An integrative mechanistic model of thymocyte dynamics

Background

The thymus plays a central role in shaping human immune function. A mechanistic, quantitative description of immune cell dynamics and thymic output under homeostatic conditions and various patho-physiological scenarios are of particular interest in drug development applications, e.g., in the identification of potential therapeutic targets and selection of lead drug candidates against infectious diseases.

Methods

We here developed an integrative mathematical model of thymocyte dynamics in human. It incorporates mechanistic features of thymocyte homeostasis as well as spatial constraints of the thymus and considerations of age-dependent involution. All model parameter estimates were obtained based on published physiological data of thymocyte dynamics and thymus properties in mouse and human. We performed model sensitivity analyses to reveal potential therapeutic targets through an identification of processes critically affecting thymic function; we further explored differences in thymic function across healthy subjects, multiple sclerosis patients, and patients on fingolimod treatment.

Results

We found thymic function to be most impacted by the egress, proliferation, differentiation and death rates of those thymocytes which are most differentiated. Model predictions also showed that the clinically observed decrease in relapse risk with age, in multiple sclerosis patients who would have discontinued fingolimod therapy, can be explained mechanistically by decreased thymic output with age. Moreover, we quantified the effects of fingolimod treatment duration on thymic output.

Conclusions

In summary, the proposed model accurately describes, in mechanistic terms, thymic output as a function of age. It may be further used to perform predictive simulations of clinically relevant scenarios which combine specific patho-physiological conditions and pharmacological interventions of interest.

Differential kinetics of splenic CD169+ macrophage death is one underlying cause of virus infection fate regulation

Acute infection and chronic infection are the two most common fates of pathogenic virus infections. While several factors that contribute to these fates are described, the critical control points and the mechanisms that underlie infection fate regulation are incompletely understood. Using the acute and chronic lymphocytic choriomeningitis virus (LCMV) infection model of mice, we find that the early dynamic pattern of the IFN-I response is a differentiating trait between both infection fates. Acute-infected mice generate a 2-wave IFN-I response while chronic-infected mice generate only a 1-wave response. The underlying cause is a temporal difference in CD8 T cell-mediated killing of splenic marginal zone CD169+ macrophages. It occurs later in acute infection and thus enables CD169+ marginal zone macrophages to produce the 2nd IFN-I wave. This is required for subsequent immune events including induction of inflammatory macrophages, generation of effector CD8+ T cells and virus clearance. Importantly, these benefits come at a cost for the host in the form of spleen fibrosis. Due to an earlier marginal zone destruction, these ordered immune events are deregulated in chronic infection. Our findings demonstrate the critical importance of kinetically well-coordinated sequential immune events for acute infection control and highlights that it may come at a cost for the host organism.

Numerical study of chronic hepatitis B infection using Marchuk-Petrov model

In this work, we briefly describe our technology developed for computing periodic solutions of time-delay systems and discuss the results of computing periodic solutions for the Marchuk-Petrov model with parameter values, corresponding to hepatitis B infection. We identified the regions in the model parameter space in which an oscillatory dynamics in the form of periodic solutions exists. The respective solutions can be interpreted as active forms of chronic hepatitis B. The period and amplitude of oscillatory solutions were traced along the parameter determining the efficacy of antigen presentation by macrophages for T- and B-lymphocytes in the model.. The oscillatory regimes are characterized by enhanced destruction of hepatocytes as a consequence of immunopathology and temporal reduction of viral load to values which can be a prerequisite of spontaneous recovery observed in chronic HBV infection. Our study presents a first step in a systematic analysis of the chronic HBV infection using Marchuk-Petrov model of antiviral immune response.

XCR1+ DCs are critical for T cell-mediated immunotherapy of chronic viral infections

The contribution of cross-presenting XCR1+ dendritic cells (DCs) and SIRPα+ DCs in maintaining T cell function during exhaustion and immunotherapeutic interventions of chronic infections remains poorly characterized. Using the mouse model of chronic LCMV infection, we found that XCR1+ DCs are more resistant to infection and highly activated compared with SIRPα+ DCs. Exploiting XCR1+ DCs via Flt3L-mediated expansion or XCR1-targeted vaccination notably reinvigorates CD8+ T cells and improves virus control. Upon PD-L1 blockade, XCR1+ DCs are not required for the proliferative burst of progenitor exhausted CD8+ T (TPEX) cells but are indispensable to sustain the functionality of exhausted CD8+ T (TEX) cells. Combining anti-PD-L1 therapy with increased frequency of XCR1+ DCs improves functionality of TPEX and TEX subsets, while increase of SIRPα+ DCs dampened their proliferation. Together, this demonstrates that XCR1+ DCs are crucial for the success of checkpoint inhibitor-based therapies through differential activation of exhausted CD8+ T cell subsets.

