Search

Most people living with HIV-1 experience rapid viral rebound once antiretroviral therapy is interrupted; however, a small fraction remain in viral remission for an extended duration. Understanding the factors that determine whether viral rebound is likely after treatment interruption can enable the development of optimal treatment regimens and therapeutic interventions to potentially achieve a functional cure for HIV-1. We built upon the theoretical framework proposed by Conway and Perelson to construct dynamic models of virus-immune interactions to study factors that influence viral rebound dynamics. We evaluated these models using viral load data from 24 individuals following antiretroviral therapy interruption. The best-performing model accurately captures the heterogeneity of viral dynamics and highlights the importance of the effector cell expansion rate. Our results show that post-treatment controllers and non-controllers can be distinguished based on the effector cell expansion rate in our models. Furthermore, these results demonstrate the potential of using dynamic models incorporating an effector cell response to understand early viral rebound dynamics post-antiretroviral therapy interruption.

To mitigate the loss of lives during the COVID-19 pandemic, emergency use authorization was given to several anti-SARS-CoV-2 monoclonal antibody (mAb) therapies for the treatment of mild-to-moderate COVID-19 in patients with a high risk of progressing to severe disease. Monoclonal antibodies used to treat SARS-CoV-2 target the spike protein of the virus and block its ability to enter and infect target cells. Monoclonal antibody therapy can thus accelerate the decline in viral load and lower hospitalization rates among high-risk patients with variants susceptible to mAb therapy. However, viral resistance has been observed, in some cases leading to a transient viral rebound that can be as large as 3-4 orders of magnitude. As mAbs represent a proven treatment choice for SARS-CoV-2 and other viral infections, evaluation of treatment-emergent mAb resistance can help uncover underlying pathobiology of SARS-CoV-2 infection and may also help in the development of the next generation of mAb therapies. Although resistance can be expected, the large rebounds observed are much more difficult to explain. We hypothesize replenishment of target cells is necessary to generate the high transient viral rebound. Thus, we formulated two models with different mechanisms for target cell replenishment (homeostatic proliferation and return from an innate immune response antiviral state) and fit them to data from persons with SARS-CoV-2 treated with a mAb. We showed that both models can explain the emergence of resistant virus associated with high transient viral rebounds. We found that variations in the target cell supply rate and adaptive immunity parameters have a strong impact on the magnitude or observability of the viral rebound associated with the emergence of resistant virus. Both variations in target cell supply rate and adaptive immunity parameters may explain why only some individuals develop observable transient resistant viral rebound. Our study highlights the conditions that can lead to resistance and subsequent viral rebound in mAb treatments during acute infection.

Mathematical models of viral infection have been developed, fitted to data, and provide insight into disease pathogenesis for multiple agents that cause chronic infection, including HIV, hepatitis C, and B virus. However, for agents that cause acute infections or during the acute stage of agents that cause chronic infections, viral load data are often collected after symptoms develop, usually around or after the peak viral load. Consequently, we frequently lack data in the initial phase of viral growth, i.e., when pre-symptomatic transmission events occur. Missing data may make estimating the time of infection, the infectious period, and parameters in viral dynamic models, such as the cell infection rate, difficult. However, having extra information, such as the average time to peak viral load, may improve the robustness of the estimation. Here, we evaluated the robustness of estimates of key model parameters when viral load data prior to the viral load peak is missing, when we know the values of some parameters and/or the time from infection to peak viral load. Although estimates of the time of infection are sensitive to the quality and amount of available data, particularly pre-peak, other parameters important in understanding disease pathogenesis, such as the loss rate of infected cells, are less sensitive. Viral infectivity and the viral production rate are key parameters affecting the robustness of data fits. Fixing their values to literature values can help estimate the remaining model parameters when pre-peak data is missing or limited. We find a lack of data in the pre-peak growth phase underestimates the time to peak viral load by several days, leading to a shorter predicted growth phase. On the other hand, knowing the time of infection (e.g., from epidemiological data) and fixing it results in good estimates of dynamical parameters even in the absence of early data. While we provide ways to approximate model parameters in the absence of early viral load data, our results also suggest that these data, when available, are needed to estimate model parameters more precisely.

PGT121 is a broadly neutralizing antibody in clinical development for the treatment and prevention of HIV-1 infection via passive administration. PGT121 targets the HIV-1 V3-glycan and demonstrated potent antiviral activity in a phase I clinical trial. Resistance to PGT121 monotherapy rapidly occurred in the majority of participants in this trial with the sampled rebound viruses being entirely resistant to PGT121 mediated neutralization. However, two individuals experienced long-term ART-free viral suppression following antibody infusion and retained sensitivity to PGT121 upon viral rebound. Here, we develop mathematical models of the HIV-1 dynamics during this phase I clinical trial. We utilize these models to understand the dynamics leading to PGT121 resistance and to identify the mechanisms driving the observed long-term viral control. Our modeling highlights the importance of the relative fitness difference between PGT121 sensitive and resistant subpopulations prior to treatment. Specifically, by fitting our models to data, we identify the treatment-induced competitive advantage of previously existing or newly generated resistant population as a primary driver of resistance. Finally, our modeling emphasizes the high neutralization ability of PGT121 in both participants who exhibited long-term viral control.

Chronic infection with hepatitis B virus (HBV) is caused by the persistence of closed circular DNA (cccDNA) in the nucleus of infected hepatocytes. Despite available therapeutic anti-HBV agents, eliminating the cccDNA remains challenging. Thus, quantifying and understanding the dynamics of cccDNA are essential for developing effective treatment strategies and new drugs. However, such study requires repeated liver biopsy to measure the intrahepatic cccDNA, which is basically not accepted because liver biopsy is potentially morbid and not common during hepatitis B treatment. We here aimed to develop a noninvasive method for quantifying cccDNA in the liver using surrogate markers in peripheral blood. We constructed a multiscale mathematical model that explicitly incorporates both intracellular and intercellular HBV infection processes. The model, based on age-structured partial differential equations, integrates experimental data from in vitro and in vivo investigations. By applying this model, we roughly predicted the amount and dynamics of intrahepatic cccDNA within a certain range using specific viral markers in serum samples, including HBV DNA, HBsAg, HBeAg, and HBcrAg. Our study represents a significant step towards advancing the understanding of chronic HBV infection. The noninvasive quantification of cccDNA using our proposed method holds promise for improving clinical analyses and treatment strategies. By comprehensively describing the interactions of all components involved in HBV infection, our multiscale mathematical model provides a valuable framework for further research and the development of targeted interventions.

Plus-strand RNA viruses are the largest group of viruses. Many are human pathogens that inflict a socio-economic burden. Interestingly, plus-strand RNA viruses share remarkable similarities in their replication. A hallmark of plus-strand RNA viruses is the remodeling of intracellular membranes to establish replication organelles (so-called "replication factories"), which provide a protected environment for the replicase complex, consisting of the viral genome and proteins necessary for viral RNA synthesis. In the current study, we investigate pan-viral similarities and virus-specific differences in the life cycle of this highly relevant group of viruses. We first measured the kinetics of viral RNA, viral protein, and infectious virus particle production of hepatitis C virus (HCV), dengue virus (DENV), and coxsackievirus B3 (CVB3) in the immuno-compromised Huh7 cell line and thus without perturbations by an intrinsic immune response. Based on these measurements, we developed a detailed mathematical model of the replication of HCV, DENV, and CVB3 and showed that only small virus-specific changes in the model were necessary to describe the in vitro dynamics of the different viruses. Our model correctly predicted virus-specific mechanisms such as host cell translation shut off and different kinetics of replication organelles. Further, our model suggests that the ability to suppress or shut down host cell mRNA translation may be a key factor for in vitro replication efficiency, which may determine acute self-limited or chronic infection. We further analyzed potential broad-spectrum antiviral treatment options in silico and found that targeting viral RNA translation, such as polyprotein cleavage and viral RNA synthesis, may be the most promising drug targets for all plus-strand RNA viruses. Moreover, we found that targeting only the formation of replicase complexes did not stop the in vitro viral replication early in infection, while inhibiting intracellular trafficking processes may even lead to amplified viral growth.

