Understanding the failure of CD8+ T-cell vaccination against simian/human immunodeficiency virus

Semi-infectious particles contribute substantially to influenza virus within-host dynamics when infection is dominated by spatial structure

Influenza is an ribonucleic acid virus with a genome that comprises eight segments. Experiments show that the vast majority of virions fail to express one or more gene segments and thus cannot cause a productive infection on their own. These particles, called semi-infectious particles (SIPs), can induce virion production through complementation when multiple SIPs are present in an infected cell. Previous within-host influenza models did not explicitly consider SIPs and largely ignore the potential effects of coinfection during virus infection. Here, we constructed and analyzed two distinct models explicitly keeping track of SIPs and coinfection: one without spatial structure and the other implicitly considering spatial structure. While the model without spatial structure fails to reproduce key aspects of within-host influenza virus dynamics, we found that the model implicitly considering the spatial structure of the infection process makes predictions that are consistent with biological observations, highlighting the crucial role that spatial structure plays during an influenza infection. This model predicts two phases of viral growth prior to the viral peak: a first phase driven by fully infectious particles at the initiation of infection followed by a second phase largely driven by coinfections of fully infectious particles and SIPs. Fitting this model to two sets of data, we show that SIPs can contribute substantially to viral load during infection. Overall, the model provides a new interpretation of the in vivo exponential viral growth observed in experiments and a mechanistic explanation for why the production of large numbers of SIPs does not strongly impede viral growth. Being simple and predictive, our model framework serves as a useful tool to understand coinfection dynamics in spatially structured acute viral infections.

A role for CD4 + helper cells in HIV control and progression

OBJECTIVE

It remains unclear why HIV persists in most untreated individuals, and why a small minority of individuals can control the virus, either spontaneously or after an early treatment. Striking differences have been discovered between patient cohorts in CD4 + T-cell avidity but not in CD8 + T-cell avidity. The present work has the aim to explain the diverse outcome of infection and identify the key virological and immunological parameters predicting the outcome.

DESIGN AND METHOD

A mathematical model informed by these experiments and taking into account the details of HIV virology is developed.

RESULTS

The model predicts an arms race between viral dissemination and the proliferation of HIV-specific CD4 + helper cells leading to one of two states: a low-viremia state (controller) or a high-viremia state (progressor). Helper CD4 + cells with a higher avidity favor virus control. The parameter segregating spontaneous and posttreatment controllers is the infectivity difference between activated and resting CD4 + T cells. The model is shown to have a better connection to experiment than a previous model based on T-cell 'exhaustion'.

CONCLUSION

Using the model informed by patient data, the timing of antiretroviral therapy can be optimized.

Thresholds for post-rebound SHIV control after CCR5 gene-edited autologous hematopoietic cell transplantation

Autologous, CCR5 gene-edited hematopoietic stem and progenitor cell (HSPC) transplantation is a promising strategy for achieving HIV remission. However, only a fraction of HSPCs can be edited ex vivo to provide protection against infection. To project the thresholds of CCR5-edition necessary for HIV remission, we developed a mathematical model that recapitulates blood T cell reconstitution and plasma simian-HIV (SHIV) dynamics from SHIV-1157ipd3N4-infected pig-tailed macaques that underwent autologous transplantation with CCR5 gene editing. The model predicts that viral control can be obtained following analytical treatment interruption (ATI) when: (1) transplanted HSPCs are at least fivefold higher than residual endogenous HSPCs after total body irradiation and (2) the fraction of protected HSPCs in the transplant achieves a threshold (76–94%) sufficient to overcome transplantation-dependent loss of SHIV immunity. Under these conditions, if ATI is withheld until transplanted gene-modified cells engraft and reconstitute to a steady state, spontaneous viral control is projected to occur.

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.

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.

Autologous Stem Cell Transplantation Disrupts Adaptive Immune Responses during Rebound Simian/Human Immunodeficiency Virus Viremia

