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

Global dynamics in an age-structured HIV model with humoral immunity

In this paper, we formulate an age-structured HIV model, in which the influence of humoral immunity and the infection age of the infected cells are considered. The model is governed by three ordinary differential equations and two first-ordered partial differential equations and admits three equilibria: disease-free, immune-inactivated and immune-activated equilibria. We introduce two important thresholds: the basic reproduction number [Formula: see text] and immune-activated reproduction number [Formula: see text] and further show the global stability of above three equilibria in terms of [Formula: see text] and [Formula: see text], respectively. The numerical simulations are presented to illustrate our results.

Mathematical analysis of an HIV model with latent reservoir, delayed CTL immune response and immune impairment

In this paper, an in-host HIV infection model with latent reservoir, delayed CTL immune response and immune impairment is investigated. By using suitable Lyapunov functions and LaSalle's invariance principle, it is shown that when time delay is equal to zero, the immunity-inactivated reproduction ratio is a threshold determining the global dynamics of the model. By means of the persistence theory for infinite dimensional systems, it is proven that if the immunity-inactivated reproduction ratio is greater than unity, the model is permanent. Choosing time delay as the bifurcation parameter and analyzing the corresponding characteristic equation of the linearized system, the existence of a Hopf bifurcation at the immunity-activated equilibrium is established. Numerical simulations are carried out to illustrate the theoretical results and reveal the effects of some key parameters on viral dynamics.

Predictions of time to HIV viral rebound following ART suspension that incorporate personal biomarkers

Antiretroviral therapy (ART) effectively controls HIV infection, suppressing HIV viral loads. Suspension of therapy is followed by rebound of viral loads to high, pre-therapy levels. However, there is significant heterogeneity in speed of rebound, with some rebounds occurring within days, weeks, or sometimes years. We present a stochastic mathematical model to gain insight into these post-treatment dynamics, specifically characterizing the dynamics of short term viral rebounds (≤ 60 days). Li et al. (2016) report that the size of the expressed HIV reservoir, i.e., cell-associated HIV RNA levels, and drug regimen correlate with the time between ART suspension and viral rebound to detectable levels. We incorporate this information and viral rebound times to parametrize our model. We then investigate insights offered by our model into the underlying dynamics of the latent reservoir. In particular, we refine previous estimates of viral recrudescence after ART interruption by accounting for heterogeneity in infection rebound dynamics, and determine a recrudescence rate of once every 2-4 days. Our parametrized model can be used to aid in design of clinical trials to study viral dynamics following analytic treatment interruption. We show how to derive informative personalized testing frequencies from our model and offer a proof-of-concept example. Our results represent first steps towards a model that can make predictions on a person living with HIV (PLWH)'s rebound time distribution based on biomarkers, and help identify PLWH with long viral rebound delays.

Stochastic Dynamics of the Latently Infected Cell Reservoir During HIV Infection

The presence of cells latently infected with HIV is currently considered to be a major barrier to viral eradication within a patient. Here, we consider birth-death-immigration models for the latent cell population in a single patient, and present analytical results for the size of this population in the absence of treatment. We provide results both at steady state (viral set point), and during the non-equilibrium setting of early infection. We obtain semi-analytic results showing how latency-reversing drugs might be expected to affect the size of the latent pool over time. We also analyze the probability of rare mutant viral strains joining the latent cell population, allowing for steady-state and dynamic viral populations within the host.

An HIV model with age-structured latently infected cells

HIV latency remains a major obstacle to viral elimination. The activation rate of latently infected cells may depend on the age of latent infection. In this paper, we develop a model of HIV infection including age-structured latently infected cells. We mathematically analyse the model and use numerical simulations with different activation functions to show that the model can explain the persistence of low-level viremia and the latent reservoir stability in patients on therapy. Sensitivity tests suggest that the model is robust to the changes of most parameters but is sensitive to the relative magnitude of the net generation rate and the long-term activation rate of latently infected cells. To reduce the sensitivity, we extend the model to include homeostatic proliferation of latently infected cells. The new model is robust in reproducing the long-term dynamics of the virus and latently infected cells observed in patients receiving prolonged combination therapy.

