Dynamics of CD8+ T cell responses during acute and chronic lymphocytic choriomeningitis virus infection

Tim-3 Is Not Required for Establishment of CD8+ T Cell Memory to Lymphocytic Choriomeningitis Virus

Tim-3 is a transmembrane protein that is best known for being highly expressed on terminally exhausted CD8+ T cells associated with chronic infection and tumors, although its expression is not limited to those settings. Tim-3 is also expressed by CD8+ T cells during acute infection and by multiple other immune cell types, including CD4+ Th1 and regulatory T cells, dendritic cells, and mast cells. In this study, we investigated the role of Tim-3 signaling on CD8+ T cell memory using a Tim-3 conditional knockout mouse model and mice lacking the signaling portion of the Tim-3 cytoplasmic domain. Together, our results indicate that Tim-3 has at most a modest effect on the formation and function of CD8+ memory T cells.

Cell volume controlled by LRRC8A-formed volume-regulated anion channels fine-tunes T cell activation and function

Biosynthesis drives the cell volume increase during T cell activation. However, the contribution of cell volume regulation in TCR signaling during T lymphoblast formation and its underlying mechanisms remain unclear. Here we show that cell volume regulation is required for optimal T cell activation. Inhibition of VRACs (volume-regulated anion channels) and deletion of leucine-rich repeat-containing protein 8A (LRRC8A) channel components impair T cell activation and function, particularly under weak TCR stimulation. Additionally, LRRC8A has distinct influences on mRNA transcriptional profiles, indicating the prominent effects of cell volume regulation for T cell functions. Moreover, cell volume regulation via LRRC8A controls T cell-mediated antiviral immunity and shapes the TCR repertoire in the thymus. Mechanistically, LRRC8A governs stringent cell volume increase via regulated volume decrease (RVD) during T cell blast formation to keep the TCR signaling molecules at an adequate density. Together, our results show a further layer of T cell activation regulation that LRRC8A functions as a cell volume controlling "valve" to facilitate T cell activation.

Large clones of pre-existing T cells drive early immunity against SARS-COV-2 and LCMV infection

T cell responses precede antibody and may provide early control of infection. We analyzed the clonal basis of this rapid response following SARS-COV-2 infection. We applied T cell receptor (TCR) sequencing to define the trajectories of individual T cell clones immediately. In SARS-COV-2 PCR+ individuals, a wave of TCRs strongly but transiently expand, frequently peaking the same week as the first positive PCR test. These expanding TCR CDR3s were enriched for sequences functionally annotated as SARS-COV-2 specific. Epitopes recognized by the expanding TCRs were highly conserved between SARS-COV-2 strains but not with circulating human coronaviruses. Many expanding CDR3s were present at high frequency in pre-pandemic repertoires. Early response TCRs specific for lymphocytic choriomeningitis virus epitopes were also found at high frequency in the preinfection naive repertoire. High-frequency naive precursors may allow the T cell response to respond rapidly during the crucial early phases of acute viral infection.

Quantification of lymphocytic choriomeningitis virus specific T cells and LCMV viral titers

Lymphocytic choriomeningitis virus (LCMV) is a frequently used animal model to study immune responses against acute and chronic viral infections. LCMV is a non-cytopathic virus, but destruction of infected cells by cytotoxic T lymphocytes (CTLs) can lead to severe damage of tissues. Virus-specific T cell responses have to be balanced. A low virus load leads to a strong T cell response and subsequently to viral control. In contrast, a high viral titer is associated with T cell exhaustion and chronic viral infections. During an intermediate LCMV viral load CD8⁺ T cells can cause immunopathology, which can have detrimental outcomes. The LCMV infection model offers the opportunity to study virus-specific CD4⁺ and CD8⁺ T cell responses during chronic and acute infections by quantifying LCMV-specific T cells by tetramer staining and measuring cytokine production and viral titers in different organs.

Turnover of Murine Cytomegalovirus-Expanded CD8+ T Cells Is Similar to That of Memory Phenotype T Cells and Independent of the Magnitude of the Response

The potential of memory T cells to provide protection against reinfection is beyond question. Yet, it remains debated whether long-term T cell memory is due to long-lived memory cells. There is ample evidence that blood-derived memory phenotype CD8⁺ T cells maintain themselves through cell division, rather than through longevity of individual cells. It has recently been proposed, however, that there may be heterogeneity in the lifespans of memory T cells, depending on factors such as exposure to cognate Ag. CMV infection induces not only conventional, contracting T cell responses, but also inflationary CD8⁺ T cell responses, which are maintained at unusually high numbers, and are even thought to continue to expand over time. It has been proposed that such inflating T cell responses result from the accumulation of relatively long-lived CMV-specific memory CD8⁺ T cells. Using in vivo deuterium labeling and mathematical modeling, we found that the average production rates and expected lifespans of mouse CMV-specific CD8⁺ T cells are very similar to those of bulk memory-phenotype CD8⁺ T cells. Even CMV-specific inflationary CD8⁺ T cell responses that differ 3-fold in size were found to turn over at similar rates.

The role of a programmatic immune response on the evolution of pathogen traits

In modelling pathogen evolution during epidemics, it is important to understand the interactions between within-host infection dynamics and between-host pathogen transmission. Multiscale models often assume an immune response that is highly responsive to pathogen dynamics. Empirical evidence, however, suggests that the immune response in acute infections is triggered and programmatic. This leads to somewhat more predictable infection trajectories where transition times and, consequently, the infectious window are non-exponentially distributed. Here, we develop a within-host model where the immune response is triggered by pathogen growth but otherwise develops independently, and use this to obtain analytic expressions for the infectious period and peak pathogen load. This allows us to model the basic reproductive number in terms of explicit functional relationships among within-host traits including the growth rate of the pathogen. We find that the dependence of pathogen load and the infectious window on within-host parameters constrains the evolution of the pathogen growth rate. At low growth rate, selection favours a higher pathogen load and therefore increasing pathogen growth rate. At high growth rates, selection for a longer infectious window trades off against selection against the effects of virulence. At intermediate growth rates the basic reproductive number is relatively insensitive to changes in the growth rate. The resulting "flat" region of the pathogen fitness landscape is due to the stability of the programmatic immune response in clearing the infection.

