Ongoing HIV replication in lymph node sanctuary sites in treated individuals contributes to the total latent HIV at a very slow rate.

Lymph nodes (LNs) serve as a sanctuary site for HIV viruses due to the heterogeneous distribution of the antiretrovirals (ARVs) inside the LNs. There is an ongoing debate whether this represents ongoing cycles of viral replication in the LNs or merely residual virus production by latently infected cells. Previous work has claimed that the measured levels of genetic variation in proviruses sampled from the blood were inconsistent with ongoing replication. However, it is not clear what rate of variation is consistent with ongoing replication in small sanctuary sites. In this study, we used a spherically symmetric compartmental ODE model to track the HIV viral dynamics in the LN and predict the contribution of ongoing replication within the LN to the whole-body proviral pool in an ARV-suppressed person living with HIV. This model tracks the reaction-diffusion dynamics of uninfected, actively infected, and latently infected T-cells as well as free virus within the LN parenchyma and the blood, and distinguishes between latently infected cells created before ARV therapy and during ARV therapy. We simulated suppressive therapy beginning in year 5 post-infection. Each LN sanctuary site had a volume of 1 ml, and we considered cases of 1 ml, 30 ml, and 250 ml total volume, which represent a single active sanctuary site, moderate systemic involvement, and involvement of the total lymphoid tissue. Viral load in the blood rapidly dropped and remained below the limit of detection in all cases but remained high in the LN sanctuary sites. Novel latent cells increased systemically over time but very slowly, taking between 25 and 50 years to reach 5 % of the total latent pool, depending on the volume of lymphoid tissue involvement. Putative sanctuary sites in LNs are limited in volume and produce novel latent cells slowly. Assays to detect genetic drift due to such sites would require very deep sequencing if sampling only from the blood. Previous studies showing a lack of genetic drift are consistent with the expected contribution of ongoing replication in lymph node sanctuary sites.

Long-term antiretroviral treatment initiated at primary HIV-1 infection affects the size, composition, and decay kinetics of the reservoir of HIV-1-infected CD4 T cells.

UNLABELLED: Initiation of antiretroviral therapy during the earliest stages of HIV-1 infection may limit the seeding of a long-lasting viral reservoir, but long-term effects of early antiretroviral treatment initiation remain unknown. Here, we analyzed immunological and virological characteristics of nine patients who started antiretroviral therapy at primary HIV-1 infection and remained on suppressive treatment for >10 years; patients with similar treatment duration but initiation of suppressive therapy during chronic HIV-1 infection served as controls. We observed that independently of the timing of treatment initiation, HIV-1 DNA in CD4 T cells decayed primarily during the initial 3 to 4 years of treatment. However, in patients who started antiretroviral therapy in early infection, this decay occurred faster and was more pronounced, leading to substantially lower levels of cell-associated HIV-1 DNA after long-term treatment. Despite this smaller size, the viral CD4 T cell reservoir in persons with early treatment initiation consisted more dominantly of the long-lasting central-memory and T memory stem cells. HIV-1-specific T cell responses remained continuously detectable during antiretroviral therapy, independently of the timing of treatment initiation. Together, these data suggest that early HIV-1 treatment initiation, even when continued for >10 years, is unlikely to lead to viral eradication, but the presence of low viral reservoirs and durable HIV-1 T cell responses may make such patients good candidates for future interventional studies aiming at HIV-1 eradication and cure. IMPORTANCE: Antiretroviral therapy can effectively suppress HIV-1 replication to undetectable levels; however, HIV-1 can persist despite treatment, and viral replication rapidly rebounds when treatment is discontinued. This is mainly due to the presence of latently infected CD4 T cells, which are not susceptible to antiretroviral drugs. Starting treatment in the earliest stages of HIV-1 infection can limit the number of these latently infected cells, raising the possibility that these viral reservoirs are naturally eliminated if suppressive antiretroviral treatment is continued for extremely long periods of time. Here, we analyzed nine patients who started on antiretroviral therapy within the earliest weeks of the disease and continued treatment for more than 10 years. Our data show that early treatment accelerated the decay of infected CD4 T cells and led to very low residual levels of detectable HIV-1 after long-term therapy, levels that were otherwise detectable in patients who are able to maintain a spontaneous, drug-free control of HIV-1 replication. Thus, long-term antiretroviral treatment started during early infection cannot eliminate HIV-1, but the reduced reservoirs of HIV-1 infected cells in such patients may increase their chances to respond to clinical interventions aiming at inducing a drug-free remission of HIV-1 infection.

