Dynamics of immune escape during HIV/SIV infection

Dynamic behaviors of a stochastic virus infection model with Beddington-DeAngelis incidence function, eclipse-stage and Ornstein-Uhlenbeck process

In this paper, we present a virus infection model that incorporates eclipse-stage and Beddington-DeAngelis function, along with perturbation in infection rate using logarithmic Ornstein-Uhlenbeck process. Rigorous analysis demonstrates that the stochastic model has a unique global solution. Through construction of appropriate Lyapunov functions and a compact set, combined with the strong law of numbers and Fatou's lemma, we obtain the existence of the stationary distribution under a critical condition, which indicates the long-term persistence of T-cells and virions. Moreover, a precise probability density function is derived around the quasi-equilibrium of the model, and spectral radius analysis is employed to identify critical condition for elimination of the virus. Finally, numerical simulations are presented to validate theoretical results, and the impact of some key parameters such as the speed of reversion, volatility intensity and mean infection rate are investigated.

Human immunodeficiency virus dynamics in secondary lymphoid tissues and the evolution of cytotoxic T lymphocyte escape mutants

In secondary lymphoid tissues, human immunodeficiency virus (HIV) can replicate in both the follicular and extrafollicular compartments. Yet, virus is concentrated in the follicular compartment in the absence of antiretroviral therapy, in part due to the lack of cytotoxic T lymphocyte (CTL)-mediated activity there. CTLs home to the extrafollicular compartment, where they can suppress virus load to relatively low levels. We use mathematical models to show that this compartmentalization can explain seemingly counter-intuitive observations. First, it can explain the observed constancy of the viral decline slope during antiviral therapy in the peripheral blood, irrespective of the presence of CTL in Simian Immunodeficiency Virus (SIV)-infected macaques, under the assumption that CTL-mediated lysis significantly contributes to virus suppression. Second, it can account for the relatively long times it takes for CTL escape mutants to emerge during chronic infection even if CTL-mediated lysis is responsible for virus suppression. The reason is the heterogeneity in CTL activity and the consequent heterogeneity in selection pressure between the follicular and extrafollicular compartments. Hence, to understand HIV dynamics more thoroughly, this analysis highlights the importance of measuring virus populations separately in the extrafollicular and follicular compartments rather than using virus load in peripheral blood as an observable; this hides the heterogeneity between compartments that might be responsible for the particular patterns seen in the dynamics and evolution of the HIV in vivo.

Modeling the effects of drugs of abuse on within-host dynamics of two HIV species

Injection drug use is one of the most significant risk factors associated with contracting human immunodeficiency virus (HIV), and drug users infected with HIV suffer from a higher viral load and rapid disease progression. While replication of HIV may result in many mutant viruses that can escape recognition of the host's immune response, the presence of morphine (a drug of abuse) can decrease the viral mutation rate and cellular immune responses. This study develops a mathematical model to explore the effects of morphine-altered mutation and cellular immune response on the within-host dynamics of two HIV species, a wild-type and a mutant. Our model predicts that the morphine-altered mutation rate and cellular immune response allow the wild-type virus to outcompete the mutant virus, resulting in a higher set point viral load and lower CD4 count. We also compute the basic reproduction numbers and show that the dominant species is determined by morphine concentration, with the mutant dominating below and the wild-type dominating above a threshold. Furthermore, we identified three biologically relevant equilibria, infection-free, mutant-only, and coexistence, which are completely characterized by the fitness cost of mutation, mutant escape rate, and morphine concentration.

Virus-immune dynamics determined by prey-predator interaction network and epistasis in viral fitness landscape

Population dynamics and evolutionary genetics underly the structure of ecosystems, changing on the same timescale for interacting species with rapid turnover, such as virus (e.g. HIV) and immune response. Thus, an important problem in mathematical modeling is to connect ecology, evolution and genetics, which often have been treated separately. Here, extending analysis of multiple virus and immune response populations in a resource-prey (consumer)-predator model from Browne and Smith (2018), we show that long term dynamics of viral mutants evolving resistance at distinct epitopes (viral proteins targeted by immune responses) are governed by epistasis in the virus fitness landscape. In particular, the stability of persistent equilibrium virus-immune (prey-predator) network structures, such as nested and one-to-one, and bifurcations are determined by a collection of circuits defined by combinations of viral fitnesses that are minimally additive within a hypercube of binary sequences representing all possible viral epitope sequences ordered according to immunodominance hierarchy. Numerical solutions of our ordinary differential equation system, along with an extended stochastic version including random mutation, demonstrate how pairwise or multiplicative epistatic interactions shape viral evolution against concurrent immune responses and convergence to the multi-variant steady state predicted by theoretical results. Furthermore, simulations illustrate how periodic infusions of subdominant immune responses can induce a bifurcation in the persistent viral strains, offering superior host outcome over an alternative strategy of immunotherapy with strongest immune response.

Stochastic dynamics of influenza infection: Qualitative analysis and numerical results

In this paper, a novel influenza $ \mathcal{S}\mathcal{I}_N\mathcal{I}_R\mathcal{R} $ model with white noise is investigated. According to the research, white noise has a significant impact on the disease. First, we explain that there is global existence and positivity to the solution. Then we show that the stochastic basic reproduction $ {{\underset{\scriptscriptstyle\centerdot}{\text{R}}}} {_r} $ is a threshold that determines whether the disease is cured or persists. When the noise intensity is high, we get $ {{\underset{\scriptscriptstyle\centerdot}{\text{R}}}}{_r} < 1 $ and the disease goes away; when the white noise intensity is low, we get $ {{\underset{\scriptscriptstyle\centerdot}{\text{R}}}}{_r} > 1 $, and a sufficient condition for the existence of a stationary distribution is obtained, which suggests that the disease is still there. However, the main objective of the study is to produce a stochastic analogue of the deterministic model that we analyze using numerical simulations to get views on the infection dynamics in a stochastic environment that we can relate to the deterministic context.

Mathematical modeling of N-803 treatment in SIV-infected non-human primates

Immunomodulatory drugs could contribute to a functional cure for Human Immunodeficiency Virus (HIV). Interleukin-15 (IL-15) promotes expansion and activation of CD8⁺ T cell and natural killer (NK) cell populations. In one study, an IL-15 superagonist, N-803, suppressed Simian Immunodeficiency Virus (SIV) in non-human primates (NHPs) who had received prior SIV vaccination. However, viral suppression attenuated with continued N-803 treatment, partially returning after long treatment interruption. While there is evidence of concurrent drug tolerance, immune regulation, and viral escape, the relative contributions of these mechanisms to the observed viral dynamics have not been quantified. Here, we utilize mathematical models of N-803 treatment in SIV-infected macaques to estimate contributions of these three key mechanisms to treatment outcomes: 1) drug tolerance, 2) immune regulation, and 3) viral escape. We calibrated our model to viral and lymphocyte responses from the above-mentioned NHP study. Our models track CD8⁺ T cell and NK cell populations with N-803-dependent proliferation and activation, as well as viral dynamics in response to these immune cell populations. We compared mathematical models with different combinations of the three key mechanisms based on Akaike Information Criterion and important qualitative features of the NHP data. Two minimal models were capable of reproducing the observed SIV response to N-803. In both models, immune regulation strongly reduced cytotoxic cell activation to enable viral rebound. Either long-term drug tolerance or viral escape (or some combination thereof) could account for changes to viral dynamics across long breaks in N-803 treatment. Theoretical explorations with the models showed that less-frequent N-803 dosing and concurrent immune regulation blockade (e.g. PD-L1 inhibition) may improve N-803 efficacy. However, N-803 may need to be combined with other immune therapies to countermand viral escape from the CD8⁺ T cell response. Our mechanistic model will inform such therapy design and guide future studies.

