Antigen-driven CD4+ T cell and HIV-1 dynamics: residual viral replication under highly active antiretroviral therapy

Stochastic modelling of viral blips in HIV-1-infected patients: effects of inhomogeneous density fluctuations

We propose a stochastic model of HIV-1 infection dynamics under HAART in order to analyse the origin and dynamics of the so-called viral blips, i.e. episodes of transient viremia that occur in the phase of where the disease remains in a latent state during which the viral load raises above the detection limit of standard clinical assays. Based on prior work in the subject, we consider an infection model in which latently infected cell compartment sustains a residual (latent) infection over long periods of time. Unlike previous models, we include the effects of inhomogeneities in cell and virus concentration in the blood stream. We further consider the effect of burst virion production. By comparing with the experimental results obtained during a study in which intensive sampling was carried out on HIV-1-infected patients undergoing HAART over a long period of time, we conclude that our model supports the hypothesis that viral blips are consistent with random fluctuations around the average viral load. We further observe that agreement between our simulation results and the blip statistics obtained in the aforementioned study improves when burst virion production is considered. We also study the effect of sample manipulation artifacts on the results produced by our model, in particular, that of the post-extraction handling time, i.e. the time elapsed between sample extraction and actual test. Our results support the notion that the statistics of viral blips can be critically affected by such artifacts.

A stochastic model of latently infected cell reactivation and viral blip generation in treated HIV patients

Motivated by viral persistence in HIV+ patients on long-term anti-retroviral treatment (ART), we present a stochastic model of HIV viral dynamics in the blood stream. We consider the hypothesis that the residual viremia in patients on ART can be explained principally by the activation of cells latently infected by HIV before the initiation of ART and that viral blips (clinically-observed short periods of detectable viral load) represent large deviations from the mean. We model the system as a continuous-time, multi-type branching process. Deriving equations for the probability generating function we use a novel numerical approach to extract the probability distributions for latent reservoir sizes and viral loads. We find that latent reservoir extinction-time distributions underscore the importance of considering reservoir dynamics beyond simply the half-life. We calculate blip amplitudes and frequencies by computing complete viral load probability distributions, and study the duration of viral blips via direct numerical simulation. We find that our model qualitatively reproduces short small-amplitude blips detected in clinical studies of treated HIV infection. Stochastic models of this type provide insight into treatment-outcome variability that cannot be found from deterministic models.

Superinfection with a heterologous HIV strain per se does not lead to faster progression

BACKGROUND

It has been suggested that superinfection of HIV positive individuals with heterologous HIV strains could lead to faster progression to AIDS, generating concern over the risks of exposure to new infections in those already infected.

METHODS

A mathematical model of the within-host dynamics of two sequential infections with strains of HIV describing activation and infection of immune cells was developed. Multiple stochastic realizations describing progression to AIDS in the individual were generated, comparing the situation with and without superinfection.

RESULTS

It was found that the susceptibility of immune cells to dual infection is crucial to the outcome of HIV superinfection. A low susceptibility leads to competitive exclusion between the strains and a high susceptibility may lead to co-existence if the superinfecting strain is sufficiently fit. It was also found that only superinfection with a fitter strain leads to faster progression to AIDS, rather than superinfection per se.

CONCLUSION

In theory, a superinfection event with a heterologous strain of HIV does not lead to faster progression to AIDS. Unless superinfection allows the spread of fitter virus, it should not be of concern for public health.

Modeling latently infected cell activation: viral and latent reservoir persistence, and viral blips in HIV-infected patients on potent therapy

Although potent combination therapy is usually able to suppress plasma viral loads in HIV-1 patients to below the detection limit of conventional clinical assays, a low level of viremia frequently can be detected in plasma by more sensitive assays. Additionally, many patients experience transient episodes of viremia above the detection limit, termed viral blips, even after being on highly suppressive therapy for many years. An obstacle to viral eradication is the persistence of a latent reservoir for HIV-1 in resting memory CD4(+) T cells. The mechanisms underlying low viral load persistence, slow decay of the latent reservoir, and intermittent viral blips are not fully characterized. The quantitative contributions of residual viral replication to viral and the latent reservoir persistence remain unclear. In this paper, we probe these issues by developing a mathematical model that considers latently infected cell activation in response to stochastic antigenic stimulation. We demonstrate that programmed expansion and contraction of latently infected cells upon immune activation can generate both low-level persistent viremia and intermittent viral blips. Also, a small fraction of activated T cells revert to latency, providing a potential to replenish the latent reservoir. By this means, occasional activation of latently infected cells can explain the variable decay characteristics of the latent reservoir observed in different clinical studies. Finally, we propose a phenomenological model that includes a logistic term representing homeostatic proliferation of latently infected cells. The model is simple but can robustly generate the multiphasic viral decline seen after initiation of therapy, as well as low-level persistent viremia and intermittent HIV-1 blips. Using these models, we provide a quantitative and integrated prospective into the long-term dynamics of HIV-1 and the latent reservoir in the setting of potent antiretroviral therapy.

