) T cell counts in HIV-infected individuals receiving highly active antiretroviral therapy (HAART) is not fully known. Here, we show that variations in CCL3L1 gene dose and CCR5 genotype, but not major histocompatibility complex HLA alleles, influence immune reconstitution, especially when HAART is initiated at <350 CD4(+) T cells/mm(3). The CCL3L1-CCR5 genotypes favoring CD4(+) T cell recovery are similar to those that blunted CD4(+) T cell depletion during the time before HAART became available (pre-HAART era), suggesting that a common CCL3L1-CCR5 genetic pathway regulates the balance between pathogenic and reparative processes from early in the disease course. Hence, CCL3L1-CCR5 variations influence HIV pathogenesis even in the presence of HAART and, therefore, may prospectively identify subjects in whom earlier initiation of therapy is more likely to mitigate immunologic failure despite viral suppression by HAART. Furthermore, as reconstitution of CD4(+) cells during HAART is more sensitive to CCL3L1 dose than to CCR5 genotypes, CCL3L1 analogs might be efficacious in supporting immunological reconstitution.