Immune therapy may be a critical component in the functional cure for Human Immunodeficiency Virus (HIV). N-803 is an immunotherapeutic drug that activates antigen-specific CD8⁺ T cells of the immune system. These CD8⁺ T cells eliminate HIV-infected cells in order to limit the spread of infection in the body. In one study, N-803 reduced plasma viremia in macaques that were infected with Simian Immunodeficiency Virus, an analog of HIV. Here, we used mathematical models to analyze the data from this study to better understand the effects of N-803 therapy on the immune system. Our models indicated that inhibitory signals may be reversing the stimulatory effect of N-803. Results also suggested the possibilities that tolerance to N-803 could build up within the CD8⁺ T cells themselves and that the treatment may be selecting for virus strains that are not targeted by CD8⁺ T cells. Our models predict that N-803 therapy may be made more effective if the time between doses is increased or if inhibitory signals are blocked by an additional drug. Also, N-803 may need to be combined with other immune therapies to target virus that would otherwise evade CD8⁺ T cells.

Cancer-induced immunosuppression can enable effectiveness of immunotherapy through bistability generation: A mathematical and computational examination

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The presence of an immunological barrier in cancer- immune system interaction (CISI) is consistent with the bistability patterns in that system.

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In CISI models, bistability patterns are consistent with immunosuppressive effects dominating immunoproliferative effects.

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Bistability could be harnessed to devise effective combination immunotherapy approaches.

Cancer immunotherapies rely on how interactions between cancer and immune system cells are constituted. The more essential to the emergence of the dynamical behavior of cancer growth these interactions are, the more effectively they may be used as mechanisms for interventions. Mathematical modeling can help unearth such connections, and help explain how they shape the dynamics of cancer growth. Here, we explored whether there exist simple, consistent properties of cancer-immune system interaction (CISI) models that might be harnessed to devise effective immunotherapy approaches. We did this for a family of three related models of increasing complexity. To this end, we developed a base model of CISI, which captures some essential features of the more complex models built on it. We find that the base model and its derivates can plausibly reproduce biological behavior that is consistent with the notion of an immunological barrier. This behavior is also in accord with situations in which the suppressive effects exerted by cancer cells on immune cells dominate their proliferative effects. Under these circumstances, the model family may display a pattern of bistability, where two distinct, stable states (a cancer-free, and a full-grown cancer state) are possible. Increasing the effectiveness of immune-caused cancer cell killing may remove the basis for bistability, and abruptly tip the dynamics of the system into a cancer-free state. Additionally, in combination with the administration of immune effector cells, modifications in cancer cell killing may be harnessed for immunotherapy without the need for resolving the bistability. We use these ideas to test immunotherapeutic interventions in silico in a stochastic version of the base model. This bistability-reliant approach to cancer interventions might offer advantages over those that comprise gradual declines in cancer cell numbers.

Simulating the entire natural course of HIV infection by extending the basic viral dynamics equations to include declining viral clearance

The basic model of viral dynamics is a relatively simple set of equations describing the most essential features of the host-pathogen interactions. Coupled with data, it has been used extensively and successfully to reproduce and explain the features of the early acute phase of HIV infection and the effects of antiretroviral treatment, as well as to estimate the lifespan of infected cells, viral growth and clearance rates and predict early outcomes under different circumstances. However, it cannot reproduce the entire natural course of untreated HIV infection consistently with constant parameters. Here we show that it is possible to qualitatively reproduce the whole course of untreated HIV infection within the general framework of the basic model by assuming progressively declining viral clearance coupled with viral load. We discuss the interpretation of this model as proof-of-concept that may inspire further research into the role of viral clearance in HIV infection.

Genetically barcoded SIV reveals the emergence of escape mutations in multiple viral lineages during immune escape

The rapidity of replication coupled with a high mutation rate enables HIV to evade selective pressures imposed by host immune responses. Investigating the ability of HIV to escape different selection forces has generally relied on population-level measures, such as the time to detectable escape mutations in plasma and the rate these mutations subsequently take over the virus population. Here we employed a barcoded synthetic swarm of simian immunodeficiency virus (SIV) in rhesus macaques to investigate the generation and selection of escape mutations within individual viral lineages at the Mamu-A*01-restricted Tat-SL8 epitope. We observed the persistence of more than 1,000 different barcode lineages following selection after acquiring escape mutations. Furthermore, the increased resolution into the virus population afforded by barcode analysis revealed changes in the population structure of the viral quasispecies as it adapted to immune pressure. The high frequency of emergence of escape mutations in parallel viral lineages at the Tat-SL8 epitope highlights the challenge posed by viral escape for the development of T cell-based vaccines. Importantly, the level of viral replication required for generating escape mutations in individual lineages can be directly estimated using the barcoded virus, thereby identifying the level of efficacy required for a successful vaccine to limit escape. Overall, assessing the survival of barcoded viral lineages during selection provides a direct and quantitative measure of the stringency of the underlying genetic bottleneck, making it possible to predict the ability of the virus to escape selective forces induced by host immune responses as well as during therapeutic interventions.

Rise and fall of the new variant of Chlamydia trachomatis in Sweden: mathematical modelling study

Objectives

A new variant of Chlamydia trachomatis (nvCT) was discovered in Sweden in 2006. The nvCT has a plasmid deletion, which escaped detection by two nucleic acid amplification tests (Abbott-Roche, AR), which were used in 14 of 21 Swedish counties. The objectives of this study were to assess when and where nvCT emerged in Sweden, the proportion of nvCT in each county and the role of a potential fitness difference between nvCT and co-circulating wild-type strains (wtCT).

Methods

We used a compartmental mathematical model describing the spatial and temporal spread of nvCT and wtCT. We parameterised the model using sexual behaviour data and Swedish spatial and demographic data. We used Bayesian inference to fit the model to surveillance data about reported diagnoses of chlamydia infection in each county and data from four counties that assessed the proportion of nvCT in multiple years.

Results

Model results indicated that nvCT emerged in central Sweden (Dalarna, Gävleborg, Västernorrland), reaching a proportion of 1% of prevalent CT infections in late 2002 or early 2003. The diagnostic selective advantage enabled rapid spread of nvCT in the presence of high treatment rates. After detection, the proportion of nvCT decreased from 30%–70% in AR counties and 5%–20% in counties that Becton Dickinson tests, to around 5% in 2015 in all counties. The decrease in nvCT was consistent with an estimated fitness cost of around 5% in transmissibility or 17% reduction in infectious duration.

Conclusions

We reconstructed the course of a natural experiment in which a mutant strain of C. trachomatis spread across Sweden. Our modelling study provides support, for the first time, of a reduced transmissibility or infectious duration of nvCT. This mathematical model improved our understanding of the first nvCT epidemic in Sweden and can be adapted to investigate the impact of future diagnostic escape mutants.

Within-host modeling of blood-stage malaria

Malaria infection continues to be a major health problem worldwide and drug resistance in the major human parasite species, Plasmodium falciparum, is increasing in South East Asia. Control measures including novel drugs and vaccines are in development, and contributions to the rational design and optimal usage of these interventions are urgently needed. Infection involves the complex interaction of parasite dynamics, host immunity, and drug effects. The long life cycle (48 hours in the common human species) and synchronized replication cycle of the parasite population present significant challenges to modeling the dynamics of Plasmodium infection. Coupled with these, variation in immune recognition and drug action at different life cycle stages leads to further complexity. We review the development and progress of "within-host" models of Plasmodium infection, and how these have been applied to understanding and interpreting human infection and animal models of infection.

Defining Kinetic Properties of HIV-Specific CD8⁺ T-Cell Responses in Acute Infection

Multiple lines of evidence indicate that CD8 + T cells are important in the control of HIV-1 (HIV) replication. However, CD8 + T cells induced by natural infection cannot eliminate the virus or reduce viral loads to acceptably low levels in most infected individuals. Understanding the basic quantitative features of CD8 + T-cell responses induced during HIV infection may therefore inform us about the limits that HIV vaccines, which aim to induce protective CD8 + T-cell responses, must exceed. Using previously published experimental data from a cohort of HIV-infected individuals with sampling times from acute to chronic infection we defined the quantitative properties of CD8 + T-cell responses to the whole HIV proteome. In contrast with a commonly held view, we found that the relative number of HIV-specific CD8 + T-cell responses (response breadth) changed little over the course of infection (first 400 days post-infection), with moderate but statistically significant changes occurring only during the first 35 symptomatic days. This challenges the idea that a change in the T-cell response breadth over time is responsible for the slow speed of viral escape from CD8 + T cells in the chronic infection. The breadth of HIV-specific CD8 + T-cell responses was not correlated with the average viral load for our small cohort of patients. Metrics of relative immunodominance of HIV-specific CD8 + T-cell responses such as Shannon entropy or the Evenness index were also not significantly correlated with the average viral load. Our mathematical-model-driven analysis suggested extremely slow expansion kinetics for the majority of HIV-specific CD8 + T-cell responses and the presence of intra- and interclonal competition between multiple CD8 + T-cell responses; such competition may limit the magnitude of CD8 + T-cell responses, specific to different epitopes, and the overall number of T-cell responses induced by vaccination. Further understanding of mechanisms underlying interactions between the virus and virus-specific CD8 + T-cell response will be instrumental in determining which T-cell-based vaccines will induce T-cell responses providing durable protection against HIV infection.