Primary HIV-1 infection induces a virus-specific adaptive/cytolytic immune response that impacts the plasma viral load set point and the rate of progression to AIDS. Combination antiretroviral therapy (cART) suppresses plasma viremia to undetectable levels that rebound upon cART treatment interruption. Following cART withdrawal, the memory component of the virus-specific adaptive immune response may improve viral control compared to primary infection. Here, using primary infection and treatment interruption data from macaques infected with simian/human immunodeficiency virus (SHIV), we observe a lower peak viral load but an unchanged viral set point during viral rebound. The addition of an autologous stem cell transplant before cART withdrawal alters viral dynamics: we found a higher rebound set point but similar peak viral loads compared to the primary infection. Mathematical modeling of the data that accounts for fundamental immune parameters achieves excellent fit to heterogeneous viral loads. Analysis of model output suggests that the rapid memory immune response following treatment interruption does not ultimately lead to better viral containment. Transplantation decreases the durability of the adaptive immune response following cART withdrawal and viral rebound. Our model's results highlight the impact of the endogenous adaptive immune response during primary SHIV infection. Moreover, because we capture adaptive immune memory and the impact of transplantation, this model will provide insight into further studies of cure strategies inspired by the Berlin patient.IMPORTANCE HIV patients who interrupt combination antiretroviral therapy (cART) eventually experience viral rebound, the return of viral loads to pretreatment levels. However, the "Berlin patient" remained free of HIV rebound over a decade after stopping cART. His cure is attributed to leukemia treatment that included an HIV-resistant stem cell transplant. Inspired by this case, we studied the impact of stem cell transplantation in a macaque simian/HIV (SHIV) system. Using a mechanistic mathematical model, we found that while primary infection generates an adaptive immune memory response, stem cell transplantation disrupts this learned immunity. The results have implications for HIV cure regimens based on stem cell transplantation.

Personalized life expectancy and treatment benefit index of antiretroviral therapy

BACKGROUND

The progression of Human Immunodeficiency Virus (HIV) within host includes typical stages and the Antiretroviral Therapy (ART) is shown to be effective in slowing down this progression. There are great challenges in describing the entire HIV disease progression and evaluating comprehensive effects of ART on life expectancy for HIV infected individuals on ART.

METHODS

We develop a novel summative treatment benefit index (TBI), based on an HIV viral dynamics model and linking the infection and viral production rates to the Weibull function. This index summarizes the integrated effect of ART on the life expectancy (LE) of a patient, and more importantly, can be reconstructed from the individual clinic data.

RESULTS

The proposed model, faithfully mimicking the entire HIV disease progression, enables us to predict life expectancy and trace back the timing of infection. We fit the model to the longitudinal data in a cohort study in China to reconstruct the treatment benefit index, and we describe the dependence of individual life expectancy on key ART treatment specifics including the timing of ART initiation, timing of emergence of drug resistant virus variants and ART adherence.

CONCLUSIONS

We show that combining model predictions with monitored CD4 counts and viral loads can provide critical information about the disease progression, to assist the design of ART regimen for maximizing the treatment benefits.

On the Role of CD8+ T Cells in Determining Recovery Time from Influenza Virus Infection

Myriad experiments have identified an important role for CD8⁺ T cell response mechanisms in determining recovery from influenza A virus infection. Animal models of influenza infection further implicate multiple elements of the immune response in defining the dynamical characteristics of viral infection. To date, influenza virus models, while capturing particular aspects of the natural infection history, have been unable to reproduce the full gamut of observed viral kinetic behavior in a single coherent framework. Here, we introduce a mathematical model of influenza viral dynamics incorporating innate, humoral, and cellular immune components and explore its properties with a particular emphasis on the role of cellular immunity. Calibrated against a range of murine data, our model is capable of recapitulating observed viral kinetics from a multitude of experiments. Importantly, the model predicts a robust exponential relationship between the level of effector CD8⁺ T cells and recovery time, whereby recovery time rapidly decreases to a fixed minimum recovery time with an increasing level of effector CD8⁺ T cells. We find support for this relationship in recent clinical data from influenza A (H7N9) hospitalized patients. The exponential relationship implies that people with a lower level of naive CD8⁺ T cells may receive significantly more benefit from induction of additional effector CD8⁺ T cells arising from immunological memory, itself established through either previous viral infection or T cell-based vaccines.

Notwithstanding Circumstantial Alibis, Cytotoxic T Cells Can Be Major Killers of HIV-1-Infected Cells

Several experiments suggest that in the chronic phase of human immunodeficiency virus type 1 (HIV-1) infection, CD8⁺ cytotoxic T lymphocytes (CTL) contribute very little to the death of productively infected cells. First, the expected life span of productively infected cells is fairly long, i.e., about 1 day. Second, this life span is hardly affected by the depletion of CD8⁺ T cells. Third, the rate at which mutants escaping a CTL response take over the viral population tends to be slow. Our main result is that all these observations are perfectly compatible with killing rates that are much faster than one per day once we invoke the fact that infected cells proceed through an eclipse phase of about 1 day before they start producing virus. Assuming that the major protective effect of CTL is cytolytic, we demonstrate that mathematical models with an eclipse phase account for the data when the killing is fast and when it varies over the life cycle of infected cells. Considering the steady state corresponding to the chronic phase of the infection, we find that the rate of immune escape and the rate at which the viral load increases following CD8⁺ T cell depletion should reflect the viral replication rate, ρ. A meta-analysis of previous data shows that viral replication rates during chronic infection vary between 0.5 ≤ ρ ≤ 1 day⁻¹. Balancing such fast viral replication requires killing rates that are several times larger than ρ, implying that most productively infected cells would die by cytolytic effects.