The interplay of immunology and cachexia in infection and cancer

Diverse inflammatory diseases, infections and malignancies are associated with wasting syndromes. In many of these conditions, the standards for diagnosis and treatment are lacking due to our limited understanding of the causative molecular mechanisms. Here, we discuss the complex immunological context of cachexia, a systemic catabolic syndrome that depletes both fat and muscle mass with profound consequences for patient prognosis. We highlight the main cytokine and immune cell-driven pathways that have been linked to weight loss and tissue wasting in the context of cancer-associated and infection-associated cachexia. Moreover, we discuss the potential immunometabolic consequences of cachexia on the basis of newly identified pathways and explore the multilayered area of immunometabolic crosstalk both upstream and downstream of tissue catabolism. Collectively, this Review highlights the intricate relationship of the immune system with cachexia in the context of malignant and infectious diseases.

A participant-derived xenograft model of HIV enables long-term evaluation of autologous immunotherapies

HIV-specific CD8⁺ T cells partially control viral replication and delay disease progression, but they rarely provide lasting protection, largely due to immune escape. Here, we show that engrafting mice with memory CD4⁺ T cells from HIV⁺ donors uniquely allows for the in vivo evaluation of autologous T cell responses while avoiding graft-versus-host disease and the need for human fetal tissues that limit other models. Treating HIV-infected mice with clinically relevant HIV-specific T cell products resulted in substantial reductions in viremia. In vivo activity was significantly enhanced when T cells were engineered with surface-conjugated nanogels carrying an IL-15 superagonist, but it was ultimately limited by the pervasive selection of a diverse array of escape mutations, recapitulating patterns seen in humans. By applying mathematical modeling, we show that the kinetics of the CD8⁺ T cell response have a profound impact on the emergence and persistence of escape mutations. This “participant-derived xenograft” model of HIV provides a powerful tool for studying HIV-specific immunological responses and facilitating the development of effective cell-based therapies.

Modeling and characterization of inter-individual variability in CD8 T cell responses in mice

To develop vaccines it is mandatory yet challenging to account for inter-individual variability during immune responses. Even in laboratory mice, T cell responses of single individuals exhibit a high heterogeneity that may come from genetic backgrounds, intra-specific processes (e.g. antigen-processing and presentation) and immunization protocols.

To account for inter-individual variability in CD8 T cell responses in mice, we propose a dynamical model coupled to a statistical, nonlinear mixed effects model. Average and individual dynamics during a CD8 T cell response are characterized in different immunization contexts (vaccinia virus and tumor). On one hand, we identify biological processes that generate inter-individual variability (activation rate of naive cells, the mortality rate of effector cells, and dynamics of the immunogen). On the other hand, introducing categorical covariates to analyze two different immunization regimens, we highlight the steps of the response impacted by immunogens (priming, differentiation of naive cells, expansion of effector cells and generation of memory cells). The robustness of the model is assessed by confrontation to new experimental data.

Our approach allows to investigate immune responses in various immunization contexts, when measurements are scarce or missing, and contributes to a better understanding of inter-individual variability in CD8 T cell immune responses.

Cellular and Molecular Mechanisms of CD8+ T Cell Differentiation, Dysfunction and Exhaustion

T cells follow a triphasic distinct pathway of activation, proliferation and differentiation before becoming functionally and phenotypically “exhausted” in settings of chronic infection, autoimmunity and in cancer. Exhausted T cells progressively lose canonical effector functions, exhibit altered transcriptional networks and epigenetic signatures and gain constitutive expression of a broad coinhibitory receptor suite. This review outlines recent advances in our understanding of exhausted T cell biology and examines cellular and molecular mechanisms by which a state of dysfunction or exhaustion is established, and mechanisms by which exhausted T cells may still contribute to pathogen or tumour control. Further, this review describes our understanding of exhausted T cell heterogeneity and outlines the mechanisms by which checkpoint blockade differentially engages exhausted T cell subsets to overcome exhaustion and recover T cell function.

Cyclophilin D Regulates Antiviral CD8+ T Cell Survival in a Cell-Extrinsic Manner

CD8+ T cell-mediated immunity is critical for host defense against viruses and requires mitochondria-mediated type I IFN (IFN-I) signaling for optimal protection. Cyclophilin D (CypD) is a mitochondrial matrix protein that modulates the mitochondrial permeability transition pore, but its role in IFN-I signaling and CD8+ T cell responses to viral infection has not been previously explored. In this study, we demonstrate that CypD plays a critical extrinsic role in the survival of Ag-specific CD8+ T cell following acute viral infection with lymphocytic choriomeningitis virus in mice. CypD deficiency resulted in reduced IFN-I and increased CD8+ T cell death, resulting in a reduced antiviral CD8+ T cell response. In addition, CypD deficiency was associated with an increase in pathogen burden at an early time-point following infection. Furthermore, our data demonstrate that transfer of wild-type macrophages (expressing CypD) to CypD-deficient mice can partially restore CD8+ T cell responses. These results establish that CypD plays an extrinsic role in regulating optimal effector CD8+ T cell responses to viral infection. Furthermore, this suggests that, under certain circumstances, inhibition of CypD function may have a detrimental impact on the host's ability to respond to viral infection.