CD8+ Cytotoxic-T-Lymphocyte Breadth Could Facilitate Early Immune Detection of Immunodeficiency Virus-Derived Epitopes with Limited Expression Levels

Cytotoxic-T-lymphocyte (CTL) responses are important to control the replication of human immunodeficiency virus (HIV) and simian immunodeficiency virus (SIV). Accumulating evidence suggests that the ability of a few immunodominant T-cell populations to detect and kill HIV/SIV-infected cells is important in individuals with a protective major histocompatibility complex class I (MHC-I) allele.

Cytotoxic-T-lymphocyte (CTL) responses are important to control the replication of human immunodeficiency virus (HIV) and simian immunodeficiency virus (SIV). Accumulating evidence suggests that the ability of a few immunodominant T-cell populations to detect and kill HIV/SIV-infected cells is important in individuals with a protective major histocompatibility complex class I (MHC-I) allele. On the other hand, immunization with live(-attenuated) viruses may be effective against superinfection of virulent viral strains regardless of the host’s MHC-I haplotypes, although the underlying mechanisms have not been fully documented. In this article, we propose a hypothesis that the early detection of infected cells in superinfected individuals may be partly facilitated by recognition of diverse CTL epitopes with limited expression levels. We further explain the hypothesis using simple mathematics that was written based on previous in vitro viral suppression assay results and by considering the physical contact of infected cells with CTLs.

Computational design of hepatitis C virus immunogens from host-pathogen dynamics over empirical viral fitness landscapes

Hepatitis C virus (HCV) afflicts 170 million people and kills 700 000 annually. Vaccination offers the most realistic and cost effective hope of controlling this epidemic, but despite 25 years of research, no vaccine is available. A major obstacle is HCV's extreme genetic variability and rapid mutational escape from immune pressure. Coupling maximum entropy inference with population dynamics simulations, we have employed a computational approach to translate HCV sequence databases into empirical landscapes of viral fitness and simulate the intrahost evolution of the viral quasispecies over these landscapes. We explicitly model the coupled host-pathogen dynamics by combining agent-based models of viral mutation with stochastically-integrated coupled ordinary differential equations for the host immune response. We validate our model in predicting the mutational evolution of the HCV RNA-dependent RNA polymerase (protein NS5B) within seven individuals for whom longitudinal sequencing data is available. We then use our approach to perform exhaustive in silico evaluation of putative immunogen candidates to rationally design tailored vaccines to simultaneously cripple viral fitness and block mutational escape within two selected individuals. By systematically identifying a small number of promising vaccine candidates, our empirical fitness landscapes and host-pathogen dynamics simulator can guide and accelerate experimental vaccine design efforts.

Inhibitory killer cell immunoglobulin-like receptors strengthen CD8+ T cell-mediated control of HIV-1, HCV, and HTLV-1

Killer cell immunoglobulin-like receptors (KIRs) are expressed predominantly on natural killer cells, where they play a key role in the regulation of innate immune responses. Recent studies show that inhibitory KIRs can also affect adaptive T cell-mediated immunity. In mice and in human T cells in vitro, inhibitory KIR ligation enhanced CD8+ T cell survival. To investigate the clinical relevance of these observations, we conducted an extensive immunogenetic analysis of multiple independent cohorts of HIV-1-, hepatitis C virus (HCV)-, and human T cell leukemia virus type 1 (HTLV-1)-infected individuals in conjunction with in vitro assays of T cell survival, analysis of ex vivo KIR expression, and mathematical modeling of host-virus dynamics. Our data suggest that functional engagement of inhibitory KIRs enhances the CD8+ T cell response against HIV-1, HCV, and HTLV-1 and is a significant determinant of clinical outcome in all three viral infections.

Modeling the immune response to HIV infection

The interplay between immune response and HIV is intensely studied via mathematical modeling, with significant insights but few direct answers. In this short review, we highlight advances and knowledge gaps across different aspects of immunity. In particular, we identify the innate immune response and its role in priming the adaptive response as ripe for modeling. The latter have been the focus of most modeling studies, but we also synthesize key outstanding questions regarding effector mechanisms of cellular immunity and development of broadly neutralizing antibodies. Thus far, most modeling studies aimed to infer general immune mechanisms; we foresee that significant progress will be made next by detailed quantitative fitting of models to data, and prediction of immune responses.

Insight into treatment of HIV infection from viral dynamics models

The odds of living a long and healthy life with HIV infection have dramatically improved with the advent of combination antiretroviral therapy. Along with the early development and clinical trials of these drugs, and new field of research emerged called viral dynamics, which uses mathematical models to interpret and predict the time-course of viral levels during infection and how they are altered by treatment. In this review, we summarize the contributions that virus dynamics models have made to understanding the pathophysiology of infection and to designing effective therapies. This includes studies of the multiphasic decay of viral load when antiretroviral therapy is given, the evolution of drug resistance, the long-term persistence latently infected cells, and the rebound of viremia when drugs are stopped. We additionally discuss new work applying viral dynamics models to new classes of investigational treatment for HIV, including latency-reversing agents and immunotherapy.

Dynamics of virus and immune response in multi-epitope network

The host immune response can often efficiently suppress a virus infection, which may lead to selection for immune-resistant viral variants within the host. For example, during HIV infection, an array of CTL immune response populations recognize specific epitopes (viral proteins) presented on the surface of infected cells to effectively mediate their killing. However HIV can rapidly evolve resistance to CTL attack at different epitopes, inducing a dynamic network of interacting viral and immune response variants. We consider models for the network of virus and immune response populations, consisting of Lotka-Volterra-like systems of ordinary differential equations. Stability of feasible equilibria and corresponding uniform persistence of distinct variants are characterized via a Lyapunov function. We specialize the model to a "binary sequence" setting, where for n epitopes there can be [Formula: see text] distinct viral variants mapped on a hypercube graph. The dynamics in several cases are analyzed and sharp polychotomies are derived characterizing persistent variants. In particular, we prove that if the viral fitness costs for gaining resistance to each epitope are equal, then the system of [Formula: see text] virus strains converges to a "perfectly nested network" with less than or equal to [Formula: see text] persistent virus strains. Overall, our results suggest that immunodominance, i.e. relative strength of immune response to an epitope, is the most important factor determining the persistent network structure.

Kinetics of HIV-Specific CTL Responses Plays a Minimal Role in Determining HIV Escape Dynamics

Cytotoxic T lymphocytes (CTLs) have been suggested to play an important role in controlling human immunodeficiency virus (HIV-1 or simply HIV) infection. HIV, due to its high mutation rate, can evade recognition of T cell responses by generating escape variants that cannot be recognized by HIV-specific CTLs. Although HIV escape from CTL responses has been well documented, factors contributing to the timing and the rate of viral escape from T cells have not been fully elucidated. Fitness costs associated with escape and magnitude of the epitope-specific T cell response are generally considered to be the key in determining timing of HIV escape. Several previous analyses generally ignored the kinetics of T cell responses in predicting viral escape by either considering constant or maximal T cell response; several studies also considered escape from different T cell responses to be independent. Here, we focus our analysis on data from two patients from a recent study with relatively frequent measurements of both virus sequences and HIV-specific T cell response to determine impact of CTL kinetics on viral escape. In contrast with our expectation, we found that including temporal dynamics of epitope-specific T cell response did not improve the quality of fit of different models to escape data. We also found that for well-sampled escape data, the estimates of the model parameters including T cell killing efficacy did not strongly depend on the underlying model for escapes: models assuming independent, sequential, or concurrent escapes from multiple CTL responses gave similar estimates for CTL killing efficacy. Interestingly, the model assuming sequential escapes (i.e., escapes occurring along a defined pathway) was unable to accurately describe data on escapes occurring rapidly within a short-time window, suggesting that some of model assumptions must be violated for such escapes. Our results thus suggest that the current sparse measurements of temporal CTL dynamics in blood bear little quantitative information to improve predictions of HIV escape kinetics. More frequent measurements using more sensitive techniques and sampling in secondary lymphoid tissues may allow to better understand whether and how CTL kinetics impacts viral escape.

