Modeling the short-, middle- and long-term viral load responses for comparing estimated dynamic parameters

A virologic marker, the number of HIV RNA copies or viral load, is currently used to evaluate antiviral therapies in AIDS clinical trials. This marker can be used to assess the antiviral potency of therapies, but is easily affected by drug exposures, drug resistance and other factors during the long-term treatment evaluation process. The study of HIV dynamics is one of the most important development in recent AIDS research for understanding the pathogenesis of HIV-1 infection and antiviral treatment strategies. Although many HIV dynamic models have been proposed by AIDS researchers in the last decade, they have only been used to quantify short-term viral dynamics and do not correctly describe long-term virologic responses to antiretroviral treatment. In other words, these simple viral dynamic models can only be used to fit short-term viral load data for estimating dynamic parameters. In this paper, a mechanism-based differential equation models is introduced for characterizing the long-term viral dynamics with antiretroviral therapy. We applied this model to fit different segments of the viral load trajectory data from a simulation experiment and an AIDS clinical trial study, and found that the estimates of dynamic parameters from our modeling approach are very consistent. We may conclude that our model can not only characterize long-term viral dynamics, but can also quantify short- and middle-term viral dynamics. It suggests that if there are enough data in the early stage of the treatment, the results from our modeling based on short-term information can be used to capture the performance of long-term care with HIV-1 infected patients.     

Design of long-term HIV dynamic studies using semiparametric mixed-effects models

Studies of HIV dynamics in AIDS research are very important in understanding the pathogenesis of HIV-1 infection and also in assessing the effectiveness of antiviral therapies. There are many AIDS clinical trials on HIV dynamics currently in development worldwide, giving rise to many design issues yet to be addressed. For example, most studies are focused on short-term viral dynamics and the existing models may not be applicable to describe long-term virologic response. In this paper, we use a simulation-based approach to study the designs of long-term viral dynamics under semiparametric nonlinear mixed-effects models. These models not only can preserve the meaningful interpretation of the short-term HIV dynamics, but also characterize the long-term virologic responses to antiretroviral (ARV) treatment. We investigate a number of feasible clinical protocol designs similar to those currently used in AIDS clinical trials. In particular, we evaluate whether earlier samplings can result in more useful information about the viral response trajectory; we also evaluate the effectiveness of two strategies: more frequent samplings per subject with fewer subjects versus fewer samplings per subject with more subjects while keeping the total number of samplings constant. The results of our investigation provide quantitative guidance for designing and selecting ARV therapy.     

Natural variation in HIV infection: Monte Carlo estimates that include CD8 effector cells

Viral load and CD4 T-cell counts in patients infected with the human immunodeficiency virus (HIV) are commonly used to guide clinical decisions regarding drug therapy or to assess therapeutic outcomes in clinical trials. However, random fluctuations in these markers of infection can obscure clinically significant change. We employ a Monte Carlo simulation to investigate contributing factors in the expected variability in CD4 T-cell count and viral load due solely to the stochastic nature of HIV infection. The simulation includes processes that contribute to the variability in HIV infection including CD4 and CD8 T-cell population dynamics as well as T-cell activation and proliferation. The simulation results may reconcile the wide range of variabilities in viral load observed in clinical studies, by quantifying correlations between viral load measurements taken days or weeks apart. The sensitivity of variability in T-cell count and viral load to changes in the lifetimes of CD4 and CD8 T-cells is investigated, as well as the effects of drug therapy.     

Population HIV-1 dynamics in vivo: applicable models and inferential tools for virological data from AIDS clinical trials

In this paper, we introduce a novel application of hierarchical nonlinear mixed-effect models to HIV dynamics. We show that a simple model with a sum of exponentials can give a good fit to the observed clinical data of HIV-1 dynamics (HIV-1 RNA copies) after initiation of potent antiviral treatments and can also be justified by a biological compartment model for the interaction between HIV and its host cells. This kind of model enjoys both biological interpretability and mathematical simplicity after reparameterization and simplification. A model simplification procedure is proposed and illustrated through examples. We interpret and justify various simplified models based on clinical data taken during different phases of viral dynamics during antiviral treatments. We suggest the hierarchical nonlinear mixed-effect model approach for parameter estimation and other statistical inferences. In the context of an AIDS clinical trial involving patients treated with a combination of potent antiviral agents, we show how the models may be used to draw biologically relevant interpretations from repeated HIV-1 RNA measurements and demonstrate the potential use of the models in clinical decision-making.     