Spatial modeling of HIV cryptic viremia and 2-LTR formation during raltegravir intensification.

Combination Antiretroviral Therapy (cART) can suppress plasma HIV below the limit of detection in normal assays. Recently reported results suggest that viral replication may continue in some patients, despite undetectable levels in the blood. It has been suggested that the appearance of the circularized episomal HIV DNA artifact 2-LTR following treatment intensification with the integrase inhibitor raltegravir is a marker of ongoing viral replication. Other work has suggested that lymphoid organs may be a site of reduced antiviral penetration and increased viral production. In this study we model the hypothesis that this ongoing replication occurs in lymphoid follicle sanctuary sites and investigate the patterns of 2-LTR formation expected after raltegravir application. Experimental data is used to estimate the reaction and diffusion parameters in the model, and Monte-Carlo simulations are used to explore model behavior subject to variation in these rates. The results suggest that conditions for the formation of an observed transient peak in 2-LTR formation following raltegravir intensification include a sanctuary site diameter larger than 0.2mm, a viral basic reproductive ratio within the site larger than 1, and a total volume of active sanctuary sites above 20mL. Significant levels of uncontrolled replication can occur in the sanctuary sites without measurable changes in the plasma viral load. By contrast, subcritical replication (where the basic reproductive ratio of the virus is less than 1 in all sites) always results in monotonic increases of measured 2-LTR following raltegravir intensification, occurring at levels below the limit of detection.

Ongoing HIV replication in lymph node sanctuary sites in treated patients contributes to the total latent HIV at a very slow rate.

Lymph nodes (LNs) serve as a sanctuary site for HIV viruses due to the heterogeneous distribution of the antiretrovirals (ARVs) inside the LNs. There is an ongoing debate whether this represents ongoing cycles of viral replication in the LNs or merely residual virus production by latently infected cells. Previous work has claimed that the measured levels of genetic variation in proviruses sampled from the blood were inconsistent with ongoing replication. However, it is not clear what rate of variation is consistent with ongoing replication in small sanctuary sites. In this study, we used a spherically symmetric compartmental ODE model to track the HIV viral dynamics in the LN and predict the contribution of ongoing replication within the LN to the wholebody proviral pool in an ARV-suppressed patient. This model tracks the reaction-diffusion dynamics of uninfected, actively infected, and latently infected T-cells as well as free virus within the LN parenchyma and the blood, and distinguishes between latently infected cells created before ARV therapy and during ARV therapy. We simulated suppressive therapy beginning in year 5 post-infection. Each LN sanctuary site had a volume of 1 ml, and we considered cases of 1ml, 30ml, and 250ml total volume, which represent a single active sanctuary site, moderate systemic involvement, and involvement of the total lymphoid tissue. Viral load in the blood rapidly dropped and remained below the limit of detection in all cases but remained high in the LN sanctuary sites. Novel latent cells increased systemically over time but very slowly, taking between 25 and 50 years to reach 5% of the total latent pool, depending on the volume of lymphoid tissue involvement. Putative sanctuary sites in LNs are limited in volume and produce novel latent cells slowly. Assays to detect genetic drift due to such sites would require very deep sequencing if sampling only from the blood. Previous studies showing a lack of genetic drift are consistent with the expected contribution of ongoing replication in lymph node sanctuary sites.

Modeling uncertainty in single-copy assays for HIV.

We present a simple computational model of measurement accuracy for single-copy sensitivity assays (SCA) of HIV RNA that was developed from first principles. The model shows that the SCA is significantly right-skewed. Measured virus concentrations of 1 and 10 virions/ml had overlapping 95% confidence intervals and were statistically indistinguishable.

Controlling the Evolution of Resistance.