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.

Asymmetric division of activated latently infected cells may explain the decay kinetics of the HIV-1 latent reservoir and intermittent viral blips

Most HIV-infected patients when treated with combination antiretroviral therapy achieve viral loads that are below the current limit of detection of standard assays after a few months. Despite this, virus eradication from the host has not been achieved. Latent, replication-competent HIV-1 can generally be identified in resting memory CD4(+) T cells in patients with "undetectable" viral loads. Turnover of these cells is extremely slow but virus can be released from the latent reservoir quickly upon cessation of therapy. In addition, a number of patients experience transient episodes of viremia, or HIV-1 blips, even with suppression of the viral load to below the limit of detection for many years. The mechanisms underlying the slow decay of the latent reservoir and the occurrence of intermittent viral blips have not been fully elucidated. In this study, we address these two issues by developing a mathematical model that explores a hypothesis about latently infected cell activation. We propose that asymmetric division of latently infected cells upon sporadic antigen encounter may both replenish the latent reservoir and generate intermittent viral blips. Interestingly, we show that occasional replenishment of the latent reservoir induced by reactivation of latently infected cells may reconcile the differences between the divergent estimates of the half-life of the latent reservoir in the literature.

Transient viremia, plasma viral load, and reservoir replenishment in HIV-infected patients on antiretroviral therapy

When antiretroviral therapy (ART) is administered for long periods to HIV-1-infected patients, most achieve viral loads that are "undetectable" by standard assay methods (ie, HIV-1 RNA <50 copies/mL). Despite sustaining viral loads lower than the level of detection, a number of patients experience unexplained episodes of transient viremia or viral "blips." We propose that transient activation of the immune system by infectious agents may explain these episodes of viremia. Using 2 different mathematical models, one in which blips arise because of target cell activation and subsequent infection and another in which latent cell activation generates blips, we establish a nonlinear (power law) relationship between blip amplitude and viral load (under ART) that suggest blips should be of lower amplitude, and thus harder to detect, as increasingly potent therapy is used. This effect can be more profound than is predicted by simply lowering the baseline viral load from which blips originate. Finally, we suggest that sporadic immune activation may elevate the level of chronically infected cells and replenish viral reservoirs, including the latent cell reservoir, providing a mechanism for recurrent viral blips and low levels of viremia under ART.

Modelling the human immune system by combining bioinformatics and systems biology approaches

Over the past decade a number of bioinformatics tools have been developed that use genomic sequences as input to predict to which parts of a microbe the immune system will react, the so-called epitopes. Many predicted epitopes have later been verified experimentally, demonstrating the usefulness of such predictions. At the same time, simulation models have been developed that describe the dynamics of different immune cell populations and their interactions with microbes. These models have been used to explain experimental findings where timing is of importance, such as the time between administration of a vaccine and infection with the microbe that the vaccine is intended to protect against. In this paper, we outline a framework for integration of these two approaches. As an example, we develop a model in which HIV dynamics are correlated with genomics data. For the first time, the fitness of wild type and mutated virus are assessed by means of a sequence-dependent scoring matrix, derived from a BLOSUM matrix, that links protein sequences to growth rates of the virus in the mathematical model. A combined bioinformatics and systems biology approach can lead to a better understanding of immune system-related diseases where both timing and genomic information are of importance.

Role of avidity and breadth of the CD4 T cell response in progression to AIDS

The great variability in the time between infection with HIV and the onset of AIDS has been the object of intense study. In the current work, we examine a mathematical model that focuses on the role of immune response variability between patients. We study the effect of variation in both the avidity and the breadth of the immune response on within-patient disease dynamics, viral setpoint and time to AIDS. We conclude that immune response variability can explain the observed variability in disease progression to a large extent. It turns out that the avidity, more than the breadth of the immune response, determines disease progression, and that the average avidity of the five best clones is a much better correlate for disease progression than the total number of clones responding. For the design of vaccines, this would suggest that, if given the choice between stimulating a broader, but average avidity response or a narrower high-avidity response, the latter option would yield better control of virus load and consequently slow down disease progression.