Fighting a virus with a virus: a dynamic model for HIV-1 therapy

A mathematical model examined a potential therapy for controlling viral infections using genetically modified viruses. The control of the infection is an indirect effect of the selective elimination by an engineered virus of infected cells that are the source of the pathogens. Therefore, this engineered virus could greatly compensate for a dysfunctional immune system compromised by AIDS. In vitro studies using engineered viruses have been shown to decrease the HIV-1 load about 1000-fold. However, the efficacy of this potential treatment for reducing the viral load in AIDS patients is unknown. The present model studied the interactions among the HIV-1 virus, its main host cell (activated CD4+ T cells), and a therapeutic engineered virus in an in vivo context; and it examined the conditions for controlling the pathogen. This model predicted a significant drop in the HIV-1 load, but the treatment does not eradicate HIV. A basic estimation using a currently engineered virus indicated an HIV-1 load reduction of 92% and a recovery of host cells to 17% of their normal level. Greater success (98% HIV reduction, 44% host cells recovery) is expected as more competent engineered viruses are designed. These results suggest that therapy using viruses could be an alternative to extend the survival of AIDS patients.     

Human immunodeficiency virus drug therapy and virus load.

Analysis of the short-term dynamics of human immunodeficiency virus (HIV) type 1 infection in response to drug therapy has elucidated crucial kinetic properties of viral dynamics in vivo (D. D. Ho et al., Nature 373:123-126, 1995; A. S. Perelson et al., Science 271:1582-1586, 1996; X. Wei et al., Nature 373:117-122, 1995). Here we investigated long-term changes in virus load in patients treated with a combination of lamivudine and zidovudine to identify principal factors responsible for the observed 10- to 100-fold sustained suppression of virus load in vivo. Interestingly, most standard accounts of virus dynamics cannot explain a large sustained reduction without shifting the virus very close to extinction. The effect can be explained by taking into consideration either (i) the immune response against HIV, (ii) the killing of uninfected CD4 cells, or (iii) the differential efficacies of the drugs in different cell populations.     

The PDZ-adaptor protein syntenin-1 regulates HIV-1 entry

Syntenin-1 is a cytosolic adaptor protein involved in several cellular processes requiring polarization. Human immunodeficiency virus type 1 (HIV-1) attachment to target CD4(+) T-cells induces polarization of the viral receptor and coreceptor, CD4/CXCR4, and cellular structures toward the virus contact area, and triggers local actin polymerization and phosphatidylinositol 4,5-bisphosphate (PIP(2)) production, which are needed for successful HIV infection. We show that syntenin-1 is recruited to the plasma membrane during HIV-1 attachment and associates with CD4, the main HIV-1 receptor. Syntenin-1 overexpression inhibits HIV-1 production and HIV-mediated cell fusion, while syntenin depletion specifically increases HIV-1 entry. Down-regulation of syntenin-1 expression reduces F-actin polymerization in response to HIV-1. Moreover, HIV-induced PIP(2) accumulation is increased in syntenin-1-depleted cells. Once the virus has entered the target cell, syntenin-1 polarization toward the viral nucleocapsid is lost, suggesting a spatiotemporal regulatory role of syntenin-1 in actin remodeling, PIP(2) production, and the dynamics of HIV-1 entry.     

Treatment-mediated alterations in HIV fitness preserve CD4+ T cell counts but have minimal effects on viral load

For most HIV-infected patients, antiretroviral therapy controls viral replication. However, in some patients drug resistance can cause therapy to fail. Nonetheless, continued therapy with a failing regimen can preserve or even lead to increases in CD4+ T cell counts. To understand the biological basis of these observations, we used mathematical models to explain observations made in patients with drug-resistant HIV treated with enfuvirtide (ENF/T-20), an HIV-1 fusion inhibitor. Due to resistance emergence, ENF was removed from the drug regimen, drug-sensitive virus regrown, and ENF was re-administered. We used our model to study the dynamics of plasma-viral RNA and CD4+ T cell levels, and the competition between drug-sensitive and resistant viruses during therapy interruption and re-administration. Focusing on resistant viruses carrying the V38A mutation in gp41, we found ENF-resistant virus to be 17±3% less fit than ENF-sensitive virus in the absence of the drug, and that the loss of resistant virus during therapy interruption was primarily due to this fitness cost. Using viral dynamic parameters estimated from these patients, we show that although re-administration of ENF cannot suppress viral load, it can, in the presence of resistant virus, increase CD4+ T cell counts, which should yield clinical benefits. This study provides a framework to investigate HIV and T cell dynamics in patients who develop drug resistance to other antiretroviral agents and may help to develop more effective strategies for treatment.     