Evolution has long been understood as the driving force for many problems of medical interest. The evolution of drug resistance in HIV and bacterial infections is recognized as one of the most significant emerging problems in medicine. In cancer therapy, the evolution of resistance to chemotherapeutic agents is often the differentiating factor between effective therapy and disease progression or death. Interventions to manage the evolution of resistance have, up to this point, been based on steady-state analysis of mutation and selection models. In this paper, we review the mathematical methods applied to studying evolution of resistance in disease. We present a broad review of several classical applications of mathematical modeling of evolution, and review in depth two recent problems which demonstrate the potential for interventions which exploit the dynamic behavior of resistance evolution models. The first problem addresses the problem of sequential treatment failures in HIV; we present a review of our recent publications addressing this problem. The second problem addresses a novel approach to gene therapy for pancreatic cancer treatment, where selection is used to encourage optimal spread of susceptibility genes through a target tumor, which is then eradicated during a second treatment phase. We review the recent in Vitro laboratory work on this topic, present a new mathematical model to describe the treatment process, and show why model-based approaches will be necessary to successfully implement this novel and promising approach.

An Integrated Spatial Dynamics-Pharmacokinetic Model Explaining Poor Penetration of Anti-retroviral Drugs in Lymph Nodes.

Although combined anti-retroviral therapy (cART) suppresses plasma HIV viremia below the limit of detection in a majority of HIV patients, evidence is emerging that the distribution of the anti-retroviral drugs is heterogeneous in tissue. Clinical studies measuring antiretroviral drug concentrations in lymph nodes (LNs) revealed lower concentrations compared to peripheral blood levels suggesting poor drug penetration properties. Our current study is an attempt to understand this poor anti-retroviral drug penetration inside lymph node lobules through integrating known pharmacokinetic and pharmacodynamic (PK/PD) parameters of the anti-retroviral drugs into a spatial model of reaction and transport dynamics within a solid lymph node lobule. Simulated drug penetration values were compared against experimental results whenever available or matched with data that is available for other drugs in a similar class. Our integrated spatial dynamics pharmacokinetic model reproduced the experimentally observed exclusion of antivirals from lymphoid sites. The strongest predictor of drug exclusion from the lymphoid lobule, independent of drug class, was lobule size; large lobules (high inflammation) exhibited high levels of drug exclusion. PK/PD characteristics associated with poor lymphoid penetration include high cellular uptake rates and low intracellular half-lives. To determine whether this exclusion might lead to ongoing replication, target CD4+ T cell, infected CD4+ T cell, free virus, and intracellular IC50 values of anti-retroviral drugs were incorporated into the model. Notably, for median estimates of PK/PD parameters and lobule diameters consistent with low to moderate inflammation, the model predicts no ongoing viral replication, despite substantial exclusion of the drugs from the lymphoid site. Monte-Carlo studies drawn from the prior distributions of the PK/PD parameters predicts increases in site-specific HIV replication in a small fraction of the patient population for lobule diameters greater than 0.2 mm; this fraction increases as the site diameter/ inflammation level increases. The model shows that cART consisting of two nRTIs and one PI is the most likely treatment combination to support formation of a sanctuary site, a finding that is consistent with clinical observations.

Optimal control modulation of HIV reservoir formation rate by antigen infusion.

The Human Immunodeficiency Virus (HIV) infects helper-T cells, and takes advantage of the naturally occurring quiescent phenotype of T cells to persist even under effective treatment conditions. If an infected cell does not produce virus and enters this quiescent state, it forms a natural reservoir that is not targeted by either the existing antiretroviral drugs or the immune system. These quiescent cells intermittently switch to an activated phenotype and begin to produce virus, and are the primary source of viral rebound following treatment cessation. Recent experimental results have shown that, despite this reservoir having a years-long half-life under treatment, most of the cells in the reservoir were infected in a few weeks prior to the start of treatment. This can only be explained by assuming that this reservoir has a short half-life off treatment and a very long half-life on treatment. In this paper, we introduce a novel model of reservoir formation and turnover explaining this difference as a result of antigen-dependent activation. We introduce a second control input through infusion of HIV antigen, mimicking the non-infection pseudovirus (PV) produced by protease inhibitor therapy. This model is coupled to an existing model of immune response to HIV. We fit the parameters of this model to the existing clinical observations of latency. We show that the use of antigen infusion therapy can result in order-of-magnitude decrease in the size of the quiescent reservoir, and that this may provide a way to rapidly stabilize a post-treatment control state in treated HIV infected individuals.

Positive feedback through inflammation creates bistable behavior in HIV tissue sanctuaries.