Adherence to antiretroviral therapy and its impact on clinical outcome in HIV-infected patients

We analyse data on patient adherence to prescribed regimens and surrogate markers of clinical outcome for 168 human immunodeficiency virus infected patients treated with antiretroviral therapy. Data on patient adherence consisted of dose-timing measurements collected for an average of 12 months per patient via electronic monitoring of bottle opening events. We first discuss how such data can be presented to highlight suboptimal adherence patterns and between-patient differences, before introducing two novel methods by which such data can be statistically modelled. Correlations between adherence and subsequent measures of viral load and CD4+T-cell counts are then evaluated. We show that summary measures of short-term adherence, which incorporate pharmacokinetic and pharmacodynamic data on the monitored regimen, predict suboptimal trends in viral load and CD4+T-cell counts better than measures based on adherence data alone.

Comparative potency of three antiretroviral therapy regimes in primary HIV infection

BACKGROUND

Virally mediated destruction of HIV-specific CD4+ T-cells in primary HIV infection (PHI) may be abrogated by potent antiretroviral therapy (ART) started in acute infection. To best achieve the most rapid reduction in primary viraemia we compared three different ART regimens in PHI.

STUDY DESIGN AND METHODS

A sequential, unblinded, non-randomized prospective cohort study. The primary endpoint was time to achieve plasma viral load (pVL) < 50 copies HIV RNA/ml. One hundred and five patients identified with PHI according to the definition: HIV antibody negative with positive HIV DNA (n = 22), HIV antibody positive with a documented negative test within the previous 6 months (n = 53), low-level incident 'detuned' assay (n = 10) or an evolving HIV-antibody test (n = 20) were recruited. Ninety of 105 individuals chose to take a short course of ART at PHI whereas 15 of 105 declined therapy. Seventy-nine of 90 were included for analysis and were allocated sequentially to either three (29 of 79) or four-drug (33 of 79) or protease inhibitor-containing ART (17 of 79).

RESULTS

A mathematical model-based analysis of viral decay indicated significantly faster viral load decline in patients receiving the four-drug regimen (P = 0.01). This conclusion was supported by a non-significant on-treatment analysis of the time taken to reach pVL <50 copies HIV RNA/ml (P = 0.07) but not by the corresponding intend-to-treat analysis. This discordance was caused by greater toxicities associated with the four-drug regimen, although the differences were not significant.

CONCLUSION

Of the three treatment regimens compared, the four-drug arm enhanced the rate of decline of primary viraemia but at the cost of toxicity.

The epidemiological impact of antiretroviral use predicted by mathematical models: a review

This review summarises theoretical studies attempting to assess the population impact of antiretroviral therapy (ART) use on mortality and HIV incidence. We describe the key parameters that determine the impact of therapy, and argue that mathematical models of disease transmission are the natural framework within which to explore the interaction between antiviral use and the dynamics of an HIV epidemic. Our review focuses on the potential effects of ART in resource-poor settings. We discuss choice of model type and structure, the potential for risk behaviour change following widespread introduction of ART, the importance of the stage of HIV infection at which treatment is initiated, and the potential for spread of drug resistance. These issues are illustrated with results from models of HIV transmission. We demonstrate that HIV transmission models predicting the impact of ART use should incorporate a realistic progression through stages of HIV infection in order to capture the effect of the timing of treatment initiation on disease spread. The realism of existing models falls short of properly reproducing patterns of diagnosis timing, incorporating heterogeneity in sexual behaviour, and describing the evolution and transmission of drug resistance. The uncertainty surrounding certain effects of ART, such as changes in sexual behaviour and transmission of ART-resistant HIV strains, demands exploration of best and worst case scenarios in modelling, but this must be complemented by surveillance and behavioural surveys to quantify such effects in settings where ART is implemented.

A modeling approach to the impact of HIV mutations on the immune system

A dynamical system modeling the HIV infection, including a mutation occurrence process, is used, after simplifications, to show the impact of the viral diversity on the immune response and disease dynamics, by introducing an indicator of the immune system behavior, the immunological recognition efficacy (IRE) index. The existence, the expression and the stability of the endemically infected steady state of the IRE index-based model, as function of this index, are mathematically analyzed. The monotony of the steady state with respect to the IRE index is studied and an asymptotic analysis of the dynamical system performed. It is shown that the IRE index-based model provides a bound to the responses of the initial complex dynamical system. The biological interpretation of these mathematical results is the exhaustion of the immune system as a consequence of the continuous generation of viral mutants.

Robust parameter estimation techniques for stochastic within-host macroparasite models

We present a stochastic model of the within-host population dynamics of lymphatic filariasis, and use a simulated goodness-of-fit (GOF) method to estimate immunological parameters and their confidence intervals from experimental data. A variety of deterministic moment closure approximations to the stochastic system are explored and compared with simulation results. For the maximum GOF parameter estimates, none of the methods of closure accurately reproduce the behaviour of the stochastic model. However, direct analysis of the stochastic model demonstrates that the high levels of variation observed in the data can be reproduced without requiring parameters to vary between hosts. This indicates that the observed aggregation of parasite load may be dynamically generated by random variation in the development of an effective immune response against parasite larvae.