Prediction of Specific Antibody- and Cell-Mediated Responses Using Baseline Immune Status Parameters of Individuals Received Measles-Mumps-Rubella Vaccine

A successful vaccination implies the induction of effective specific immune responses. We intend to find biomarkers among various immune cell subpopulations, cytokines and antibodies that could be used to predict the levels of specific antibody- and cell-mediated responses after measles-mumps-rubella vaccination. We measured 59 baseline immune status parameters (frequencies of 42 immune cell subsets, levels of 13 cytokines, immunoglobulins) before vaccination and 13 response variables (specific IgA and IgG, antigen-induced IFN-γ production, CD107a expression on CD8+ T lymphocytes, and cellular proliferation levels by CFSE dilution) 6 weeks after vaccination for 19 individuals. Statistically significant Spearman correlations between some baseline parameters and response variables were found for each response variable (p < 0.05). Because of the low number of observations relative to the number of baseline parameters and missing data for some observations, we used three feature selection strategies to select potential predictors of the post-vaccination responses among baseline variables: (a) screening of the variables based on correlation analysis; (b) supervised screening based on the information of changes of baseline variables at day 7; and (c) implicit feature selection using regularization-based sparse regression. We identified optimal multivariate linear regression models for predicting the effectiveness of vaccination against measles-mumps-rubella using the baseline immune status parameters. It turned out that the sufficient number of predictor variables ranges from one to five, depending on the response variable of interest.

An integrative systems biology view of host-pathogen interactions: The regulation of immunity and homeostasis is concomitant, flexible, and smart

The systemic bio-organization of humans and other mammals is essentially "preprogrammed", and the basic interacting units, the cells, can be crudely mapped into discrete sets of developmental lineages and maturation states. Over several decades, however, and focusing on the immune system, we and others invoked evidence - now overwhelming - suggesting dynamic acquisition of cellular properties and functions, through tuning, re-networking, chromatin remodeling, and adaptive differentiation. The genetically encoded "algorithms" that govern the integration of signals and the computation of new states are not fully understood but are believed to be "smart", designed to enable the cells and the system to discriminate meaningful perturbations from each other and from "noise". Cellular sensory and response properties are shaped in part by recurring temporal patterns, or features, of the signaling environment. We compared this phenomenon to associative brain learning. We proposed that interactive cell learning is subject to selective pressures geared to performance, allowing the response of immune cells to injury or infection to be progressively coordinated with that of other cell types across tissues and organs. This in turn is comparable to supervised brain learning. Guided by feedback from both the tissue itself and the neural system, resident or recruited antigen-specific and innate immune cells can eradicate a pathogen while simultaneously sustaining functional homeostasis. As informative memories of immune responses are imprinted both systemically and within the targeted tissues, it is desirable to enhance tissue preparedness by incorporating attenuated-pathogen vaccines and informed choice of tissue-centered immunomodulators in vaccination schemes. Fortunately, much of the "training" that a living system requires to survive and function in the face of disturbances from outside or within is already incorporated into its design, so it does not need to deep-learn how to face a new challenge each time from scratch. Instead, the system learns from experience how to efficiently select a built-in strategy, or a combination of those, and can then use tuning to refine its organization and responses. Efforts to identify and therapeutically augment such strategies can take advantage of existing integrative modeling approaches. One recently explored strategy is boosting the flux of uninfected cells into and throughout an infected tissue to rinse and replace the infected cells.

Stochastic Modelling of HIV-1 Replication in a CD4 T Cell with an IFN Response

A mathematical model of the human immunodeficiency virus Type 1 (HIV-1) life cycle in CD4 T cells was constructed and calibrated. It describes the activation of the intracellular Type I interferon (IFN-I) response and the IFN-induced suppression of viral replication. The model includes viral replication inhibition by interferon-induced antiviral factors and their inactivation by the viral proteins Vpu and Vif. Both deterministic and stochastic model formulations are presented. The stochastic model was used to predict efficiency of IFN-I-induced suppression of viral replication in different initial conditions for autocrine and paracrine effects. The probability of virion excretion for various MOIs and various amounts of IFN-I was evaluated and the statistical properties of the heterogeneity of HIV-1 and IFN-I production characterised.

Functional cure of a chronic virus infection by shifting the virus - host equilibrium state

The clinical handling of chronic virus infections remains a challenge. Here we describe recent progress in the understanding of virus - host interaction dynamics. Based on the systems biology concept of multi-stability and the prediction of multiplicative cooperativity between virus-specific cytotoxic T cells and neutralising antibodies, we argue for the requirements to engage multiple immune system components for functional cure strategies. Our arguments are derived from LCMV model system studies and are translated to HIV-1 infection.