The Goldilocks Window of Personalized Chemotherapy: Getting the Immune Response Just Right

The immune system is a robust and often untapped accomplice of many standard cancer therapies. A majority of tumors exist in a state of immune tolerance where the patient's immune system has become insensitive to the cancer cells. Because of its lymphodepleting effects, chemotherapy has the potential to break this tolerance. To investigate this, we created a mathematical modeling framework of tumor-immune dynamics. Our results suggest that optimal chemotherapy scheduling must balance two opposing objectives: maximizing tumor reduction while preserving patient immune function. Successful treatment requires therapy to operate in a "Goldilocks Window" where patient immune health is not overly compromised. By keeping therapy "just right," we show that the synergistic effects of immune activation and chemotherapy can maximize tumor reduction and control. SIGNIFICANCE: To maximize the synergy between chemotherapy and antitumor immune response, lymphodepleting therapy must be balanced in a "Goldilocks Window" of optimal dosing.Graphical Abstract: http://cancerres.aacrjournals.org/content/canres/79/20/5302/F1.large.jpg.

Endogenous n-3 Polyunsaturated Fatty Acids Are Beneficial to Dampen CD8+ T Cell-Mediated Inflammatory Response upon the Viral Infection in Mice

Omega-3 (n-3) polyunsaturated fatty acids (PUFAs) have been known to exert anti-inflammatory effects on various disease states. However, its effect on CD8⁺ T cell-mediated immunopathology upon viral infection has not been well elucidated yet. In this study, we investigated the possible implication of n-3 PUFAs in CD8⁺ T cell responses against an acute viral infection. Infection of FAT-1 transgenic mice that are capable of synthesizing n-3 PUFAs from n-6 PUFAs with lymphocytic choriomeningitis virus (LCMV) resulted in significant reduction of anti-viral CD8⁺ T cell responses. Interestingly, expansion of adoptively transferred wild-type (WT) LCMV-specific T cell receptor (TCR) transgenic CD8⁺ (P14) T cells into FAT-1 mice was significantly decreased. Also, activation of anti-viral CD4⁺ helper T cells was reduced in FAT-1 mice. Importantly, P14 cells carrying the fat-1 gene that were adoptively transferred into WT mice exhibited a substantially decreased ability to proliferate and produce cytokines against LCMV infection. Together, n-3 PUFAs attenuated anti-viral CD8⁺ T cell responses against an acute viral infection and thus could be used to alleviate immunopathology mediated by the viral infection.

Investigating the Dynamics of MCMV-Specific CD8+ T Cell Responses in Individual Hosts

Infection by Cytomegalovirus (CMV) is characterized by the massive expansion and continued maintenance of CMV-specific CD8⁺ T cells for certain CMV-derived peptides. This phenomenon called “memory inflation" has made CMV a primary target for the generation of T cell based vaccine vectors against various diseases. However, many aspects concerning the generation and maintenance of the inflationary CD8⁺ T cell response still remain to be resolved. In this study, we combined experimental data and mathematical models to analyze the dynamics of circulatory inflationary CD8⁺ T cells within individual mice infected by MCMV. Obtaining frequent measurements on the number and frequency of CMV-specific CD8⁺ T cells up to 70 days post infection, we find that mathematical models assuming differing viral stimuli during acute infection and the inflationary phase provide a better description for the observed dynamics than models relying on similar viral stimuli during both phases. In addition, our analysis allowed a detailed quantification of the different phases of memory inflation within individual mice (1^st-expansion - contraction - 2^nd expansion/maintenance) indicating remarkable consistency of the timing of these phases across mice, but considerable variation in the size of the individual responses between mice. Our analysis provides a first step toward generating a mechanistic framework for analyzing the generation and maintenance of inflationary CD8⁺ T cells while accounting for individual heterogeneity. Extending these analyses by incorporating measurements from additional compartments and more prolonged sampling will help to obtain a systematic and quantitative understanding of the factors regulating the process of memory inflation.

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.

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.

Fas Ligand-mediated cytotoxicity of CD4+ T cells during chronic retrovirus infection

CD4+ helper T cells and cytotoxic CD8+ T cells are key players for adaptive immune responses against acute infections with retroviruses. Similar to textbook knowledge the most important function of CD4+ T cells during an acute retrovirus infection seems to be their helper function for other immune cells. Whereas there was no direct anti-viral activity of CD4+ T cells during acute Friend Virus (FV) infection, they were absolutely required for the control of chronic infection. During chronic FV infection a population of activated FV-specific CD4+ T cells did not express cytotoxic molecules, but Fas Ligand that can induce Fas-induced apoptosis in target cells. Using an MHC II-restricted in vivo CTL assay we demonstrated that FV-specific CD4+ T cells indeed mediated cytotoxic effects against FV epitope peptide loaded targets. CD4 + CTL killing was also detected in FV-infected granzyme B knockout mice confirming that the exocytosis pathway was not involved. However, killing could be blocked by antibodies against FasL, which identified the Fas/FasL pathway as critical cytotoxic mechanism during chronic FV infection. Interestingly, targeting the co-stimulatory receptor CD137 with an agonistic antibody enhanced CD4+ T cell cytotoxicity. This immunotherapy may be an interesting new approach for the treatment of chronic viral infections.

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.

About Training and Memory: NK-Cell Adaptation to Viral Infections

Viral infections continuously challenge and shape our immune system. Due to their fine antigen recognition ability, adaptive lymphocytes protect against pathogen reencounter by generating specific immunological memory. Innate cells such as macrophages also adapt to pathogen challenge and mount resistance to reinfection, a phenomenon termed trained immunity. As part of the innate immunity, natural killer (NK) cells can display rapid effector functions and play a crucial role in the control of viral infections, especially by the β-herpesvirus cytomegalovirus (CMV). CMV activates the NK-cell pool by inducing proinflammatory signals, which prime NK cells, paralleling macrophage training. In addition, CMV dramatically shapes the NK-cell repertoire due to its ability to trigger specific NK cell-activating receptors, and enables the expansion and persistence of a specific NK-cell subset displaying adaptive and memory features. In this chapter, we will discuss how different signals during CMV infection contribute to NK-cell training and acquisition of classical memory properties and how these events can impact on reinfection and cross-resistance.