In HIV-1-infected individuals, transmitted/founder (TF) virus contributes to establish new infection and expands during the acute phase of infection, while chronic control (CC) virus emerges during the chronic phase of infection. TF viruses are more resistant to interferon-alpha (IFN-α)-mediated antiviral effects than CC virus, however, its virological relevance in infected individuals remains unclear. Here we perform an experimental-mathematical investigation and reveal that IFN-α strongly inhibits cell-to-cell infection by CC virus but only weakly affects that by TF virus. Surprisingly, IFN-α enhances cell-free infection of HIV-1, particularly that of CC virus, in a virus-cell density-dependent manner. We further demonstrate that LY6E, an IFN-stimulated gene, can contribute to the density-dependent enhancement of cell-free HIV-1 infection. Altogether, our findings suggest that the major difference between TF and CC viruses can be explained by their resistance to IFN-α-mediated inhibition of cell-to-cell infection and their sensitivity to IFN-α-mediated enhancement of cell-free infection.

While the liver, specifically hepatocytes, are widely accepted as the main source of hepatitis C virus (HCV) production, the role of the liver/hepatocytes in clearance of circulating HCV remains unknown. Frequent HCV kinetic data were recorded and mathematically modeled from five liver transplant patients throughout the anhepatic (absence of liver) phase and for 4 hr post-reperfusion. During the anhepatic phase, HCV remained at pre-anhepatic levels (n = 3) or declined (n = 2) with t1/2~1 hr. Immediately post-reperfusion, virus declined in a biphasic manner in four patients consisting of a rapid decline (t1/2 = 5 min) followed by a slower decline (t1/2 = 67 min). Consistent with the majority of patients in the anhepatic phase, when we monitored HCV clearance at 37°C from culture medium in the absence/presence of chronically infected hepatoma cells that were inhibited from secreting HCV, the HCV t1/2 in cell culture was longer in the absence of chronically HCV-infected cells. The results suggest that the liver plays a major role in the clearance of circulating HCV and that hepatocytes may be involved.

BackgroundDevelopment of an effective antiviral drug for Coronavirus Disease 2019 (COVID-19) is a global health priority. Although several candidate drugs have been identified through in vitro and in vivo models, consistent and compelling evidence from clinical studies is limited. The lack of evidence from clinical trials may stem in part from the imperfect design of the trials. We investigated how clinical trials for antivirals need to be designed, especially focusing on the sample size in randomized controlled trials.Methods and findingsA modeling study was conducted to help understand the reasons behind inconsistent clinical trial findings and to design better clinical trials. We first analyzed longitudinal viral load data for Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) without antiviral treatment by use of a within-host virus dynamics model. The fitted viral load was categorized into 3 different groups by a clustering approach. Comparison of the estimated parameters showed that the 3 distinct groups were characterized by different virus decay rates (p-value < 0.001). The mean decay rates were 1.17 d-1 (95% CI: 1.06 to 1.27 d-1), 0.777 d-1 (0.716 to 0.838 d-1), and 0.450 d-1 (0.378 to 0.522 d-1) for the 3 groups, respectively. Such heterogeneity in virus dynamics could be a confounding variable if it is associated with treatment allocation in compassionate use programs (i.e., observational studies). Subsequently, we mimicked randomized controlled trials of antivirals by simulation. An antiviral effect causing a 95% to 99% reduction in viral replication was added to the model. To be realistic, we assumed that randomization and treatment are initiated with some time lag after symptom onset. Using the duration of virus shedding as an outcome, the sample size to detect a statistically significant mean difference between the treatment and placebo groups (1:1 allocation) was 13,603 and 11,670 (when the antiviral effect was 95% and 99%, respectively) per group if all patients are enrolled regardless of timing of randomization. The sample size was reduced to 584 and 458 (when the antiviral effect was 95% and 99%, respectively) if only patients who are treated within 1 day of symptom onset are enrolled. We confirmed the sample size was similarly reduced when using cumulative viral load in log scale as an outcome. We used a conventional virus dynamics model, which may not fully reflect the detailed mechanisms of viral dynamics of SARS-CoV-2. The model needs to be calibrated in terms of both parameter settings and model structure, which would yield more reliable sample size calculation.ConclusionsIn this study, we found that estimated association in observational studies can be biased due to large heterogeneity in viral dynamics among infected individuals, and statistically significant effect in randomized controlled trials may be difficult to be detected due to small sample size. The sample size can be dramatically reduced by recruiting patients immediately after developing symptoms. We believe this is the first study investigated the study design of clinical trials for antiviral treatment using the viral dynamics model.

Treating macaques with an anti-α4β7 antibody under the umbrella of combination antiretroviral therapy (cART) during early SIV infection can lead to viral remission, with viral loads maintained at < 50 SIV RNA copies/ml after removal of all treatment in a subset of animals. Depletion of CD8+ lymphocytes in controllers resulted in transient recrudescence of viremia, suggesting that the combination of cART and anti-α4β7 antibody treatment led to a state where ongoing immune responses kept the virus undetectable in the absence of treatment. A previous mathematical model of HIV infection and cART incorporates immune effector cell responses and exhibits the property of two different viral load set-points. While the lower set-point could correspond to the attainment of long-term viral remission, attaining the higher set-point may be the result of viral rebound. Here we expand that model to include possible mechanisms of action of an anti-α4β7 antibody operating in these treated animals. We show that the model can fit the longitudinal viral load data from both IgG control and anti-α4β7 antibody treated macaques, suggesting explanations for the viral control associated with cART and an anti-α4β7 antibody treatment. This effective perturbation to the virus-host interaction can also explain observations in other nonhuman primate experiments in which cART and immunotherapy have led to post-treatment control or resetting of the viral load set-point. Interestingly, because the viral kinetics in the various treated animals differed-some animals exhibited large fluctuations in viral load after cART cessation-the model suggests that anti-α4β7 treatment could act by different primary mechanisms in different animals and still lead to post-treatment viral control. This outcome is nonetheless in accordance with a model with two stable viral load set-points, in which therapy can perturb the system from one set-point to a lower one through different biological mechanisms.

The scientific community is focused on developing antiviral therapies to mitigate the impacts of the ongoing novel coronavirus disease 2019 (COVID-19) outbreak. This will be facilitated by improved understanding of viral dynamics within infected hosts. Here, using a mathematical model in combination with published viral load data, we compare within-host viral dynamics of SARS-CoV-2 with analogous dynamics of MERS-CoV and SARS-CoV. Our quantitative analyses using a mathematical model revealed that the within-host reproduction number at symptom onset of SARS-CoV-2 was statistically significantly larger than that of MERS-CoV and similar to that of SARS-CoV. In addition, the time from symptom onset to the viral load peak for SARS-CoV-2 infection was shorter than those of MERS-CoV and SARS-CoV. These findings suggest the difficulty of controlling SARS-CoV-2 infection by antivirals. We further used the viral dynamics model to predict the efficacy of potential antiviral drugs that have different modes of action. The efficacy was measured by the reduction in the viral load area under the curve (AUC). Our results indicate that therapies that block de novo infection or virus production are likely to be effective if and only if initiated before the viral load peak (which appears 2-3 days after symptom onset), but therapies that promote cytotoxicity of infected cells are likely to have effects with less sensitivity to the timing of treatment initiation. Furthermore, combining a therapy that promotes cytotoxicity and one that blocks de novo infection or virus production synergistically reduces the AUC with early treatment. Our unique modeling approach provides insights into the pathogenesis of SARS-CoV-2 and may be useful for development of antiviral therapies.

