Investigation of bacteriophage MS2 viral dynamics using model discrimination analysis and the implications for phage therapy

Lytic phages infect their bacterial hosts, use the host machinery to replicate, and finally lyse and kill their hosts, releasing progeny phages. Various mathematical models have been developed that describe these phage-host viral dynamics. The aim of this study was to determine which of these models best describes the viral dynamics of lytic RNA phage MS2 and its host Escherichia coli C-3000. Experimental data consisted of uninfected and infected bacterial cell densities, free phage density, and substrate concentration. Parameters of various models were either determined directly through other experimental techniques or estimated using regression analysis of the experimental data. The models were evaluated using a Bayesian-based model discrimination technique. Through model discrimination it was shown that phage-resistant cells inhibited the growth of phage population. It was also shown that the uninfected bacterial population was a quasispecies consisting of phage-sensitive and phage-resistant bacterial cells. When there was a phage attack the phage-sensitive cells died out and the phage-resistant cells were selected for and became the dominant strain of the bacterial population.     

A model of HIV-1 infection with two time delays: mathematical analysis and comparison with patient data

Mathematical models have made considerable contributions to our understanding of HIV dynamics. Introducing time delays to HIV models usually brings challenges to both mathematical analysis of the models and comparison of model predictions with patient data. In this paper, we incorporate two delays, one the time needed for infected cells to produce virions after viral entry and the other the time needed for the adaptive immune response to emerge to control viral replication, into an HIV-1 model. We begin model analysis with proving the positivity and boundedness of the solutions, local stability of the infection-free and infected steady states, and uniform persistence of the system. By developing a few Lyapunov functionals, we obtain conditions ensuring global stability of the steady states. We also fit the model including two delays to viral load data from 10 patients during primary HIV-1 infection and estimate parameter values. Although the delay model provides better fits to patient data (achieving a smaller error between data and modeling prediction) than the one without delays, we could not determine which one is better from the statistical standpoint. This highlights the need of more data sets for model verification and selection when we incorporate time delays into mathematical models to study virus dynamics.     

Modeling the short-, middle- and long-term viral load responses for comparing estimated dynamic parameters

A virologic marker, the number of HIV RNA copies or viral load, is currently used to evaluate antiviral therapies in AIDS clinical trials. This marker can be used to assess the antiviral potency of therapies, but is easily affected by drug exposures, drug resistance and other factors during the long-term treatment evaluation process. The study of HIV dynamics is one of the most important development in recent AIDS research for understanding the pathogenesis of HIV-1 infection and antiviral treatment strategies. Although many HIV dynamic models have been proposed by AIDS researchers in the last decade, they have only been used to quantify short-term viral dynamics and do not correctly describe long-term virologic responses to antiretroviral treatment. In other words, these simple viral dynamic models can only be used to fit short-term viral load data for estimating dynamic parameters. In this paper, a mechanism-based differential equation models is introduced for characterizing the long-term viral dynamics with antiretroviral therapy. We applied this model to fit different segments of the viral load trajectory data from a simulation experiment and an AIDS clinical trial study, and found that the estimates of dynamic parameters from our modeling approach are very consistent. We may conclude that our model can not only characterize long-term viral dynamics, but can also quantify short- and middle-term viral dynamics. It suggests that if there are enough data in the early stage of the treatment, the results from our modeling based on short-term information can be used to capture the performance of long-term care with HIV-1 infected patients.     

Population HIV-1 dynamics in vivo: applicable models and inferential tools for virological data from AIDS clinical trials

In this paper, we introduce a novel application of hierarchical nonlinear mixed-effect models to HIV dynamics. We show that a simple model with a sum of exponentials can give a good fit to the observed clinical data of HIV-1 dynamics (HIV-1 RNA copies) after initiation of potent antiviral treatments and can also be justified by a biological compartment model for the interaction between HIV and its host cells. This kind of model enjoys both biological interpretability and mathematical simplicity after reparameterization and simplification. A model simplification procedure is proposed and illustrated through examples. We interpret and justify various simplified models based on clinical data taken during different phases of viral dynamics during antiviral treatments. We suggest the hierarchical nonlinear mixed-effect model approach for parameter estimation and other statistical inferences. In the context of an AIDS clinical trial involving patients treated with a combination of potent antiviral agents, we show how the models may be used to draw biologically relevant interpretations from repeated HIV-1 RNA measurements and demonstrate the potential use of the models in clinical decision-making.     