Modelling and Simulation of the Dynamics of the Antigen-Specific T Cell Response Using Variable Structure Control Theory

Experimental and mathematical studies in immunology have revealed that the dynamics of the programmed T cell response to vigorous infection can be conveniently modelled using a sigmoidal or a discontinuous immune response function. This paper hypothesizes strong synergies between this existing work and the dynamical behaviour of engineering systems with a variable structure control (VSC) law. These findings motivate the interpretation of the immune system as a variable structure control system. It is shown that dynamical properties as well as conditions to analytically assess the transition from health to disease can be developed for the specific T cell response from the theory of variable structure control. In particular, it is shown that the robustness properties of the specific T cell response as observed in experiments can be explained analytically using a VSC perspective. Further, the predictive capacity of the VSC framework to determine the T cell help required to overcome chronic Lymphocytic Choriomeningitis Virus (LCMV) infection is demonstrated. The findings demonstrate that studying the immune system using variable structure control theory provides a new framework for evaluating immunological dynamics and experimental observations. A modelling and simulation tool results with predictive capacity to determine how to modify the immune response to achieve healthy outcomes which may have application in drug development and vaccine design.

Modeling the dynamics of neonatal CD8+ T-cell responses

Neonates are particularly susceptible to a number of infections, and the neonatal CD8+ T cell response demonstrates differences in both the phenotype and magnitude of responses to infection compared with adults. However, the underlying basis for these differences is unclear. We have used a mathematical modeling approach to analyze the dynamics of neonatal and adult CD8+ T cell responses following in vitro stimulation and in vivo infection, which allows us to dissect key cell-intrinsic differences in expansion, differentiation and memory formation. We found that neonatal cells started dividing 8 hrs earlier and proliferated at a faster rate (0.077 day⁻¹ vs 0.105 day⁻¹) than adult cells in vitro. In addition, neonatal cells also differentiated more rapidly, as measured by the loss in CD62L and Ly6C expression. We extended our mathematical modeling to analysis of neonatal and adult CD8+ T cells responding in vivo and demonstrated that neonatal cells divide more slowly than adult cells after day 4 post-infection. However, neonatal cells differentiate more rapidly, up-regulating more KLRG-1 per division than adult cells (20% vs. 5%). The dynamics of memory formation were also found to be different, with neonatal effector cells showing increased death (1.0 day⁻¹ vs. 2.45 day⁻¹). Comparison of the division of human cord blood and adult naïve cells stimulated in vitro showed more division in cord blood derived cells, consistent with the observations in mice. This work highlights differences of the cell-intrinsic division and differentiation program in neonatal CD8+ T cells.

Stem-cell dynamics and lineage topology from in vivo fate mapping in the hematopoietic system

In recent years, sophisticated fate-mapping tools have been developed to study the behavior of stem cells in the intact organism. These experimental approaches are beginning to yield a quantitative picture of how cell numbers are regulated during steady state and in response to challenges. Focusing on hematopoiesis and immune responses, we discuss how novel mathematical approaches driven by these fate-mapping data have provided insights into the dynamics and topology of cellular differentiation pathways in vivo. The combination of experiment and theory has allowed to quantify the degree of self-renewal in stem and progenitor cells, shown how native hematopoiesis differs fundamentally from post-transplantation hematopoiesis, and uncovered that the diversification of T lymphocytes during immune responses resembles tissue renewal driven by stem cells.

Understanding Experimental LCMV Infection of Mice: The Role of Mathematical Models

Virus infections represent complex biological systems governed by multiple-level regulatory processes of virus replication and host immune responses. Understanding of the infection means an ability to predict the systems behaviour under various conditions. Such predictions can only rely upon quantitative mathematical models. The model formulations should be tightly linked to a fundamental step called “coordinatization” (Hermann Weyl), that is, the definition of observables, parameters, and structures that enable the link with a biological phenotype. In this review, we analyse the mathematical modelling approaches to LCMV infection in mice that resulted in quantification of some fundamental parameters of the CTL-mediated virus control including the rates of T cell turnover, infected target cell elimination, and precursor frequencies. We show how the modelling approaches can be implemented to address diverse aspects of immune system functioning under normal conditions and in response to LCMV and, importantly, make quantitative predictions of the outcomes of immune system perturbations. This may highlight the notion that data-driven applications of meaningful mathematical models in infection biology remain a challenge.

Interaction between unrelated viruses during in vivo co-infection to limit pathology and immunity

Great progress has been made in understanding immunity to viral infection. However, infection can occur in the context of co-infection by unrelated pathogens that modulate immune responses and/or disease. We have studied immunity and disease during co-infection with two unrelated viruses: Ectromelia virus (ECTV) and Lymphocytic Choriomeningitis virus (LCMV). ECTV infection can be a lethal in mice due in part to the blockade of Type I Interferons (IFN-I). We show that ECTV/LCMV co-infection results in decreased ECTV viral load and amelioration of ECTV-induced disease, likely due to IFN-I induction by LCMV, as rescue is not observed in IFN-I receptor deficient mice. However, immune responses to LCMV in ECTV co-infected mice were also lower compared to mice infected with LCMV alone and potentially biased toward effector-memory cell generation. Thus, we provide evidence for bi-directional effects of viral co-infection that modulate disease and immunity.