HIV-1 infection and low steady state viral loads

Highly active antiretroviral therapy (HAART) reduces the viral burden in human immunodeficiency virus type 1 (HIV-1) infected patients below the threshold of detectability. However, substantial evidence indicates that viral replication persists in these individuals. In this paper we examine the ability of several biologically motivated models of HIV-1 dynamics to explain sustained low viral loads. At or near drug efficacies that result in steady state viral loads below detectability, most models are extremely sensitive to small changes in drug efficacy. We argue that if these models reflect reality many patients should have cleared the virus, contrary to observation. We find that a model in which the infected cell death rate is dependent on the infected cell density does not suffer this shortcoming. The shortcoming is also overcome in two more conventional models that include small populations of cells in which the drug is less effective than in the main population, suggesting that difficulties with drug penetrance and maintenance of effective intracellular drug concentrations in all cells susceptible to HIV infection may underlie ongoing viral replication.     

A model of HIV-1 infection with two time delays: mathematical analysis and comparison with patient data

Mathematical models have made considerable contributions to our understanding of HIV dynamics. Introducing time delays to HIV models usually brings challenges to both mathematical analysis of the models and comparison of model predictions with patient data. In this paper, we incorporate two delays, one the time needed for infected cells to produce virions after viral entry and the other the time needed for the adaptive immune response to emerge to control viral replication, into an HIV-1 model. We begin model analysis with proving the positivity and boundedness of the solutions, local stability of the infection-free and infected steady states, and uniform persistence of the system. By developing a few Lyapunov functionals, we obtain conditions ensuring global stability of the steady states. We also fit the model including two delays to viral load data from 10 patients during primary HIV-1 infection and estimate parameter values. Although the delay model provides better fits to patient data (achieving a smaller error between data and modeling prediction) than the one without delays, we could not determine which one is better from the statistical standpoint. This highlights the need of more data sets for model verification and selection when we incorporate time delays into mathematical models to study virus dynamics.     

Hierarchical Bayesian methods for estimation of parameters in a longitudinal HIV dynamic system

HIV dynamics studies have significantly contributed to the understanding of HIV infection and antiviral treatment strategies. But most studies are limited to short-term viral dynamics due to the difficulty of establishing a relationship of antiviral response with multiple treatment factors such as drug exposure and drug susceptibility during long-term treatment. In this article, a mechanism-based dynamic model is proposed for characterizing long-term viral dynamics with antiretroviral therapy, described by a set of nonlinear differential equations without closed-form solutions. In this model we directly incorporate drug concentration, adherence, and drug susceptibility into a function of treatment efficacy, defined as an inhibition rate of virus replication. We investigate a Bayesian approach under the framework of hierarchical Bayesian (mixed-effects) models for estimating unknown dynamic parameters. In particular, interest focuses on estimating individual dynamic parameters. The proposed methods not only help to alleviate the difficulty in parameter identifiability, but also flexibly deal with sparse and unbalanced longitudinal data from individual subjects. For illustration purposes, we present one simulation example to implement the proposed approach and apply the methodology to a data set from an AIDS clinical trial. The basic concept of the longitudinal HIV dynamic systems and the proposed methodologies are generally applicable to any other biomedical dynamic systems.     

Modeling adaptive regulatory T-cell dynamics during early HIV infection

Regulatory T-cells (Tregs) are a subset of CD4(+) T-cells that have been found to suppress the immune response. During HIV viral infection, Treg activity has been observed to have both beneficial and deleterious effects on patient recovery; however, the extent to which this is regulated is poorly understood. We hypothesize that this dichotomy in behavior is attributed to Treg dynamics changing over the course of infection through the proliferation of an 'adaptive' Treg population which targets HIV-specific immune responses. To investigate the role Tregs play in HIV infection, a delay differatial equation model was constructed to examine (1) the possible existence of two distinct Treg populations, normal (nTregs) and adaptive (aTregs), and (2) their respective effects in limiting viral load. Sensitivity analysis was performed to test parameter regimes that show the proportionality of viral load with adaptive regulatory populations and also gave insight into the importance of downregulation of CD4(+) cells by normal Tregs on viral loads. Through the inclusion of Treg populations in the model, a diverse array of viral dynamics was found. Specifically, oscillatory and steady state behaviors were both witnessed and it was seen that the model provided a more accurate depiction of the effector cell population as compared with previous models. Through further studies of adaptive and normal Tregs, improved treatments for HIV can be constructed for patients and the viral mechanisms of infection can be further elucidated.     