Intra-Host Diversity and Emergence of Unique GBV-C Viral Lineages in HIV Infected Subjects in Central China

GB virus C (GBV-C), which is highly prevalent among HIV/AIDS, seemed to slow the HIV disease progression. The HIV/GBV-C co-infected individuals may represent an interesting model for the investigation of the role played by HIV infection and/or the immune system in driving the evolution of the GBV-C viral populations. The present study investigated the prevalence and population dynamics of GB virus C in HIV infected individuals representing 13 geographic regions of Hubei Province of China. Approximately 37% of HIV-1 infected individuals were infected with GBV-C and genotype 3 is appeared to be predominant. Utilizing the 196 complete E2 nucleotide sequence data from 10 HIV/GBV-C infected individuals and employing coalescence based phylogenetic approaches; the present study has investigated the intra-host dynamics of GBV-C. The results revealed patient-specific unique GBV-C viral lineages and each viral lineage showed the evidence of rapid population expansion in respective HIV-1 infected patients, thus suggesting HIV-1 was unlikely to have been inhibiting effect on the GBV-C viral replication. GBV-C in all patients has experienced intense purifying selection, suggesting the GBV-C viral invasion and subsequent expansion within the HIV-1 infected hosts without any modification of the functional epitopes at their membrane protein. The finding of within host GBV-C recombinant sequences indicated recombination was one of the significant forces in the evolution and divergence of GBV-C.     

Non-linear dynamics models characterizing long-term virological data from AIDS clinical trials

Human immunodeficiency virus (HIV) dynamics represent a complicated variant of the text-book case of non-linear dynamics: predator-prey interaction. The interaction can be described as naturally reproducing T-cells (prey) hunted and killed by virus (predator). Virus reproduce and increase in number as a consequence of successful predation; this is countered by the production of T-cells and the reaction of the immune system. Multi-drug anti-HIV therapy attempts to alter the natural dynamics of the predator-prey interaction by decreasing the reproductive capability of the virus and hence predation. These dynamics are further complicated by varying compliance to treatment and insurgence of resistance to treatment. When following the temporal progression of viral load in plasma during therapy one observes a short-term (1-12 weeks) decrease in viral load. In the long-term (more than 12 weeks from the beginning of therapy) the reduction in viral load is either sustained, or it is followed by a rebound, oscillations and a new (generally lower than at the beginning of therapy) viral load level. Biomathematicians have investigated these dynamics by means of simulations. However the estimation of the parameters associated with the dynamics from real data has been mostly limited to the case of simplified, in particular linearized, models. Linearized model can only describe the short-term changes of viral load during therapy and can only predict (apparent) suppression. In this paper we put forward relatively simple models to characterize long-term virus dynamics which can incorporate different factors associated with resurgence: (Fl) the intrinsic non-linear HIV-1 dynamics, (F2) drug exposure and in particular compliance to treatment, and (F3) insurgence of resistant HIV-1 strains. The main goal is to obtain models which are mathematically identifiable given only measurements of viral load, while retaining the most crucial features of HIV dynamics. For the purpose of illustration we demonstrate an application of the models using real AIDS clinical trial data involving patients treated with a combination of anti-retroviral agents using a model which incorporates compliance data.     

The molecular population genetics of HIV-1 group O

HIV-1 group O originated through cross-species transmission of SIV from chimpanzees to humans and has established a relatively low prevalence in Central Africa. Here, we infer the population genetics and epidemic history of HIV-1 group O from viral gene sequence data and evaluate the effect of variable evolutionary rates and recombination on our estimates. First, model selection tools were used to specify suitable evolutionary and coalescent models for HIV group O. Second, divergence times and population genetic parameters were estimated in a Bayesian framework using Markov chain Monte Carlo sampling, under both strict and relaxed molecular clock methods. Our results date the origin of the group O radiation to around 1920 (1890-1940), a time frame similar to that estimated for HIV-1 group M. However, group O infections, which remain almost wholly restricted to Cameroon, show a slower rate of exponential growth during the twentieth century, explaining their lower current prevalence. To explore the effect of recombination, the Bayesian framework is extended to incorporate multiple unlinked loci. Although recombination can bias estimates of the time to the most recent common ancestor, this effect does not appear to be important for HIV-1 group O. In addition, we show that evolutionary rate estimates for different HIV genes accurately reflect differential selective constraints along the HIV genome.     