Subpopulations of long-lived and short-lived T cells in advanced HIV-1 infection

Antigenic stimulation of T cells gives rise to short-lived effector cells and long-lived memory cells. We used two stable isotope-labeling techniques to identify kinetically distinct subpopulations of T cells and to determine the effect of advanced infection with HIV-1. Long-term deuterated water (2H2O) incorporation into DNA demonstrated biphasic accrual of total and of memory/effector (m/e)-phenotype but not naive-phenotype T cells, consistent with the presence of short-lived and longer-lived subpopulations within the m/e-phenotype T cell pool. These results were mirrored by biphasic die-away kinetics in m/e- but not naive-phenotype T cells after short-term 2H-glucose labeling. Persistent label retention was observed in a subset of m/e-phenotype T cells (presumably memory T cells), confirming the presence of T cells with very different life spans in humans. In advanced HIV-1 infection, much higher proportions of T cells were short-lived, compared to healthy controls. Effective long-term anti-retroviral therapy restored values to normal. These results provide the first quantitative evidence that long-lived and quiescent T cells do indeed predominate in the T cell pool in humans and determine T cell pool size, as in rodents. The greatest impact of advanced HIV-1 infection is to reduce the generation of long-lived, potential progenitor T cells.

The role of the cytotoxic T-lymphocyte response and virus cytopathogenicity in the virus decline during antiviral therapy

Although it is clear that HIV can lyse HIV-infected CD4 T cells, it is still controversial whether the depletion of CD4 T cells seen in HIV-infected patients after years of asymptomatic disease is caused by the direct cytopathic effects of the virus or is mediated by the immune response. Assuming the initial decline in viraemia during highly active antiretroviral therapy (HAART) is caused by the death of cells productively infected with HIV, I investigate how the rate of the virus decline is affected by the efficiency of the cytotoxic T-lymphocyte (CTL) response. I find that whether the stronger immune response causes a more rapid virus decline depends critically on how the virus is controlled by the CTL response (lytic versus non-lytic mechanisms). Moreover, variation in the efficiency of the immune response does not always cause variation in the rate of the virus decline (and, therefore, in the death rate of infected cells), implying that the constancy of the virus decline rate measured in different patients does not necessarily indicate that the virus is cytopathic. The potential problems associated with the model and the approach undertaken are also discussed.

The race between initial T-helper expansion and virus growth upon HIV infection influences polyclonality of the response and viral set-point

Infection with HIV is characterized by very diverse disease-progression patterns across patients, associated with a wide variation in viral set-points. Progression is a multifactorial process, but an important role has been attributed to the HIV-specific T-cell response. To explore the conditions under which different set-points may be explained by differences in initial CD4 and CD8 T-cell responses and virus inoculum, we have formulated a model assuming that HIV-specific CD4 cells are both targets for infection and mediators of a monoclonal or polyclonal immune response. Clones differ in functional avidity for HIV epitopes. Importantly, in contrast to previous models, in this model we obtained coexistence of multiple clones at steady-state viral set-point, as seen in HIV infection. We found that, for certain parameter conditions, multiple steady states are possible: with few initial CD4 helper cells and high virus inoculum, no immune response is established and target-cell-limited infection follows, with associated high viral load; when CD4 clones are initially large and virus inoculum is low, infection can be controlled by several clones. The conditions for the dependence of viral set-point on initial inoculum and CD4 T-helper clone availability are investigated in terms of the effector mechanism of the clones involved.

Modelling the dynamics of LCMV infection in mice: II. Compartmental structure and immunopathology

In this study, we develop a mathematical model for analysis of the compartmental aspects and immunopathology of lymphocytic choriomeningitis virus (LCMV) infection in mice. We used sets of original and published data on systemic (extrasplenic) virus distribution to estimate the parameters of virus growth and elimination for spleen and other anatomical compartments, such as the liver, kidney, thymus and lung as well as transfer rates between blood and the above organs. A mathematical model quantitatively integrating the virus distribution kinetics in the host, the specific cytotoxic T lymphocyte (CTL) response in spleen and the re-circulation of effector CTL between spleen, blood and liver is advanced to describe the CTL-mediated immunopathology (hepatitis) in mice infected with LCMV. For intravenous and "peripheral" routes of infection we examine the severity of the liver disease, as a function of the virus dose and the host's immune status characterized by the numbers of precursor and/or cytolytic effector CTL. The model is used to predict the efficacy of protection against virus persistence and disease in a localized viral infection as a function of the composition of CTL population. The modelling analysis suggests quantitative demands to CTL memory for maximal protection against a wide range of doses of infection with a primarily peripheral site of virus replication without the risk of favoring immunopathology. It specifies objectives for CTL vaccination to ensure virus elimination with minimal immunopathology vs. vaccination for disease.