Repurposed drugs that are safe and immediately available constitute a first line of defense against new viral infections. Despite limited antiviral activity against SARS-CoV-2, several drugs are being tested as medication or as prophylaxis to prevent infection. Using a stochastic model of early phase infection, we evaluate the success of prophylactic treatment with different drug types to prevent viral infection. We find that there exists a critical efficacy that a treatment must reach in order to block viral establishment. Treatment by a combination of drugs reduces the critical efficacy, most effectively by the combination of a drug blocking viral entry into cells and a drug increasing viral clearance. Below the critical efficacy, the risk of infection can nonetheless be reduced. Drugs blocking viral entry into cells or enhancing viral clearance reduce the risk of infection more than drugs that reduce viral production in infected cells. The larger the initial inoculum of infectious virus, the less likely is prevention of an infection. In our model, we find that as long as the viral inoculum is smaller than 10 infectious virus particles, viral infection can be prevented almost certainly with drugs of 90% efficacy (or more). Even when a viral infection cannot be prevented, antivirals delay the time to detectable viral loads. The largest delay of viral infection is achieved by drugs reducing viral production in infected cells. A delay of virus infection flattens the within-host viral dynamic curve, possibly reducing transmission and symptom severity. Thus, antiviral prophylaxis, even with reduced efficacy, could be efficiently used to prevent or alleviate infection in people at high risk.

Experimental Zika virus infection in non-human primates results in acute viral load dynamics that can be well-described by mathematical models. The inoculum dose that would be received in a natural infection setting is likely lower than the experimental infections and how this difference affects the viral dynamics and immune response is unclear. Here we study a dataset of experimental infection of non-human primates with a range of doses of Zika virus. We develop new models of infection incorporating both an innate immune response and viral interference with that response. We find that such a model explains the data better than models with no interaction between virus and the immune response. We also find that larger inoculum doses lead to faster dynamics of infection, but approximately the same total amount of viral production.

Hepatitis C virus (HCV) causes acute hepatitis C and can lead to life-threatening complications if it becomes chronic. The HCV genome is a single plus strand of RNA. Its intracellular replication is a spatiotemporally coordinated process of RNA translation upon cell infection, RNA synthesis within a replication compartment, and virus particle production. While HCV is mainly transmitted via mature infectious virus particles, it has also been suggested that HCV-infected cells can secrete HCV RNA carrying exosomes that can infect cells in a receptor independent manner. In order to gain insight into these two routes of transmission, we developed a series of intracellular HCV replication models that include HCV RNA secretion and/or virus assembly and release. Fitting our models to in vitro data, in which cells were infected with HCV, suggests that initially most secreted HCV RNA derives from intracellular cytosolic plus-strand RNA, but subsequently secreted HCV RNA derives equally from the cytoplasm and the replication compartments. Furthermore, our model fits to the data suggest that the rate of virus assembly and release is limited by host cell resources. Including the effects of direct acting antivirals in our models, we found that in spite of decreasing intracellular HCV RNA and extracellular virus concentration, low level HCV RNA secretion may continue as long as intracellular RNA is available. This may possibly explain the presence of detectable levels of plasma HCV RNA at the end of treatment even in patients that ultimately attain a sustained virologic response.

Mathematical modelling has successfully been used to provide quantitative descriptions of many viral infections, but for the Ebola virus, which requires biosafety level 4 facilities for experimentation, modelling can play a crucial role. Ebola virus modelling efforts have primarily focused on in vivo virus kinetics, e.g., in animal models, to aid the development of antivirals and vaccines. But, thus far, these studies have not yielded a detailed specification of the infection cycle, which could provide a foundational description of the virus kinetics and thus a deeper understanding of their clinical manifestation. Here, we obtain a diverse experimental data set of the Ebola virus infection in vitro, and then make use of Bayesian inference methods to fully identify parameters in a mathematical model of the infection. Our results provide insights into the distribution of time an infected cell spends in the eclipse phase (the period between infection and the start of virus production), as well as the rate at which infectious virions lose infectivity. We suggest how these results can be used in future models to describe co-infection with defective interfering particles, which are an emerging alternative therapeutic.

In order to assess the efficacy of novel HIV-1 treatments leading to a functional cure, the time to viral rebound is frequently used as a surrogate endpoint. The longer the time to viral rebound, the more efficacious the therapy. In support of such an approach, mathematical models serve as a connection between the size of the latent reservoir and the time to HIV-1 rebound after treatment interruption. The simplest of such models assumes that a single successful latent cell reactivation event leads to observable viremia after a period of exponential viral growth. Here we consider a generalization developed by Pinkevych et al. and Hill et al. of this simple model in which multiple reactivation events can occur, each contributing to the exponential growth of the viral load. We formalize and improve the previous derivation of the dynamics predicted by this model, and use the model to estimate relevant biological parameters from SIV rebound data. We confirm a previously described effect of very early antiretroviral therapy (ART) initiation on the rate of recrudescence and the viral load growth rate after treatment interruption. We find that every day ART initiation is delayed results in a 39% increase in the recrudescence rate (95% credible interval: [18%, 62%]), and a 11% decrease of the viral growth rate (95% credible interval: [4%, 20%]). We show that when viral rebound occurs early relative to the viral load doubling time, a model with multiple successful reactivation events fits the data better than a model with only a single successful reactivation event.

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.

CD8+ lymphocytes play an important role in suppressing in vivo viral replication in HIV infection. However, both the extent to which and the mechanisms by which CD8+ lymphocytes contribute to viral control are not completely understood. A recent experiment depleted CD8+ lymphocytes in simian immunodeficiency virus (SIV)-infected rhesus macaques (RMs) on antiretroviral treatment (ART) to study the role of CD8+ lymphocytes. CD8+ lymphocytes depletion resulted in temporary plasma viremia in all studied RMs. Viral control was restored when CD8+ lymphocytes repopulated. We developed a viral dynamic model to fit the viral load (VL) data from the CD8 depletion experiment. We explicitly modeled the dynamics of the latent reservoir and the SIV-specific effector cell population including their exhaustion and their potential cytolytic and noncytolytic functions. We found that the latent reservoir significantly contributes to the size of the peak VL after CD8 depletion, while drug efficacy plays a lesser role. Our model suggests that the overall CD8+ lymphocyte cytolytic killing rate is dynamically changing depending on the levels of antigen-induced effector cell activation and exhaustion. Based on estimated parameters, our model suggests that before ART or without ART the overall CD8 cytolytic killing rate is small due to exhaustion. However, after the start of ART, the overall CD8 cytolytic killing rate increases due to an expansion of SIV-specific CD8 effector cells. Further, we estimate that the cytolytic killing rate can be significantly larger than the cytopathic death rate in some animals during the second phase of ART-induced viral decay. Lastly, our model provides a new explanation for the puzzling findings by Klatt et al. and Wong et al. that CD8 depletion done immediately before ART has no noticeable effect on the first phase viral decay slope seen after ART initiation Overall, by incorporating effector cells and their exhaustion, our model can explain the effects of CD8 depletion on VL during ART, reveals a detailed dynamic role of CD8+ lymphocytes in controlling viral infection, and provides a unified explanation for CD8 depletion experimental data.

Fundamental to biological decision-making is the ability to generate bimodal expression patterns where 2 alternate expression states simultaneously exist. Here, we use a combination of single-cell analysis and mathematical modeling to examine the sources of bimodality in the transcriptional program controlling HIV's fate decision between active replication and viral latency. We find that the HIV transactivator of transcription (Tat) protein manipulates the intrinsic toggling of HIV's promoter, the long terminal repeat (LTR), to generate bimodal ON-OFF expression and that transcriptional positive feedback from Tat shifts and expands the regime of LTR bimodality. This result holds for both minimal synthetic viral circuits and full-length virus. Strikingly, computational analysis indicates that the Tat circuit's noncooperative "nonlatching" feedback architecture is optimized to slow the promoter's toggling and generate bimodality by stochastic extinction of Tat. In contrast to the standard Poisson model, theory and experiment show that nonlatching positive feedback substantially dampens the inverse noise-mean relationship to maintain stochastic bimodality despite increasing mean expression levels. Given the rapid evolution of HIV, the presence of a circuit optimized to robustly generate bimodal expression appears consistent with the hypothesis that HIV's decision between active replication and latency provides a viral fitness advantage. More broadly, the results suggest that positive-feedback circuits may have evolved not only for signal amplification but also for robustly generating bimodality by decoupling expression fluctuations (noise) from mean expression levels.