IMPORTANCE Most current data suggest that cytotoxic T cells (CTL) mediate their control of human immunodeficiency virus type 1 (HIV-1) infection by nonlytic mechanisms; i.e., the data suggest that CTL hardly kill. This interpretation of these data has been based upon the general mathematical model for HIV infection. Because this model ignores the eclipse phase between the infection of a target cell and the start of viral production by that cell, we reanalyze the same data sets with novel models that do account for the eclipse phase. We find that the data are perfectly consistent with lytic control by CTL and predict that most productively infected cells are killed by CTL. Because the killing rate should balance the viral replication rate, we estimate both parameters from a large set of published experiments in which CD8⁺ T cells were depleted in simian immunodeficiency virus (SIV)-infected monkeys. This confirms that the killing rate can be much faster than is currently appreciated.

Orally Administered Salacia reticulata Extract Reduces H1N1 Influenza Clinical Symptoms in Murine Lung Tissues Putatively Due to Enhanced Natural Killer Cell Activity

Influenza is a major cause of respiratory tract infection. Although most cases do not require further hospitalization, influenza periodically causes epidemics in humans that can potentially infect and kill millions of people. To countermeasure this threat, new vaccines need to be developed annually to match emerging influenza viral strains with increased resistance to existing vaccines. Thus, there is a need for finding and developing new anti-influenza viral agents as alternatives to current treatments. Here, we tested the antiviral effects of an extract from the stems and roots of Salacia reticulata (SSRE), a plant rich in phytochemicals, such as salacinol, kotalanol, and catechins, on H1N1 influenza virus-infected mice. Following oral administration of 0.6 mg/day of SSRE, the incidence of coughing decreased in 80% of mice, and only one case of severe pulmonary inflammation was detected. Moreover, when compared with mice given Lactobacillus casei JCM1134, a strain previously shown to help increase in vitro natural killer (NK) cell activity, SSRE-administered mice showed greater and equal NK cell activity in splenocytes and pulmonary cells, respectively, at high effector cell:target cell ratios. Next, to test whether or not SSRE would exert protective effects against influenza in the absence of gut microbiota, mice were given antibiotics before being inoculated influenza virus and subsequently administered SSRE. SSRE administration induced an increase in NK cell activity in splenocytes and pulmonary cells at levels similar to those detected in mice not treated with antibiotics. Based on our results, it can be concluded that phytochemicals in the SSRE exerted protective effects against influenza infection putatively via modulation of the immune response, including enhancement of NK cell activity, although some protective effects were not necessarily through modulation of gut microbiota. Further investigation is necessary to elucidate the molecular mechanisms underlying the protective effects of SSRE against influenza infection.

Timing of CD8 T cell effector responses in viral infections

CD8 T cell or cytotoxic T lymphocyte (CTL) responses are an important branch of the immune system in the fight against viral infections. The dynamics of anti-viral CTL responses have been characterized in some detail, both experimentally and with mathematical models. An interesting experimental observation concerns the timing of CTL responses. A recent study reported that in pneumonia virus of mice the effector CTL tended to arrive in the lung only after maximal virus loads had been achieved, an observation that seems at first counterintuitive because prevention of pathology would require earlier CTL-mediated activity. A delay in CTL-mediated effector activity has also been quoted as a possible explanation for the difficulties associated with CTL-based vaccines. This paper uses mathematical models to show that in specific parameter regimes, delayed CTL effector activity can be advantageous for the host in the sense that it can increase the chances of virus clearance. The increased ability of the CTL to clear the infection, however, is predicted to come at the cost of acute pathology, giving rise to a trade-off, which is discussed in the light of evolutionary processes. This work provides a theoretical basis for understanding the described experimental observations.

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.