BISTABILITY ANALYSIS OF AN HIV MODEL WITH IMMUNE RESPONSE

Some HIV-infected patients (the so-called post-treatment controllers) can control the virus after cessation of antiretroviral therapy. A small fraction of patients can even naturally maintain undetectable viral load without therapy (they are called elite controllers). The immune response may play an important role in viral control in these patients. In this paper, we analyze a within-host model including immune response to study the virus dynamics in HIV-infected patients. We derived two threshold values for the immune cell proliferation parameter. Below the lower immune proliferation rate, the model has a stable immune-free steady state, which predicts that patients have a high viral load. Above the higher immune proliferation rate, the model has a stable low infected steady state, which indicates that patients are under elite control. Between the two immune thresholds, the model exhibits the dynamic behavior of bistability, which suggests that patients either undergo viral rebound after treatment termination or achieve the post-treatment control. These results may explain the different virus dynamics in HIV-infected patients.

Modeling Kick-Kill Strategies toward HIV Cure

Although combinatorial antiretroviral therapy (cART) potently suppresses the virus, a sterile or functional cure still remains one of the greatest therapeutic challenges worldwide. Reservoirs are infected cells that can maintain HIV persistence for several years in patients with optimal cART, which is a leading obstacle to eradicate the virus. Despite the significant progress that has been made in our understanding of the diversity of cells that promote HIV persistence, many aspects that are critical to the development of effective therapeutic approaches able to purge the latent CD4+ T cell reservoir are poorly understood. Simultaneous purging strategies known as “kick-kill” have been pointed out as promising therapeutic approaches to eliminate the viral reservoir. However, long-term outcomes of purging strategies as well as the effect on the HIV reservoir are still largely fragmented. In this context, mathematical modeling can provide a rationale not only to evaluate the impact on the HIV reservoir but also to facilitate the formulation of hypotheses about potential therapeutic strategies. This review aims to discuss briefly the most recent mathematical modeling contributions, harnessing our knowledge toward the uncharted territory of HIV eradication. In addition, problems associated with current models are discussed, in particular, mathematical models consider only T cell responses but HIV control may also depend on other cell responses as well as chemokines and cytokines dynamics.

Role of Different Subpopulations of CD8+ T Cells during HIV Exposure and Infection

During HIV infection, specific responses exhibited by CD8⁺ T cells are crucial to establish an early, effective, and sustained viral control, preventing severe immune alterations and organ dysfunction. Several CD8⁺ T cells subsets have been identified, exhibiting differences in terms of activation, functional profile, and ability to limit HIV replication. Some of the most important CD8⁺ T cells subsets associated with viral control, production of potent antiviral molecules, and strong polyfunctional responses include Th1-like cytokine pattern and Tc17 cells. In addition, the expression of specific activation markers has been also associated with a more effective response of CD8⁺ T cells, as evidenced in HLA-DR⁺ CD38⁻ cells. CD8⁺ T cells in both, peripheral blood and gut mucosa, are particularly important in individuals with a resistant phenotype, including HIV-exposed seronegative individuals (HESNs), long-term non-progressors (LTNPs) and HIV-controllers. Although the role of CD8⁺ T cells has been extensively explored in the context of an established HIV-1 infection, the presence of HIV-specific cells with effector abilities and a defined functional profile in HESNs, remain poorly understood. Here, we reviewed studies carried out on different subpopulations of CD8⁺ T cells in relation with natural resistance to HIV infection and progression.

Within-Epitope Interactions Can Bias CTL Escape Estimation in Early HIV Infection

As human immunodeficiency virus (HIV) begins to replicate within hosts, immune responses are elicited against it. Escape mutations in viral epitopes—immunogenic peptide parts presented on the surface of infected cells—allow HIV to partially evade these responses, and thus rapidly go to fixation. The faster they go to fixation, i.e., the higher their escape rate, the larger the selective pressure exerted by the immune system is assumed to be. This relation underpins the rationale for using escapes to assess the strength of immune responses. However, escape rate estimates are often obtained by employing an aggregation procedure, where several mutations that affect the same epitope are aggregated into a single, composite epitope mutation. The aggregation procedure thus rests upon the assumption that all within-epitope mutations have indistinguishable effects on immune recognition. In this study, we investigate how violation of this assumption affects escape rate estimates. To this end, we extend a previously developed simulation model of HIV that accounts for mutation, selection, and recombination to include different distributions of fitness effects (DFEs) and inter-mutational genomic distances. We use this discrete time Wright–Fisher based model to simulate early within-host evolution of HIV for DFEs and apply standard estimation methods to infer the escape rates. We then compare true with estimated escape rate values. We also compare escape rate values obtained by applying the aggregation procedure with values estimated without use of that procedure. We find that across the DFEs analyzed, the aggregation procedure alters the detectability of escape mutations: large-effect mutations are overrepresented while small-effect mutations are concealed. The effect of the aggregation procedure is similar to extracting the largest-effect mutation appearing within an epitope. Furthermore, the more pronounced the over-exponential decay of the DFEs, the more severely true escape rates are underestimated. We conclude that the aggregation procedure has two main consequences. On the one hand, it leads to a misrepresentation of the DFE of fixed mutations. On the other hand, it conceals within-epitope interactions that may generate irregularities in mutation frequency trajectories that are thus left unexplained.

Global properties of nested network model with application to multi-epitope HIV/CTL dynamics

Mathematical modeling and analysis can provide insight on the dynamics of ecosystems which maintain biodiversity in the face of competitive and prey-predator interactions. Of primary interests are the underlying structure and features which stabilize diverse ecological networks. Recently Korytowski and Smith (Theor Ecol 8(1):111-120, 2015) proved that a perfectly nested infection network, along with appropriate life history trade-offs, leads to coexistence and persistence of bacteria-phage communities in a chemostat model. In this article, we generalize their model in order to apply it to the within-host dynamics virus and immune response, in particular HIV and CTL (Cytotoxic T Lymphocyte) cells. Our model can describe sequential viral escape from dominant immune responses and rise in subdominant immune responses, consistent with observed patterns of HIV/CTL evolution. We find a Lyapunov function for the system which leads to rigorous characterization of persistent viral and immune variants, along with informing upon equilibria stability and global dynamics. Results are interpreted in the context of within-host HIV/CTL evolution and numerical simulations are provided.

Solving Immunology?

Emergent responses of the immune system result from the integration of molecular and cellular networks over time and across multiple organs. High-content and high-throughput analysis technologies, concomitantly with data-driven and mechanistic modeling, hold promise for the systematic interrogation of these complex pathways. However, connecting genetic variation and molecular mechanisms to individual phenotypes and health outcomes has proven elusive. Gaps remain in data, and disagreements persist about the value of mechanistic modeling for immunology. Here, we present the perspectives that emerged from the National Institute of Allergy and Infectious Disease (NIAID) workshop 'Complex Systems Science, Modeling and Immunity' and subsequent discussions regarding the potential synergy of high-throughput data acquisition, data-driven modeling, and mechanistic modeling to define new mechanisms of immunological disease and to accelerate the translation of these insights into therapies.

Ad26/MVA therapeutic vaccination with TLR7 stimulation in SIV-infected rhesus monkeys

The development of immunologic interventions that can target the viral reservoir in HIV-1-infected individuals is a major goal of the HIV-1 cure field^1,2. However, little evidence exists that the viral reservoir can be sufficiently targeted to improve virologic control following discontinuation of antiretroviral therapy (ART). Here we show that Ad26/MVA^3,4 therapeutic vaccination with toll-like receptor 7 (TLR7) stimulation improves virologic control and delays viral rebound following ART discontinuation in SIV-infected rhesus monkeys that initiated ART during acute infection. Ad26/MVA therapeutic vaccination resulted in a dramatic increase in the magnitude and breadth of SIV-specific cellular immune responses in virologically suppressed, SIV-infected monkeys. TLR7 agonist administration led to innate immune stimulation and cellular immune activation. The combination of Ad26/MVA vaccination and TLR7 stimulation resulted in decreased levels of viral DNA in lymph nodes and peripheral blood, as well as improved virologic control and delayed viral rebound following ART discontinuation. Cellular immune breadth correlated inversely with setpoint viral loads and correlated directly with time to viral rebound. These data demonstrate the potential of therapeutic vaccination with innate immune stimulation as a strategy aimed at an HIV-1 functional cure.

