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

Mathematical modeling indicates that regulatory inhibition of CD8+ T cell cytotoxicity can limit efficacy of IL-15 immunotherapy in cases of high pre-treatment SIV viral load

Immunotherapeutic cytokines can activate immune cells against cancers and chronic infections. N-803 is an IL-15 superagonist that expands CD8+ T cells and increases their cytotoxicity. N-803 also temporarily reduced viral load in a limited subset of non-human primates infected with simian immunodeficiency virus (SIV), a model of HIV. However, viral suppression has not been observed in all SIV cohorts and may depend on pre-treatment viral load and the corresponding effects on CD8+ T cells. Starting from an existing mechanistic mathematical model of N-803 immunotherapy of SIV, we develop a model that includes activation of SIV-specific and non-SIV-specific CD8+ T cells by antigen, inflammation, and N-803. Also included is a regulatory counter-response that inhibits CD8+ T cell proliferation and function, representing the effects of immune checkpoint molecules and immunosuppressive cells. We simultaneously calibrate the model to two separate SIV cohorts. The first cohort had low viral loads prior to treatment (≈3-4 log viral RNA copy equivalents (CEQ)/mL), and N-803 treatment transiently suppressed viral load. The second had higher pre-treatment viral loads (≈5-7 log CEQ/mL) and saw no consistent virus suppression with N-803. The mathematical model can replicate the viral and CD8+ T cell dynamics of both cohorts based on different pre-treatment viral loads and different levels of regulatory inhibition of CD8+ T cells due to those viral loads (i.e. initial conditions of model). Our predictions are validated by additional data from these and other SIV cohorts. While both cohorts had high numbers of activated SIV-specific CD8+ T cells in simulations, viral suppression was precluded in the high viral load cohort due to elevated inhibition of cytotoxicity. Thus, we mathematically demonstrate how the pre-treatment viral load can influence immunotherapeutic efficacy, highlighting the in vivo conditions and combination therapies that could maximize efficacy and improve treatment outcomes.

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.

Mathematical modeling to reveal breakthrough mechanisms in the HIV Antibody Mediated Prevention (AMP) trials

The ongoing Antibody Mediated Prevention (AMP) trials will uncover whether passive infusion of the broadly neutralizing antibody (bNAb) VRC01 can protect against HIV acquisition. Previous statistical simulations indicate these trials may be partially protective. In that case, it will be crucial to identify the mechanism of breakthrough infections. To that end, we developed a mathematical modeling framework to simulate the AMP trials and infer the breakthrough mechanisms using measurable trial outcomes. This framework combines viral dynamics with antibody pharmacokinetics and pharmacodynamics, and will be generally applicable to forthcoming bNAb prevention trials. We fit our model to human viral load data (RV217). Then, we incorporated VRC01 neutralization using serum pharmacokinetics (HVTN 104) and in vitro pharmacodynamics (LANL CATNAP database). We systematically explored trial outcomes by reducing in vivo potency and varying the distribution of sensitivity to VRC01 in circulating strains. We found trial outcomes could be used in a clinical trial regression model (CTRM) to reveal whether partially protective trials were caused by large fractions of VRC01-resistant (IC50>50 μg/mL) circulating strains or rather a global reduction in VRC01 potency against all strains. The former mechanism suggests the need to enhance neutralizing antibody breadth; the latter suggests the need to enhance VRC01 delivery and/or in vivo binding. We will apply the clinical trial regression model to data from the completed trials to help optimize future approaches for passive delivery of anti-HIV neutralizing antibodies.

Infusions of broadly neutralizing antibodies are currently being tested as a novel HIV prevention modality. To help interpret the results of these antibody mediated prevention (AMP) studies we developed a mathematical modeling framework. The approach combines antibody potency and drug levels with models of HIV viral dynamics, which will be generally applicable to future studies. Through simulating these clinical trials, we found trial outcomes can be used in combination to infer whether breakthrough infections are caused by large fractions of antibody-resistant circulating strains or some reduction in potency against all strains. This distinction helps to focus future trials on enhancing neutralizing antibody breadth or antibody delivery and/or in vivo binding.