Transmission selects for HIV-1 strains of intermediate virulence: a modelling approach

Recent data shows that HIV-1 is characterised by variation in viral virulence factors that is heritable between infections, which suggests that viral virulence can be naturally selected at the population level. A trade-off between transmissibility and duration of infection appears to favour viruses of intermediate virulence. We developed a mathematical model to simulate the dynamics of putative viral genotypes that differ in their virulence. As a proxy for virulence, we use set-point viral load (SPVL), which is the steady density of viral particles in blood during asymptomatic infection. Mutation, the dependency of survival and transmissibility on SPVL, and host effects were incorporated into the model. The model was fitted to data to estimate unknown parameters, and was found to fit existing data well. The maximum likelihood estimates of the parameters produced a model in which SPVL converged from any initial conditions to observed values within 100-150 years of first emergence of HIV-1. We estimated the 1) host effect and 2) the extent to which the viral virulence genotype mutates from one infection to the next, and found a trade-off between these two parameters in explaining the variation in SPVL. The model confirms that evolution of virulence towards intermediate levels is sufficiently rapid for it to have happened in the early stages of the HIV epidemic, and confirms that existing viral loads are nearly optimal given the assumed constraints on evolution. The model provides a useful framework under which to examine the future evolution of HIV-1 virulence.     

The relationship between tumor necrosis factor and human immunodeficiency virus gene expression in lymphoid tissue.

In tissue culture models of chronic human immunodeficiency virus type 1 (HIV-1) infection, cytokines such as tumor necrosis factor alpha (TNF-alpha) activate viral gene expression. We sought evidence that TNF-alpha might similarly regulate viral gene expression in vivo in the major lymphoid tissue (LT) reservoir. We used in situ hybridization, quantitative image analysis, and double-label techniques to compare cytokine and HIV-1 RNA levels in sections of tonsil and lymph node tissues obtained from individuals in early and later stages of HIV-1 infection. The levels of TNF-alpha gene expression in LT from HIV-1-infected an uninfected individuals were indistinguishable, and we found no correlation between TNF-alpha gene expression in LT and the level of HIV-1 gene expression in LT. There is thus little evidence that in vivo TNF-alpha significantly influences HIV production in LT.     

Maximum Likelihood Estimation of Long‐Term HIV Dynamic Models and Antiviral Response

Summary HIV dynamics studies, based on differential equations, have significantly improved the knowledge on HIV infection. While first studies used simplified short‐term dynamic models, recent works considered more complex long‐term models combined with a global analysis of whole patient data based on nonlinear mixed models, increasing the accuracy of the HIV dynamic analysis. However statistical issues remain, given the complexity of the problem. We proposed to use the SAEM (stochastic approximation expectation‐maximization) algorithm, a powerful maximum likelihood estimation algorithm, to analyze simultaneously the HIV viral load decrease and the CD4 increase in patients using a long‐term HIV dynamic system. We applied the proposed methodology to the prospective COPHAR2–ANRS 111 trial. Very satisfactory results were obtained with a model with latent CD4 cells defined with five differential equations. One parameter was fixed, the 10 remaining parameters (eight with between‐patient variability) of this model were well estimated. We showed that the efficacy of nelfinavir was reduced compared to indinavir and lopinavir.     

HIV-1 Tropism Dynamics and Phylogenetic Analysis from Longitudinal Ultra-Deep Sequencing Data of CCR5- and CXCR4-Using Variants

Objective

Coreceptor switch from CCR5 to CXCR4 is associated with HIV disease progression. The molecular and evolutionary mechanisms underlying the CCR5 to CXCR4 switch are the focus of intense recent research. We studied the HIV-1 tropism dynamics in relation to coreceptor usage, the nature of quasispecies from ultra deep sequencing (UDPS) data and their phylogenetic relationships.

