Machine Learning Bolsters Evidence That D1, Nef, and Tat Influence HIV Reservoir Dynamics.

Background: The primary hurdle to curing HIV is due to the establishment of a reservoir early in infection. In an effort to find new treatment strategies, we and others have focused on understanding the selection pressures exerted on the reservoir by studying how proviral sequences change over time. Methods: To gain insights into the dynamics of the HIV reservoir we analyzed longitudinal near full-length sequences from 7 people living with HIV between 1 and 20 years following the initiation of antiretroviral treatment. We used this data to employ Bayesian mixed effects models to characterize the decay of the reservoir using single-phase and multiphasic decay models based on near full-length sequencing. In addition, we developed a machine-learning approach utilizing logistic regression to identify elements within the HIV genome most associated with proviral decay and persistence. By systematically analyzing proviruses that are deleted for a specific element, we gain insights into their role in reservoir contraction and expansion. Results: Our analyses indicate that biphasic decay models of intact reservoir dynamics were better than single-phase models with a stronger statistical fit. Based on the biphasic decay pattern of the intact reservoir, we estimated the half-lives of the first and second phases of decay to be 18.2 (17.3 to 19.2, 95%CI) and 433 (227 to 6400, 95%CI) months, respectively.In contrast, the dynamics of defective proviruses differed favoring neither model definitively, with an estimated half-life of 87.3 (78.1 to 98.8, 95% CI) months during the first phase of the biphasic model. Machine-learning analysis of HIV genomes at the nucleotide level revealed that the presence of the splice donor site D1 was the principal genomic element associated with contraction. This role of D1 was then validated in an in vitro system. Using the same approach, we additionally found supporting evidence that HIV nef may confer a protective advantage for latently infected T cells while tat was associated with clonal expansion. Conclusions: The nature of intact reservoir decay suggests that the long-lived HIV reservoir contains at least 2 distinct compartments. The first compartment decays faster than the second compartment. Our machine-learning analysis of HIV proviral sequences reveals specific genomic elements are associated with contraction while others are associated with persistence and expansion. Together, these opposing forces shape the reservoir over time.

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.

Persistence of an intact HIV reservoir in phenotypically naive T cells.

Despite the efficacy of antiretroviral therapy (ART), HIV persists in a latent form and remains a hurdle to eradication. CD4+ T lymphocytes harbor the majority of the HIV reservoir, but the role of individual subsets remains unclear. CD4+ T cells were sorted into central, transitional, effector memory, and naive T cells. We measured HIV DNA and performed proviral sequencing of more than 1900 proviruses in 2 subjects at 2 and 9 years after ART initiation to estimate the contribution of each subset to the reservoir. Although our study was limited to 2 subjects, we obtained comparable findings with publicly available sequences. While the HIV integration levels were lower in naive compared with memory T cells, naive cells were a major contributor to the intact proviral reservoir. Notably, proviral sequences isolated from naive cells appeared to be unique, while those retrieved from effector memory cells were mainly clonal. The number of clones increased as cells differentiated from a naive to an effector memory phenotype, suggesting naive cells repopulate the effector memory reservoir as previously shown for central memory cells. Naive T cells contribute substantially to the intact HIV reservoir and represent a significant hurdle for HIV eradication.

Longitudinal HIV sequencing reveals reservoir expression leading to decay which is obscured by clonal expansion.

After initiating antiretroviral therapy (ART), a rapid decline in HIV viral load is followed by a long period of undetectable viremia. Viral outgrowth assay suggests the reservoir continues to decline slowly. Here, we use full-length sequencing to longitudinally study the proviral landscape of four subjects on ART to investigate the selective pressures influencing the dynamics of the treatment-resistant HIV reservoir. We find intact and defective proviruses that contain genetic elements favoring efficient protein expression decrease over time. Moreover, proviruses that lack these genetic elements, yet contain strong donor splice sequences, increase relatively to other defective proviruses, especially among clones. Our work suggests that HIV expression occurs to a significant extent during ART and results in HIV clearance, but this is obscured by the expansion of proviral clones. Paradoxically, clonal expansion may also be enhanced by HIV expression that leads to splicing between HIV donor splice sites and downstream human exons.

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.

Experiment Design for Early Molecular Events in HIV Infection.

The recent introduction of integrase inhibitors to the HIV antiviral repertoire permits us to create in vitro experiments that reliably terminate HIV infection at the point of chromosomal integration. This allows us to isolate the dynamics of a single round of infection, without needing to account for the influence of multiple overlapping rounds of infection. By measuring the various nucleic acid concentrations in a population of infected target cells at multiple time points, we can infer the rates of these molecular events with great accuracy, which allows us to compare the rates between target cells with different functional phenotypes. This information will help in understanding the behavior of the various populations of reservoir cells such as active and quiescent T-cells which maintain HIV infection in treated patients. In this paper, we introduce a family of models of the early molecular events in HIV infection, with either linear dynamics or age-structured delays at each step. We introduce an experimental design metric based on the delta AIC (Akaike Information Criteria) between a model fit for simulated data from a matching model vs a mismatched model, which allows us to determine a candidate experiment design's ability to discriminate between models. Using parameters values drawn from experimentally-derived priors corrupted with appropriate measurement noise, we confirm that a proposed sampling schedule at different time points allows us to consistently discriminate between candidate models.

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.

Order preservation of expected information content using Unscented Transform approximation of multivariate prior distributions in HIV 2-LTR experiment design.

Numerical computation of the expected information content of a prospective experimental design is computationally expensive, requiring calculating the Kullback-Leibler divergence of the posterior distribution from the prior for simulated data from a large sample of points from the prior distribution. In this work, we investigate whether the Unscented Transform (UT) of the prior distribution can provide an adequate estimate of the expected information content in the context of experiment design for a previously validated HIV-1 2-LTR model. Three different schedules with evenly distributed time points have been used to generate the experimental data along with the incorporation of qPCR noise for the study. The UT shows promise in estimating information content by preserving the optimal ordering of 2-LTR sample collection schedules, when compared to completely stochastic sampling from the underlying multivariate distributions.

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.