Recent Insights into the HIV/AIDS Pandemic

Etiology, transmission and protection: Transmission of HIV, the causative agent of AIDS, occurs predominantly through bodily fluids. Factors that significantly alter the risk of HIV transmission include male circumcision, condom use, high viral load, and the presence of other sexually transmitted diseases. Pathology/Symptomatology: HIV infects preferentially CD4+ T lymphocytes, and Monocytes. Because of their central role in regulating the immune response, depletion of CD4+ T cells renders the infected individual incapable of adequately responding to microorganisms otherwise inconsequential. Epidemiology, incidence and prevalence: New HIV infections affect predominantly young heterosexual women and homosexual men. While the mortality rates of AIDS related causes have decreased globally in recent years due to the use of highly active antiretroviral therapy (HAART) treatment, a vaccine remains an elusive goal. Treatment and curability: For those afflicted HIV infection remains a serious illness. Nonetheless, the use of advanced therapeutics have transformed a dire scenario into a chronic condition with near average life spans. When to apply those remedies appears to be as important as the remedies themselves. The high rate of HIV replication and the ability to generate variants are central to the viral survival strategy and major barriers to be overcome. Molecular mechanisms of infection: In this review, we assemble new details on the molecular events from the attachment of the virus, to the assembly and release of the viral progeny. Yet, much remains to be learned as understanding of the molecular mechanisms used in viral replication and the measures engaged in the evasion of immune surveillance will be important to develop effective interventions to address the global HIV pandemic.

Recursion-based depletion of human immunodeficiency virus-specific naive CD4(+) T cells may facilitate persistent viral replication and chronic viraemia leading to acquired immunodeficiency syndrome

Although antiretroviral therapy has made human immunodeficiency virus (HIV) infection a controllable disease, it is still unclear how viral replication persists in untreated patients and causes CD4(+) T-cell depletion leading to acquired immunodeficiency syndrome (AIDS) in several years. Theorists tried to explain it with the diversity threshold theory in which accumulated mutations in the HIV genome make the virus so diverse that the immune system will no longer be able to recognize all the variants and fail to control the viraemia. Although the theory could apply to a number of cases, macaque AIDS models using simian immunodeficiency virus (SIV) have shown that failed viral control at the set point is not always associated with T-cell escape mutations. Moreover, even monkeys without a protective major histocompatibility complex (MHC) allele can contain replication of a super infected SIV following immunization with a live-attenuated SIV vaccine, while those animals are not capable of fighting primary SIV infection. Here we propose a recursion-based virus-specific naive CD4(+) T-cell depletion hypothesis through thinking on what may happen in individuals experiencing primary immunodeficiency virus infection. This could explain the mechanism for impairment of virus-specific immune response in the course of HIV infection.

Investigating the Consequences of Interference between Multiple CD8+ T Cell Escape Mutations in Early HIV Infection

During early human immunodeficiency virus (HIV) infection multiple CD8⁺ T cell responses are elicited almost simultaneously. These responses exert strong selective pressures on different parts of HIV’s genome, and select for mutations that escape recognition and are thus beneficial to the virus. Some studies reveal that the later these escape mutations emerge, the more slowly they go to fixation. This pattern of escape rate decrease(ERD) can arise by distinct mechanisms. In particular, in large populations with high beneficial mutation rates interference among different escape strains –an effect that can emerge in evolution with asexual reproduction and results in delayed fixation times of beneficial mutations compared to sexual reproduction– could significantly impact the escape rates of mutations. In this paper, we investigated how interference between these concurrent escape mutations affects their escape rates in systems with multiple epitopes, and whether it could be a source of the ERD pattern. To address these issues, we developed a multilocus Wright-Fisher model of HIV dynamics with selection, mutation and recombination, serving as a null-model for interference. We also derived an interference-free null model assuming initial neutral evolution before immune response elicitation. We found that interference between several equally selectively advantageous mutations can generate the observed ERD pattern. We also found that the number of loci, as well as recombination rates substantially affect ERD. These effects can be explained by the underexponential decline of escape rates over time. Lastly, we found that the observed ERD pattern in HIV infected individuals is consistent with both independent, interference-free mutations as well as interference effects. Our results confirm that interference effects should be considered when analyzing HIV escape mutations. The challenge in estimating escape rates and mutation-associated selective coefficients posed by interference effects cannot simply be overcome by improved sampling frequencies or sizes. This problem is a consequence of the fundamental shortcomings of current estimation techniques under interference regimes. Hence, accounting for the stochastic nature of competition between mutations demands novel estimation methodologies based on the analysis of HIV strains, rather than mutation frequencies.

Within-host evolution of human immunodeficiency virus (HIV) is shaped by strong immune responses mounted against the virus. Multiple CD8⁺ T cell populations, each recognizing a specific part of an HIV protein, simultaneously suppress HIV growth. Escape mutations that arise in HIV genome regions coding for these virion protein parts, impair CD8⁺ T cell recognition and are consequently strongly selected. The emergence and rise of these escape mutations exhibits an intriguing temporal pattern: the earlier an escape mutation arises, the faster it goes to fixation. This pattern is termed escape rate decrease (ERD). In this paper, we tested computationally whether interference, i.e. the coexistence of multiple genetically distinct HIV strains engaged in competitive interaction within the host, could be a possible source of ERD. As an alternative, we also mathematically derived the temporal pattern of escapes under interference-free conditions, and compared this with data. We found that interference between multiple beneficial mutations could generate ERD. However, ERD does not imply the presence of interference. Thus, more detailed data is required to unambiguously determine whether interference effects influence ERD generation. Nevertheless, interference should be considered when studying the within-host evolution of HIV. Ignoring its effects on population dynamics can severely underestimate the protective capacity of CD8⁺ T cells.

Third-Kind Encounters in Biomedicine: Immunology Meets Mathematics and Informatics to Become Quantitative and Predictive

The understanding of the immune response is right now at the center of biomedical research. There are growing expectations that immune-based interventions will in the midterm provide new, personalized, and targeted therapeutic options for many severe and highly prevalent diseases, from aggressive cancers to infectious and autoimmune diseases. To this end, immunology should surpass its current descriptive and phenomenological nature, and become quantitative, and thereby predictive.Immunology is an ideal field for deploying the tools, methodologies, and philosophy of systems biology, an approach that combines quantitative experimental data, computational biology, and mathematical modeling. This is because, from an organism-wide perspective, the immunity is a biological system of systems, a paradigmatic instance of a multi-scale system. At the molecular scale, the critical phenotypic responses of immune cells are governed by large biochemical networks, enriched in nested regulatory motifs such as feedback and feedforward loops. This network complexity confers them the ability of highly nonlinear behavior, including remarkable examples of homeostasis, ultra-sensitivity, hysteresis, and bistability. Moving from the cellular level, different immune cell populations communicate with each other by direct physical contact or receiving and secreting signaling molecules such as cytokines. Moreover, the interaction of the immune system with its potential targets (e.g., pathogens or tumor cells) is far from simple, as it involves a number of attack and counterattack mechanisms that ultimately constitute a tightly regulated multi-feedback loop system. From a more practical perspective, this leads to the consequence that today's immunologists are facing an ever-increasing challenge of integrating massive quantities from multi-platforms.In this chapter, we support the idea that the analysis of the immune system demands the use of systems-level approaches to ensure the success in the search for more effective and personalized immune-based therapies.

What do mathematical models tell us about killing rates during HIV-1 infection?