Evaluating contribution of the cellular and humoral immune responses to the control of shedding of Mycobacterium avium spp. paratuberculosis in cattle

Mycobacterium avium spp. paratuberculosis (MAP) causes a persistent infection and chronic inflammation of the gut in ruminants leading to bacterial shedding in feces in many infected animals. Although there are often strong MAP-specific immune responses in infected animals, immunological correlates of protection against progression to disease remain poorly defined. Analysis of cross-sectional data has suggested that the cellular immune response observed early in infection is effective at containing bacterial growth and shedding, in contrast to humoral immune responses. In this study, 20 MAP-infected calves were followed for nearly 5 years during which MAP shedding, antigen-specific cellular (LPT) and humoral (ELISA) immune responses were measured. We found that MAP-specific cellular immune response developed slowly, with the peak of the immune response occurring one year post infection. MAP-specific humoral immunity expanded only in a subset of animals. Only in a subset of animals there was a statistically significant negative correlation between the amount of MAP shedding and magnitude of the MAP-specific cellular immune response. Direct fitting of simple mechanistic mathematical models to the shedding data suggested that MAP-specific immune responses contributed significantly to the kinetics of MAP shedding in most animals. However, whereas the MAP-specific cellular immune response was predicted to suppress shedding in some animals, in other animals it was predicted to increase shedding. In contrast, MAP-specific humoral response was always predicted to increase shedding. Our results illustrate the use of mathematical methods to understand relationships between mycobacteria and immunity in vivo but also highlight problems with establishing cause-effect links from observational data.

Predicting pathogen-specific CD8 T cell immune responses from a modeling approach

The primary CD8 T cell immune response constitutes a major mechanism to fight an infection by intra-cellular pathogens. We aim at assessing whether pathogen-specific dynamical parameters of the CD8 T cell response can be identified, based on measurements of CD8 T cell counts, using a modeling approach. We generated experimental data consisting in CD8 T cell counts kinetics during the response to three different live intra-cellular pathogens: two viruses (influenza, vaccinia) injected intranasally, and one bacteria (Listeria monocytogenes) injected intravenously. All pathogens harbor the same antigen (NP68), but differ in their interaction with the host. In parallel, we developed a mathematical model describing the evolution of CD8 T cell counts and pathogen amount during an immune response. This model is characterized by 9 parameters and includes relevant feedback controls. The model outputs were compared with the three data series and an exhaustive estimation of the parameter values was performed. By focusing on the ability of the model to fit experimental data and to produce a CD8 T cell population mainly composed of memory cells at the end of the response, critical parameters were identified. We show that a small number of parameters (2-4) define the main features of the CD8 T cell immune response and are characteristic of a given pathogen. Among these parameters, two are related to the effector CD8 T cell mediated control of cell and pathogen death. The parameter associated with memory cell death is shown to play no relevant role during the main phases of the CD8 T cell response, yet it becomes essential when looking at the predictions of the model several months after the infection.

Mathematical modeling provides kinetic details of the human immune response to vaccination

With major advances in experimental techniques to track antigen-specific immune responses many basic questions on the kinetics of virus-specific immunity in humans remain unanswered. To gain insights into kinetics of T and B cell responses in human volunteers we combined mathematical models and experimental data from recent studies employing vaccines against yellow fever and smallpox. Yellow fever virus-specific CD8 T cell population expanded slowly with the average doubling time of 2 days peaking 2.5 weeks post immunization. Interestingly, we found that the peak of the yellow fever-specific CD8 T cell response was determined by the rate of T cell proliferation and not by the precursor frequency of antigen-specific cells as has been suggested in several studies in mice. We also found that while the frequency of virus-specific T cells increased slowly, the slow increase could still accurately explain clearance of yellow fever virus in the blood. Our additional mathematical model described well the kinetics of virus-specific antibody-secreting cell and antibody response to vaccinia virus in vaccinated individuals suggesting that most of antibodies in 3 months post immunization were derived from the population of circulating antibody-secreting cells. Taken together, our analysis provided novel insights into mechanisms by which live vaccines induce immunity to viral infections and highlighted challenges of applying methods of mathematical modeling to the current, state-of-the-art yet limited immunological data.

Plasmodium suppresses expansion of T cell responses to heterologous infections

Plasmodium remains a major pathogen causing malaria and impairing defense against other infections. Defining how Plasmodium increases susceptibility to heterologous pathogens may lead to interventions that mitigate the severity of coinfections. Previous studies proposed that reduced T cell responses during coinfections are due to diminished recruitment of naive T cells through infection-induced decreases in chemokine CCL21. We found that, although Listeria infections reduced expression of CCL21 in murine spleens, lymphocytic choriomeningitis virus (LCMV)-specific T cell responses were not impaired during Listeria + LCMV coinfection, arguing against a major role for this chemokine in coinfection-induced T cell suppression. In our experiments, Plasmodium yoelii infection led to a reduced CD8(+) T cell response to a subsequent Listeria infection. We propose an alternative mechanism whereby P. yoelii suppresses Listeria-specific T cell responses. We found that Listeria-specific T cells expanded more slowly and resulted in lower numbers in response to coinfection with P. yoelii. Mathematical modeling and experimentation revealed greater apoptosis of Listeria-specific effector T cells as the main mechanism, because P. yoelii infections did not suppress the recruitment or proliferation rates of Listeria-specific T cells. Our results suggest that P. yoelii infections suppress immunity to Listeria by causing increased apoptosis in Listeria-specific T cells, resulting in a slower expansion rate of T cell responses.

Functional switching and stability of regulatory T cells

It is widely accepted that the primary immune system contains a subpopulation of cells, known as regulatory T cells whose function is to regulate the immune response. There is conflicting biological evidence regarding the ability of regulatory cells to lose their regulatory capabilities and turn into immune promoting cells. In this paper, we develop mathematical models to investigate the effects of regulatory T cell switching on the immune response. Depending on environmental conditions, regulatory T cells may transition, becoming effector T cells that are immunostimulatory rather than immunoregulatory. We consider this mechanism both in the context of a simple, ordinary differential equation (ODE) model and in the context of a more biologically detailed, delay differential equation (DDE) model of the primary immune response. It is shown that models that incorporate such a mechanism express the usual characteristics of an immune response (expansion, contraction, and memory phases), while being more robust with respect to T cell precursor frequencies. We characterize the affects of regulatory T cell switching on the peak magnitude of the immune response and identify a biologically testable range for the switching parameter. We conclude that regulatory T cell switching may play a key role in controlling immune contraction.