Quantifying the turnover of transcriptional subclasses of HIV-1-infected cells

HIV-1-infected cells in peripheral blood can be grouped into different transcriptional subclasses. Quantifying the turnover of these cellular subclasses can provide important insights into the viral life cycle and the generation and maintenance of latently infected cells. We used previously published data from five patients chronically infected with HIV-1 that initiated combination antiretroviral therapy (cART). Patient-matched PCR for unspliced and multiply spliced viral RNAs combined with limiting dilution analysis provided measurements of transcriptional profiles at the single cell level. Furthermore, measurement of intracellular transcripts and extracellular virion-enclosed HIV-1 RNA allowed us to distinguish productive from non-productive cells. We developed a mathematical model describing the dynamics of plasma virus and the transcriptional subclasses of HIV-1-infected cells. Fitting the model to the data allowed us to better understand the phenotype of different transcriptional subclasses and their contribution to the overall turnover of HIV-1 before and during cART. The average number of virus-producing cells in peripheral blood is small during chronic infection. We find that a substantial fraction of cells can become defectively infected. Assuming that the infection is homogenous throughout the body, we estimate an average in vivo viral burst size on the order of 10⁴ virions per cell. Our study provides novel quantitative insights into the turnover and development of different subclasses of HIV-1-infected cells, and indicates that cells containing solely unspliced viral RNA are a good marker for viral latency. The model illustrates how the pool of latently infected cells becomes rapidly established during the first months of acute infection and continues to increase slowly during the first years of chronic infection. Having a detailed understanding of this process will be useful for the evaluation of viral eradication strategies that aim to deplete the latent reservoir of HIV-1.

Gaining a quantitative understanding of the development and turnover of different HIV-1-infected subpopulations of cells is crucial to improve the outcome of patients on combination antiretroviral therapy (cART). The population of latently infected cells is of particular interest as they represent the major barrier to a cure of HIV-1 infection. We developed a mathematical model that describes the dynamics of different transcriptionally active subclasses of HIV-1-infected cells and the viral load in peripheral blood. The model was fitted to previously published data from five chronically HIV-1-infected patients starting cART. This allowed us to estimate critical parameters of the within-host dynamics of HIV-1, such as the the number of virions produced by a single infected cell. The model further allowed investigation of HIV-1 dynamics during the acute phase. Computer simulations illustrate that latently infected cells become rapidly established during the first months of acute infection and continue to increase slowly during the first years of chronic infection. This illustrates the opportunity for strategies that aim to eradicate the virus during early cART as the pool of HIV-1 infected cells is substantially smaller during acute infection than during chronic infection.

Mathematical models of viral latency

While viral latency remains one of the biggest challenges for successful antiviral therapy, it has also inspired mathematical modelers to develop dynamical system approaches with the aim of predicting the impact of drug efficacy on disease progression and the persistence of latent viral reservoirs. In this review we present several differential equation models and assess their relative success in giving advice to the working clinician and their predictive power for inferring long term viral eradication from short term abatement. Many models predict that there is a considerable likelihood of viral rebound due to continuous reseeding of latent reservoirs. Most mathematical models of HIV latency suffer from being reductionist by ignoring the growing variety of different cell types harboring latent virus, the considerable intercellular delay involved in reactivation, and host-related epigenetic modifications which may alter considerably the dynamical system of immune cell populations.

Impact of latently infected cells on strain archiving within HIV hosts

Latently infected cells are a barrier to HIV eradication on therapy due to long half-lives of between 6 and 44 months. The mechanism behind this long term maintenance is unclear although bystander proliferation and asymmetric division have both been put forward for consideration in mathematical models. The latently infected cell reservoir seems to act as an archive for strains of HIV no longer dominant in the blood, such as wild-type virus when the individual is on therapy. This is particularly significant when patients wish to come off medication and wild-type virus re-emerges. We use a two target cell model capable of producing low-level viral load on therapy and include latent cells and two strains of virus, wild-type and drug resistant, to investigate the impact of two possible mechanisms of latent cell reservoir maintenance on strain archiving. We find that although short term (less than a year) archiving of viral strains is possible in a model with no mechanism for reservoir maintenance, both bystander proliferation and asymmetric division of latent cells allow archiving to occur over much longer timescales (2 or more years). We suggest that regardless of the mechanism involved, latent cell reservoir maintenance allows strain archiving to occur. We interpret our results for clinical consideration.