Modeling the effects of vaccination on chronically infected HIV-positive patients

T-cell activation plays a critical role in the initiation and propagation of HIV-1 infection and yet transient activation of the immune system is a normal response to immunization. While it is now considered wise to vaccinate HIV-1-positive patients, it is crucial to anticipate any lasting effects of vaccination on plasma HIV-1 RNA levels and on infected T-cell populations. We extend a simple dynamic model of HIV infection to include T-cell activation by vaccination. We show that the model can reproduce many but not all of the features of the post-tetanus immunization rise in viral load observed and reported on by Stanley et al. in 1966 ( 334:1222-1230). Amplitudes and approximate timing of postimmunization peak viral loads were matched in 10 of 12 cases; in patients with double postimmunization peaks of nearly equal amplitude the later peaks were matched. Furthermore, our simulations suggest that productively infected cell populations track postvaccination increases in plasma viral load, rising and falling in concert over a period of about 4 weeks, whereas chronically infected cells peak later and remain elevated over baseline levels for up to 6 weeks postvaccination.

Antigen-driven T-cell turnover

A mathematical model is developed to characterize the distribution of cell turnover rates within a population of T lymphocytes. Previous models of T-cell dynamics have assumed a constant uniform turnover rate; here we consider turnover in a cell pool subject to clonal proliferation in response to diverse and repeated antigenic stimulation. A basic framework is defined for T-cell proliferation in response to antigen, which explicitly describes the cell cycle during antigenic stimulation and subsequent cell division. The distribution of T-cell turnover rates is then calculated based on the history of random exposures to antigens. This distribution is found to be bimodal, with peaks in cell frequencies in the slow turnover (quiescent) and rapid turnover (activated) states. This distribution can be used to calculate the overall turnover for the cell pool, as well as individual contributions to turnover from quiescent and activated cells. The impact of heterogeneous turnover on the dynamics of CD4(+) T-cell infection by HIV is explored. We show that our model can resolve the paradox of high levels of viral replication occurring while only a small fraction of cells are infected.

HIV-1 reservoirs

In most infected individuals, HIV-1 replicates high levels throughout the duration of infection, including the clinically quiescent phase of disease. The level of this active viral replication correlates directly with disease progression and survival. The advent of combination therapeutics for HIV-1 (i.e., highly active antiretroviral therapy [HAART]) has led to dramatic reductions in viral replication in vivo and morbidity and mortality, at least in the developed world.

Decelerating decay of latently infected cells during prolonged therapy for human immunodeficiency virus type 1 infection

Antiviral therapy induces a rapid drop in human immunodeficiency virus type 1 viremia, but the decline of virus levels decelerates over time. Mathematical modeling demonstrates that the source of residual virus production might be a single compartment of latently infected cells with an extended distribution of activation rates.

A Bayesian approach to parameter estimation in HIV dynamical models

In the context of a mathematical model describing HIV infection, we discuss a Bayesian modelling approach to a non-linear random effects estimation problem. The model and the data exhibit a number of features that make the use of an ordinary non-linear mixed effects model intractable: (i) the data are from two compartments fitted simultaneously against the implicit numerical solution of a system of ordinary differential equations; (ii) data from one compartment are subject to censoring; (iii) random effects for one variable are assumed to be from a beta distribution. We show how the Bayesian framework can be exploited by incorporating prior knowledge on some of the parameters, and by combining the posterior distributions of the parameters to obtain estimates of quantities of interest that follow from the postulated model.

Viral replication under combination antiretroviral therapy: a comparison of four different regimens

A mathematical model of the interaction among CD4+ T-cells, HIV-1, and antiretroviral drugs was fitted to the viral load decline following initiation of combination therapy to estimate differences in the residual reproductive capacity of virus (R(0)) in the average patient in each group. Four regimens were studied: 12 patients on 5-drug nucleoside reverse transcriptase inhibitor (NRTIs), nonnucleoside reverse transcriptase inhibitor (NNRTIs) and protease inhibitor (PI)-containing combination therapy, 11 patients on PI-containing triple therapy, 10 patients on double NRTI therapy, and 10 patients on NNRTI-containing triple therapy. Model fits were used to estimate R(0). The NNRTI-containing triple therapy and the 5-drug regimen blocked viral replication to the greatest extent (R(0) = 0.85; 95% confidence interval [CI], 0.79-0.91; and 0.90, 95% CI, 0.82-0.98, respectively), with the former being significantly better than the PI-containing triple regimen (R(0) = 0.98; 95% CI, 0.92-1.03; p =.007). Both the NNRTI-containing and the 5-drug regimen, as well as the PI-containing triple therapy, were significantly better at blocking viral replication than the double NRTI therapy (R(0) = 1.04; 95% CI, 1.0-1.07). Measurement of viral load after approximately 7 days provided the most accurate measure of the degree of viral suppression induced by a given drug regimen.