Simple mathematical models do not accurately predict early SIV dynamics

Upon infection of a new host, human immunodeficiency virus (HIV) replicates in the mucosal tissues and is generally undetectable in circulation for 1–2 weeks post-infection. Several interventions against HIV including vaccines and antiretroviral prophylaxis target virus replication at this earliest stage of infection. Mathematical models have been used to understand how HIV spreads from mucosal tissues systemically and what impact vaccination and/or antiretroviral prophylaxis has on viral eradication. Because predictions of such models have been rarely compared to experimental data, it remains unclear which processes included in these models are critical for predicting early HIV dynamics. Here we modified the “standard” mathematical model of HIV infection to include two populations of infected cells: cells that are actively producing the virus and cells that are transitioning into virus production mode. We evaluated the effects of several poorly known parameters on infection outcomes in this model and compared model predictions to experimental data on infection of non-human primates with variable doses of simian immunodifficiency virus (SIV). First, we found that the mode of virus production by infected cells (budding vs. bursting) has a minimal impact on the early virus dynamics for a wide range of model parameters, as long as the parameters are constrained to provide the observed rate of SIV load increase in the blood of infected animals. Interestingly and in contrast with previous results, we found that the bursting mode of virus production generally results in a higher probability of viral extinction than the budding mode of virus production. Second, this mathematical model was not able to accurately describe the change in experimentally determined probability of host infection with increasing viral doses. Third and finally, the model was also unable to accurately explain the decline in the time to virus detection with increasing viral dose. These results suggest that, in order to appropriately model early HIV/SIV dynamics, additional factors must be considered in the model development. These may include variability in monkey susceptibility to infection, within-host competition between different viruses for target cells at the initial site of virus replication in the mucosa, innate immune response, and possibly the inclusion of several different tissue compartments. The sobering news is that while an increase in model complexity is needed to explain the available experimental data, testing and rejection of more complex models may require more quantitative data than is currently available.

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 role of chance in primate lentiviral infectivity: from protomer to host organism

Infection is best described as a stochastic process. Whether a host becomes infected upon exposure has a strong random element. The same applies to cells exposed to virions. In this review, we show how the mathematical formalism for stochastic processes has been used to describe and understand the infection by the Human and Simian Immunodeficiency Virus on different levels. We survey quantitative studies on the establishment of infection in the host (the organismal level) and on the infection of target cells (the cellular and molecular level). We then discuss how a synthesis of the approaches across these levels could give rise to a predictive framework for assessing the efficacy of microbicides and vaccines.

Modeling inoculum dose dependent patterns of acute virus infections

Inoculum dose, i.e. the number of pathogens at the beginning of an infection, often affects key aspects of pathogen and immune response dynamics. These in turn determine clinically relevant outcomes, such as morbidity and mortality. Despite the general recognition that inoculum dose is an important component of infection outcomes, we currently do not understand its impact in much detail. This study is intended to start filling this knowledge gap by analyzing inoculum dependent patterns of viral load dynamics in acute infections. Using experimental data for adenovirus and infectious bronchitis virus infections as examples, we demonstrate inoculum dose dependent patterns of virus dynamics. We analyze the data with the help of mathematical models to investigate what mechanisms can reproduce the patterns observed in experimental data. We find that models including components of both the innate and adaptive immune response are needed to reproduce the patterns found in the data. We further analyze which types of innate or adaptive immune response models agree with observed data. One interesting finding is that only models for the adaptive immune response that contain growth terms partially independent of viral load can properly reproduce observed patterns. This agrees with the idea that an antigen-independent, programmed response is part of the adaptive response. Our analysis provides useful insights into the types of model structures that are required to properly reproduce observed virus dynamics for varying inoculum doses. We suggest that such models should be taken as basis for future models of acute viral infections.

Viral Dynamics and Mathematical Models

Mathematical tools have been widely applied in understanding the dynamics and control of viral infections. Here we present some fundamental aspects of infection dynamics, starting with acute immunising infections as a case study for herd immunity and other important factors in the spread and control of infection. We then discuss the dynamics of infections with more complex life histories, including chronic infections, and those showing evolution for immune escape. We conclude with a discussion of important gaps in our current understanding of viral dynamics, along with future research needs.

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.

Computational inference methods for selective sweeps arising in acute HIV infection

During the first weeks of human immunodeficiency virus-1 (HIV-1) infection, cytotoxic T-lymphocytes (CTLs) select for multiple escape mutations in the infecting HIV population. In recent years, methods that use escape mutation data to estimate rates of HIV escape have been developed, thereby providing a quantitative framework for exploring HIV escape from CTL response. Current methods for escape-rate inference focus on a specific HIV mutant selected by a single CTL response. However, recent studies have shown that during the first weeks of infection, CTL responses occur at one to three epitopes and HIV escape occurs through complex mutation pathways. Consequently, HIV escape from CTL response forms a complex, selective sweep that is difficult to analyze. In this work, we develop a model of initial infection, based on the well-known standard model, that allows for a description of multi-epitope response and the complex mutation pathways of HIV escape. Under this model, we develop Bayesian and hypothesis-test inference methods that allow us to analyze and estimate HIV escape rates. The methods are applied to two HIV patient data sets, concretely demonstrating the utility of our approach.