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.

Intracellular transactivation of HIV can account for the decelerating decay of virus load during drug therapy

Linking the intracellular transactivation circuit of HIV into a virus dynamics model can account for activation of infected cells and reversion into latency.

We hypothesize that the activation of latently infected cells is governed by the basal transcription rate of the integrated provirus rather than through extracellular stimuli.

This systems approach to modelling virus dynamics offers a promising framework to infer the extracellular dynamics of cell populations from their intracellular reaction networks.

The viral reservoir of latently infected cells is considered to be one of the major barriers for eradicating the virus from patients infected with HIV. During prolonged antiretroviral therapy, it has been shown that the pool of latently infected cells decays very slowly and at a decreasing rate. The underlying mechanisms causing this decelerating decay are still unclear (Lassen et al, 2004a, 2004b; Han et al, 2007). A recent study has shown that HIV can exhibit a switch-like behavior where infected cells can either be activated or become resting in a latent state (Weinberger et al, 2005). To investigate the effect of this switch-like behavior on the viral infection dynamics, we devise a new model that links the intracellular transactivation of the virus with the extracellular virus dynamics (Box 1). The model can explain the typical decelerating decay of HIV that is observed during antiretroviral therapy. We find that the activation of latently infected cells is governed by the basal transcription rate of the inserted provirus. Therefore, our analysis suggests that increasing the basal transcription rate of the HIV provirus could serve as a new therapeutic intervention for eradicating the pool of latently infected cells. In addition, our systems approach to modeling virus dynamics offers a promising framework for inferring the extracellular dynamics of cell populations from their intracellular reaction networks.

Basic virus dynamics models have been essential in understanding quantitative issues of HIV replication. However, several parts of the viral life cycle remain elusive. One of the most critical steps is the start of viral transcription, which is governed by the regulatory protein trans-activator of transcription (Tat) that induces a positive feedback loop. It has been shown that this feedback loop can alternate between two states leading to a transient activation of viral transcription. Using Monte Carlo simulations, we integrate the transactivation circuit into a new virus dynamics model having an age-dependent transactivation rate and reversion into latency. The cycling of infected cells between an activated and latent state results in the typical decelerating decay of virus load following therapy. Further, we hypothesize that the activation of latently infected cells is governed by the basal transcription rate of the integrated provirus rather than the intra- or extracellular environment. Finally, our systems approach to modeling virus dynamics offers a promising framework to infer the extracellular dynamics of cell populations from their intracellular reaction networks.

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.

Pharmaceutical approaches to eradication of persistent HIV infection

Highly active antiretroviral therapy (HAART) has markedly decreased morbidity and mortality in human immunodeficiency virus type 1 (HIV-1)-infected individuals in the developed world. Successful therapy often results in stable plasma levels of HIV-1 RNA below the limits of detection of commercial assays. Nonetheless, HIV-1 has not been cured by HAART. The causes of persistence of HIV infection in the face of current therapy appear to be multifactorial: latent but replication-competent provirus in resting CD4+ T cells, cryptic viral expression below the limits of detection of clinical assays, and viral sanctuary sites might all contribute to persistence. Clearance of HIV infection will almost certainly require a multimodality approach that includes potent suppression of HIV replication, therapies that reach all compartments of residual HIV replication and depletion of any reservoirs of persistent, quiescent proviral infection. This review highlights the basic mechanisms for the establishment and maintenance of viral reservoirs and pharmaceutical approaches towards their elimination.

Constraints on the dominant mechanism for HIV viral dynamics in patients on raltegravir

Background

Raltegravir is the first publicly released HIV integrase inhibitor. In clinical trials, patients on a raltegravir-based highly active antiretroviral therapy (HAART) regimen were observed to have 70% less viraemia in the second-phase decay of viraemia than patients on an efavirenz- based HAART regimen. Because of this accelerated decay of viraemia, raltegravir has been speculated to have greater antiretroviral activity than efavirenz. Alternative explanations for this phenomenon are also possible. For example, the stage in the viral life cycle at which raltegravir acts might explain the distinct viral dynamics produced by this drug.