Over the past few decades the extent to which cytotoxic T lymphocytes (CTLs) control human immunodeficiency virus (HIV) replication has been studied extensively, yet their role and mode of action remain controversial. In some studies, CTLs were found to kill a large fraction of the productively infected cells relative to the viral cytopathicity, whereas in others CTLs were suggested to kill only a small fraction of infected cells. In this review, we compile published estimates of CTL-mediated death rates, and examine whether these studies permit determining the rate at which CTLs kill HIV-1 infected cells. We highlight potential misinterpretations of the CTL-killing rates from the escape rates of mutants, and from perturbations of the steady state viral load during chronic infection. Our major conclusion is that CTL-mediated killing rates remain unknown. But contrary to current consensus, we argue that killing rates higher than one per day are perfectly consistent with the experimental data, which would imply that the majority of the productively infected cells could still die from CTL-mediated killing rather than from viral cytopathicity.

Global stability of an age-structured virus dynamics model with Beddington-DeAngelis infection function

In this paper, we study an age-structured virus dynamics model with Beddington-DeAngelis infection function. An explicit formula for the basic reproductive number R0 of the model is obtained. We investigate the global behavior of the model in terms of R0: if R0 ≤ 1, then the infection-free equilibrium is globally asymptotically stable, whereas if R0 > 1, then the infection equilibrium is globally asymptotically stable. Finally, some special cases, which reduce to some known HIV infection models studied by other researchers, are considered.

The Oral Tolerance as a Complex Network Phenomenon

The phenomenon of oral tolerance refers to a local and systemic state of tolerance induced in the gut after its exposure to innocuous antigens. Recent findings have shown the interrelationship between cellular and molecular components of oral tolerance, but its representation through a network of interactions has not been investigated. Our work aims at identifying the causal relationship of each element in an oral tolerance network, and also to propose a phenomenological model that's capable of predicting the stochastic behavior of this network when under manipulation. We compared the changes of a "healthy" network caused by "knock-outs" (KOs) in two approaches: an analytical approach by the Perron Frobenius theory; and a computational approach, which we describe within this work in order to find numerical results for the model. Both approaches have shown the most relevant immunological components for this phenomena, that happens to corroborate the empirical results from animal models. Besides explain in a intelligible fashion how the components interacts in a complex manner, we also managed to describe and quantify the importance of KOs that hasn't been empirically tested.

Optimal Treatment Strategies in the Context of 'Treatment for Prevention' against HIV-1 in Resource-Poor Settings

An estimated 2.7 million new HIV-1 infections occurred in 2010. `Treatment-for-prevention’ may strongly prevent HIV-1 transmission. The basic idea is that immediate treatment initiation rapidly decreases virus burden, which reduces the number of transmittable viruses and thereby the probability of infection. However, HIV inevitably develops drug resistance, which leads to virus rebound and nullifies the effect of `treatment-for-prevention’ for the time it remains unrecognized. While timely conducted treatment changes may avert periods of viral rebound, necessary treatment options and diagnostics may be lacking in resource-constrained settings. Within this work, we provide a mathematical platform for comparing different treatment paradigms that can be applied to many medical phenomena. We use this platform to optimize two distinct approaches for the treatment of HIV-1: (i) a diagnostic-guided treatment strategy, based on infrequent and patient-specific diagnostic schedules and (ii) a pro-active strategy that allows treatment adaptation prior to diagnostic ascertainment. Both strategies are compared to current clinical protocols (standard of care and the HPTN052 protocol) in terms of patient health, economic means and reduction in HIV-1 onward transmission exemplarily for South Africa. All therapeutic strategies are assessed using a coarse-grained stochastic model of within-host HIV dynamics and pseudo-codes for solving the respective optimal control problems are provided. Our mathematical model suggests that both optimal strategies (i)-(ii) perform better than the current clinical protocols and no treatment in terms of economic means, life prolongation and reduction of HIV-transmission. The optimal diagnostic-guided strategy suggests rare diagnostics and performs similar to the optimal pro-active strategy. Our results suggest that ‘treatment-for-prevention’ may be further improved using either of the two analyzed treatment paradigms.

HIV-1 continues to spread globally. Antiviral treatment cannot cure patients, but it slows disease progression and may prevent HIV transmission by decreasing the amount of transmittable viruses in treated individuals. ‘Treatment-for-prevention’ argues for immediate treatment initiation and may reduce transmission by 96% (CI: 73–99%), according to the results of a large clinical study (HPTN052). In order to ensure long-lasting treatment success, early therapy initiation demands more sophisticated treatment strategies & exceeding funds. However, countries facing the highest HIV burden are among the poorest. Within this work, we provide a mathematical framework that allows assessing different treatment paradigms using optimal control theory together with stochastic modelling of within-host viral dynamics and drug resistance development. We use this framework to compute and evaluate two distinct optimal long-term treatment strategies for resource-constrained settings: (i) a diagnostic-guided and (ii) a pro-active treatment strategy. The cost of a strategy is evaluated from a national economic perspective, valuating a severe patient health status in terms of an economic loss. The optimal strategies are compared with current clinical treatment protocols and no treatment in terms of costs, life expectation and reduction of secondary cases. Our simulations indicate that the pro-active treatment strategy performs comparably to the diagnostic-guided treatment strategy. Both strategies perform better than current clinical protocols, suggesting directions for improvement.

Antibody escape kinetics of equine infectious anemia virus infection of horses

Lentivirus escape from neutralizing antibodies (NAbs) is not well understood. In this work, we quantified antibody escape of a lentivirus, using antibody escape data from horses infected with equine infectious anemia virus. We calculated antibody blocking rates of wild-type virus, fitness costs of mutant virus, and growth rates of both viruses. These quantitative kinetic estimates of antibody escape are important for understanding lentiviral control by antibody neutralization and in developing NAb-eliciting vaccine strategies.

The Effect of Interference on the CD8(+) T Cell Escape Rates in HIV

In early human immunodeficiency virus (HIV) infection, the virus population escapes from multiple CD8⁺ cell responses. The later an escape mutation emerges, the slower it outgrows its competition, i.e., the escape rate is lower. This pattern could indicate that the strength of the CD8⁺ cell responses is waning, or that later viral escape mutants carry a larger fitness cost. In this paper, we investigate whether the pattern of decreasing escape rates could also be caused by genetic interference among different escape strains. To this end, we developed a mathematical multi-epitope model of HIV dynamics, which incorporates stochastic effects, recombination, and mutation. We used cumulative linkage disequilibrium measures to quantify the amount of interference. We found that nearly synchronous, similarly strong immune responses in two-locus systems enhance the generation of genetic interference. This effect, combined with a scheme of densely spaced sampling times at the beginning of infection and sparse sampling times later, leads to decreasing successive escape rate estimates, even when there were no selection differences among alleles. These predictions are supported by empirical data from one HIV-infected patient. Thus, interference could explain why later escapes are slower. Considering escape mutations in isolation, neglecting their genetic linkage, conceals the underlying haplotype dynamics and can affect the estimation of the selective pressure exerted by CD8⁺ cells. In systems in which multiple escape mutations appear, the occurrence of interference dynamics should be assessed by measuring the linkage between different escape mutations.

The route of HIV escape from immune response targeting multiple sites is determined by the cost-benefit tradeoff of escape mutations

Cytotoxic T lymphocytes (CTL) are a major factor in the control of HIV replication. CTL arise in acute infection, causing escape mutations to spread rapidly through the population of infected cells. As a result, the virus develops partial resistance to the immune response. The factors controlling the order of mutating epitope sites are currently unknown and would provide a valuable tool for predicting conserved epitopes. In this work, we adapt a well-established mathematical model of HIV evolution under dynamical selection pressure from multiple CTL clones to include partial impairment of CTL recognition, , as well as cost to viral replication, . The process of escape is described in terms of the cost-benefit tradeoff of escape mutations and predicts a trajectory in the cost-benefit plane connecting sequentially escaped sites, which moves from high recognition loss/low fitness cost to low recognition loss/high fitness cost and has a larger slope for early escapes than for late escapes. The slope of the trajectory offers an interpretation of positive correlation between fitness costs and HLA binding impairment to HLA-A molecules and a protective subset of HLA-B molecules that was observed for clinically relevant escape mutations in the Pol gene. We estimate the value of from published experimental studies to be in the range (0.01–0.86) and show that the assumption of complete recognition loss () leads to an overestimate of mutation cost. Our analysis offers a consistent interpretation of the commonly observed pattern of escape, in which several escape mutations are observed transiently in an epitope. This non-nested pattern is a combined effect of temporal changes in selection pressure and partial recognition loss. We conclude that partial recognition loss is as important as fitness loss for predicting the order of escapes and, ultimately, for predicting conserved epitopes that can be targeted by vaccines.