The dynamics of simian immunodeficiency virus after depletion of CD8+ cells

Human immunodeficiency virus infection is still one of the most important causes of morbidity and mortality in the world, with a disproportionate human and economic burden especially in poorer countries. Despite many years of intense research, an aspect that still is not well understood is what (immune) mechanisms control the viral load during the prolonged asymptomatic stage of infection. Because CD8+ T cells have been implicated in this control by multiple lines of evidence, there has been a focus on understanding the potential mechanisms of action of this immune effector population. One type of experiment used to this end has been depleting these cells with monoclonal antibodies in the simian immunodeficiency virus-macaque model and then studying the effect of that depletion on the viral dynamics. Here we review what these experiments have told us. We emphasize modeling studies to interpret the changes in viral load observed in these experiments, including discussion of alternative models, assumptions and interpretations, as well as potential future experiments.

Towards multiscale modeling of the CD8+ T cell response to viral infections

The CD8⁺ T cell response is critical to the control of viral infections. Yet, defining the CD8⁺ T cell response to viral infections quantitatively has been a challenge. Following antigen recognition, which triggers an intracellular signaling cascade, CD8⁺ T cells can differentiate into effector cells, which proliferate rapidly and destroy infected cells. When the infection is cleared, they leave behind memory cells for quick recall following a second challenge. If the infection persists, the cells may become exhausted, retaining minimal control of the infection while preventing severe immunopathology. These activation, proliferation and differentiation processes as well as the mounting of the effector response are intrinsically multiscale and collective phenomena. Remarkable experimental advances in the recent years, especially at the single cell level, have enabled a quantitative characterization of several underlying processes. Simultaneously, sophisticated mathematical models have begun to be constructed that describe these multiscale phenomena, bringing us closer to a comprehensive description of the CD8⁺ T cell response to viral infections. Here, we review the advances made and summarize the challenges and opportunities ahead. This article is categorized under: Analytical and Computational Methods > Computational Methods Biological Mechanisms > Cell Fates Biological Mechanisms > Cell Signaling Models of Systems Properties and Processes > Mechanistic Models.

CD8+ lymphocyte control of SIV infection during antiretroviral therapy

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

CD8⁺ lymphocytes play an important role in suppressing in vivo viral replication in HIV infection. However, both the extent to which and the mechanisms by which CD8⁺ lymphocytes contribute to viral control are not completely understood. By mathematically modeling data from a recent CD8 depletion experiment done in antiretroviral (ART) treated animals, our results suggest that the overall CD8⁺ lymphocyte cytolytic killing rate is dynamically changing depending on the levels of antigen-induced effector cell activation and exhaustion, i.e. before ART or without ART the overall CD8 cytolytic killing rate is small due to exhaustion. However, after the start of ART, the overall CD8 cytolytic killing rate increases due to an expansion of SIV-specific CD8 effector cells. By incorporating effector cells and their exhaustion, our model explains the effects on viral load of CD8 depletion done before ART or during ART, reveals a detailed dynamic role of CD8⁺ lymphocytes in controlling viral infection, and provides a unified explanation for CD8 depletion experimental data.

Killing of Latently HIV-Infected CD4 T Cells by Autologous CD8 T Cells Is Modulated by Nef

The role of HIV-specific CD8 T cell activity in the course of HIV infection and the way it affects the virus that resides in the latent reservoir resting memory cells is debated. The PBMC of HIV-infected patients contain HIV-specific CD8 T cells and their potential targets, CD4 T cells latently infected by HIV. CD4 T cells and CD8 T cells procured from PBMC of HIV-infected patients were co-incubated and analyzed: Formation of CD8 T cells and HIV-infected CD4 T cell conjugates and apoptosis of these CD4 T cells were observed by fluorescence microscopy with in situ PCR of HIV LTR DNA. Furthermore, conjugation of CD8 T cells with CD4 T cells and apoptosis of CD4 T cells was observed and quantified by imaging flow cytometry using anti-human activated caspase 3 antibody and TUNEL assay. The conjugation activity and apoptosis were found to be much higher in patients with acute HIV infection or AIDS compared to patients in chronic infection on antiretroviral therapy (ART) or not. Patients on ART had low grade conjugation and apoptosis of isolated CD69, CD25, and HLA-DR-negative CD4 T cells (latent reservoir cells) by CD8 T cells. Using in situ PCR The latent reservoir CD4 T cells were shown to contain most of the HIV DNA. We demonstrate in HIV-infected patients, that CD8 T cells conjugate with and kill HIV-infected CD4 T cells, including HIV-infected resting memory CD4 T cells, throughout the course of HIV infection. We propose that in HIV-infected patients CD4 T cell annihilation is caused in part by ongoing activity of HIV-specific CD8 T cells. HIV Nef protein interacts with ASK 1 and inhibits its pro-apoptotic death signaling by Fas/FasL, thus protecting HIV-infected cells from CD8 T cells killing. A peptide that interrupts Nef-ASK1 interaction that had been delivered into CD4 T cells procured from patients on ART resulted in the increase of their apoptosis inflicted by autologous CD8 T cells. We suggest that elimination of the HIV-infected latent reservoir CD4 T cells can be achieved by Nef inhibition.

