The race between initial T-helper expansion and virus growth upon HIV infection influences polyclonality of the response and viral set-point

A mathematical study on the drug resistant virus emergence with HIV/AIDS treatment cases

HIV/AIDS drug treatments, one of which is highly active anti-retroviral ther-apy (HAART), often fail by the emergence of drug resistant virus. In this paper we study a quantitative method to evaluate the chance of resistant virus gen-eration. To this end we develop a mathematical description of the possibility of the emergence of resistant virus species against drug treatments, depend-ing on the trajectories of the state variables of HIV infection dynamic model. By simulation studies of mathematical models we apply the proposed analy-sis method to HIV/AIDS drug therapies, improved gradual dosage reduction (iGDR) and structured treatment interruption (STI). Based on the analysis it can be explained the reason why STI therapy often fails. Moreover it is con-cluded that iGDR is desirable particularly by decreasing the threat of resistant virus emergence.

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.

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.

Post-treatment control of HIV infection

Antiretroviral therapy (ART) for HIV is not a cure. However, recent studies suggest that ART, initiated early during primary infection, may induce post-treatment control (PTC) of HIV infection with HIV RNA maintained at <50 copies per mL. We investigate the hypothesis that ART initiated early during primary infection permits PTC by limiting the size of the latent reservoir, which, if small enough at treatment termination, may allow the adaptive immune response to prevent viral rebound (VR) and control infection. We use a mathematical model of within host HIV dynamics to capture interactions among target cells, productively infected cells, latently infected cells, virus, and cytotoxic T lymphocytes (CTLs). Analysis of our model reveals a range in CTL response strengths where a patient may show either VR or PTC, depending on the size of the latent reservoir at treatment termination. Below this range, patients will always rebound, whereas above this range, patients are predicted to behave like elite controllers. Using data on latent reservoir sizes in patients treated during primary infection, we also predict population-level VR times for noncontrollers consistent with observations.

Modeling T cell responses to antigenic challenge

T cell responses are a crucial part of the adaptive immune system in the fight against infections. This article discusses the use of mathematical models for understanding the dynamics of cytotoxic T lymphocyte (CTL) responses against viral infections. Complementing experimental research, mathematical models have been very useful for exploring new hypotheses, interpreting experimental data, and for defining what needs to be measured to improve understanding. This review will start with minimally parameterized models of CTL responses, which have generated some valuable insights into basic dynamics and correlates of control. Subsequently, more biological complexity is incorporated into this modeling framework, examining different mechanisms of CTL expansion, different effector activities, and the influence of T cell help. Models and results are discussed in the context of data from specific infections.

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.

Infection of HIV-specific CD4 T helper cells and the clonal composition of the response

A hallmark of human immunodeficiency virus is its ability to infect CD4+ T helper cells, thus impairing helper cell responses and consequently effector responses whose maintenance depends on help (such as killer T cells and B cells). In particular, the virus has been shown to infect HIV-specific helper cells preferentially. Using mathematical models, we investigate the consequence of this assumption for the basic dynamics between HIV and its target cells, assuming the existence of two independently regulated helper cell clones, directed against different epitopes of the virus. In contrast to previous studies, we examine a relatively simple scenario, only concentrating on the interactions between the virus and its target cells, not taking into account any helper-dependent effector responses. Further, there is no direct competition for space or antigenic stimulation in the model. Yet, a set of interesting outcomes is observed that provide further insights into factors that shape helper cell responses. Despite the absence of competition, a stronger helper cell clone can still exclude a weaker one because the two clones are infected by the same pathogen, an ecological concept called "apparent competition". Moreover, we also observe "facilitation": if one of the helper cell clones is too weak to become established in isolation, the presence of a stronger clone can provide enhanced antigenic stimulation, thus allowing the weaker clone to persist. The dependencies of these outcomes on parameters is explored. Factors that reduce viral infectivity and increase the death rate of infected cells promote coexistence, which is in agreement with the observation that stronger immunity correlates with broader helper cell responses. The basic model is extended to explicitly take into account helper-dependent CTL responses and direct competition. This study sheds further light onto the factors that can influence the clonal composition of HIV-specific helper cell responses, which has implications for the overall pattern of disease progression.

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.