Methods

Here, we characterized C2-V3-C3 sequences of HIV obtained from 19 patients followed up for 54 to 114 months using UDPS, with further genotyping and phylogenetic analysis for coreceptor usage. HIV quasispecies diversity and variability as well as HIV plasma viral load were measured longitudinally and their relationship with the HIV coreceptor usage was analyzed. The longitudinal UDPS data were submitted to phylogenetic analysis and sampling times and coreceptor usage were mapped onto the trees obtained.

Results

Although a temporal viral genetic structuring was evident, the persistence of several viral lineages evolving independently along the infection was statistically supported, indicating a complex scenario for the evolution of viral quasispecies. HIV X4-using variants were present in most of our patients, exhibiting a dissimilar inter- and intra-patient predominance as the component of quasispecies even on antiretroviral therapy. The viral populations from some of the patients studied displayed evidences of the evolution of X4 variants through fitness valleys, whereas for other patients the data favored a gradual mode of emergence.

Conclusions

CXCR4 usage can emerge independently, in multiple lineages, along the course of HIV infection. The mode of emergence, i.e. gradual or through fitness valleys seems to depend on both virus and patient factors. Furthermore, our analyses suggest that, besides becoming dominant after population-level switches, minor proportions of X4 viruses might exist along the infection, perhaps even at early stages of it. The fate of these minor variants might depend on both viral and host factors.     

HIV-1 infection and low steady state viral loads

Highly active antiretroviral therapy (HAART) reduces the viral burden in human immunodeficiency virus type 1 (HIV-1) infected patients below the threshold of detectability. However, substantial evidence indicates that viral replication persists in these individuals. In this paper we examine the ability of several biologically motivated models of HIV-1 dynamics to explain sustained low viral loads. At or near drug efficacies that result in steady state viral loads below detectability, most models are extremely sensitive to small changes in drug efficacy. We argue that if these models reflect reality many patients should have cleared the virus, contrary to observation. We find that a model in which the infected cell death rate is dependent on the infected cell density does not suffer this shortcoming. The shortcoming is also overcome in two more conventional models that include small populations of cells in which the drug is less effective than in the main population, suggesting that difficulties with drug penetrance and maintenance of effective intracellular drug concentrations in all cells susceptible to HIV infection may underlie ongoing viral replication.     

Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models

The dynamics of HIV-1 infection consist of three distinct phases starting with primary infection, then latency and finally AIDS or drug therapy. In this paper we model the dynamics of primary infection and the beginning of latency. We show that allowing for time delays in the model better predicts viral load data when compared to models with no time delays. We also find that our model of primary infection predicts the turnover rates for productively infected T cells and viral totals to be much longer than compared to data from patients receiving anti-viral drug therapy. Hence the dynamics of the infection can change dramatically from one stage to the next. However, we also show that with the data available the results are highly sensitive to the chosen model. We compare the results using analysis and Monte Carlo techniques for three different models and show how each predicts rather dramatic differences between the fitted parameters. We show, using a chi(2) test, that these differences between models are statistically significant and using a jackknifing method, we find the confidence intervals for the parameters. These differences in parameter estimations lead to widely varying conclusions about HIV pathogenesis. For instance, we find in our model with time delays the existence of a Hopf bifurcation that leads to sustained oscillations and that these oscillations could simulate the rapid turnover between viral strains and the appropriate CTL response necessary to control the virus, similar to that of a predator-prey type system.     

Design of long-term HIV dynamic studies using semiparametric mixed-effects models

Studies of HIV dynamics in AIDS research are very important in understanding the pathogenesis of HIV-1 infection and also in assessing the effectiveness of antiviral therapies. There are many AIDS clinical trials on HIV dynamics currently in development worldwide, giving rise to many design issues yet to be addressed. For example, most studies are focused on short-term viral dynamics and the existing models may not be applicable to describe long-term virologic response. In this paper, we use a simulation-based approach to study the designs of long-term viral dynamics under semiparametric nonlinear mixed-effects models. These models not only can preserve the meaningful interpretation of the short-term HIV dynamics, but also characterize the long-term virologic responses to antiretroviral (ARV) treatment. We investigate a number of feasible clinical protocol designs similar to those currently used in AIDS clinical trials. In particular, we evaluate whether earlier samplings can result in more useful information about the viral response trajectory; we also evaluate the effectiveness of two strategies: more frequent samplings per subject with fewer subjects versus fewer samplings per subject with more subjects while keeping the total number of samplings constant. The results of our investigation provide quantitative guidance for designing and selecting ARV therapy.     