Examining the cooperativity mode of antibody and CD8+ T cell immune responses for vaccinology

A fundamental unsolved issue in vaccine design is how neutralizing antibodies and cytotoxic CD8⁺ T cells cooperate numerically in controlling virus infections. We hypothesize on a viewpoint for the multiplicative cooperativity between neutralizing antibodies and CD8⁺ T cells and propose how this might be exploited for improving vaccine-induced protective immunity.

Intracellular Life Cycle Kinetics of SARS-CoV-2 Predicted Using Mathematical Modelling

SARS-CoV-2 infection represents a global threat to human health. Various approaches were employed to reveal the pathogenetic mechanisms of COVID-19. Mathematical and computational modelling is a powerful tool to describe and analyze the infection dynamics in relation to a plethora of processes contributing to the observed disease phenotypes. In our study here, we formulate and calibrate a deterministic model of the SARS-CoV-2 life cycle. It provides a kinetic description of the major replication stages of SARS-CoV-2. Sensitivity analysis of the net viral progeny with respect to model parameters enables the identification of the life cycle stages that have the strongest impact on viral replication. These three most influential parameters are (i) degradation rate of positive sense vRNAs in cytoplasm (negative effect), (ii) threshold number of non-structural proteins enhancing vRNA transcription (negative effect), and (iii) translation rate of non-structural proteins (positive effect). The results of our analysis could be used for guiding the search for antiviral drug targets to combat SARS-CoV-2 infection.

Topological Structure and Robustness of the Lymph Node Conduit System

Fibroblastic reticular cells (FRCs) form a road-like cellular network in lymph nodes (LNs) that provides essential chemotactic, survival, and regulatory signals for immune cells. While the topological characteristics of the FRC network have been elaborated, the network properties of the micro-tubular conduit system generated by FRCs, which drains lymph fluid through a pipeline-like system to distribute small molecules and antigens, has remained unexplored. Here, we quantify the crucial 3D morphometric parameters and determine the topological properties governing the structural organization of the intertwined networks. We find that the conduit system exhibits lesser small-worldness and lower resilience to perturbation compared to the FRC network, while the robust topological organization of both networks is maintained in a lymphotoxin-β-receptor-independent manner. Overall, the high-resolution topological analysis of the "roads-and-pipes" networks highlights essential parameters underlying the functional organization of LN micro-environments and will, hence, advance the development of multi-scale LN models.

The spatiotemporal dynamics of type I IFN response determine viral infection outcome

Type I interferons (IFN-I) play a critical role in shaping the antiviral immune response early after an infection. However, the dynamics by which different immune cell subsets regulate the IFN-I response during the early stages of acute and chronic infections is not completely understood. Here we used the Lymphocytic Choriomeningitis Virus (LCMV)-infection mouse model system to characterize the dynamics of the IFN-I response in acute and chronic infections. Time-resolved spleen-transcriptomes revealed that during an acute infection, IFN-I showed two peaks of expression at days 2 and 5 post-infection. In contrast, in chronically infected mice a single peak of IFN-I genes appeared at day 1. Further analysis revealed that IFN-I genes in acute infection were co-expressed with genes related to inflammatory macrophages, suggesting an important role of these cells determining infection fate. Indeed, we identified metallophilic macrophages as an important source of Ifnb only during acute infection and demonstrated that the subsequent IFN-I receptor (IFNAR) signaling is necessary to induce pro-inflammatory macrophages. In contrast, during chronic infection, early depletion of marginal zone macrophages results in a lack of IFN-I production and the inflammatory response is not induced. Importantly, blockage of the second peak of IFN-I response by IFNAR blockage during an acute infection also resulted in exhaustion of virus-specific CD8 T cells and prevention of lymphoid tissue fibrosis. Further studies are ongoing to decipher the regulatory mechanisms underlying the characterized events, thus revealing universal concepts related to infection fate decisions that are also relevant for persistent human infections such as HIV or HCV.

Prediction of PD-L1 inhibition effects for HIV-infected individuals

The novel therapies with immune checkpoint inhibitors hold great promises for patients with chronic virus infections and cancers. This is based mainly on the partial reversal of the exhausted phenotype of antigen-specific cytotoxic CD8 T cells (CTL). Recently, we have shown that the restoration of HIV-specific T cell function depends on the HIV infection stage of an infected individual. Here we aimed to answer two fundamental questions: (i) Can one estimate growth parameters for the HIV-specific proliferative responsiveness upon PD-L1 blockade ex vivo? (ii) Can one use these parameter estimates to predict clinical benefit for HIV-infected individuals displaying diverse infection phenotypes? To answer these questions, we first analyzed HIV-1 Gag-specific CD8 T cell proliferation by time-resolved CFSE assays and estimated the effect of PD-L1 blockade on division and death rates, and specific precursor frequencies. These values were then incorporated into a model for CTL-mediated HIV control and the effects on CTL frequencies, viral loads and CD4 T cell counts were predicted for different infection phenotypes. The biggest absolute increase in CD4 T cell counts was in the group of slow progressors while the strongest reduction in virus loads was observed in progressor patients. These results suggest a significant clinical benefit only for a subgroup of HIV-infected individuals. However, as PD1 is a marker of lymphocyte activation and expressed on several lymphocyte subsets including also CD4 T cells and B cells, we subsequently examined the multiple effects of anti-PD-L1 blockade beyond those on CD8 T cells. This extended model then predicts that the net effect on HIV load and CD4 T cell number depends on the interplay between positive and negative effects of lymphocyte subset activation. For a physiologically relevant range of affected model parameters, PD-L1 blockade is likely to be overall beneficial for HIV-infected individuals.