Combination Antiretroviral Therapy (cART) consists of a cocktail of drugs administered to HIV-infected patients that can suppress the amount of HIV in the patient's blood plasma to an undetectable level. Our previous work has suggested that some HIV-infected patients, despite being placed on cART, can still have ongoing viral replication occurring in self-sustaining inflamed lymph node follicle sanctuary sites. Spatial models of the putative sites show that inflammation is a necessary condition for ongoing HIV replication. In this study, we model the hypothesis that ongoing HIV replication may provide a sufficiently strong pro-inflammatory signal to maintain inflammation levels consistent with continued HIV replication. A system of ordinary differential equations integrated with a reactive-diffusion system is used to model the HIV dynamics and the diameter of a lymph node follicle as a function of time and external influence. The estimates of the parameters in our model come from prior data when available. The results of our study show that these dynamics have two stable steady-state solutions, one with low inflammation and no ongoing HIV replication in the site, and one with high inflammation and high levels of ongoing HIV replication in the site. We furthermore show that the system can transition between the two outcomes in response to a transient exogenous addition of pro-inflammatory signaling, consistent with the antigenic stimulus of a secondary infection. The spatial isolation of the sites results in a low viral load in the blood plasma for both conditions.

HIV 2-LTR experiment design optimization.

Clinical trials are necessary in order to develop treatments for diseases; however, they can often be costly, time consuming, and demanding to the patients. This paper summarizes several common methods used for optimal design that can be used to address these issues. In addition, we introduce a novel method for optimizing experiment designs applied to HIV 2-LTR clinical trials. Our method employs Bayesian techniques to optimize the experiment outcome by maximizing the Expected Kullback-Leibler Divergence (EKLD) between the a priori knowledge of system parameters before the experiment and the a posteriori knowledge of the system parameters after the experiment. We show that our method is robust and performs equally well if not better than traditional optimal experiment design techniques.

Implications of Measurement Assay Type in Design of HIV Experiments.

Time series measurements of circular viral episome (2-LTR) concentrations enable indirect quantification of persistent low-level Human Immunodeficiency Virus (HIV) replication in patients on Integrase-Inhibitor intensified Combined Antiretroviral Therapy (cART). In order to determine the magnitude of these low level infection events, blood has to be drawn from a patients at a frequency and volume that is strictly regulated by the Institutional Review Board (IRB). Once the blood is drawn, the 2-LTR concentration is determined by quantifying the amount of HIV DNA present in the sample via a PCR (Polymerase Chain Reaction) assay. Real time quantitative Polymerase Chain Reaction (qPCR) is a widely used method of performing PCR; however, a newer droplet digital Polymerase Chain Reaction (ddPCR) method has been shown to provide more accurate quantification of DNA. Using a validated model of HIV viral replication, this paper demonstrates the importance of considering DNA quantification assay type when optimizing experiment design conditions. Experiments are optimized using a Genetic Algorithm (GA) to locate a family of suboptimal sample schedules which yield the highest fitness. Fitness is defined as the expected information gained in the experiment, measured by the Kullback-Leibler Divergence (KLD) between the prior and posterior distributions of the model parameters. We compare the information content of the optimized schedules to uniform schedules as well as two clinical schedules implemented by researchers at UCSF and the University of Melbourne. This work shows that there is a significantly greater gain information in experiments using a ddPCR assay vs. a qPCR assay and that certain experiment design considerations should be taken when using either assay.

Increased inflammation in sanctuary sites may explain viral blips in HIV infection.

Combined antiretroviral therapy (cART) suppress HIV-1 viral replication, such that viral load in plasma remains below the limit of detection in standard assays. However, intermittent episodes of transient viremia (blips) occur in a set of HIV-patients. Given that follicular hyperplasia occurs during lymphoid inflammation as a normal response to infection, it is hypothesised that when the diameter of the lymph node follicle (LNF) increases and crosses a critical size, a viral blip occurs due to cryptic viremia. To study this hypothesis, a theoretical analysis of a mathematical model is performed to find the conditions for virus suppression in all compartments and different scenarios of LNF size changes are simulated. According to the analysis, blips with duration of around 30 days arise when the diameter rise rate is between 0.02 and 0.03 days(-1). Moreover, the final diameter of the site is directly related to the steady states of the virus load after the occurrence of a blip. When the value of R0 is around 2.1, to have a steady-state below the limit of detection after the viral blip, the maximum final diameters should be greater than 0.7 mm so that there is a relative loss of connection between compartments.