The kinetics of HIV-1 decay under treatment depends on the class of antiretrovirals used. Mathematical models are useful to interpret the different profiles, providing quantitative information about the kinetics of virus replication and the cell populations contributing to viral decay. We modeled proviral integration in short- and long-lived infected cells to compare viral kinetics under treatment with and without the integrase inhibitor raltegravir (RAL). We fitted the model to data obtained from participants treated with RAL-containing regimes or with a four-drug regimen of protease and reverse transcriptase inhibitors. Our model explains the existence and quantifies the three phases of HIV-1 RNA decay in RAL-based regimens vs. the two phases observed in therapies without RAL. Our findings indicate that HIV-1 infection is mostly sustained by short-lived infected cells with fast integration and a short viral production period, and by long-lived infected cells with slow integration but an equally short viral production period. We propose that these cells represent activated and resting infected CD4+ T-cells, respectively, and estimate that infection of resting cells represent ~4% of productive reverse transcription events in chronic infection. RAL reveals the kinetics of proviral integration, showing that in short-lived cells the pre-integration population has a half-life of ~7 hours, whereas in long-lived cells this half-life is ~6 weeks. We also show that the efficacy of RAL can be estimated by the difference in viral load at the start of the second phase in protocols with and without RAL. Overall, we provide a mechanistic model of viral infection that parsimoniously explains the kinetics of viral load decline under multiple classes of antiretrovirals.

Hepatitis C virus (HCV) RNA is synthesized by the replicase complex (RC), a macromolecular assembly composed of viral non-structural proteins and cellular co-factors. Inhibitors of the HCV NS5A protein block formation of new RCs but do not affect RNA synthesis by pre-formed RCs. Without new RC formation, existing RCs turn over and are eventually lost from the cell. We aimed to use NS5A inhibitors to estimate the half-life of the functional RC of HCV. We compared different cell culture-infectious strains of HCV that may be grouped based on their sensitivity to lipid peroxidation: robustly replicating, lipid peroxidation resistant (LPOR) viruses (e.g. JFH-1 or H77D) and more slowly replicating, lipid peroxidation sensitive (LPOS) viruses (e.g. H77S.3 and N.2). In luciferase assays, LPOS HCV strains declined under NS5A inhibitor therapy with much slower kinetics compared to LPOR HCV strains. This difference in rate of decline was not observed for inhibitors of the NS5B RNA-dependent RNA polymerase suggesting that the difference was not simply a consequence of differences in RNA stability. In further analyses, we compared two isoclonal HCV variants: the LPOS H77S.3 and the LPOR H77D that differ only by 12 amino acids. Differences in rate of decline between H77S.3 and H77D following NS5A inhibitor addition were not due to amino acid sequences in NS5A but rather due to a combination of amino acid differences in the non-structural proteins that make up the HCV RC. Mathematical modeling of intracellular HCV RNA dynamics suggested that differences in RC stability (half-lives of 3.5 and 9.9 hours, for H77D and H77S.3, respectively) are responsible for the different kinetics of antiviral suppression between LPOS and LPOR viruses. In nascent RNA capture assays, the rate of RNA synthesis decline following NS5A inhibitor addition was significantly faster for H77D compared to H77S.3 indicating different half-lives of functional RCs.

Complications of HIV-1 infection in individuals who utilize drugs of abuse is a significant problem, because these drugs have been associated with higher virus replication and accelerated disease progression as well as severe neuropathogenesis. To gain further insight it is important to quantify the effects of drugs of abuse on HIV-1 infection dynamics. Here, we develop a mathematical model that incorporates experimentally observed effects of morphine on inducing HIV-1 co-receptor expression. For comparison we also considered viral dynamic models with cytolytic or noncytolytic effector cell responses. Based on the small sample size Akaike information criterion, these models were inferior to the new model based on changes in co-receptor expression. The model with morphine affecting co-receptor expression agrees well with the experimental data from simian immunodeficiency virus infections in morphine-addicted macaques. Our results show that morphine promotes a target cell subpopulation switch from a lower level of susceptibility to a state that is about 2-orders of magnitude higher in susceptibility to SIV infection. As a result, the proportion of target cells with higher susceptibility remains extremely high in morphine conditioning. Such a morphine-induced population switch not only has adverse effects on the replication rate, but also results in a higher steady state viral load and larger CD4 count drops. Moreover, morphine conditioning may pose extra obstacles to controlling viral load during antiretroviral therapy, such as pre-exposure prophylaxis and post infection treatments. This study provides, for the first time, a viral dynamics model, viral dynamics parameters, and related analytical and simulation results for SIV dynamics under drugs of abuse.

Antiretroviral therapy (ART) effectively controls HIV infection, suppressing HIV viral loads. However, some residual virus remains, below the level of detection, in HIV-infected patients on ART. The source of this viremia is an area of debate: does it derive primarily from activation of infected cells in the latent reservoir, or from ongoing viral replication? Observations seem to be contradictory: there is evidence of short term evolution, implying that there must be ongoing viral replication, and viral strains should thus evolve. However, phylogenetic analyses, and rare emergent drug resistance, suggest no long-term viral evolution, implying that virus derived from activated latent cells must dominate. We use simple deterministic and stochastic models to gain insight into residual viremia dynamics in HIV-infected patients. Our modeling relies on two underlying assumptions for patients on suppressive ART: that latent cell activation drives viral dynamics and that the reproductive ratio of treated infection is less than 1. Nonetheless, the contribution of viral replication to residual viremia in patients on ART may be non-negligible. However, even if the portion of viremia attributable to viral replication is significant, our model predicts (1) that latent reservoir re-seeding remains negligible, and (2) some short-term viral evolution is permitted, but long-term evolution can still be limited: stochastic analysis of our model shows that de novo emergence of drug resistance is rare. Thus, our simple models reconcile the seemingly contradictory observations on residual viremia and, with relatively few parameters, recapitulates HIV viral dynamics observed in patients on suppressive therapy.

HIV-1 is subject to immune pressure exerted by the host, giving variants that escape the immune response an advantage. Virus released from activated latent cells competes against variants that have continually evolved and adapted to host immune pressure. Nevertheless, there is increasing evidence that virus displaying a signal of latency survives in patient plasma despite having reduced fitness due to long-term immune memory. We investigated the survival of virus with latent envelope genomic fragments by simulating within-host HIV-1 sequence evolution and the cycling of viral lineages in and out of the latent reservoir. Our model incorporates a detailed mutation process including nucleotide substitution, recombination, latent reservoir dynamics, diversifying selection pressure driven by the immune response, and purifying selection pressure asserted by deleterious mutations. We evaluated the ability of our model to capture sequence evolution in vivo by comparing our simulated sequences to HIV-1 envelope sequence data from 16 HIV-infected untreated patients. Empirical sequence divergence and diversity measures were qualitatively and quantitatively similar to those of our simulated HIV-1 populations, suggesting that our model invokes realistic trends of HIV-1 genetic evolution. Moreover, reconstructed phylogenies of simulated and patient HIV-1 populations showed similar topological structures. Our simulation results suggest that recombination is a key mechanism facilitating the persistence of virus with latent envelope genomic fragments in the productively infected cell population. Recombination increased the survival probability of latent virus forms approximately 13-fold. Prevalence of virus with latent fragments in productively infected cells was observed in only 2% of simulations when we ignored recombination, while the proportion increased to 27% of simulations when we allowed recombination. We also found that the selection pressures exerted by different fitness landscapes influenced the shape of phylogenies, diversity trends, and survival of virus with latent genomic fragments. Our model predicts that the persistence of latent genomic fragments from multiple different ancestral origins increases sequence diversity in plasma for reasonable fitness landscapes.