Predicting differential responses to structured treatment interruptions during HAART

Highly active antiretroviral therapy (HAART) has been used clinically in various administration schemes for several years. However, due to the development of drug resistance, evolution of viral strains, serious side effects, and poor patient compliance, the combination of drugs used in HAART fails to effectively contain virus long term in a high proportion of patients. Our group and others have suggested a change to the usual regimen of continuous HAART through structured treatment interruptions (STIs). STIs may provide similar clinical benefits as continuous treatment such as reduced viral loads and reestablishment of CD4⁺ T cells while allowing patients drug holidays. We explore the use of STIs using a previously published model that accurately represents CD4⁺ T-cell counts and viral loads during both untreated HIV-1 infection and HAART therapy. We simulate the effects of different STI regimens including weekly and monthly interruptions together with variations in treatment initiation time. We predict that differential responses to STIs as observed in conflicting clinical trial data are impacted by the duration of the interruption, stage of infection at initiation of treatment, strength of the immune system in suppressing virus, or pre-therapy CD4⁺ T-cell count or virus load. Our results indicate that dynamics occurring below the limit of detection (LOD) are influenced by these factors, and contribute to reemergence or suppression of virus during interruptions. Simulations predict that short-term viral suppression with varying interruptions strategies does not guarantee long-term clinical benefit.     

Inclusion of Vpr accessory gene in a plasmid vaccine cocktail markedly reduces Nef vaccine effectiveness in vivo resulting in CD4 cell loss and increased viral loads in rhesus macaques

We compared the immunogenicity of plasmid vaccines containing multiple human immunodeficiency virus (HIV) antigens and found that covaccination with plasmids expressing HIV-1 14 kDa vpr gene product profoundly reduces antigen-specific CD8-mediated cytotoxic T-cell activity (CTL). Interestingly, Th1 type responses against codelivered antigens (pGag-Pol, pNef, etc.) encoded by the plasmid vaccines were suppressed. This suggested that vpr might compromise CD8 T-cell immunity in vivo during infection. A pilot primate vaccine study was designed to test the hypothesis to compare the following groups: unvaccinated controls, animals vaccinated without simean immunodeficiency virus (SIV)-Nef antigen plasmid, and animals covaccinated with the identical plasmid antigen and a plasmid construct encoding SIV Vpr/Vpx. Animals were subsequently challenged intrarectally with pathogenic SIVmac251 after the final vaccination of a multiple immunization protocol. Control animals were all infected and exhibited high viral loads and rapid CD4+ T-cell loss. In contrast, the Nef plasmid-vaccinated animals were also infected but exhibited preservation of CD4+ T-cells and a multilog reduction in viral load compared with controls. Animals covaccinated multiple times with the Nef vaccine and pVpr/Vpx plasmid suffered rapid and profound loss of CD4+ T-cells. These results have important implications for the design of multicomponent and particle vaccines for HIV-1 as well as for our understanding of HIV/SIV pathogenesis in vivo.     

Correlates of cytotoxic T-lymphocyte-mediated virus control: implications for immunosuppressive infections and their treatment

A very important question in immunology is to determine which factors decide whether an immune response can efficiently clear or control a viral infection, and under what circumstances we observe persistent viral replication and pathology. This paper summarizes how mathematical models help us gain new insights into these questions, and explores the relationship between antiviral therapy and long-term immunological control in human immunodeficiency virus (HIV) infection. We find that cytotoxic T lymphocyte (CTL) memory, defined as antigen-independent persistence of CTL precursors, is necessary for the CTL response to clear an infection. The presence of such a memory response is associated with the coexistence of many CTL clones directed against multiple epitopes. If CTL memory is inefficient, then persistent replication can be established. This outcome is associated with a narrow CTL response directed against only one or a few viral epitopes. If the virus replicates persistently, occurrence of pathology depends on the level of virus load at equilibrium, and this can be determined by the overall efficacy of the CTL response. Mathematical models suggest that controlled replication is reflected by a positive correlation between CTLs and virus load. On the other hand, uncontrolled viral replication results in higher loads and the absence of a correlation between CTLs and virus load. A negative correlation between CTLs and virus load indicates that the virus actively impairs immunity, as observed with HIV. Mathematical models and experimental data suggest that HIV persistence and pathology are caused by the absence of sufficient CTL memory. We show how mathematical models can help us devise therapy regimens that can restore CTL memory in HIV patients and result in long-term immunological control of the virus in the absence of life-long treatment.     