Like many viruses, HIV has evolved mechanisms to evade the host immune response. As early as a few weeks after infection is initiated, mutations appear in the viral genome that reduce the ability of cytotoxic T lymphocytes (CTL) to control virus replication. However, of the many mutations in the viral genome that could potentially mediate viral escape from the CTL response, a specific subset are typically observed. This suggests that some mutations either entail too high a fitness cost for the virus, or are relatively inefficient escape mutations. A successful vaccine would target the CTL response to these regions in such a way that escape would not be possible. We use a computational model of HIV infection in order to study the factors that determine whether a given escape mutation will occur, how long it will be maintained in the population, and how these changes in the viral genome will affect the CTL response. Our analysis highlights the important role of partial recognition loss conferred by a mutation in producing the complex dynamics of escape that are observed during the course of infection.

Quantifying the turnover of transcriptional subclasses of HIV-1-infected cells

HIV-1-infected cells in peripheral blood can be grouped into different transcriptional subclasses. Quantifying the turnover of these cellular subclasses can provide important insights into the viral life cycle and the generation and maintenance of latently infected cells. We used previously published data from five patients chronically infected with HIV-1 that initiated combination antiretroviral therapy (cART). Patient-matched PCR for unspliced and multiply spliced viral RNAs combined with limiting dilution analysis provided measurements of transcriptional profiles at the single cell level. Furthermore, measurement of intracellular transcripts and extracellular virion-enclosed HIV-1 RNA allowed us to distinguish productive from non-productive cells. We developed a mathematical model describing the dynamics of plasma virus and the transcriptional subclasses of HIV-1-infected cells. Fitting the model to the data allowed us to better understand the phenotype of different transcriptional subclasses and their contribution to the overall turnover of HIV-1 before and during cART. The average number of virus-producing cells in peripheral blood is small during chronic infection. We find that a substantial fraction of cells can become defectively infected. Assuming that the infection is homogenous throughout the body, we estimate an average in vivo viral burst size on the order of 10⁴ virions per cell. Our study provides novel quantitative insights into the turnover and development of different subclasses of HIV-1-infected cells, and indicates that cells containing solely unspliced viral RNA are a good marker for viral latency. The model illustrates how the pool of latently infected cells becomes rapidly established during the first months of acute infection and continues to increase slowly during the first years of chronic infection. Having a detailed understanding of this process will be useful for the evaluation of viral eradication strategies that aim to deplete the latent reservoir of HIV-1.

Gaining a quantitative understanding of the development and turnover of different HIV-1-infected subpopulations of cells is crucial to improve the outcome of patients on combination antiretroviral therapy (cART). The population of latently infected cells is of particular interest as they represent the major barrier to a cure of HIV-1 infection. We developed a mathematical model that describes the dynamics of different transcriptionally active subclasses of HIV-1-infected cells and the viral load in peripheral blood. The model was fitted to previously published data from five chronically HIV-1-infected patients starting cART. This allowed us to estimate critical parameters of the within-host dynamics of HIV-1, such as the the number of virions produced by a single infected cell. The model further allowed investigation of HIV-1 dynamics during the acute phase. Computer simulations illustrate that latently infected cells become rapidly established during the first months of acute infection and continue to increase slowly during the first years of chronic infection. This illustrates the opportunity for strategies that aim to eradicate the virus during early cART as the pool of HIV-1 infected cells is substantially smaller during acute infection than during chronic infection.

A comparison of elasticities of viral levels to specific immune response mechanisms in human immunodeficiency virus infection

BACKGROUND

The presence of an asymptomatic phase in an HIV infection indicates that the immune system can partially control the infection. Determining the immune mechanisms that contribute significantly to the partial control of the infection enhance the HIV infection intervention strategies and is important in vaccine development. Towards this goal, a discrete time HIV model, which incorporates the life cycle aspects of the virus, the antibody (humoral) response and the cell-mediated immune response is formulated to determine immune system components that are most efficient in controlling viral levels. Ecological relationships are used to model the interplay between the immune system components and the HIV pathogen. Model simulations and transient elasticity analysis of the viral levels to immune response parameters are used to compare the different immune mechanisms.

RESULTS

It is shown that cell-mediated immune response is more effective in controlling the viral levels than the antibody response. Killing of infected cells is shown to be crucial in controlling the viral levels. Our results show a negative correlation between the antibody response and the viral levels in the early stages of the infection, but we predicted this immune mechanism to be positively correlated with the viral levels in the late stage of the infection. A result that suggests lack of relevance of antibody response with infection progression. On the contrary, we predicted the cell-mediated immune response to be always negatively correlated with viral levels.

CONCLUSION

Neutralizing antibodies can only control the viral levels in the early days of the HIV infection whereas cell-mediated immune response is beneficial during all the stages of the infection. This study predicts that vaccine design efforts should also focus on stimulating killer T cells that target infected cells.

On the laws of virus spread through cell populations

The dynamics of viral infections have been investigated extensively, often with a combination of experimental and mathematical approaches. Mathematical descriptions of virus spread through cell populations are well established in the literature and have yielded important insights, yet the formulation of certain fundamental aspects of virus dynamics models remains uncertain and untested. Here, we investigate the process of infection and, in particular, the effect of varying the target cell population size on the number of productively infected cells generated. Using an in vitro single-round HIV-1 infection system, we find that the established modeling framework cannot accurately fit the data. If the model is fit to data with the lowest number of cells and is used to predict data generated with larger cell populations, the model significantly overestimates the number of productively infected cells generated. Interestingly, this deviation becomes stronger under experimental conditions that promote mixing of cells and viruses. The reason for the deviation is that the standard model makes certain oversimplifying assumptions about the fate of viruses that fail to find a cell in their immediate proximity. We derive from stochastic processes a different model that assumes simultaneous access of the virus to multiple target cells. In this scenario, if no cell is available to the virus at its location, it has a chance to interact with other cells, a process that can be promoted by mixing of the populations. This model can accurately fit the experimental data and suggests a new interpretation of mass action in virus dynamics models.

IMPORTANCE

Understanding the principles of virus growth through cell populations is of fundamental importance to virology. It helps us make informed decisions about intervention strategies aimed at preventing virus growth, such as drug treatment or vaccination approaches, e.g., in HIV infection, yet considerable uncertainty remains in this respect. An important variable in this context is the number of susceptible cells available for virus replication. How does the number of susceptible cells influence the growth potential of the virus? Besides the importance of such information for clinical responses, a thorough understanding of this is also important for the prediction of virus levels in patients and the estimation of crucial patient parameters through the use of mathematical models. This paper investigates the relationship between target cell availability and the virus growth potential with a combination of experimental and mathematical approaches and provides significant new insights.

Reliable reconstruction of HIV-1 whole genome haplotypes reveals clonal interference and genetic hitchhiking among immune escape variants

BACKGROUND

Following transmission, HIV-1 evolves into a diverse population, and next generation sequencing enables us to detect variants occurring at low frequencies. Studying viral evolution at the level of whole genomes was hitherto not possible because next generation sequencing delivers relatively short reads.

RESULTS

We here provide a proof of principle that whole HIV-1 genomes can be reliably reconstructed from short reads, and use this to study the selection of immune escape mutations at the level of whole genome haplotypes. Using realistically simulated HIV-1 populations, we demonstrate that reconstruction of complete genome haplotypes is feasible with high fidelity. We do not reconstruct all genetically distinct genomes, but each reconstructed haplotype represents one or more of the quasispecies in the HIV-1 population. We then reconstruct 30 whole genome haplotypes from published short sequence reads sampled longitudinally from a single HIV-1 infected patient. We confirm the reliability of the reconstruction by validating our predicted haplotype genes with single genome amplification sequences, and by comparing haplotype frequencies with observed epitope escape frequencies.