Recent efforts to cure human immunodeficiency virus type-1 (HIV-1) infection have focused on developing latency reversing agents as a first step to eradicate the latent reservoir. The histone deacetylase inhibitor, vorinostat, has been shown to activate HIV RNA transcription in CD4+ T-cells and alter host cell gene transcription in HIV-infected individuals on antiretroviral therapy. In order to understand how latently infected cells respond dynamically to vorinostat treatment and determine the impact of vorinostat on reservoir size in vivo, we have constructed viral dynamic models of latency that incorporate vorinostat treatment. We fitted these models to data collected from a recent clinical trial in which vorinostat was administered daily for 14 days to HIV-infected individuals on suppressive ART. The results show that HIV transcription is increased transiently during the first few hours or days of treatment and that there is a delay before a sustained increase of HIV transcription, whose duration varies among study participants and may depend on the long term impact of vorinostat on host gene expression. Parameter estimation suggests that in latently infected cells, HIV transcription induced by vorinostat occurs at lower levels than in productively infected cells. Furthermore, the estimated loss rate of transcriptionally induced cells remains close to baseline in most study participants, suggesting vorinostat treatment does not induce latently infected cell killing and thus reduce the latent reservoir in vivo.

Control of virus replication in HIV-1 infection is critical to delaying disease progression. While cellular immune responses are a key determinant of control, relatively little is known about the contribution of the infecting virus to this process. To gain insight into this interplay between virus and host in viral control, we conducted a detailed analysis of two heterosexual HIV-1 subtype A transmission pairs in which female recipients sharing three HLA class I alleles exhibited contrasting clinical outcomes: R880F controlled virus replication while R463F experienced high viral loads and rapid disease progression. Near full-length single genome amplification defined the infecting transmitted/founder (T/F) virus proteome and subsequent sequence evolution over the first year of infection for both acutely infected recipients. T/F virus replicative capacities were compared in vitro, while the development of the earliest cellular immune response was defined using autologous virus sequence-based peptides. The R880F T/F virus replicated significantly slower in vitro than that transmitted to R463F. While neutralizing antibody responses were similar in both subjects, during acute infection R880F mounted a broad T cell response, the most dominant components of which targeted epitopes from which escape was limited. In contrast, the primary HIV-specific T cell response in R463F was focused on just two epitopes, one of which rapidly escaped. This comprehensive study highlights both the importance of the contribution of the lower replication capacity of the transmitted/founder virus and an associated induction of a broad primary HIV-specific T cell response, which was not undermined by rapid epitope escape, to long-term viral control in HIV-1 infection. It underscores the importance of the earliest CD8 T cell response targeting regions of the virus proteome that cannot mutate without a high fitness cost, further emphasizing the need for vaccines that elicit a breadth of T cell responses to conserved viral epitopes.

Chronic liver infection by hepatitis C virus (HCV) is a major public health concern. Despite partly successful treatment options, several aspects of intrahepatic HCV infection dynamics are still poorly understood, including the preferred mode of viral propagation, as well as the proportion of infected hepatocytes. Answers to these questions have important implications for the development of therapeutic interventions. In this study, we present methods to analyze the spatial distribution of infected hepatocytes obtained by single cell laser capture microdissection from liver biopsy samples of patients chronically infected with HCV. By characterizing the internal structure of clusters of infected cells, we are able to evaluate hypotheses about intrahepatic infection dynamics. We found that individual clusters on biopsy samples range in size from 4-50 infected cells. In addition, the HCV RNA content in a cluster declines from the cell that presumably founded the cluster to cells at the maximal cluster extension. These observations support the idea that HCV infection in the liver is seeded randomly (e.g. from the blood) and then spreads locally. Assuming that the amount of intracellular HCV RNA is a proxy for how long a cell has been infected, we estimate based on models of intracellular HCV RNA replication and accumulation that cells in clusters have been infected on average for less than a week. Further, we do not find a relationship between the cluster size and the estimated cluster expansion time. Our method represents a novel approach to make inferences about infection dynamics in solid tissues from static spatial data.

Simple models of therapy for viral diseases such as hepatitis C virus (HCV) or human immunodeficiency virus assume that, once therapy is started, the drug has a constant effectiveness. More realistic models have assumed either that the drug effectiveness depends on the drug concentration or that the effectiveness varies over time. Here a previously introduced varying-effectiveness (VE) model is studied mathematically in the context of HCV infection. We show that while the model is linear, it has no closed-form solution due to the time-varying nature of the effectiveness. We then show that the model can be transformed into a Bessel equation and derive an analytic solution in terms of modified Bessel functions, which are defined as infinite series, with time-varying arguments. Fitting the solution to data from HCV infected patients under therapy has yielded values for the parameters in the model. We show that for biologically realistic parameters, the predicted viral decay on therapy is generally biphasic and resembles that predicted by constant-effectiveness (CE) models. We introduce a general method for determining the time at which the transition between decay phases occurs based on calculating the point of maximum curvature of the viral decay curve. For the parameter regimes of interest, we also find approximate solutions for the VE model and establish the asymptotic behavior of the system. We show that the rate of second phase decay is determined by the death rate of infected cells multiplied by the maximum effectiveness of therapy, whereas the rate of first phase decline depends on multiple parameters including the rate of increase of drug effectiveness with time.

Hepatitis B is a DNA virus that infects liver cells and can cause both acute and chronic disease. It is believed that both viral and host factors are responsible for determining whether the infection is cleared or becomes chronic. Here we investigate the mechanism of protection by developing a mathematical model of the antibody response following hepatitis B virus (HBV) infection. We fitted the model to data from seven infected adults identified during acute infection and determined the ability of the virus to escape neutralization through overproduction of non-infectious subviral particles, which have HBs proteins on their surface, but do not contain nucleocapsid protein and viral nucleic acids. We showed that viral clearance can be achieved for high anti-HBV antibody levels, as in vaccinated individuals, when: (1) the rate of synthesis of hepatitis B subviral particles is slow; (2) the rate of synthesis of hepatitis B subviral particles is high but either anti-HBV antibody production is fast, the antibody affinity is high, or the levels of pre-existent HBV-specific antibody at the time of infection are high, as could be attained by vaccination. We further showed that viral clearance can be achieved for low equilibrium anti-HBV antibody levels, as in unvaccinated individuals, when a strong cellular immune response controls early infection.

Several studies have proven oseltamivir to be efficient in reducing influenza viral titer and symptom intensity. However, the usefulness of oseltamivir can be compromised by the emergence and spread of drug-resistant virus. The selective pressure exerted by different oseltamivir therapy regimens have received little attention. Combining models of drug pharmacokinetics, pharmacodynamics, viral kinetics and symptom dynamics, we explored the efficacy of oseltamivir in reducing both symptoms (symptom efficacy) and viral load (virological efficacy). We simulated samples of 1000 subjects using previously estimated between-subject variability in viral and symptom dynamic parameters to describe the observed heterogeneity in a patient population. We simulated random mutations conferring resistance to oseltamivir. We explored the effect of therapy initiation time, dose, intake frequency and therapy duration on influenza infection, illness dynamics, and emergence of viral resistance. Symptom and virological efficacies were strongly associated with therapy initiation time. The proportion of subjects shedding resistant virus was 27-fold higher when prophylaxis was initiated during the incubation period compared with no treatment. It fell to below 1% when treatment was initiated after symptom onset for twice-a-day intakes. Lower doses and prophylaxis regimens led to lower efficacies and increased risk of resistance emergence. We conclude that prophylaxis initiated during the incubation period is the main factor leading to resistance emergence.

Immune escape mutations that revert back to the consensus sequence frequently occur in newly HIV-1-infected individuals and have been thought to render the viruses more fit. However, their impact on viral fitness and their interaction with other immune escape mutations have not been evaluated in the background of their cognate transmitted/founder (T/F) viral genomes. To precisely determine the role of reversion mutations, we introduced reversion mutations alone or together with CD8+ T cell escape mutations in their unmodified cognate T/F viral genome and determined their impact on viral fitness in primary CD4+ T cells. Two reversion mutations, V247I and I64T, were identified in Gag and Tat, respectively, but neither had measurable effect on the fitness of their cognate T/F virus. The V247I and G248A mutations that were detected before and concurrently with the potent T cell escape mutation T242N, respectively, were selected by early T cell responses. The V247I or the G248A mutation alone partially restored the fitness loss caused by the T242N mutation. Together they could fully restore the fitness of the T242N mutant to the T/F level. These results demonstrate that the fitness loss caused by a T cell escape mutation could be compensated by preexisting or concurrent reversion and other T cell escape mutations. Our findings indicate that the overall viral fitness is modulated by the complex interplay among T cell escape, compensatory and reversion mutations to maintain the balance between immune escape and viral replication capacity.