Quantifying T lymphocyte turnover

Peripheral T cell populations are maintained by production of naive T cells in the thymus, clonal expansion of activated cells, cellular self-renewal (or homeostatic proliferation), and density dependent cell life spans. A variety of experimental techniques have been employed to quantify the relative contributions of these processes. In modern studies lymphocytes are typically labeled with 5-bromo-2'-deoxyuridine (BrdU), deuterium, or the fluorescent dye carboxy-fluorescein diacetate succinimidyl ester (CFSE), their division history has been studied by monitoring telomere shortening and the dilution of T cell receptor excision circles (TRECs) or the dye CFSE, and clonal expansion has been documented by recording changes in the population densities of antigen specific cells. Proper interpretation of such data in terms of the underlying rates of T cell production, division, and death has proven to be notoriously difficult and involves mathematical modeling. We review the various models that have been developed for each of these techniques, discuss which models seem most appropriate for what type of data, reveal open problems that require better models, and pinpoint how the assumptions underlying a mathematical model may influence the interpretation of data. Elaborating various successful cases where modeling has delivered new insights in T cell population dynamics, this review provides quantitative estimates of several processes involved in the maintenance of naive and memory, CD4(+) and CD8(+) T cell pools in mice and men.

PD-1 promotes immune exhaustion by inducing antiviral T cell motility paralysis

Immune responses to persistent viral infections and cancer often fail because of intense regulation of antigen-specific T cells-a process referred to as immune exhaustion. The mechanisms that underlie the induction of exhaustion are not completely understood. To gain novel insights into this process, we simultaneously examined the dynamics of virus-specific CD8(+) and CD4(+) T cells in the living spleen by two-photon microscopy (TPM) during the establishment of an acute or persistent viral infection. We demonstrate that immune exhaustion during viral persistence maps anatomically to the splenic marginal zone/red pulp and is defined by prolonged motility paralysis of virus-specific CD8(+) and CD4(+) T cells. Unexpectedly, therapeutic blockade of PD-1-PD-L1 restored CD8(+) T cell motility within 30 min, despite the presence of high viral loads. This result was supported by planar bilayer data showing that PD-L1 localizes to the central supramolecular activation cluster, decreases antiviral CD8(+) T cell motility, and promotes stable immunological synapse formation. Restoration of T cell motility in vivo was followed by recovery of cell signaling and effector functions, which gave rise to a fatal disease mediated by IFN-γ. We conclude that motility paralysis is a manifestation of immune exhaustion induced by PD-1 that prevents antiviral CD8(+) T cells from performing their effector functions and subjects them to prolonged states of negative immune regulation.

Evolution of viral life-cycle in response to cytotoxic T lymphocyte-mediated immunity

Viruses in mammals are constantly faced with the problem of elimination by the host immunity. Cytotoxic T lymphocyte (CTL) responses are thought to play a major role in the control and clearance of several viral infections in mice and humans. It is therefore expected that over evolutionary time, viruses would be forced to evolve to avoid recognition by CTLs. Indeed, a number of studies have documented the accumulation of viral variants with escape mutations. These mutations allow viruses to hide from CTL responses common in the host population. CTLs recognize viruses by short protein sequences, named epitopes, derived from viral proteins. The efficiency of viral recognition by epitope-specific CTL responses depends on the expression pattern of the proteins carrying these epitopes, and the total amount of that protein (and thus epitopes) in the cell. When a virus replicates in a cell, some viral genes are expressed early in the life cycle of the virus, while other proteins are expressed late. For example, HIV infected cells first express Rev and Tat proteins, and the Gag proteins are expressed late. Here we propose a dynamical model of the viral life cycle to study how expression level of early vs. late genes may affect viral dynamics within the host and virus transmission over the course of infection. We find that for acute and chronic viral infections lower expression of early genes than that of the late genes is expected to give selective advantage and higher transmission to viruses.

Predator-prey dynamics in a uniform medium lead to directed percolation and wave-train propagation

The dynamics of birth-death processes with extinction points that are unstable in the deterministic average description has been extensively studied, mainly in the context of the stochastic transition from the mean-field attracting fixed point to the absorbing state. Here we study the opposite case of a small perturbation from the zero-population absorbing state. We show that such perturbations can grow beyond the mean-field attracting fixed point and then can collapse back into the absorbing state. Such dynamics can represent, for example, the fast growth of a pathogen and then its destruction by the immune system. We show that when the prey perturbation extinction probability is high, the loss of synchronization between the prey densities in different regions in space leads to two possible dynamic regimes: (a) a directed percolation regime based on the balance between regions escaping the absorbing state and regions absorbed into it, and (b) wave trains representing the transition of the entire space to the mean-field stable positive fixed point.

A low dimensional dynamical model of the initial pulmonary innate response to infection

In order to gain a deeper understanding of the onset and progression of pulmonary infections we present and analyze a low dimensional, phenomenological model of infection and the innate immune response in the lungs. Because pulmonary innate immunity has features unique to itself, general mathematical models of the immune system may not be appropriate. The differential equations model that we propose is based on current knowledge of the biology of pulmonary innate immunity and accurately reproduces known features of the initial phase of the dynamics of pulmonary innate system as exhibited in recent experiments. Further, we propose to use the model as a starting point for interrogation with clinical data from a new noninvasive technique for sampling alveolar lining fluid.