Mechanisms and Dynamics of T Cell-Mediated Cytotoxicity In Vivo

Cytotoxic T lymphocytes (CTLs) are critical in the elimination of infected or malignant cells and are emerging as a major therapeutic target. How CTLs recognize and kill harmful cells has been characterized in vitro but little is known about these processes in the living organism. Here we review recent insights into CTL-mediated killing with an emphasis on in vivo CTL biology. Specifically, we focus on the possible rate-limiting steps determining the efficiency of CTL-mediated killing. We also highlight the need for cell-based datasets that permit the quantification of CTL dynamics, including CTL location, migration, and killing rates. A better understanding of these factors is required to predict protective CD8 T cell immunity in vivo and to design optimized vaccination protocols.

Mathematical Models for Immunology: Current State of the Art and Future Research Directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.

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.

The gut microbiome in human immunodeficiency virus infection

HIV/AIDS causes severe dysfunction of the immune system through CD4+ T cell depletion, leading to dysregulation of both the adaptive and innate immune arms. A primary target for viral infection is the gastrointestinal tract, which is a reservoir of CD4+ T cells. In addition to being a major immune hub, the human gastrointestinal tract harbors trillions of commensal microorganisms, the microbiota, which have recently been shown to play critical roles in health. Alterations in the composition and function of microbiota have been implicated in a variety of 'multi-factorial' disorders, including infectious, autoimmune, metabolic, and neoplastic disorders. It is widely accepted that, in addition to its direct role in altering the gastrointestinal CD4+ T cell compartment, HIV infection is characterized by gut microbiota compositional and functional changes. Herein, we review such alterations and discuss their potential local and systemic effects on the HIV-positive host, as well as potential roles of novel microbiota-targeting treatments in modulating HIV progression and associated adverse systemic manifestations.

T cell and reticular network co-dependence in HIV infection

Fibroblastic reticular cells (FRC) are arranged on a network in the T cell zone of lymph nodes, forming a scaffold for T cell migration, and providing survival factors, especially interleukin-7 (IL-7). Conversely, CD4(+) T cells are the major producers of lymphotoxin-β (LT-β), necessary for the construction and maintenance of the FRC network. This interdependence creates the possibility of a vicious cycle, perpetuating loss of both FRC and T cells. Furthermore, evidence that HIV infection is responsible for collagenation of the network suggests that long term loss of network function might be responsible for the attenuated recovery in T cell count seen in HIV patients undergoing antiretroviral therapy (ART). We present computational and mathematical models of this interaction mechanism and subsequent naive CD4(+) T-cell depletion in which (1) collagen deposition impedes access of naive T cells to IL-7 on the FRC and loss of IL-7 production by loss of FRC network itself, leading to the depletion of naive T cells through increased apoptosis; and (2) depletion of naive T cells as the source of LT-β on which the FRC depend for survival leads to loss of the network, thereby amplifying and perpetuating the cycle of depletion of both naive T cells and stromal cells. Our computational model explicitly includes an FRC network and its cytokine exchange with a heterogeneous T-cell population. We also derive lumped models, in terms of partial differential equations and reduced to ordinary differential equations, that provide additional insight into the mechanisms at work. The central conclusions are that (1) damage to the reticular network, caused by HIV infection is a plausible mechanism for attenuated recovery post-ART; (2) within this, the production of T cell survival factors by FRCs may be the key rate-limiting step; and (3) the methods of model reduction and analysis presented are useful for both immunological studies and other contexts in which agent-based models are severely limited by computational cost.