Which of our modeling predictions are robust?

In theoretical ecology it is well known that the steady state expressions of the variables in a food chain crucially depend on the parity of the length of the chain. This poses a major problem for modeling real food webs because it is difficult to establish their true number of trophic levels, with sometimes rare predators and often rampant pathogens. Similar problems arise in the modeling of chronic viral infections. We review examples where seemingly general interpretations strongly depend on the number of levels in a model, and on its specific equations. This Perspective aims to open the discussion on this problem.

Impaired immune evasion in HIV through intracellular delays and multiple infection of cells

With its high mutation rate, HIV is capable of escape from recognition, suppression and/or killing by CD8(+) cytotoxic T lymphocytes (CTLs). The rate at which escape variants replace each other can give insights into the selective pressure imposed by single CTL clones. We investigate the effects of specific characteristics of the HIV life cycle on the dynamics of immune escape. First, it has been found that cells in HIV-infected patients can carry multiple copies of proviruses. To investigate how this process affects the emergence of immune escape, we develop a mathematical model of HIV dynamics with multiple infections of cells. Increasing the frequency of multiple-infected cells delays the appearance of immune escape variants, slows down the rate at which they replace the wild-type variant and can even prevent escape variants from taking over the quasi-species. Second, we study the effect of the intracellular eclipse phase on the rate of escape and show that escape rates are expected to be slower than previously anticipated. In summary, slow escape rates do not necessarily imply inefficient CTL-mediated killing of HIV-infected cells, but are at least partly a result of the specific characteristics of the viral life cycle.

A race between tumor immunoescape and genome maintenance selects for optimum levels of (epi)genetic instability

The human immune system functions to provide continuous body-wide surveillance to detect and eliminate foreign agents such as bacteria and viruses as well as the body's own cells that undergo malignant transformation. To counteract this surveillance, tumor cells evolve mechanisms to evade elimination by the immune system; this tumor immunoescape leads to continuous tumor expansion, albeit potentially with a different composition of the tumor cell population ("immunoediting"). Tumor immunoescape and immunoediting are products of an evolutionary process and are hence driven by mutation and selection. Higher mutation rates allow cells to more rapidly acquire new phenotypes that help evade the immune system, but also harbor the risk of an inability to maintain essential genome structure and functions, thereby leading to an error catastrophe. In this paper, we designed a novel mathematical framework, based upon the quasispecies model, to study the effects of tumor immunoediting and the evolution of (epi)genetic instability on the abundance of tumor and immune system cells. We found that there exists an optimum number of tumor variants and an optimum magnitude of mutation rates that maximize tumor progression despite an active immune response. Our findings provide insights into the dynamics of tumorigenesis during immune system attacks and help guide the choice of treatment strategies that best inhibit diverse tumor cell populations.

The role of recombination for the coevolutionary dynamics of HIV and the immune response

The evolutionary implications of recombination in HIV remain not fully understood. A plausible effect could be an enhancement of immune escape from cytotoxic T lymphocytes (CTLs). In order to test this hypothesis, we constructed a population dynamic model of immune escape in HIV and examined the viral-immune dynamics with and without recombination. Our model shows that recombination (i) increases the genetic diversity of the viral population, (ii) accelerates the emergence of escape mutations with and without compensatory mutations, and (iii) accelerates the acquisition of immune escape mutations in the early stage of viral infection. We see a particularly strong impact of recombination in systems with broad, non-immunodominant CTL responses. Overall, our study argues for the importance of recombination in HIV in allowing the virus to adapt to changing selective pressures as imposed by the immune system and shows that the effect of recombination depends on the immunodominance pattern of effector T cell responses.

Implications of CTL-mediated killing of HIV-infected cells during the non-productive stage of infection

Patients infected with HIV exhibit orders of magnitude differences in their set-point levels of the plasma viral load. As to what extent this variation is due to differences in the efficacy of the cytotoxic T lymphocyte (CTL) response in these patients is unclear. Several studies have shown that HIV-infected CD4⁺ T cells also present viral epitopes that are recognized by CTLs before the productive stage of infection, i.e., during the intracellular eclipse phase before the infected cell starts to produce new viral particles. Here, we use mathematical modeling to investigate the potential impact of early killing of HIV-infected cells on viral replication. We suggest that the majority of CTL-mediated killing could occur during the viral eclipse phase, and that the killing of virus-producing cells could be substantially lower at later stages due to MHC-I-down-regulation. Such a mechanism is in agreement with several experimental observations that include CD8⁺ T cell depletion and antiretroviral drug treatment. This indicates a potentially important role of CTL-mediated killing during the non-productive stage of HIV-infected cells.