Mathematical model of the primary CD8 T cell immune response: stability analysis of a nonlinear age-structured system

The primary CD8 T cell immune response, due to a first encounter with a pathogen, happens in two phases: an expansion phase, with a fast increase of T cell count, followed by a contraction phase. This contraction phase is followed by the generation of memory cells. These latter are specific of the antigen and will allow a faster and stronger response when encountering the antigen for the second time. We propose a nonlinear mathematical model describing the T CD8 immune response to a primary infection, based on three nonlinear ordinary differential equations and one nonlinear age-structured partial differential equation, describing the evolution of CD8 T cell count and pathogen amount. We discuss in particular the roles and relevance of feedback controls that regulate the response. First we reduce our system to a system with a nonlinear differential equation with a distributed delay. We study the existence of two steady states, and we analyze the asymptotic stability of these steady states. Second we study the system with a discrete delay, and analyze global asymptotic stability of steady states. Finally, we show some simulations that we can obtain from the model and confront them to experimental data.

Fitness costs and diversity of the cytotoxic T lymphocyte (CTL) response determine the rate of CTL escape during acute and chronic phases of HIV infection

HIV-1 often evades cytotoxic T cell (CTL) responses by generating variants that are not recognized by CTLs. We used single-genome amplification and sequencing of complete HIV genomes to identify longitudinal changes in the transmitted/founder virus from the establishment of infection to the viral set point at 1 year after the infection. We found that the rate of viral escape from CTL responses in a given patient decreases dramatically from acute infection to the viral set point. Using a novel mathematical model that tracks the dynamics of viral escape at multiple epitopes, we show that a number of factors could potentially contribute to a slower escape in the chronic phase of infection, such as a decreased magnitude of epitope-specific CTL responses, an increased fitness cost of escape mutations, or an increased diversity of the CTL response. In the model, an increase in the number of epitope-specific CTL responses can reduce the rate of viral escape from a given epitope-specific CTL response, particularly if CD8+ T cells compete for killing of infected cells or control virus replication nonlytically. Our mathematical framework of viral escape from multiple CTL responses can be used to predict the breadth and magnitude of HIV-specific CTL responses that need to be induced by vaccination to reduce (or even prevent) viral escape following HIV infection.

Comparing the kinetics of NK cells, CD4, and CD8 T cells in murine cytomegalovirus infection

NK cells recognize virus-infected cells with germline-encoded activating and inhibitory receptors that do not undergo genetic recombination or mutation. Accordingly, NK cells are often considered part of the innate immune response. The innate response comprises rapid early defenders that do not form immune memory. However, there is increasing evidence that experienced NK cells provide increased protection to secondary infection, a hallmark of the adaptive response. In this study, we compare the dynamics of the innate and adaptive immune responses by examining the kinetic profiles of the NK and T cell response to murine CMV infection. We find that, unexpectedly, the kinetics of NK cell proliferation is neither earlier nor faster than the CD4 or CD8 T cell response. Furthermore, early NK cell contraction after the peak of the response is slower than that of T cells. Finally, unlike T cells, experienced NK cells do not experience biphasic decay after the response peak, a trait associated with memory formation. Rather, NK cell contraction is continuous, constant, and returns to below endogenous preinfection levels. This indicates that the reason why Ag-experienced NK cells remain detectable for a prolonged period after adoptive transfer and infection is in part due to the high precursor frequency, slow decay rate, and low background levels of Ly49H(+) NK cells in recipient DAP12-deficient mice. Thus, the quantitative contribution of Ag-experienced NK cells in an endogenous secondary response, with higher background levels of Ly49H(+) NK cells, may be not be as robust as the secondary response observed in T cells.

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.

Persistence of viral infection despite similar killing efficacy of antiviral CD8(+) T cells during acute and chronic phases of infection

Why some viruses establish chronic infections while others do not is poorly understood. One possibility is that the host's immune response is impaired during chronic infections and is unable to clear the virus from the host. In this report, we use a recently proposed framework to estimate the per capita killing efficacy of CD8(+) T cells, specific for the polyoma virus (PyV), which establishes a chronic infection in mice. Surprisingly, the estimated per cell killing efficacy of PyV-specific effector CD8(+) T cells during the acute phase of the infection was very similar to the efficacy of effector CD8(+) T cells specific to lymphocytic choriomeningitis virus (LCMV-Armstrong), which is cleared from the host. Our results suggest that persistence of PyV does not result from the generation of an inefficient PyV-specific CD8(+) T cell response, and that other host or viral factors are responsible for the ability of PyV to establish chronic infection.

Lifelong dynamics of human CD4+CD25+ regulatory T cells: insights from in vivo data and mathematical modeling

Despite their limited proliferation capacity, regulatory T cells (T(regs)) constitute a population maintained over the entire lifetime of a human organism. The means by which T(regs) sustain a stable pool in vivo are controversial. Using a mathematical model, we address this issue by evaluating several biological scenarios of the origins and the proliferation capacity of two subsets of T(regs): precursor CD4(+)CD25(+)CD45RO(-) and mature CD4(+)CD25(+)CD45RO(+) cells. The lifelong dynamics of T(regs) are described by a set of ordinary differential equations, driven by a stochastic process representing the major immune reactions involving these cells. The model dynamics are validated using data from human donors of different ages. Analysis of the data led to the identification of two properties of the dynamics: (1) the equilibrium in the CD4(+)CD25(+)FoxP3(+)T(regs) population is maintained over both precursor and mature T(regs) pools together, and (2) the ratio between precursor and mature T(regs) is inverted in the early years of adulthood. Then, using the model, we identified three biologically relevant scenarios that have the above properties: (1) the unique source of mature T(regs) is the antigen-driven differentiation of precursors that acquire the mature profile in the periphery and the proliferation of T(regs) is essential for the development and the maintenance of the pool; there exist other sources of mature T(regs), such as (2) a homeostatic density-dependent regulation or (3) thymus- or effector-derived T(regs), and in both cases, antigen-induced proliferation is not necessary for the development of a stable pool of T(regs). This is the first time that a mathematical model built to describe the in vivo dynamics of regulatory T cells is validated using human data. The application of this model provides an invaluable tool in estimating the amount of regulatory T cells as a function of time in the blood of patients that received a solid organ transplant or are suffering from an autoimmune disease.