CONCLUSIONS

Phylogenetic analysis shows that the HIV-1 population undergoes selection driven evolution, with successive replacement of the viral population by novel dominant strains. We demonstrate that immune escape mutants evolve in a dependent manner with various mutations hitchhiking along with others. As a consequence of this clonal interference, selection coefficients have to be estimated for complete haplotypes and not for individual immune escapes.

Predicting the impact of CD8+ T cell polyfunctionality on HIV disease progression

During the chronic phase of HIV-1 infection, polyfunctional CD8+ T cell responses, which are characterized by a high frequency of cells able to secrete multiple cytokines simultaneously, are associated with lower virus loads and slower disease progression. This relationship may arise for different reasons. Polyfunctional responses may simply be stronger. Alternatively, it could be that the increased functional diversity in polyfunctional responses leads to lower virus loads and slower disease progression. Lastly, polyfunctional responses could contain more CD8+ T cells that mediate a specific key function that is primarily responsible for viral control. Disentangling the influences of overall strength, functional diversity, and specific function on viral control and disease progression is very relevant for the rational design of vaccines and immunotherapy using cellular immune responses. We developed a mathematical model to study how polyfunctional CD8+ T cell responses mediating lytic and nonlytic effector functions affect the CD4+ T cell count and plasma viral load. We based our model on in vitro data on the efficacy of gamma interferon (IFN-γ) and macrophage inflammatory protein 1β (MIP-1β)/RANTES against HIV. We find that the strength of the response is a good predictor of disease progression, while functional diversity has only a minor influence. In addition, our model predicts for realistic levels of cytotoxicity that immune responses dominated by nonlytic effector functions most positively influence disease outcome.

IMPORTANCE

It is an open question in HIV research why polyfunctional CD8+ T cell responses are associated with better viral control, while individual functional correlates of protection have not been identified so far. Identifying the role of CD8+ T cells in HIV-1 infection has important implications for the potential development of effective T cell-based vaccines. Our analysis provides new ways to think about a causative role of CD8+ T cells by studying different hypotheses regarding why polyfunctional CD8+ T cells might be more advantageous. We identify measurements that have to be obtained in order to evaluate the role of CD8+ T cells in HIV-1 infection. In addition, our method shows how individual cell functionality data can be used in population-based virus dynamics models.

T cells translate individual, quantal activation into collective, analog cytokine responses via time-integrated feedbacks

Variability within isogenic T cell populations yields heterogeneous ‘local’ signaling responses to shared antigenic stimuli, but responding clones may communicate ‘global’ antigen load through paracrine messengers, such as cytokines. Such coordination of individual cell responses within multicellular populations is critical for accurate collective reactions to shared environmental cues. However, cytokine production may saturate as a function of antigen input, or be dominated by the precursor frequency of antigen-specific T cells. Surprisingly, we found that T cells scale their collective output of IL-2 to total antigen input over a large dynamic range, independently of population size. Through experimental quantitation and computational modeling, we demonstrate that this scaling is enforced by an inhibitory cross-talk between antigen and IL-2 signaling, and a nonlinear acceleration of IL-2 secretion per cell. Our study reveals how time-integration of these regulatory loops within individual cell signaling generates scaled collective responses and can be leveraged for immune monitoring.

DOI:http://dx.doi.org/10.7554/eLife.01944.001

The cells of the immune system face the challenge of removing viruses and other pathogens without endangering healthy tissues. Cells called T cells plays a variety of roles in the immune response: some T cells directly destroy infected cells, some recruit other cells called phagocytes to the site of infection, and some release small proteins called cytokines. These cytokines help cells to communicate with other cells and, therefore, to tailor the overall immune responses to deal with a particular pathogen.

It is known that mammals are capable of adjusting the T cell response to match the overall severity of an infection. However, it is not clear how individual T cells coordinate their seemingly binary response—they are either activated when they recognize a pathogen, or they are not activated—into a response at the collective cell level that can be varied continuously over a wide range of values.

Here, Tkach et al. show that T cell populations match their production of the cytokine interleukin 2 (IL-2) to the abundance of antigens—molecules released by the pathogen—over an unexpectedly large range of concentrations. Through a combination of experimental and computational analyses, Tkach et al. identified two novel IL-2 feedback loops that help to generate the correct quantity of cytokine, irrespective of the total number of T cells. Furthermore, this model can be used to estimate antigen quantities within diseased tissues. The work of Tkach et al. illustrates the potential of feedback integration in cell signalling and gene regulation as a mechanism to allow cellular populations to respond to environmental stimuli in a graded, collective fashion.

DOI:http://dx.doi.org/10.7554/eLife.01944.002

Constructing lower-bounds for CTL escape rates in early SIV infection

Intrahost human and simian immunodeficiency virus (HIV and SIV) evolution is marked by repeated viral escape from cytotoxic T-lymphocyte (CTL) response. Typically, the first such CTL escape starts around the time of peak viral load and completes within one or two weeks. Many authors have developed methods to quantify CTL escape rates, but existing methods depend on sampling at two or more timepoints. Since many datasets capture the dynamics of the first CTL escape at a single timepoint, we develop inference methods applicable to single timepoint datasets. To account for model uncertainty, we construct estimators which serve as lower bounds for the escape rate. These lower-bound estimators allow for statistically meaningful comparison of escape rates across different times and different compartments. We apply our methods to two SIV datasets, showing that escape rates are relatively high during the initial days of the first CTL escape and drop to lower levels as the escape proceeds.

Spin models inferred from patient-derived viral sequence data faithfully describe HIV fitness landscapes

Mutational escape from vaccine-induced immune responses has thwarted the development of a successful vaccine against AIDS, whose causative agent is HIV, a highly mutable virus. Knowing the virus' fitness as a function of its proteomic sequence can enable rational design of potent vaccines, as this information can focus vaccine-induced immune responses to target mutational vulnerabilities of the virus. Spin models have been proposed as a means to infer intrinsic fitness landscapes of HIV proteins from patient-derived viral protein sequences. These sequences are the product of nonequilibrium viral evolution driven by patient-specific immune responses and are subject to phylogenetic constraints. How can such sequence data allow inference of intrinsic fitness landscapes? We combined computer simulations and variational theory á la Feynman to show that, in most circumstances, spin models inferred from patient-derived viral sequences reflect the correct rank order of the fitness of mutant viral strains. Our findings are relevant for diverse viruses.

Modeling the within-host dynamics of HIV infection

The new field of viral dynamics, based on within-host modeling of viral infections, began with models of human immunodeficiency virus (HIV), but now includes many viral infections. Here we review developments in HIV modeling, emphasizing quantitative findings about HIV biology uncovered by studying acute infection, the response to drug therapy and the rate of generation of HIV variants that escape immune responses. We show how modeling has revealed many dynamical features of HIV infection and how it may provide insight into the ultimate cure for this infection.

The rate of immune escape vanishes when multiple immune responses control an HIV infection

During the first months of HIV infection, the virus typically evolves several immune escape mutations. These mutations are found in epitopes in viral proteins and reduce the impact of the CD8⁺ T cells specific for these epitopes. Recent data show that only a subset of the epitopes escapes, that most of these escapes evolve early, and that the rate of immune escape slows down considerably. To investigate why the evolution of immune escape slows down over the time of infection, we have extended a consensus mathematical model to allow several immune responses to control the virus together. In the extended model, most escapes also occur early, and the immune escape rate becomes small later, and typically only a minority of the epitopes escape. We show that escaping one of the many immune responses provides little advantage after viral setpoint has been approached because the total killing rate hardly depends on the breadth of the immune response. If the breadth of the immune response slowly wanes during disease progression, the model predicts an increase in the rate of immune escape at late stages of infection. Overall, the most striking prediction of the model is that HIV evolves a small number of immune escapes, in both relative and absolute terms, when the CTL immune response is broad.

Modeling antiretroviral drug responses for HIV-1 infected patients using differential equation models

We review mathematical modeling and related statistical issues of HIV dynamics primarily in response to antiretroviral drug therapy in this article. We start from a basic model of virus infection and then review a number of more advanced models with consideration of pharmacokinetic factors, adherence and drug resistance. Specifically, we illustrate how mathematical models can be developed and parameterized to understand the effects of long-term treatment and different treatment strategies on disease progression. In addition, we discuss a variety of parameter estimation methods for differential equation models that are applicable to either within- or between-host viral dynamics.