Carbohydrate targets in HIV vaccine research: lessons from failures

Learning from the successes of other vaccines that enhance natural and existing protective responses to pathogens, the current effort in HIV vaccine research is directed toward inducing cytotoxic responses. Nevertheless, antibodies are fundamental players in vaccine development and are still considered in the context of passive specific immunotherapy of HIV, especially since several broadly neutralizing monoclonals are available. Special interest is directed toward antibodies binding to the glycan array on gp120 since they have the potential of broader reactivity and cross-clade neutralizing capacity. Humoral responses to carbohydrate antigens have proven effective against other pathogens, why not HIV? The variability of the epitope targets on HIV may not be the only problem to developing active or passive immunotherapeutic strategies. The dynamics of the infected immune system leads to ambiguous effects of most of the effector mechanisms calling for new approaches; some may already be available, while others are in the making.

Killing of targets by CD8 T cells in the mouse spleen follows the law of mass action

It has been difficult to correlate the quality of CD8 T cell responses with protection against viral infections. To investigate the relationship between efficacy and magnitude of T cell responses, we quantify the rate at which individual CD8 effector and memory T cells kill target cells in the mouse spleen. Using mathematical modeling, we analyze recent data on the loss of target cells pulsed with three different peptides from the mouse lymphocytic choriomeningitis virus (LCMV) in mouse spleens with varying numbers of epitope-specific CD8 T cells. We find that the killing of targets follows the law of mass-action, i.e., the death rate of individual target cells remains proportional to the frequency (or the total number) of specific CD8 T cells in the spleen despite the fact that effector cell densities and effector to target ratios vary about a 1000-fold. The killing rate of LCMV-specific CD8 T cells is largely independent of T cell specificity and differentiation stage. Our results thus allow one to calculate the critical T cell concentration at which growth of a virus with a given replication rate can be prevented from the start of infection by memory CD8 T cell response.

Interpreting the effect of vaccination on steady state infection in animals challenged with Simian immunodeficiency virus

A representative vaccinated macaque challenged with SIVmac251 establishes a persistent infection with a lower virus load, higher CTL frequencies, and much higher helper cell frequencies, than a representative control animal. The reasons for the difference are not fully understood. Here we interpret this effect using a mathematical model we developed recently to explain results of various experiments on virus and CTL dynamics in SIV-infected macaques and HIV-infected humans. The model includes two types of cytotoxic lymphocytes (CTLs) regulated by antigen-activated helper cells and directly by infected cells, respectively, and predicts the existence of two steady states with different viremia, helper cell and CTL levels. Depending on the initial level of CTL memory cells and helper cells, a representative animal ends up in either the high-virus state or the low-virus state, which accounts for the observed differences between the two animal groups. Viremia in the low-virus state is proportional to the antigen sensitivity threshold of helper cells. Estimating the infectivity ratio of activated and resting CD4 T cells at 200-300, the correct range for the critical memory cell percentage and the viremia peak suppression is predicted. However, the model does not explain why viremia in the "low-virus state" is surprisingly high , relative to vaccinated animals infected with SHIV, and broadly distributed among challenged animals. We conclude that the model needs an update explaining extremely low sensitivity of uninfected helper cells to antigen in vaccinated animals.

Model with two types of CTL regulation and experiments on CTL dynamics

Recently, we developed a mathematical model of interaction between the HIV and the immune system to match various dynamic experiments carried out in HIV-infected humans and SIV-infected macaques. The model includes helper cell-dependent and helper cell-independent cytotoxic lymphocytes (CTLs) and predicts two stable steady states, a state with a high virus load and few helper cells, and another state with a low virus load and many helper cells. Here we upgrade the model to take into account recent reports on the link between the activation status of infected cells and their ability to produce virus, the effect of helper cells at the time of priming on CTL differentiation, and virus dynamics in unvaccinated macaques with a broad genetic background acutely infected with SIVmac251. We also discuss in detail the experimental justification of the CTL block and the robustness of model predictions with respect to the hypothesis of two CTL subtypes.