IL-21 and IL-15 cytokine DNA augments HSV specific effector and memory CD8+ T cell response

The recurrence of lesions and transmission of Herpes simplex virus is dependent on the number and function of viral specific CD8(+) T cells, especially the memory T cells. The generation, turnover and set point of this cell population is maintained by different factors like exposure to antigen, cytokines and co-stimulatory molecules. However, the contribution of these factors in the generation and maintenance of the memory CD8(+) T cell population is still controversial, since it is not clear if homeostatic proliferation driven by cytokines can overcome T cell receptor (TCR) signaling. Since, interleukin 15 (IL-15) and interleukin 21 (IL-21) are cytokines implicated in homeostatic control of CD8(+) T cell pool, we constructed and used expression plasmids coding for IL-15 (pIL-15) and IL-21 (pIL-21) to expand HSV specific CD8(+) T cells in an animal model. Our results showed that the IL-21 increased the frequency of CD8(+) T cells in the absence of antigen, although the magnitude of this response was dependent on TCR signaling. Both pIL-15 and pIL-21 boosted the numbers of antigen specific CD8(+) IFNgamma producing cells in the primary response. In the memory phase, numbers of CD8(+) CD44(high) as well as CD8(+) T cells producing IFN-gamma and TNF-alpha were increased when pIL-15 and pIL-21 were used alone or in combination, compared to vector treatment only, and association of antigen further increased the proliferative response. Our data suggest that genetic treatment with pIL-15 and pIL-21 in the presence or absence of cognate antigen can contribute to immune-enhancement against HSV.

Naive precursor frequencies and MHC binding rather than the degree of epitope diversity shape CD8+ T cell immunodominance

The primary CD8(+) T cell response of C57BL/6J mice against the 28 known epitopes of lymphocytic choriomeningitis virus (LCMV) is associated with a clear immunodominance hierarchy whose mechanism has yet to be defined. To evaluate the role of epitope competition in immunodominance, we manipulated the number of CD8(+) T cell epitopes that could be recognized during LCMV infection. Decreasing epitope numbers, using a viral variant lacking dominant epitopes or C57BL/6J mice lacking H-2K(b), resulted in minor response increases for the remaining epitopes and no new epitopes being recognized. Increasing epitope numbers by using F(1) hybrid mice, delivery by recombinant vaccinia virus, or epitope delivery as a pool in IFA maintained the overall response pattern; however, changes in the hierarchy did become apparent. MHC binding affinity of these epitopes was measured and was found to not strictly predict the hierarchy since in several cases similarly high binding affinities were associated with differences in immunodominance. In these instances the naive CD8(+) T cell precursor frequency, directly measured by tetramer staining, correlated with the response hierarchy seen after LCMV infection. Finally, we investigated an escape mutant of the dominant GP33-41 epitope that elicited a weak response following LCMV variant virus infection. Strikingly, dominance loss likely reflects a substantial reduction in frequencies of naive precursors specific for this epitope. Thus, our results indicate that an intrinsic property of the epitope (MHC binding affinity) and an intrinsic property of the host (naive precursor frequency) jointly dictate the immunodominance hierarchy of CD8(+) T cell responses.

A simple model of pathogen-immune dynamics including specific and non-specific immunity

We present and analyze a model for the dynamics of the interactions between a pathogen and its host's immune response. The model consists of two differential equations, one for pathogen load, the other one for an index of specific immunity. Differently from other simple models in the literature, this model exhibits, according to the hosts' or pathogen's parameter values, or to the initial infection size, a rich repertoire of behaviours: immediate clearing of the pathogen through aspecific immune response; or acute infection followed by clearing of the pathogen through specific immune response; or uncontrolled infections; or acute infection followed by convergence to a stable state of chronic infection; or periodic solutions with intermittent acute infections. The model can also mimic some features of immune response after vaccination. This model could be a basis on which to build epidemic models including immunological features.

Robust model matching control of immune systems under environmental disturbances: dynamic game approach

A robust model matching control of immune response is proposed for therapeutic enhancement to match a prescribed immune response under uncertain initial states and environmental disturbances, including continuous intrusion of exogenous pathogens. The worst-case effect of all possible environmental disturbances and uncertain initial states on the matching for a desired immune response is minimized for the enhanced immune system, i.e. a robust control is designed to track a prescribed immune model response from the minimax matching perspective. This minimax matching problem could herein be transformed to an equivalent dynamic game problem. The exogenous pathogens and environmental disturbances are considered as a player to maximize (worsen) the matching error when the therapeutic control agents are considered as another player to minimize the matching error. Since the innate immune system is highly nonlinear, it is not easy to solve the robust model matching control problem by the nonlinear dynamic game method directly. A fuzzy model is proposed to interpolate several linearized immune systems at different operating points to approximate the innate immune system via smooth fuzzy membership functions. With the help of fuzzy approximation method, the minimax matching control problem of immune systems could be easily solved by the proposed fuzzy dynamic game method via the linear matrix inequality (LMI) technique with the help of Robust Control Toolbox in Matlab. Finally, in silico examples are given to illustrate the design procedure and to confirm the efficiency and efficacy of the proposed method.

Do most lymphocytes in humans really reside in the gut?

It is widely believed that the gut, and particularly the lamina propria (LP) of the gut, contains most of the lymphocytes in humans. The strong depletion of CD4(+) T cells from the gut LP of HIV-infected patients was, therefore, suggested to be such a large, irreversible insult that it could explain HIV disease progression. However, reviewing data from different mammalian species, we found that only 5%-20% of all lymphocytes reside in the gut, and that only 1%-9% of the total lymphocyte number is located in the gut LP. Our findings suggest that spleen and lymph nodes, rather than the gut, are the largest immune compartments in mammals.