The B cell response to influenza infection of the respiratory tract contributes to viral clearance and establishes profound resistance to reinfection by related viruses. Numerous studies have measured virus-specific antibody-secreting cell (ASC) frequencies in different anatomical compartments after influenza infection and provided a general picture of the kinetics of ASC formation and dispersion. However, the dynamics of ASC populations are difficult to determine experimentally and have received little attention. Here, we applied mathematical modeling to investigate the dynamics of ASC growth, death, and migration over the 2-week period following primary influenza infection in mice. Experimental data for model fitting came from high frequency measurements of virus-specific IgM, IgG, and IgA ASCs in the mediastinal lymph node (MLN), spleen, and lung. Model construction was based on a set of assumptions about ASC gain and loss from the sampled sites, and also on the directionality of ASC trafficking pathways. Most notably, modeling results suggest that differences in ASC fate and trafficking patterns reflect the site of formation and the expressed antibody class. Essentially all early IgA ASCs in the MLN migrated to spleen or lung, whereas cell death was likely the major reason for IgM and IgG ASC loss from the MLN. In contrast, the spleen contributed most of the IgM and IgG ASCs that migrated to the lung, but essentially none of the IgA ASCs. This finding points to a critical role for regional lymph nodes such as the MLN in the rapid generation of IgA ASCs that seed the lung. Results for the MLN also suggest that ASC death is a significant early feature of the B cell response. Overall, our analysis is consistent with accepted concepts in many regards, but it also indicates novel features of the B cell response to influenza that warrant further investigation.

Cytotoxic T-lymphocytes (CTLs) recognize viral protein fragments displayed by major histocompatibility complex (MHC) molecules on the surface of virally infected cells and generate an anti-viral response that can kill the infected cells. Virus variants whose protein fragments are not efficiently presented on infected cells or whose fragments are presented but not recognized by CTLs therefore have a competitive advantage and spread rapidly through the population. We present a method that allows a more robust estimation of these escape rates from serially sampled sequence data. The proposed method accounts for competition between multiple escapes by explicitly modeling the accumulation of escape mutations and the stochastic effects of rare multiple mutants. Applying our method to serially sampled HIV sequence data, we estimate rates of HIV escape that are substantially larger than those previously reported. The method can be extended to complex escapes that require compensatory mutations. We expect our method to be applicable in other contexts such as cancer evolution where time series data is also available.

Secondary bacterial infections are a leading cause of illness and death during epidemic and pandemic influenza. Experimental studies suggest a lethal synergism between influenza and certain bacteria, particularly Streptococcus pneumoniae, but the precise processes involved are unclear. To address the mechanisms and determine the influences of pathogen dose and strain on disease, we infected groups of mice with either the H1N1 subtype influenza A virus A/Puerto Rico/8/34 (PR8) or a version expressing the 1918 PB1-F2 protein (PR8-PB1-F2(1918)), followed seven days later with one of two S. pneumoniae strains, type 2 D39 or type 3 A66.1. We determined that, following bacterial infection, viral titers initially rebound and then decline slowly. Bacterial titers rapidly rise to high levels and remain elevated. We used a kinetic model to explore the coupled interactions and study the dominant controlling mechanisms. We hypothesize that viral titers rebound in the presence of bacteria due to enhanced viral release from infected cells, and that bacterial titers increase due to alveolar macrophage impairment. Dynamics are affected by initial bacterial dose but not by the expression of the influenza 1918 PB1-F2 protein. Our model provides a framework to investigate pathogen interaction during coinfections and to uncover dynamical differences based on inoculum size and strain.

The current paradigm for studying hepatitis C virus (HCV) dynamics in patients utilizes a standard viral dynamic model that keeps track of uninfected (target) cells, infected cells, and virus. The model does not account for the dynamics of intracellular viral replication, which is the major target of direct-acting antiviral agents (DAAs). Here we describe and study a recently developed multiscale age-structured model that explicitly considers the potential effects of DAAs on intracellular viral RNA production, degradation, and secretion as virus into the circulation. We show that when therapy significantly blocks both intracellular viral RNA production and virus secretion, the serum viral load decline has three phases, with slopes reflecting the rate of serum viral clearance, the rate of loss of intracellular viral RNA, and the rate of loss of intracellular replication templates and infected cells, respectively. We also derive analytical approximations of the multiscale model and use one of them to analyze data from patients treated for 14 days with the HCV protease inhibitor danoprevir. Analysis suggests that danoprevir significantly blocks intracellular viral production (with mean effectiveness 99.2%), enhances intracellular viral RNA degradation about 5-fold, and moderately inhibits viral secretion (with mean effectiveness 56%). The multiscale model can be used to study viral dynamics in patients treated with other DAAs and explore their mechanisms of action in treatment of hepatitis C.

The linker for activation of T cells (LAT), the linker for activation of B cells (LAB), and the linker for activation of X cells (LAX) form a family of transmembrane adaptor proteins widely expressed in lymphocytes. These scaffolding proteins have multiple binding motifs that, when phosphorylated, bind the SH2 domain of the cytosolic adaptor Grb2. Thus, the valence of LAT, LAB and LAX for Grb2 is variable, depending on the strength of receptor activation that initiates phosphorylation. During signaling, the LAT population will exhibit a time-varying distribution of Grb2 valences from zero to three. In the cytosol, Grb2 forms 1:1 and 2:1 complexes with the guanine nucleotide exchange factor SOS1. The 2:1 complex can bridge two LAT molecules when each Grb2, through their SH2 domains, binds to a phosphorylated site on a separate LAT. In T cells and mast cells, after receptor engagement, receptor phosphoyrlation is rapidly followed by LAT phosphorylation and aggregation. In mast cells, aggregates containing more than one hundred LAT molecules have been detected. Previously we considered a homogeneous population of trivalent LAT molecules and showed that for a range of Grb2, SOS1 and LAT concentrations, an equilibrium theory for LAT aggregation predicts the formation of a gel-like phase comprising a very large aggregate (superaggregate). We now extend this theory to investigate the effects of a distribution of Grb2 valence in the LAT population on the formation of LAT aggregates and superaggregate and use stochastic simulations to calculate the fraction of the total LAT population in the superaggregate.

Spontaneous disease extinction can occur due to a rare stochastic fluctuation. We explore this process, both numerically and theoretically, in two minimal models of stochastic viral infection dynamics. We propose a method that reduces the complexity in models of viral infections so that the remaining dynamics can be studied by previously developed techniques for analyzing epidemiological models. Using this technique, we obtain an expression for the infection clearance time as a function of kinetic parameters. We apply our theoretical results to study stochastic infection clearance for specific stages of HIV and HCV dynamics. Our results show that the typical time for stochastic clearance of a viral infection increases exponentially with the size of the population, but infection still can be cleared spontaneously within a reasonable time interval in a certain population of cells. We also show that the clearance time is exponentially sensitive to the viral decay rate and viral infectivity but only linearly dependent on the lifetime of an infected cell. This suggests that if standard drug therapy fails to clear an infection then intensifying therapy by adding a drug that reduces the rate of cell infection rather than immune modulators that hasten infected cell death may be more useful in ultimately clearing remaining pockets of infection.