Viral Dynamics during Structured Treatment Interruptions of Chronic Human Immunodeficiency Virus Type 1 Infection

Although antiviral agents which block human immunodeficiency virus (HIV) replication can result in long-term suppression of viral loads to undetectable levels in plasma, long-term therapy fails to eradicate virus, which generally rebounds after a single treatment interruption. Multiple structured treatment interruptions (STIs) have been suggested as a possible strategy that may boost HIV-specific immune responses and control viral replication. We analyze viral dynamics during four consecutive STI cycles in 12 chronically infected patients with a history (>2 years) of viral suppression under highly active antiretroviral therapy. We fitted a simple model of viral rebound to the viral load data from each patient by using a novel statistical approach that allows us to overcome problems of estimating viral dynamics parameters when there are many viral load measurements below the limit of detection. There is an approximate halving of the average viral growth rate between the first and fourth STI cycles, yet the average time between treatment interruption and detection of viral loads in the plasma is approximately the same in the first and fourth interruptions. We hypothesize that reseeding of viral reservoirs during treatment interruptions can account for this discrepancy, although factors such as stochastic effects and the strength of HIV-specific immune responses may also affect the time to viral rebound. We also demonstrate spontaneous drops in viral load in later STIs, which reflect fluctuations in the rates of viral production and/or clearance that may be caused by a complex interaction between virus and target cells and/or immune responses.     

Residual Viremia in Treated HIV+ Individuals

Antiretroviral therapy (ART) effectively controls HIV infection, suppressing HIV viral loads. However, some residual virus remains, below the level of detection, in HIV-infected patients on ART. The source of this viremia is an area of debate: does it derive primarily from activation of infected cells in the latent reservoir, or from ongoing viral replication? Observations seem to be contradictory: there is evidence of short term evolution, implying that there must be ongoing viral replication, and viral strains should thus evolve. However, phylogenetic analyses, and rare emergent drug resistance, suggest no long-term viral evolution, implying that virus derived from activated latent cells must dominate. We use simple deterministic and stochastic models to gain insight into residual viremia dynamics in HIV-infected patients. Our modeling relies on two underlying assumptions for patients on suppressive ART: that latent cell activation drives viral dynamics and that the reproductive ratio of treated infection is less than 1. Nonetheless, the contribution of viral replication to residual viremia in patients on ART may be non-negligible. However, even if the portion of viremia attributable to viral replication is significant, our model predicts (1) that latent reservoir re-seeding remains negligible, and (2) some short-term viral evolution is permitted, but long-term evolution can still be limited: stochastic analysis of our model shows that de novo emergence of drug resistance is rare. Thus, our simple models reconcile the seemingly contradictory observations on residual viremia and, with relatively few parameters, recapitulates HIV viral dynamics observed in patients on suppressive therapy.     

Association between virus-specific T-cell responses and plasma viral load in human immunodeficiency virus type 1 subtype C infection

Virus-specific T-cell immune responses are important in restraint of human immunodeficiency virus type 1 (HIV-1) replication and control of disease. Plasma viral load is a key determinant of disease progression and infectiousness in HIV infection. Although HIV-1 subtype C (HIV-1C) is the predominant virus in the AIDS epidemic worldwide, the relationship between HIV-1C-specific T-cell immune responses and plasma viral load has not been elucidated. In the present study we address (i) the association between the level of plasma viral load and virus-specific immune responses to different HIV-1C proteins and their subregions and (ii) the specifics of correlation between plasma viral load and T-cell responses within the major histocompatibility complex (MHC) class I HLA supertypes. Virus-specific immune responses in the natural course of HIV-1C infection were analyzed in the gamma interferon (IFN-gamma)-enzyme-linked immunospot assay by using synthetic overlapping peptides corresponding to the HIV-1C consensus sequence. For Gag p24, a correlation was seen between better T-cell responses and lower plasma viral load. For Nef, an opposite trend was observed where a higher T-cell response was more likely to be associated with a higher viral load. At the level of the HLA supertypes, a lower viral load was associated with higher T-cell responses to Gag p24 within the HLA A2, A24, B27, and B58 supertypes, in contrast to the absence of such a correlation within the HLA B44 supertype. The present study demonstrated differential correlations (or trends to correlation) in various HIV-1C proteins, suggesting (i) an important role of the HIV-1C Gag p24-specific immune responses in control of viremia and (ii) more rapid viral escape from immune responses to Nef with no restraint of plasma viral load. Correlations between the level of IFN-gamma-secreting T cells and viral load within the MHC class I HLA supertypes should be considered in HIV vaccine design and efficacy trials.