Dynamics of naive and memory CD4+ T lymphocytes in HIV-1 disease progression

Understanding the dynamics of naive and memory CD4+ T cells in the immune response to HIV-1 infection can help elucidate typical disease progression patterns observed in HIV-1 patients. Although infection markers such as CD4+ T-cell count and viral load are monitored in patient blood, the lymphatic tissues (LT) have been shown to be an important viral reservoir. Here, we introduce the first comprehensive theoretical model of disease progression based on T-cell subsets and virus circulating between the two compartments of LT and blood. We use this model to predict several trademarks observed in adult HIV-1 disease progression such as the establishment of a setpoint in the asymptomatic stage. Our model predicts that both host and viral elements play a role in determining different disease progression patterns. Viral factors include viral infectivity and production rates, whereas host factors include elements of specific immunity. We also predict the effect of highly active antiretroviral therapy and treatment cessation on cellular and viral dynamics in both blood and LT.

Non-linear dynamics models characterizing long-term virological data from AIDS clinical trials

Human immunodeficiency virus (HIV) dynamics represent a complicated variant of the text-book case of non-linear dynamics: predator-prey interaction. The interaction can be described as naturally reproducing T-cells (prey) hunted and killed by virus (predator). Virus reproduce and increase in number as a consequence of successful predation; this is countered by the production of T-cells and the reaction of the immune system. Multi-drug anti-HIV therapy attempts to alter the natural dynamics of the predator-prey interaction by decreasing the reproductive capability of the virus and hence predation. These dynamics are further complicated by varying compliance to treatment and insurgence of resistance to treatment. When following the temporal progression of viral load in plasma during therapy one observes a short-term (1-12 weeks) decrease in viral load. In the long-term (more than 12 weeks from the beginning of therapy) the reduction in viral load is either sustained, or it is followed by a rebound, oscillations and a new (generally lower than at the beginning of therapy) viral load level. Biomathematicians have investigated these dynamics by means of simulations. However the estimation of the parameters associated with the dynamics from real data has been mostly limited to the case of simplified, in particular linearized, models. Linearized model can only describe the short-term changes of viral load during therapy and can only predict (apparent) suppression. In this paper we put forward relatively simple models to characterize long-term virus dynamics which can incorporate different factors associated with resurgence: (Fl) the intrinsic non-linear HIV-1 dynamics, (F2) drug exposure and in particular compliance to treatment, and (F3) insurgence of resistant HIV-1 strains. The main goal is to obtain models which are mathematically identifiable given only measurements of viral load, while retaining the most crucial features of HIV dynamics. For the purpose of illustration we demonstrate an application of the models using real AIDS clinical trial data involving patients treated with a combination of anti-retroviral agents using a model which incorporates compliance data.

Quantification of intrinsic residual viral replication in treated HIV-infected patients

The intrinsic rate of viral replication in HIV-infected patients treated with antiretroviral combination therapy is estimated by using a mathematical model of viral dynamics. This intrinsic replication is found to be episodic, varying considerably in quantity between patients (even among those achieving long-term undetectable levels of viremia) and is always reduced by increasing the potency of the antiviral drug regimen. The analysis reveals that even in conditions of perfect patient adherence and drug penetration a substantial level of residual viral replication is expected. The rate of evolution in the viral quasispecies, and thus also the probability of new drug-resistant viral strains being created, is proportional to the total amount of residual viral replication. Under most circumstances, the viral population continues to turn over rapidly during therapy, albeit at a much reduced level.

The role of antigenic stimulation and cytotoxic T cell activity in regulating the long-term immunopathogenesis of HIV: mechanisms and clinical implications

This paper develops a predictive mathematical model of cell infection, host immune response and viral replication that reproduces observed long-term trends in human immunodeficiency virus (HIV) pathogenesis. Cell activation induced by repeated exposure to many different antigens is proposed as the principal mechanism of providing target cells for HIV infection and, hence, of CD4+ T cell depletion, with regulation of the overall T cell pool size causing concomitant CD8 pool increases. The model correctly predicts the cross-patient variability in disease progression, the rate of which is found to depend on the efficacy of anti-HIV cytotoxic T lymphocyte responses, overall viral pathogenicity and random effects. The model also predicts a variety of responses to anti-viral therapy, including episodic residual viral replication and discordant responses and we find that such effects can be suppressed by increasing the potency of treatment.