A precise molecular identification of transmitted hepatitis C virus (HCV) genomes could illuminate key aspects of transmission biology, immunopathogenesis and natural history. We used single genome sequencing of 2,922 half or quarter genomes from plasma viral RNA to identify transmitted/founder (T/F) viruses in 17 subjects with acute community-acquired HCV infection. Sequences from 13 of 17 acute subjects, but none of 14 chronic controls, exhibited one or more discrete low diversity viral lineages. Sequences within each lineage generally revealed a star-like phylogeny of mutations that coalesced to unambiguous T/F viral genomes. Numbers of transmitted viruses leading to productive clinical infection were estimated to range from 1 to 37 or more (median = 4). Four acutely infected subjects showed a distinctly different pattern of virus diversity that deviated from a star-like phylogeny. In these cases, empirical analysis and mathematical modeling suggested high multiplicity virus transmission from individuals who themselves were acutely infected or had experienced a virus population bottleneck due to antiviral drug therapy. These results provide new quantitative and qualitative insights into HCV transmission, revealing for the first time virus-host interactions that successful vaccines or treatment interventions will need to overcome. Our findings further suggest a novel experimental strategy for identifying full-length T/F genomes for proteome-wide analyses of HCV biology and adaptation to antiviral drug or immune pressures.

Single genome sequencing of early HIV-1 genomes provides a sensitive, dynamic assessment of virus evolution and insight into the earliest anti-viral immune responses in vivo. By using this approach, together with deep sequencing, site-directed mutagenesis, antibody adsorptions and virus-entry assays, we found evidence in three subjects of neutralizing antibody (Nab) responses as early as 2 weeks post-seroconversion, with Nab titers as low as 1∶20 to 1∶50 (IC(50)) selecting for virus escape. In each of the subjects, Nabs targeted different regions of the HIV-1 envelope (Env) in a strain-specific, conformationally sensitive manner. In subject CH40, virus escape was first mediated by mutations in the V1 region of the Env, followed by V3. HIV-1 specific monoclonal antibodies from this subject mapped to an immunodominant region at the base of V3 and exhibited neutralizing patterns indistinguishable from polyclonal antibody responses, indicating V1-V3 interactions within the Env trimer. In subject CH77, escape mutations mapped to the V2 region of Env, several of which selected for alterations of glycosylation. And in subject CH58, escape mutations mapped to the Env outer domain. In all three subjects, initial Nab recognition was followed by sequential rounds of virus escape and Nab elicitation, with Nab escape variants exhibiting variable costs to replication fitness. Although delayed in comparison with autologous CD8 T-cell responses, our findings show that Nabs appear earlier in HIV-1 infection than previously recognized, target diverse sites on HIV-1 Env, and impede virus replication at surprisingly low titers. The unexpected in vivo sensitivity of early transmitted/founder virus to Nabs raises the possibility that similarly low concentrations of vaccine-induced Nabs could impair virus acquisition in natural HIV-1 transmission, where the risk of infection is low and the number of viruses responsible for transmission and productive clinical infection is typically one.

Influenza virus infection remains a public health problem worldwide. The mechanisms underlying viral control during an uncomplicated influenza virus infection are not fully understood. Here, we developed a mathematical model including both innate and adaptive immune responses to study the within-host dynamics of equine influenza virus infection in horses. By comparing modeling predictions with both interferon and viral kinetic data, we examined the relative roles of target cell availability, and innate and adaptive immune responses in controlling the virus. Our results show that the rapid and substantial viral decline (about 2 to 4 logs within 1 day) after the peak can be explained by the killing of infected cells mediated by interferon activated cells, such as natural killer cells, during the innate immune response. After the viral load declines to a lower level, the loss of interferon-induced antiviral effect and an increased availability of target cells due to loss of the antiviral state can explain the observed short phase of viral plateau in which the viral level remains unchanged or even experiences a minor second peak in some animals. An adaptive immune response is needed in our model to explain the eventual viral clearance. This study provides a quantitative understanding of the biological factors that can explain the viral and interferon kinetics during a typical influenza virus infection.

Hepatitis C virus (HCV) is present in the host with multiple variants generated by its error prone RNA-dependent RNA polymerase. Little is known about the initial viral diversification and the viral life cycle processes that influence diversity. We studied the diversification of HCV during acute infection in 17 plasma donors, with frequent sampling early in infection. To analyze these data, we developed a new stochastic model of the HCV life cycle. We found that the accumulation of mutations is surprisingly slow: at 30 days, the viral population on average is still 46% identical to its transmitted viral genome. Fitting the model to the sequence data, we estimate the median in vivo viral mutation rate is 2.5×10⁻⁵ mutations per nucleotide per genome replication (range 1.6-6.2×10⁻⁵), about 5-fold lower than previous estimates. To confirm these results we analyzed the frequency of stop codons (N = 10) among all possible non-sense mutation targets (M = 898,335), and found a mutation rate of 2.8-3.2×10⁻⁵, consistent with the estimate from the dynamical model. The slow accumulation of mutations is consistent with slow turnover of infected cells and replication complexes within infected cells. This slow turnover is also inferred from the viral load kinetics. Our estimated mutation rate, which is similar to that of other RNA viruses (e.g., HIV and influenza), is also compatible with the accumulation of substitutions seen in HCV at the population level. Our model identifies the relevant processes (long-lived cells and slow turnover of replication complexes) and parameters involved in determining the rate of HCV diversification.

Relatively little is known about the viral factors contributing to the lethality of the 1918 pandemic, although its unparalleled virulence was likely due in part to the newly discovered PB1-F2 protein. This protein, while unnecessary for replication, increases apoptosis in monocytes, alters viral polymerase activity in vitro, enhances inflammation and increases secondary pneumonia in vivo. However, the effects the PB1-F2 protein have in vivo remain unclear. To address the mechanisms involved, we intranasally infected groups of mice with either influenza A virus PR8 or a genetically engineered virus that expresses the 1918 PB1-F2 protein on a PR8 background, PR8-PB1-F2(1918). Mice inoculated with PR8 had viral concentrations peaking at 72 hours, while those infected with PR8-PB1-F2(1918) reached peak concentrations earlier, 48 hours. Mice given PR8-PB1-F2(1918) also showed a faster decline in viral loads. We fit a mathematical model to these data to estimate parameter values. The model supports a higher viral production rate per cell and a higher infected cell death rate with the PR8-PB1-F2(1918) virus. We discuss the implications these mechanisms have during an infection with a virus expressing a virulent PB1-F2 on the possibility of a pandemic and on the importance of antiviral treatments.

Viral production from infected cells can occur continuously or in a burst that generally kills the cell. For HIV infection, both modes of production have been suggested. Standard viral dynamic models formulated as sets of ordinary differential equations can not distinguish between these two modes of viral production, as the predicted dynamics is identical as long as infected cells produce the same total number of virions over their lifespan. Here we show that in stochastic models of viral infection the two modes of viral production yield different early term dynamics. Further, we analytically determine the probability that infections initiated with any number of virions and infected cells reach extinction, the state when both the population of virions and infected cells vanish, and show this too has different solutions for continuous and burst production. We also compute the distributions of times to establish infection as well as the distribution of times to extinction starting from both a single virion as well as from a single infected cell for both modes of virion production.

Widespread resistance among circulating influenza A strains to at least one of the anti-influenza drugs is a major public health concern. A triple combination antiviral drug (TCAD) regimen comprised of amantadine, oseltamivir, and ribavirin has been shown to have synergistic and broad spectrum activity against influenza A strains, including drug resistant strains. Here, we used mathematical modeling along with three different experimental approaches to understand the effects of single agents, double combinations, and the TCAD regimen on resistance in influenza in vitro, including: 1) serial passage at constant drug concentrations, 2) serial passage at escalating drug concentrations, and 3) evaluation of the contribution of each component of the TCAD regimen to the suppression of resistance. Consistent with the modeling which demonstrated that three drugs were required to suppress the emergence of resistance in influenza A, treatment with the TCAD regimen resulted in the sustained suppression of drug resistant viruses, whereas treatment with amantadine alone or the amantadine-oseltamivir double combination led to the rapid selection of resistant variants which comprised ∼100% of the population. Furthermore, the TCAD regimen imposed a high genetic barrier to resistance, requiring multiple mutations in order to escape the effects of all the drugs in the regimen. Finally, we demonstrate that each drug in the TCAD regimen made a significant contribution to the suppression of virus breakthrough and resistance at clinically achievable concentrations. Taken together, these data demonstrate that the TCAD regimen was superior to double combinations and single agents at suppressing resistance, and that three drugs at a minimum were required to impede the selection of drug resistant variants in influenza A virus. The use of mathematical modeling with multiple experimental designs and molecular readouts to evaluate and optimize combination drug regimens for the suppression of resistance may be broadly applicable to other infectious diseases.