Mathematical modeling of viral kinetics under immune control during primary HIV-1 infection

Primary human immunodeficiency virus (HIV) infection is characterized by an initial exponential increase of viral load in peripheral blood reaching a peak, followed by a rapid decline to the viral setpoint. Although the target-cell-limited model can account for part of the viral kinetics observed early in infection [Phillips, 1996. Reduction of HIV concentration during acute infection: independence from a specific immune response. Science 271 (5248), 497-499], it frequently predicts highly oscillatory kinetics after peak viremia, which is not typically observed in clinical data. Furthermore, the target-cell-limited model is unable to predict long-term viral kinetics, unless a delayed immune effect is assumed [Stafford et al., 2000. Modeling plasma virus concentration during primary HIV infection. J. Theor. Biol. 203 (3), 285-301]. We show here that extending the target-cell-limited model, by implementing a saturation term for HIV-infected cell loss dependent upon infected cell levels, is able to reproduce the diverse observed viral kinetic patterns without the assumption of a delayed immune response. Our results suggest that the immune response may have significant effect on the control of the virus during primary infection and may support experimental observations that an anti-HIV immune response is already functional during peak viremia.

Modeling HIV persistence, the latent reservoir, and viral blips

HIV-1 eradication from infected individuals has not been achieved with the prolonged use of highly active antiretroviral therapy (HAART). The cellular reservoir for HIV-1 in resting memory CD4(+) T cells remains a major obstacle to viral elimination. The reservoir does not decay significantly over long periods of time but is able to release replication-competent HIV-1 upon cell activation. Residual ongoing viral replication may likely occur in many patients because low levels of virus can be detected in plasma by sensitive assays and transient episodes of viremia, or HIV-1 blips, are often observed in patients even with successful viral suppression for many years. Here we review our current knowledge of the factors contributing to viral persistence, the latent reservoir, and blips, and mathematical models developed to explore them and their relationships. We show how mathematical modeling has helped improve our understanding of HIV-1 dynamics in patients on HAART and of the quantitative events underlying HIV-1 latency, reservoir stability, low-level viremic persistence, and emergence of intermittent viral blips. We also discuss treatment implications related to these studies.

Novel humanized murine models for HIV research

There are few models in which HIV pathogenesis, particularly gut-associated lymphoid tissue CD4(+) T-cell depletion, can be studied and in which potential clinical interventions against HIV disease can be evaluated. HIV cannot be studied in normal mice due to the limited species tropism of the virus. Through the pioneering efforts of many investigators, humanized mice are now routinely used to rapidly advance HIV research. It is important to recognize that not all humanized murine models are equal, and their strengths and weaknesses must be taken into consideration to obtain information that is most relevant to the human condition. This review distinguishes the major humanization protocols and highlights each model's recent contributions to HIV research, including mucosal transmission, gut-associated lymphoid tissue pathogenesis, and the evaluation of novel therapeutic and prevention approaches to potentially treat HIV disease and prevent the further spread of AIDS.

Estimating in vivo death rates of targets due to CD8 T-cell-mediated killing

Despite recent advances in immunology, several key parameters determining virus dynamics in infected hosts remain largely unknown. For example, the rate at which specific effector and memory CD8 T cells clear virus-infected cells in vivo is hardly known for any viral infection. We propose a framework to quantify T-cell-mediated killing of infected or peptide-pulsed target cells using the widely used in vivo cytotoxicity assay. We have reanalyzed recently published data on killing of peptide-pulsed splenocytes by cytotoxic T lymphocytes and memory CD8 T cells specific to NP396 and GP276 epitopes of lymphocytic choriomeningitis virus (LCMV) in the mouse spleen. Because there are so many effector CD8 T cells in spleens of mice at the peak of the immune response, NP396- and GP276-pulsed targets are estimated to have very short half-lives of 2 and 14 min, respectively. After the effector numbers have diminished, i.e., in LCMV-immune mice, the half-lives become 48 min and 2.8 h for NP396- and GP276-expressing targets, respectively. Analysis of several alternative models demonstrates that the estimates of half-life times of peptide-pulsed targets are not affected when changes are made in the model assumptions. Our report provides a unifying framework to compare killing efficacies of CD8 T-cell responses specific to different viral and bacterial infections in vivo, which may be used to compare efficacies of various cytotoxic-T-lymphocyte-based vaccines.