Prospective HIV Clinical Trial Comparison by Expected Kullback-Leibler Divergence.

The sample frequency and volume of blood that can be drawn from a single patient is meticulously restricted under the human subject protection protocols established by an institutional review board (IRB). Consequently, the amount of samples that can be taken during a particular experiment is limited. In order to ensure an effective experiment design, considerations must be taken choosing when to take patient samples. A validated model of HIV-1 viral replication and 2-LTR production is exploited to find sub-optimal sampling schedules that maximize information content of the experiment outcome. This is done through a Forward Stepwise Regression (FSR) process with Kullback Liebler Divergence (KLD) as a selection criterion. Suboptimal schedules are found for an experiment taking four sample points over a possible span of 20 weeks. All schedules found with the FSR process contain significantly more information than both a uniform schedule and a schedule used in a previous experiment with 4 sample points. This work demonstrates the advantages of using KLD as a tool in the experiment design process to increase information content.

Modelling HIV-1 2-LTR dynamics following raltegravir intensification.

A model of reservoir activation and viral replication is introduced accounting for the production of 2-LTR HIV-1 DNA circles following antiviral intensification with the HIV integrase inhibitor raltegravir, considering contributions of de novo infection events and exogenous sources of infected cells, including quiescent infected cell activation. The model shows that a monotonic increase in measured 2-LTR concentration post intensification is consistent with limited de novo infection primarily maintained by sources of infected cells unaffected by raltegravir, such as quiescent cell activation, while a transient increase in measured 2-LTR concentration is consistent with significant levels of efficient (R0 > 1) de novo infection. The model is validated against patient data from the INTEGRAL study and is shown to have a statistically significant fit relative to the null hypothesis of random measurement variation about a mean. We obtain estimates and confidence intervals for the model parameters, including 2-LTR half-life. Seven of the 13 patients with detectable 2-LTR concentrations from the INTEGRAL study have measured 2-LTR dynamics consistent with significant levels of efficient replication of the virus prior to treatment intensification.

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

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

Quantitative analysis of viral persistence and transient viral load rebound from HIV clinical data.

Highly active antiretroviral therapy (HAART) suppresses HIV RNA viral load below the limit of detection for many patients. However, clinical data demonstrates that the HIV virus is not eradicated by HAART, even in patients who have had no detectable virus for 7 years [1]. One possible reason is that a stable resting latent reservoir with a long half-life exists in resting memory CD4(+)T cells [2]. In this paper, we propose a mathematical model with a constant contribution of a stable latent reservoir and identified this constant by using one patient's data from AutoVac HAART interruption study [3]. Many patients also have transient rebounds of plasma viral RNA (viral blips) under otherwise successful control of the virus by HAART. Activation of latently infected cells can explain these transient rebounds of viral load. Little quantitative analysis about the activation of reservoir has been done based on any clinical experiment data. Here, we model the activation dynamics of the reservoir by a time-independent activation rate and estimate this rate by using the clinical data from the AutoVac HAART interruption study [3].

Optimal antiviral switching to minimize resistance risk in HIV therapy.

The development of resistant strains of HIV is the most significant barrier to effective long-term treatment of HIV infection. The most common causes of resistance development are patient noncompliance and pre-existence of resistant strains. In this paper, methods of antiviral regimen switching are developed that minimize the risk of pre-existing resistant virus emerging during therapy switches necessitated by virological failure. Two distinct cases are considered; a single previous virological failure and multiple virological failures. These methods use optimal control approaches on experimentally verified mathematical models of HIV strain competition and statistical models of resistance risk. It is shown that, theoretically, order-of-magnitude reduction in risk can be achieved, and multiple previous virological failures enable greater success of these methods in reducing the risk of subsequent treatment failures.

Modeling-error robustness of a viral-load preconditioning strategy for HIV treatment switching.

In previous work, we have developed optimal-control based approaches that seek to minimize the risk of subsequent virological failure by "pre-conditioning" the viral load during therapy switches. In this paper, we use Monte-Carlo methods to evaluate the sensitivity of an open-loop implementation of these approaches to modeling errors. To account for hidden parameter dependencies, we use parameter distributions obtained from the convergence of Bayesian parameter estimation techniques applied to sets of clinical data obtained during serial therapy interruptions as the distribution from which the Monte-Carlo method samples.