Mucosal transmission of the human immunodeficiency virus (HIV) results in a bottleneck in viral genetic diversity. Gnanakaran and colleagues used a computational strategy to identify signature amino acids at particular positions in Envelope that were associated either with transmitted sequences sampled very early in infection, or sequences sampled during chronic infection. Among the strongest signatures observed was an enrichment for the stable presence of histidine at position 12 at transmission and in early infection, and a recurrent loss of histidine at position 12 in chronic infection. This amino acid lies within the leader peptide of Envelope, a region of the protein that has been shown to influence envelope glycoprotein expression and virion infectivity. We show a strong association between a positively charged amino acid like histidine at position 12 in transmitted/founder viruses with more efficient trafficking of the nascent envelope polypeptide to the endoplasmic reticulum and higher steady-state glycoprotein expression compared to viruses that have a non-basic position 12 residue, a substitution that was enriched among viruses sampled from chronically infected individuals. When expressed in the context of other viral proteins, transmitted envelopes with a basic amino acid position 12 were incorporated at higher density into the virus and exhibited higher infectious titers than did non-signature envelopes. These results support the potential utility of using a computational approach to examine large viral sequence data sets for functional signatures and indicate the importance of Envelope expression levels for efficient HIV transmission.

For most HIV-infected patients, antiretroviral therapy controls viral replication. However, in some patients drug resistance can cause therapy to fail. Nonetheless, continued therapy with a failing regimen can preserve or even lead to increases in CD4+ T cell counts. To understand the biological basis of these observations, we used mathematical models to explain observations made in patients with drug-resistant HIV treated with enfuvirtide (ENF/T-20), an HIV-1 fusion inhibitor. Due to resistance emergence, ENF was removed from the drug regimen, drug-sensitive virus regrown, and ENF was re-administered. We used our model to study the dynamics of plasma-viral RNA and CD4+ T cell levels, and the competition between drug-sensitive and resistant viruses during therapy interruption and re-administration. Focusing on resistant viruses carrying the V38A mutation in gp41, we found ENF-resistant virus to be 17±3% less fit than ENF-sensitive virus in the absence of the drug, and that the loss of resistant virus during therapy interruption was primarily due to this fitness cost. Using viral dynamic parameters estimated from these patients, we show that although re-administration of ENF cannot suppress viral load, it can, in the presence of resistant virus, increase CD4+ T cell counts, which should yield clinical benefits. This study provides a framework to investigate HIV and T cell dynamics in patients who develop drug resistance to other antiretroviral agents and may help to develop more effective strategies for treatment.

It has recently been estimated that a single HIV-1 infected cell produces between and more than viral particles over its life span. Since body-wide estimates of the ratio of free virus to productively infected cells are smaller than and much smaller than , individual virions must be cleared rapidly. This seems difficult to reconcile with the fact that most of the total body virus is trapped on follicular dendritic cells where it can survive for many months. It has also been difficult to reconcile the vast difference in the rates at which the virus is cleared from the blood in rhesus macaques and in chronically infected patients. Here we attempt to reconcile these seemingly contradictory observations by considering the virion clearance rate in various organs and the virion exchange rates between them. The main results are that the per capita clearance rate of free virus in lymphoid tissue should be fast, the virion exchange rate between lymphoid tissue and the blood should be slow, and the comparatively slow previous estimates for the virion clearance rate from the blood correspond to the rate of virion efflux from the blood to other organs where the virus is ultimately cleared.

Quantitative understanding of the kinetics of lymphocyte proliferation and death upon activation with an antigen is crucial for elucidating factors determining the magnitude, duration and efficiency of the immune response. Recent advances in quantitative experimental techniques, in particular intracellular labeling and multi-channel flow cytometry, allow one to measure the population structure of proliferating and dying lymphocytes for several generations with high precision. These new experimental techniques require novel quantitative methods of analysis. We review several recent mathematical approaches used to describe and analyze cell proliferation data. Using a rigorous mathematical framework, we show that two commonly used models that are based on the theories of age-structured cell populations and of branching processes, are mathematically identical. We provide several simple analytical solutions for a model in which the distribution of inter-division times follows a gamma distribution and show that this model can fit both simulated and experimental data. We also show that the estimates of some critical kinetic parameters, such as the average inter-division time, obtained by fitting models to data may depend on the assumed distribution of inter-division times, highlighting the challenges in quantitative understanding of cell kinetics.

We used ultra-deep sequencing to obtain tens of thousands of HIV-1 sequences from regions targeted by CD8+ T lymphocytes from longitudinal samples from three acutely infected subjects, and modeled viral evolution during the critical first weeks of infection. Previous studies suggested that a single virus established productive infection, but these conclusions were tempered because of limited sampling; now, we have greatly increased our confidence in this observation through modeling the observed earliest sample diversity based on vastly more extensive sampling. Conventional sequencing of HIV-1 from acute/early infection has shown different patterns of escape at different epitopes; we investigated the earliest escapes in exquisite detail. Over 3-6 weeks, ultradeep sequencing revealed that the virus explored an extraordinary array of potential escape routes in the process of evading the earliest CD8 T-lymphocyte responses--using 454 sequencing, we identified over 50 variant forms of each targeted epitope during early immune escape, while only 2-7 variants were detected in the same samples via conventional sequencing. In contrast to the diversity seen within epitopes, non-epitope regions, including the Envelope V3 region, which was sequenced as a control in each subject, displayed very low levels of variation. In early infection, in the regions sequenced, the consensus forms did not have a fitness advantage large enough to trigger reversion to consensus amino acids in the absence of immune pressure. In one subject, a genetic bottleneck was observed, with extensive diversity at the second time point narrowing to two dominant escape forms by the third time point, all within two months of infection. Traces of immune escape were observed in the earliest samples, suggesting that immune pressure is present and effective earlier than previously reported; quantifying the loss rate of the founder virus suggests a direct role for CD8 T-lymphocyte responses in viral containment after peak viremia. Dramatic shifts in the frequencies of epitope variants during the first weeks of infection revealed a complex interplay between viral fitness and immune escape.

Elucidating virus-host interactions responsible for HIV-1 transmission is important for advancing HIV-1 prevention strategies. To this end, single genome amplification (SGA) and sequencing of HIV-1 within the context of a model of random virus evolution has made possible for the first time an unambiguous identification of transmitted/founder viruses and a precise estimation of their numbers. Here, we applied this approach to HIV-1 env analyses in a cohort of acutely infected men who have sex with men (MSM) and found that a high proportion (10 of 28; 36%) had been productively infected by more than one virus. In subjects with multivariant transmission, the minimum number of transmitted viruses ranged from 2 to 10 with viral recombination leading to rapid and extensive genetic shuffling among virus lineages. A combined analysis of these results, together with recently published findings based on identical SGA methods in largely heterosexual (HSX) cohorts, revealed a significantly higher frequency of multivariant transmission in MSM than in HSX [19 of 50 subjects (38%) versus 34 of 175 subjects (19%); Fisher's exact p = 0.008]. To further evaluate the SGA strategy for identifying transmitted/founder viruses, we analyzed 239 overlapping 5' and 3' half genome or env-only sequences from plasma viral RNA (vRNA) and blood mononuclear cell DNA in an MSM subject who had a particularly well-documented virus exposure history 3-6 days before symptom onset and 14-17 days before peak plasma viremia (47,600,000 vRNA molecules/ml). All 239 sequences coalesced to a single transmitted/founder virus genome in a time frame consistent with the clinical history, and a molecular clone of this genome encoded replication competent virus in accord with model predictions. Higher multiplicity of HIV-1 infection in MSM compared with HSX is consistent with the demonstrably higher epidemiological risk of virus acquisition in MSM and could indicate a greater challenge for HIV-1 vaccines than previously recognized.