Early exposure to broadly neutralizing antibodies may trigger a dynamical switch from progressive disease to lasting control of SHIV infection.

Antiretroviral therapy (ART) for HIV-1 infection is life-long. Stopping therapy typically leads to the reignition of infection and progressive disease. In a major breakthrough, recent studies have shown that early initiation of ART can lead to sustained post-treatment control of viremia, raising hopes of long-term HIV-1 remission. ART, however, elicits post-treatment control in a small fraction of individuals treated. Strikingly, passive immunization with broadly neutralizing antibodies (bNAbs) of HIV-1 early in infection was found recently to elicit long-term control in a majority of SHIV-infected macaques, suggesting that HIV-1 remission may be more widely achievable. The mechanisms underlying the control elicited by bNAb therapy, however, remain unclear. Untreated infection typically leads to progressive disease. We hypothesized that viremic control represents an alternative but rarely realized outcome of the infection and that early bNAb therapy triggers a dynamical switch to this outcome. To test this hypothesis, we constructed a model of viral dynamics with bNAb therapy and applied it to analyse clinical data. The model fit quantitatively the complex longitudinal viral load data from macaques that achieved lasting control. The model predicted, consistently with our hypothesis, that the underlying system exhibited bistability, indicating two potential outcomes of infection. The first had high viremia, weak cytotoxic effector responses, and high effector exhaustion, marking progressive disease. The second had low viremia, strong effector responses, and low effector exhaustion, indicating lasting viremic control. Further, model predictions suggest that early bNAb therapy elicited lasting control via pleiotropic effects. bNAb therapy lowers viremia, which would also limit immune exhaustion. Simultaneously, it can improve effector stimulation via cross-presentation. Consequently, viremia may resurge post-therapy, but would encounter a primed effector population and eventually get controlled. ART suppresses viremia but does not enhance effector stimulation, explaining its limited ability to elicit post-treatment control relative to bNAb therapy

Interferon at the cellular, individual, and population level in hepatitis C virus infection: Its role in the interferon-free treatment era

The advent of powerful direct-acting antiviral agents (DAAs) has revolutionized the treatment of hepatitis C. DAAs cure nearly all patients with short duration, oral treatments. Significant efforts are now underway to optimize DAA-based treatments. We discuss the potential role of interferon in this optimization. Clinical studies present compelling evidence that DAAs perform better in treatment-naive individuals than in individuals who previously failed treatment with interferon, a surprising correlation because interferon and DAAs are thought to act independently. Recent mathematical models explore a mechanistic hypothesis underlying this correlation. The hypothesis invokes the action of interferon at the cellular, individual, and population levels. Strong interferon responses prevent the productive infection of cells, reduce viral replication, and impede the development of resistance to DAAs in infected individuals and improve cure rates elicited by DAAs in treated populations. The models develop descriptions of these processes, integrate them into a comprehensive framework, and capture clinical data quantitatively, providing a successful test of the hypothesis. Individuals with strong endogenous interferon responses thus present a promising subpopulation for reducing DAA treatment durations. This review discusses the conceptual advances made by the models, highlights the new insights they unravel, and examines their applicability to optimize DAA-based treatments

Leveraging mathematical modeling to analyze nonadherence for hydroxyurea therapy in sickle cell disease

Abstract Nonadherence is common in individuals with sickle cell disease (SCD) on hydroxyurea therapy and can be observed with waning improvements in hematologic parameters or biomarkers like mean cell volume and fetal hemoglobin level over time. We modeled the impact of hydroxyurea nonadherence on longitudinal biomarker profiles. We estimated the potential nonadherent days in individuals exhibiting a drop in biomarker levels by modifying the dosing profile using a probabilistic approach. Incorporating additional nonadherence using our approach besides existing ones in the dosing profile improves the model fits. We also studied how different patterns in adherence give rise to various physiological profiles of biomarkers. The key finding is consecutive days of nonadherence are less favorable than when nonadherence is interspersed. These findings improve our understanding of nonadherence and how appropriate intervention strategies can be applied for individuals with SCD susceptible to the severe impacts of nonadherence

Mutational pathway maps and founder effects define the within-host spectrum of hepatitis C virus mutants resistant to drugs.