Immune impairment in HIV infection: existence of risky and immunodeficiency thresholds

Results of several studies show that some DC populations are susceptible to HIV. Modulation of DCs by HIV infection, in particular interference of the antigen-presenting function of DCs, is a key aspect in viral pathogenesis and contributes to viral evasion from immunity because the loss of the DC function engenders some impairment effects for a proliferation of CTL responses, which play an important role in the immune response to HIV. As described herein, we use a simple mathematical model to examine virus-immune dynamics over the course of HIV infection in the context of the immune impairment effects. A decrease of the DC number and function during the course of HIV-1 infection is observed. Therefore, we simply assumed that the immune impairment rate increases over the HIV infection. Under the assumption, four processes of the disease progression dynamics of our model are classifiable according to their virological properties. It is particularly interesting a typical disease progression presents a "risky threshold" and an "immunodeficiency threshold". Regarding the former, the immune system might collapse when the impairment rate of HIV exceeds a threshold value (which corresponds to a transcritical bifurcation point). For the latter, the immune system always collapses when the impairment rate exceeds the value (which corresponds to a saddle-node bifurcation point). To test our theoretical framework, we investigate the existence and distribution of these thresholds in 10 patients.

Control of the transition to long-term nonprogressor in tristable HIV dynamics

The human immunodeficiency virus (HIV) infection, that causes acquired immune deficiency syndrome (AIDS), is a dynamic process that can be modeled via differential equations. In this paper we apply a control strategy to boost the immune response for a tristable HIV dynamic model. The purpose of this control method is to steer the system to an equilibrium condition known as long-term nonprogressor, which corresponds to an infected patient that does not develop the symptoms of AIDS. The control strategy is implemented by controlled drug scheduling based on the understanding of the immune boosting mechanism. The feasibility of the methodology is illustrated via simulations.

Infection dynamics in HIV-specific CD4 T cells: does a CD4 T cell boost benefit the host or the virus?

Recent experimental data have shown that HIV-specific CD4 T cells provide a very important target for HIV replication. We use mathematical models to explore the effect of specific CD4 T cell infection on the dynamics of virus spread and immune responses. Infected CD4 T cells can provide antigen for their own stimulation. We show that such autocatalytic cell division can significantly enhance virus spread, and can also provide an additional reservoir for virus persistence during anti-viral drug therapy. In addition, the initial number of HIV-specific CD4 T cells is an important determinant of acute infection dynamics. A high initial number of HIV-specific CD4 T cells can lead to a sudden and fast drop of the population of HIV-specific CD4 T cells which results quickly in their extinction. On the other hand, a low initial number of HIV-specific CD4 T cells can lead to a prolonged persistence of HIV-specific CD4 T cell help at higher levels. The model suggests that boosting the population of HIV-specific CD4 T cells can increase the amount of virus-induced immune impairment, lead to less efficient anti-viral effector responses, and thus speed up disease progression, especially if effector responses such as CTL have not been sufficiently boosted at the same time.

Understanding the mechanisms and limitations of immune control of HIV

A large number of experimental studies have been performed over the past decade in an attempt to develop a vaccine for human immunodeficiency virus (HIV). These studies have used a variety of approaches aimed at stimulating both antibody-mediated and cell-mediated immunity. Many of these experiments have been performed in macaque models of HIV. Analysis and modeling of the results of these studies provide the opportunity to investigate the mechanisms and limitations of viral control by humoral and cell-mediated immunity. These studies suggest that CD8(+) T cells do 'too little too late' to prevent the establishment of viral infection and latency. By contrast, passively administered antibody acts extremely early to reduce the initial inoculum and slow viral growth. In both cases, reduction in peak viral load appears crucial to the maintenance of CD4(+) T cells in acute infection and for effective long-term viral control. The insights gained from studies of simian human immunodeficiency virus infection have important implications for HIV vaccination. However, important questions remain as to whether differences in pathogenesis in HIV will lead to different 'rules of engagement' for immune control of virus.

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

Although CD8+ T cells play an important role in controlling viral infections, boosting specific CD8+ T cells by prophylactic vaccination with simian immunodeficiency virus (SIV) epitopes fails to provide sterilizing immunity. Viral replication rates and viral contraction rates after the peak viremia hardly depend on the presence of memory CD8+ T cells. To study these paradoxical findings, we parameterize novel mathematical models for acute SIV and human immunodeficiency virus infection. These models explain that failure of vaccination is due to the fact that effector/target ratios are too low during the viral expansion phase. Because CD8+ T cells require cell-to-cell contacts, immune protection requires high effector/target ratios at the primary site of infection. Effector/target ratios become favorable for immune control at the time of the peak in the viral load when the virus becomes limited by other factors, such as the availability of uninfected target cells. At the viral set point, effector/target ratios are much higher, and perturbations of the number of CD8+ effector cells have a large impact on the viral load. Such protective effector/target ratios are difficult to achieve with nucleic acid- or protein-based vaccines.