T-cell re-population in HIV-infected children on highly active anti-retroviral therapy (HAART)

In this pilot study, we address the nature of the re-population of the T-cell compartment in HIV-1+ (Human Immunodeficiency Virus 1), vertically infected children placed on successful regimens of HAART (highly active anti-retroviral therapy) incorporating 2 NRTI and a protease inhibitor. The clonality of the T-cell compartment and the abundance of RTEs (Recent Thymic Emigrants) were determined 2 weeks before and 20 weeks after initiation of HAART in a subgroup of children taking part in the PENTA (Paediatric European Network for the Treatment of AIDS) 5 trial. Analysis of the clonality of the circulating T-cell compartment was assessed using CDR3 spectratyping and analysed using the Kolmogorov-Smirnov two sample test. This revealed that a high degree of T-cell clonal restriction still exists 5 months into therapy, despite the appearance of previously undetectable T-cell clones within the periphery. We detected no increase in RTE abundance in this 5 month period, as determined by PCR detection of TRECs (T-Cell Receptor Excision Circles). We conclude that the observed re-population of T cells within the periphery of treated children is heavily reliant upon the maintenance/expansion of pre-existing cells during the 5 month period immediately following the initiation of therapy.

Effect of drug efficacy and the eclipse phase of the viral life cycle on estimates of HIV viral dynamic parameters

Fits of mathematic models to the decline in HIV-1 RNA after antiretroviral therapies have yielded estimates for the life span of productively infected cells of 1 to 2 days. In a previous report, we described the mathematic properties of an extended model that accounts for imperfect viral suppression and the eclipse phase of the viral life cycle (the intracellular delay between initial infection and release of progeny virions). In this article, we fit this extended model to detailed data on the decline of plasma HIV-1 RNA after treatment with the protease inhibitor ritonavir. Because the therapy in this study was most likely not completely suppressive, we allowed the drug efficacy parameter to vary from 70% to 100%. Estimates for the clearance rate of free virus, c, increased with the addition of the intracellular delay (as reported previously) but were not appreciably affected by changes in the drug efficacy parameter. By contrast, the estimated death rate of virus-producing cells, delta, increased from an average of 0.49 day-1 to 0.90 day-1 (an increase of 84%) because the drug efficacy parameter was reduced from 100% to 70%. Neglecting the intracellular delay, the comparable increase in delta was only about 55%. The inferred increases in delta doubled when the model was extended to account for possible increases in target cell densities after treatment initiation. This work suggests that estimates for delta may be greater than previously reported and that the half-life of a cell in vivo that is producing virus, on average, may be 1 day.

Release of virus from lymphoid tissue affects human immunodeficiency virus type 1 and hepatitis C virus kinetics in the blood

Kinetic parameters of human immunodeficiency virus type 1 (HIV-1) and hepatitis C virus (HCV) infections have been estimated from plasma virus levels following perturbation of the chronically infected (quasi-) steady state. We extend previous models by also considering the large pool of virus localized in the lymphoid tissue (LT) compartment. The results indicate that the fastest time scale of HIV-1 plasma load decay during therapy probably reflects the clearance rate of LT virus and not, as previously supposed, the clearance rate of virus in plasma. This resolves the discrepancy between the clearance rate estimates during therapy and those based on plasma apheresis experiments. In the extended models plasma apheresis measurements are indeed expected to reflect the plasma decay rate. We can reconcile all current HIV-1 estimates with this model when, on average, the clearance rate of virus in plasma is approximately 20 day(-1), that of LT virus is approximately 3 day(-1), and the death rate of virus-producing cells is approximately 0.5 day(-1). The fast clearance in the LT compartment increases current estimates for total daily virus production. Because HCV is produced in the liver, we let virus be produced into the blood compartment of our model. The results suggest that extending current HCV models with an LT compartment is not likely to affect current estimates for kinetic parameters and virus production. Estimates for treatment efficacy might be affected, however.

Viral dynamics and anti-viral pharmacodynamics: rethinking in vitro measures of drug potency

Most current assays used to quantitate the pharmacodynamic effect of anti-viral agents measure the net inhibitory effect of a drug on virus replication over several days in an in vitro cell culture. Such endpoint experiments give cumulative measures of inhibition that vary with the assay used and therefore provide suboptimal information on likely in vivo drug performance. We argue that instantaneous inhibition (proportion of cell infection prevented at a point in time) is a more robust pharmacodynamic measure, and propose techniques to estimate this quantity from endpoint data. Implications for the quantification of drug interactions are discussed.

Slower decline of plasma HIV-1 RNA following highly suppressive antiretroviral therapy in primary compared with chronic infection

OBJECTIVES

To study the effect of highly suppressive antiretroviral therapy on the slopes of HIV-1 RNA decline in primary compared with chronic HIV-1 infection.