Knowledge of the within-host frequencies of resistance-associated amino acid variants (RAVs) is important to the identification of optimal drug combinations for the treatment of hepatitis C virus (HCV) infection. Multiple RAVs may exist in infected individuals, often below detection limits, at any resistance locus, defining the diversity of accessible resistance pathways. We developed a multiscale mathematical model to estimate the pre-treatment frequencies of the entire spectrum of mutants at chosen loci. Using a codon-level description of amino acids, we performed stochastic simulations of intracellular dynamics with every possible nucleotide variant as the infecting strain and estimated the relative infectivity of each variant and the resulting distribution of variants produced. We employed these quantities in a deterministic multi-strain model of extracellular dynamics and estimated mutant frequencies. Our predictions captured database frequencies of the RAV R155K, resistant to NS3/4A protease inhibitors, presenting a successful test of our formalism. We found that mutational pathway maps, interconnecting all viable mutants, and strong founder effects determined the mutant spectrum. The spectra were vastly different for HCV genotypes 1a and 1b, underlying their differential responses to drugs. Using a fitness landscape determined recently, we estimated that 13 amino acid variants, encoded by 44 codons, exist at the residue 93 of the NS5A protein, illustrating the massive diversity of accessible resistance pathways at specific loci. Accounting for this diversity, which our model enables, would help optimize drug combinations. Our model may be applied to describe the within-host evolution of other flaviviruses and inform vaccine design strategies

Modelling how responsiveness to interferon improves interferon-free treatment of hepatitis C virus infection

Direct-acting antiviral agents (DAAs) for hepatitis C treatment tend to fare better in individuals who are also likely to respond well to interferon-alpha (IFN), a surprising correlation given that DAAs target specific viral proteins whereas IFN triggers a generic antiviral immune response. Here, we posit a causal relationship between IFN-responsiveness and DAA treatment outcome. IFN-responsiveness restricts viral replication, which would prevent the growth of viral variants resistant to DAAs and improve treatment outcome. To test this hypothesis, we developed a multiscale mathematical model integrating IFN-responsiveness at the cellular level, viral kinetics and evolution leading to drug resistance at the individual level, and treatment outcome at the population level. Model predictions quantitatively captured data from over 50 clinical trials demonstrating poorer response to DAAs in previous non-responders to IFN than treatment-naïve individuals, presenting strong evidence supporting the hypothesis. Model predictions additionally described several unexplained clinical observations, viz., the percentages of infected individuals who 1) spontaneously clear HCV, 2) get chronically infected but respond to IFN-based therapy, and 3) fail IFN-based therapy but respond to DAA-based therapy, resulting in a comprehensive understanding of HCV infection and treatment. An implication of the causal relationship is that failure of DAA-based treatments may be averted by adding IFN, a strategy of potential use in settings with limited access to DAAs. A second, wider implication is that individuals with greater IFN-responsiveness would require shorter DAA-based treatment durations, presenting a basis and a promising population for response-guided therapy

Mathematical Modeling of Hydroxyurea Therapy in Individuals with Sickle Cell Disease

Sickle cell disease (SCD) is a chronic hemolytic anemia affecting millions worldwide with acute and chronic clinical manifestations and early mortality. While hydroxyurea (HU) and other treatment strategies managed to ameliorate disease severity, high inter-individual variability in clinical response and a lack of an ability to predict those variations need to be addressed to maximize the clinical efficacy of HU. We developed pharmacokinetics (PK) and pharmacodynamics (PD) models to study the dosing, efficacy, toxicity, and clinical response of HU treatment in more than eighty children with SCD. The clinical PK parameters were used to model the HU plasma concentration for a 24 h period, and the estimated daily average HU plasma concentration was used as an input to our PD models with approximately 1 to 9 years of data connecting drug exposure with drug response. We modeled the biomarkers mean cell volume and fetal hemoglobin to study treatment efficacy. For myelosuppression, we modeled red blood cells and absolute neutrophil count. Our models provided excellent fits for individuals with known or correctly inferred adherence. Our models can be used to determine the optimal dosing regimens and study the effect of non-adherence on HU-treated individuals

Strategies to overcome DAA failure.