Methods

In this report, we use a mathematical model of HIV viral dynamics to explore several hypotheses for why raltegravir causes different viral dynamics than efavirenz. Using the experimentally observed viral dynamics of raltegravir, we calculated constraints on the mechanisms possibly responsible for the unique viral dynamics produced by raltegravir.

Results

We predicted that the dominant mechanism for the 70% reduction in the second-phase viraemia is not antiviral efficacy but the stage of the HIV viral life cycle at which raltegravir acts. Furthermore, we found that the kinetic constraints placed on the identity of the virus-producing cells of the second phase were most consistent with monocytes/macrophages.

Conclusions

Our model predictions have important implications for the motivation behind the use of raltegravir and our understanding of the virus-producing cells of the second-phase viraemia. Our results also highlight that the viral dynamics produced by different antiretroviral drugs should not be directly compared with each other.

Constraints on the dominant mechanism for HIV viral dynamics in patients on raltegravir

BACKGROUND

Raltegravir is the first publicly released HIV integrase inhibitor. In clinical trials, patients on a raltegravir-based highly active antiretroviral therapy (HAART) regimen were observed to have 70% less viraemia in the second-phase decay of viraemia than patients on an efavirenz-based HAART regimen. Because of this accelerated decay of viraemia, raltegravir has been speculated to have greater antiretroviral activity than efavirenz. Alternative explanations for this phenomenon are also possible. For example, the stage in the viral life cycle at which raltegravir acts might explain the distinct viral dynamics produced by this drug.

METHODS

In this report, we use a mathematical model of HIV viral dynamics to explore several hypotheses for why raltegravir causes different viral dynamics than efavirenz. Using the experimentally observed viral dynamics of raltegravir, we calculated constraints on the mechanisms possibly responsible for the unique viral dynamics produced by raltegravir.

RESULTS

We predicted that the dominant mechanism for the 70% reduction in the second-phase viraemia is not antiviral efficacy but the stage of the HIV viral life cycle at which raltegravir acts. Furthermore, we found that the kinetic constraints placed on the identity of the virus-producing cells of the second phase were most consistent with monocytes/macrophages.

CONCLUSIONS

Our model predictions have important implications for the motivation behind the use of raltegravir and our understanding of the virus-producing cells of the second-phase viraemia. Our results also highlight that the viral dynamics produced by different antiretroviral drugs should not be directly compared with each other.

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.

Low-level HIV-1 replication and the dynamics of the resting CD4+ T cell reservoir for HIV-1 in the setting of HAART

Background

In the setting of highly active antiretroviral therapy (HAART), plasma levels of human immunodeficiency type-1 (HIV-1) rapidly decay to below the limit of detection of standard clinical assays. However, reactivation of remaining latently infected memory CD4⁺ T cells is a source of continued virus production, forcing patients to remain on HAART despite clinically undetectable viral loads. Unfortunately, the latent reservoir decays slowly, with a half-life of up to 44 months, making it the major known obstacle to the eradication of HIV-1 infection. However, the mechanism underlying the long half-life of the latent reservoir is unknown. The most likely potential mechanisms are low-level viral replication and the intrinsic stability of latently infected cells.

Methods

Here we use a mathematical model of T cell dynamics in the setting of HIV-1 infection to probe the decay characteristics of the latent reservoir upon initiation of HAART. We compare the behavior of this model to patient derived data in order to gain insight into the role of low-level viral replication in the setting of HAART.

Results

By comparing the behavior of our model to patient derived data, we find that the viral dynamics observed in patients on HAART could be consistent with low-level viral replication but that this replication would not significantly affect the decay rate of the latent reservoir. Rather than low-level replication, the intrinsic stability of latently infected cells and the rate at which they are reactivated primarily determine the observed reservoir decay rate according to the predictions of our model.