Role of avidity and breadth of the CD4 T cell response in progression to AIDS

The great variability in the time between infection with HIV and the onset of AIDS has been the object of intense study. In the current work, we examine a mathematical model that focuses on the role of immune response variability between patients. We study the effect of variation in both the avidity and the breadth of the immune response on within-patient disease dynamics, viral setpoint and time to AIDS. We conclude that immune response variability can explain the observed variability in disease progression to a large extent. It turns out that the avidity, more than the breadth of the immune response, determines disease progression, and that the average avidity of the five best clones is a much better correlate for disease progression than the total number of clones responding. For the design of vaccines, this would suggest that, if given the choice between stimulating a broader, but average avidity response or a narrower high-avidity response, the latter option would yield better control of virus load and consequently slow down disease progression.

High epitope expression levels increase competition between T cells

Both theoretical predictions and experimental findings suggest that T cell populations can compete with each other. There is some debate on whether T cells compete for aspecific stimuli, such as access to the surface on antigen-presenting cells (APCs) or for specific stimuli, such as their cognate epitope ligand. We have developed an individual-based computer simulation model to study T cell competition. Our model shows that the expression level of foreign epitopes per APC determines whether T cell competition is mainly for specific or aspecific stimuli. Under low epitope expression, competition is mainly for the specific epitope stimuli, and, hence, different epitope-specific T cell populations coexist readily. However, if epitope expression levels are high, aspecific competition becomes more important. Such between-specificity competition can lead to competitive exclusion between different epitope-specific T cell populations. Our model allows us to delineate the circumstances that facilitate coexistence of T cells of different epitope specificity. Understanding mechanisms of T cell coexistence has important practical implications for immune therapies that require a broad immune response.

Pathogens are masters of disguise, and frequently escape recognition by the immune response. Therefore, broad immune responses, directed at many epitopes of the pathogen, are thought to improve control of infection. There is evidence that competition between immune cells of different epitope specificity reduces the breadth of the immune response. It has been suggested that the resource that T cells compete for is access to antigen-presenting cells (APCs). However, the experimental data regarding competition for access to APCs is controversial. In this study, Scherer, Salathé, and Bonhoeffer have used an individual-based model to investigate the mechanisms of T cell competition. They find that T cells only compete for access to APCs when epitopes are expressed abundantly on APCs. In contrast, when epitope expression is limiting, competition is for the specific epitope rather than for access to APCs. The distinction between competition for epitope and for access to APCs is relevant because the model predicts qualitatively different outcomes for either case. When competition is for the specific epitope, different epitope-specific T cell responses coexist readily and hence the immune response is broad. However, when T cells compete for access to APCs, immunodominant T cell responses can outcompete subdominant ones, which leads to narrow immune responses.

Viral load distribution in SARS outbreak

Airborne transmission may have resulted in an outbreak of SARS in Hong Kong.

An unprecedented community outbreak of severe acute respiratory syndrome (SARS) occurred in the Amoy Gardens, a high-rise residential complex in Hong Kong. Droplet, air, contaminated fomites, and rodent pests have been proposed to be mechanisms for transmitting SARS in a short period. We studied nasopharyngeal viral load of SARS patients on admission and their geographic distribution. Higher nasopharyngeal viral load was found in patients living in adjacent units of the same block inhabited by the index patient, while a lower but detectable nasopharyngeal viral load was found in patients living further away from the index patient. This pattern of nasopharyngeal viral load suggested that airborne transmission played an important part in this outbreak in Hong Kong. Contaminated fomites and rodent pests may have also played a role.

Virus evolution within patients increases pathogenicity

Viruses like the human immunodeficiency virus (HIV), the hepatitis B virus (HBV), the hepatitis C virus (HCV) and many others undergo numerous rounds of inaccurate reproduction within an infected host. The resulting viral quasispecies is heterogeneous and sensitive to any selection pressure. Here we extend earlier work by showing that for a wide class of models describing the interaction between the virus population and the immune system, virus evolution has a well-defined direction toward increased pathogenicity. In particular, we study virus-induced impairment of the immune response and certain cross-reactive stimulation of specific immune responses. For eight different mathematical models, we show that virus evolution reduces the equilibrium abundance of uninfected cells and increases the rate at which uninfected cells are infected. Thus, in general, virus evolution makes things worse. An idea for combating HIV infection, however, is constructing a virus mutant that could outcompete the existing infection without being pathogenic itself.