<p>The best-fit (solid line) and 95% CIs (dashed lines) of Eq (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.e185" target="_blank">18</a>) (Methods) to data (symbols) of SVR rates in treatment-naïve versus treatment-experienced patients <b>(A)</b> without liver cirrhosis and <b>(B)</b> with liver cirrhosis, treated with DAAs with (filled) or without (open) PR. The list of clinical trials from which data has been collated is presented in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s005" target="_blank">S2</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s006" target="_blank">S3</a> Tables, respectively. The fits yielded and 33±14% in the two subpopulations, respectively, and using which, we estimated the corresponding <i>ϕ</i>_<i>null</i> = 0.07 and 0.12. <b>(C)</b> Regions in the phase diagram (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.g002" target="_blank">Fig 2A</a>) where addition of PR to the DAA would elicit cure in otherwise failing patients with (orange) or without (orange and red) liver cirrhosis. SVR would be elicited in the dark blue region of the phase diagram. <b>(D)</b> The yellow box in (C) zoomed to demonstrate the influence of adding PR to an individual with a cirrhotic (small white arrow) or a non-cirrhotic (large white arrow) liver, adding a new DAA or increasing DAA dosage (yellow arrow), or adding PR and a new DAA (green arrow). <b>(E-H)</b> Dynamics of wild-type (solid) and RAV (dashed) viral populations following treatment initiation for the different conditions marked in (D). <b>(I)</b> The duration of treatment in weeks required to achieve SVR for a range of values of IFN-responsiveness, , and the relative fitness of the RAV, <i>γ</i>_<i>t</i>. <b>(J)</b> Dynamics of wild-type (solid) and RAV (dashed) viral populations following treatment initiation for the different conditions marked in (I), corresponding to daclatasvir treatment (Methods). <i>Inset</i>: The percentage of patients predicted to achieve SVR as a function of the duration of treatment with daclatasvir. The percentages corresponding to the conditions marked in (I) are indicated. Thus, 19.2%, 46% and 60.6% SVR rates are expected in 8, 10, and 12 weeks of treatment, respectively.</p

Response to PR+DAA treatment.

<p><b>(A)</b> Phase diagram indicating regimes of IFN-responsiveness pre- and during treatment, and , leading to SVR (dark blue) and treatment failure due to virological breakthrough by the RAV (light blue) for a fixed relative fitness of the RAV during treatment, <i>γ</i>_<i>t</i>. <b>(B)</b> Dynamics of wild-type (solid) and RAV (dashed) viral populations following treatment initiation for parameter combinations numbered in (A). <b>(C)</b> Phase diagram on a plot for fixed . <b>(D)</b> Dynamics for the points numbered in (C). In (A)-(D), the DAA efficacy against the wild-type, . Also, <i>γ</i> = 0.4. <b>(E)-(H)</b> Corresponding predictions with . In (E) and (G), treatment failure occurred due to the RAV (light blue), wild-type (green), or both (brown). Here, <i>γ</i> = 0.2. Other parameter values employed are in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s008" target="_blank">S5 Table</a>. Phase diagrams for other values of are in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s003" target="_blank">S3 Fig</a>.</p

Pre-treatment frequencies and populations of virions.

<p>Model predictions (lines) and analytical approximations (symbols) (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s009" target="_blank">S1</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s011" target="_blank">S3 Texts</a>) of the mutant frequencies (left) and viral populations (right) in the pre-treatment steady state as a function of the level of IFN-responsiveness, , for different combinations of the mutation rate, <i>μ</i>, and the relative fitness of the RAV, <i>γ</i>: (<i>μ</i>,<i>γ</i>) = (3×10⁻⁴,0.9) (blue), (3×10⁻⁴,0.8) (red), (3×10⁻⁴,0.7) (green) and (3×10⁻⁵,0.8) (black). Here, <i>γ</i> = <i>p</i>₁/<i>p</i>₀, the ratio of the viral production rates, or equivalently the replicative abilities, of the mutant and wild-type strains; without loss of generality, the RAV was assumed not to compromise viral infectivity (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s009" target="_blank">S1</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s011" target="_blank">S3 Texts</a>). Single mutant frequencies (<b>A)</b> and the populations of wild-type <b>(B)</b> and single mutant <b>(C)</b> virions when the genetic barrier is 1. Double mutant frequencies <b>(D)</b> and the populations of wild-type <b>(E)</b>, single mutant <b>(F)</b>, and double mutant <b>(G)</b> virions when the genetic barrier is 2. In the latter case, the two single mutants have the same relative fitness, <i>γ</i>, and the double mutant, <i>γ</i>². In (B) and (E), the different lines and symbols are indistinguishable. Parameter values employed are in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s008" target="_blank">S5 Table</a>. The parameters to which these predictions are sensitive are as expected from the analytical approximations (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s001" target="_blank">S1 Fig</a>).</p

Response to DAA-based treatments.

<p>SVR rates elicited by various IFN-free and IFN-containing DAA combinations in treatment-naïve and prior null responders to PR from recent clinical trials. The treated population size is indicated in brackets. The significance of the difference in the SVR rates in the two populations is computed using the χ² test. The HCV genotype and whether the patients had liver cirrhosis is indicated. The details of the treatment regimens along with the sources of the data are in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s004" target="_blank">S1 Table</a>.</p