METHODS

Slopes of HIV-1 RNA decline in plasma were compared before and after the start of highly suppressive antiretroviral therapy from five acutely infected patients who started treatment 2 to 5 weeks following the onset of clinical symptoms. Slopes of decline after the initiation of therapy were also compared with those found in 12 chronically infected individuals on the same therapy. Numbers and percentages of activated CD4 and CD8 T cells at baseline were compared as well.

RESULTS

The pre-treatment slopes of HIV-1 RNA decline in the acutely infected individuals increased significantly (P = 0.0001) after the start of anti-retroviral therapy. However, these post-treatment slopes were lower than those found in the chronically infected individuals (P= 0.012). Slopes were inversely correlated (P= 0.012) with baseline HIV-1 RNA. Although the number of CD38+HLA-DR+ CD4 cells was higher in primary infection (P= 0.02), the percentage did not differ between primary and chronic infection.

CONCLUSIONS

These findings indicate that antiretroviral therapy contributes significantly to the clearance of HIV-1 during primary infection. Based on the mathematical model the less steep RNA slope following the start of treatment in primary infection can be predicted to be the result of lower clearance of productively infected cells and higher burst size per cell per unit time. This may indicate a growing immune response to HIV-1 in this very early stage of infection.

Therapeutic targeting of human immunodeficiency virus type-1 latency: current clinical realities and future scientific possibilities

Factors affecting HIV-1 latency present formidable obstacles for therapeutic intervention. As these obstacles have become a clinical reality, even with the use of potent anti-retroviral regimens, the need for novel therapeutic strategies specifically targeting HIV-1 latency is evident. However, therapeutic targeting of HIV-1 latency requires an understanding of the mechanisms regulating viral quiescence and activation. These mechanisms have been partially delineated using chronically infected cell models and, clearly, HIV-1 activation from latency involves several key viral and cellular components. Among these distinctive therapeutic targets, cellular factors involved in HIV-1 transcription especially warrant further consideration for rational drug design. Exploring the scientific possibilities of new therapies targeting HIV-1 latency may hold new promise of eventual HIV-1 eradication.

Mathematical models of the transmission and control of sexually transmitted diseases

BACKGROUND

The development of mathematical models to describe and interpret the epidemiology of sexually transmitted infections has involved the incremental addition of various forms of biological and behavioral complexity to simple mathematical templates.

GOAL

To review simple and complex models used in study of observed epidemiologic pattern.

STUDY DESIGN

An overview of modeling in sexually transmitted disease epidemiology identifies the function of different types of models.

RESULTS

Simple models have the advantage of transparency and analytical tractability and can illustrate the relative merits of different intervention options. However, real life is replete with complexities that can have effects that are difficult to predict in the absence of a mathematical framework.

CONCLUSIONS

Research should increasingly be based on robust parameterization of model structures and try to capture individual behaviors. Progress will be most rapid by interdisciplinary work where the clinician, epidemiologist, and mathematician work collaboratively to help improve our knowledge of how to best control infection and disease.

Reduction of the HIV-1-infected T-cell reservoir by immune activation treatment is dose-dependent and restricted by the potency of antiretroviral drugs

BACKGROUND

Treatments combining T-cell activating agents and potent antiretroviral drugs have been proposed as a possible means of reducing the reservoir of long-lived HIV-1 infected quiescent CD4 T-cells.

OBJECTIVE

To analyse the effect of such therapies on HIV-1 dynamics and T-cell homeostasis.

DESIGN AND METHODS

A mathematical framework describing HIV-1 dynamics and T-cell homeostasis was developed. Three patients who were kept on a particularly potent course of highly active antiretroviral therapy (HAART) were treated with the anti-CD3 monoclonal antibody OKT3 and interleukin (IL)-2. Plasma HIV-RNA, and HIV-RNA and DNA in peripheral blood mononuclear cells and lymph node mononuclear cells were measured. These results and other published studies on the use of IL-2 alone were assessed using our mathematical framework.

RESULTS

We show that outcome of treatment is determined by the relative rates of depletion of the infected quiescent T-cell population by activation and of its replenishment through new infection. Which of these two processes dominates is critically dependent on both the potency of HAART and also the degree of T-cell activation induced. We demonstrate that high-level T-cell stimulation is likely to produce negative outcomes, both by failing to reduce viral reservoirs and by depleting the CD4 T-cell pool and disrupting CD4/CD8 T-cell homeostasis. In contrast, repeated low-level stimulation may both aid CD4 T-cell pool expansion and achieve a substantial reduction in the long-lived HIV-1 reservoir.

CONCLUSIONS

Our analysis suggests that although treatment that activates T-cells can reduce the long-lived HIV-1 reservoir, caution should be used as high-level stimulation may result in a negative outcome.