Evolution of intrahost HIV-1 genetic diversity during chronic infection

HIV-1 is one of the fastest evolving entities known. Given that census population sizes of HIV-1 within individuals are much greater than the inverse mutation rate, every possible single point mutation in the viral genome occurs each generation. This enormous capability to generate genetic variation allows for escape from immune surveillance and antiviral therapy. However, compared to this potential, populations of HIV-1 within individuals exhibit little genetic variation. This discrepancy between the known mutation rate of HIV-1 and the average level of genetic variation in the env gene observed in vivo is reflected in comparisons of the actual numbers of productively infected cells, estimated as 10(7), and the effective population size, estimated as 10(3). Using approximate Bayesian computation, we evaluated several hypotheses based on a variety of selective and demographic processes to explain the low effective population size of HIV-1. Of the models we examined, the metapopulation model, in which HIV-1 evolves within an individual as a large collection of small subpopulations subject to frequent migration, extinction, and recolonization, was most consistent with the observed levels of genetic variation and the average frequencies of those variants. The metapopulation model links previous studies of viral dynamics and population genetics.     

Treatment-mediated alterations in HIV fitness preserve CD4+ T cell counts but have minimal effects on viral load

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.     

Species-specific treatment effects of helminth/HIV-1 co-infection: a systematic review and meta-analysis

In sub-Saharan Africa, over 22 million people are estimated to be co-infected with both helminths and HIV-1. Several studies have suggested that de-worming individuals with HIV-1 may delay HIV-1 disease progression, and that the benefit of de-worming may vary by individual helminth species. We conducted a systematic review and meta-analysis of the published literature to determine the effect of treatment of individual helminth infections on markers of HIV-1 progression (CD4 count and HIV viral load). There was a trend towards an association between treatment for Schistosoma mansoni and a decrease in HIV viral load (Weighted mean difference (WMD)=-0·10; 95% Confidence interval (CI): -0·24, 0·03), although this association was not seen for Ascaris lumbricoides, hookworm or Trichuris trichiura. Treatment of A. lumbricoides, S. mansoni, hookworm or T. trichiura was not associated with a change in CD4 count. While pooled data from randomized trials suggested clinical benefit of de-worming for individual helminth species, these effects decreased when observational data were included in the pooled analysis. While further trials are needed to confirm the role of anthelmintic treatment in HIV-1 co-infected individuals, providing anthelmintics to individuals with HIV-1 may be a safe, inexpensive and practical intervention to slow progression of HIV-1.     

Dating the Age of the SIV Lineages That Gave Rise to HIV-1 and HIV-2

Great strides have been made in understanding the evolutionary history of simian immunodeficiency virus (SIV) and the zoonoses that gave rise to HIV-1 and HIV-2. What remains unknown is how long these SIVs had been circulating in non-human primates before the transmissions to humans. Here, we use relaxed molecular clock dating techniques to estimate the time of most recent common ancestor for the SIVs infecting chimpanzees and sooty mangabeys, the reservoirs of HIV-1 and HIV-2, respectively. The date of the most recent common ancestor of SIV in chimpanzees is estimated to be 1492 (1266–1685), and the date in sooty mangabeys is estimated to be 1809 (1729–1875). Notably, we demonstrate that SIV sequences sampled from sooty mangabeys possess sufficient clock-like signal to calibrate a molecular clock; despite the differences in host biology and viral dynamics, the rate of evolution of SIV in sooty mangabeys is indistinguishable from that of its human counterpart, HIV-2. We also estimate the ages of the HIV-2 human-to-human transmissible lineages and provide the first age estimate for HIV-1 group N at 1963 (1948–1977). Comparisons between the SIV most recent common ancestor dates and those of the HIV lineages suggest a difference on the order of only hundreds of years. Our results suggest either that SIV is a surprisingly young lentiviral lineage or that SIV and, perhaps, HIV dating estimates are seriously compromised by unaccounted-for biases.