Conclusion

The intrinsic stability of the latent reservoir has important implications for efforts to eradicate HIV-1 infection and suggests that intensified HAART would not accelerate the decay of the latent reservoir.

Viral and latent reservoir persistence in HIV-1-infected patients on therapy

Despite many years of potent antiretroviral therapy, latently infected cells and low levels of plasma virus have been found to persist in HIV-infected patients. The factors influencing this persistence and their relative contributions have not been fully elucidated and remain controversial. Here, we address these issues by developing and employing a simple, but mechanistic viral dynamics model. The model has two novel features. First, it assumes that latently infected T cells can undergo bystander proliferation without transitioning into active viral production. Second, it assumes that the rate of latent cell activation decreases with time on antiretroviral therapy due to the activation and subsequent loss of latently infected cells specific for common antigens, leaving behind cells that are successively less frequently activated. Using the model, we examined the quantitative contributions of T cell bystander proliferation, latent cell activation, and ongoing viral replication to the stability of the latent reservoir and persisting low-level viremia. Not surprisingly, proliferation of latently infected cells helped maintain the latent reservoir in spite of loss of latent infected cells through activation and death, and affected viral dynamics to an extent that depended on the magnitude of latent cell activation. In the limit of zero latent cell activation, the latent cell pool and viral load became uncoupled. However, as the activation rate increased, the plasma viral load could be maintained without depleting the latent reservoir, even in the absence of viral replication. The influence of ongoing viral replication on the latent reservoir remained insignificant for drug efficacies above the "critical efficacy" irrespective of the activation rate. However, for lower drug efficacies viral replication enabled the stable maintenance of both the latent reservoir and the virus. Our model and analysis methods provide a quantitative and qualitative framework for probing how different viral and host factors contribute to the dynamics of the latent reservoir and the virus, offering new insights into the principal determinants of their persistence.

Density-dependent decay in HIV-1 dynamics

The decay of HIV-1-infected cell populations after treatment with antiretroviral therapy has been measured using simple exponential decay models. These models are unlikely to be realistic over periods longer than a few months, however, because the population dynamics of HIV are complex. We considered an alternate model developed by Perelson and colleagues that extends the standard model for biphasic viral load decline and allows for nonlinear log decay of infected cell populations. Using data from 6 children on highly active antiretroviral therapy (HAART) and a single parameter in the new model, the assumption of log linear decay of infected cell populations is tested. Our analysis indicates that the short-lived and long-lived infected cell populations do not decay according to a simple exponential model. Furthermore, the resulting estimates of time to eradication of infected cell compartments are dramatically longer than those previously reported (eg, decades vs. years for long-lived infected cell populations and years vs. weeks for short-lived infected cell populations). Furthermore, estimates of the second-phase decay rates are significantly different than 0 for most children when obtained using the Perelson biphasic decay model. In contrast, this rate is not significantly different than 0 when the density-dependent decay model is used for parameter estimation and inference. Thus, the density-dependent decay model but not the simple exponential decay model is consistent with recent data showing that even under consistent HAART-mediated suppression of viral replication, decay rates of infected cell reservoirs decay little over several years. This suggests that conclusions about long-term viral dynamics of HIV infection based on simple exponential decay models should be carefully re-evaluated.

Heterogeneous clearance rates of long-lived lymphocytes infected with HIV: intrinsic stability predicts lifelong persistence

Viral replication and latently infected cellular reservoirs persist in HIV-infected patients achieving undetectable plasma virus levels with potent antiretroviral therapy. We exploited a predictable drug resistance mutation in the HIV reverse transcriptase to label and track cells infected during defined intervals of treatment and to identify cells replenished by ongoing replication. Decay rates of subsets of latently HIV-infected cells paradoxically decreased with time since establishment, reflecting heterogeneous lymphocyte activation and clearance. Residual low-level replication can replenish cellular reservoirs; however, it does not account for prolonged clearance rates in patients without detectable viremia. In patients receiving potent antiretroviral therapy, the latent pool has a heterogeneous and dynamic composition that comprises a progressively increasing proportion of stable lymphocytes. Eradication will not be achieved with complete inhibition of viral replication alone.