Dynamics of immune escape during HIV/SIV infection

Several studies have shown that cytotoxic T lymphocytes (CTLs) play an important role in controlling HIV/SIV infection. Notably, the observation of escape mutants suggests a selective pressure induced by the CTL response. However, it remains difficult to assess the definite role of the cellular immune response. We devise a computational model of HIV/SIV infection having a broad cellular immune response targeting different viral epitopes. The CTL clones are stimulated by viral antigen and interact with the virus population through cytotoxic killing of infected cells. Consequently, the virus population reacts through the acquisition of CTL escape mutations. Our model provides realistic virus dynamics and describes several experimental observations. We postulate that inter-clonal competition and immunodominance may be critical factors determining the sequential emergence of escapes. We show that even though the total killing induced by the CTL response can be high, escape rates against a single CTL clone are often slow and difficult to estimate from infrequent sequence measurements. Finally, our simulations show that a higher degree of immunodominance leads to more frequent escape with a reduced control of viral replication but a substantially impaired replicative capacity of the virus. This result suggests two strategies for vaccine design: Vaccines inducing a broad CTL response should decrease the viral load, whereas vaccines stimulating a narrow but dominant CTL response are likely to induce escape but may dramatically reduce the replicative capacity of the virus.

As a result of their high mutation rate, HIV and its counterpart SIV in non-human primates can evade recognition by the host immune response through the generation of viral variants, the so-called escape mutants. This avoidance of cytotoxic T lymphocyte (CTL) mediated killing seems to be one of the major reasons why virus replication is not controlled effectively. However, it remains difficult to investigate the critical properties of the dynamics of immune escape. To this end, we developed a new computational model of HIV/SIV infection consisting of several CTL clones that can recognize specific parts of viral proteins, i.e., epitopes. The simulations allow us to follow the dynamics of immune escape in detail and help to interpret longitudinal data of HIV/SIV infections. Interestingly, changing the relative sizes of the CTL clones leads to a different evolution of the virus. Instead of reducing the number of infected cells, an alternative strategy of vaccine design could be to reduce the replicative capacity of the virus that might have implications for disease progression.

Natural killer cells promote early CD8 T cell responses against cytomegalovirus

Understanding the mechanisms that help promote protective immune responses to pathogens is a major challenge in biomedical research and an important goal for the design of innovative therapeutic or vaccination strategies. While natural killer (NK) cells can directly contribute to the control of viral replication, whether, and how, they may help orchestrate global antiviral defense is largely unknown. To address this question, we took advantage of the well-defined molecular interactions involved in the recognition of mouse cytomegalovirus (MCMV) by NK cells. By using congenic or mutant mice and wild-type versus genetically engineered viruses, we examined the consequences on antiviral CD8 T cell responses of specific defects in the ability of the NK cells to control MCMV. This system allowed us to demonstrate, to our knowledge for the first time, that NK cells accelerate CD8 T cell responses against a viral infection in vivo. Moreover, we identify the underlying mechanism as the ability of NK cells to limit IFN-α/β production to levels not immunosuppressive to the host. This is achieved through the early control of cytomegalovirus, which dramatically reduces the activation of plasmacytoid dendritic cells (pDCs) for cytokine production, preserves the conventional dendritic cell (cDC) compartment, and accelerates antiviral CD8 T cell responses. Conversely, exogenous IFN-α administration in resistant animals ablates cDCs and delays CD8 T cell activation in the face of NK cell control of viral replication. Collectively, our data demonstrate that the ability of NK cells to respond very early to cytomegalovirus infection critically contributes to balance the intensity of other innate immune responses, which dampens early immunopathology and promotes optimal initiation of antiviral CD8 T cell responses. Thus, the extent to which NK cell responses benefit the host goes beyond their direct antiviral effects and extends to the prevention of innate cytokine shock and to the promotion of adaptive immunity.

To fight viral infections, vertebrates have developed a battery of innate and adaptive immune responses aimed at inhibiting viral replication or at killing infected cells. These responses include the early production of innate antiviral cytokines, especially interferons α and β (IFN-α/β), and the activation of cytotoxic lymphocytes such as the innate natural killer (NK) cells and the adaptive CD8 T cells. While critical for antiviral defense, cytokine or CD8 T cell responses can be detrimental or even fatal to the host when deregulated. Therefore, we need to better understand how the different arms of antiviral immunity are regulated. In particular, NK cells are proposed to play a protective role in a variety of viral infection in humans, but the underlying mechanisms remain poorly understood. Here, in a mouse model of cytomegalovirus infection, we demonstrate that NK cells prevent an excessive production of IFN-α/β and promote more efficient antiviral CD8 T cell responses. We thus show that NK cells can help promote health over disease during viral infections by regulating both innate and adaptive immune responses. It will be important to examine in humans whether NK cells control innate cytokine production to prevent immunopathology and to promote adaptive immunity against herpesviruses, HIV-1, influenza, or SARS.