Immune checkpoint inhibitors can revitalize exhausted virus-specific CD8 T cells (CTL) and thus hold great promises for patients with chronic virus infections. Based on the hypothesis that gain in the proliferation of CTL by such interventions may positively influence HIV-1 disease progression, we developed a general framework of how to quantify the proliferative CTL responsiveness after PD-L1 blockade, and translate it to patient outcome predictions. However, PD-L1 blockade also activates (i) exhausted CD4 T cells generating additional HIV target cells for virus expansion as well as (ii) exhausted B cells producing increasing antibody levels that potentially inhibit HIV spread. To assess these virus-specific effects of a PD-L1 blockade, we then extended our basic model and incorporated experimentally determined CD4 T cell proliferation gains and estimates on HIV-specific antibody increases. Altogether, the blockade effect is predicted to be infection phenotype-dependent and in most cases beneficial. Our general approach can be expanded to other immunotherapies and is an important step forward towards personalized treatment strategies in infectious diseases and cancers.

Spatial Lymphocyte Dynamics in Lymph Nodes Predicts the Cytotoxic T Cell Frequency Needed for HIV Infection Control

The surveillance of host body tissues by immune cells is central for mediating their defense function. In vivo imaging technologies have been used to quantitatively characterize target cell scanning and migration of lymphocytes within lymph nodes (LNs). The translation of these quantitative insights into a predictive understanding of immune system functioning in response to various perturbations critically depends on computational tools linking the individual immune cell properties with the emergent behavior of the immune system. By choosing the Newtonian second law for the governing equations, we developed a broadly applicable mathematical model linking individual and coordinated T-cell behaviors. The spatial cell dynamics is described by a superposition of autonomous locomotion, intercellular interaction, and viscous damping processes. The model is calibrated using in vivo data on T-cell motility metrics in LNs such as the translational speeds, turning angle speeds, and meandering indices. The model is applied to predict the impact of T-cell motility on protection against HIV infection, i.e., to estimate the threshold frequency of HIV-specific cytotoxic T cells (CTLs) that is required to detect productively infected cells before the release of viral particles starts. With this, it provides guidance for HIV vaccine studies allowing for the migration of cells in fibrotic LNs.

Systems analysis reveals complex biological processes during virus infection fate decisions

The processes and mechanisms of virus infection fate decisions that are the result of a dynamic virus-immune system interaction with either an efficient effector response and virus elimination or an alleviated immune response and chronic infection are poorly understood. Here, we characterized the host response to acute and chronic lymphocytic choriomeningitis virus (LCMV) infections by gene coexpression network analysis of time-resolved splenic transcriptomes. First, we found an early attenuation of inflammatory monocyte/macrophage prior to the onset of T cell exhaustion, and second, a critical role of the XCL1-XCR1 communication axis during the functional adaptation of the T cell response to the chronic infection state. These findings not only reveal an important feedback mechanism that couples T cell exhaustion with the maintenance of a lower level of effector T cell response but also suggest therapy options to better control virus levels during the chronic infection phase.

Linking Cell Dynamics With Gene Coexpression Networks to Characterize Key Events in Chronic Virus Infections

The host immune response against infection requires the coordinated action of many diverse cell subsets that dynamically adapt to a pathogen threat. Due to the complexity of such a response, most immunological studies have focused on a few genes, proteins, or cell types. With the development of “omic”-technologies and computational analysis methods, attempts to analyze and understand complex system dynamics are now feasible. However, the decomposition of transcriptomic data sets generated from complete organs remains a major challenge. Here, we combined Weighted Gene Coexpression Network Analysis (WGCNA) and Digital Cell Quantifier (DCQ) to analyze time-resolved mouse splenic transcriptomes in acute and chronic Lymphocytic Choriomeningitis Virus (LCMV) infections. This enabled us to generate hypotheses about complex immune functioning after a virus-induced perturbation. This strategy was validated by successfully predicting several known immune phenomena, such as effector cytotoxic T lymphocyte (CTL) expansion and exhaustion. Furthermore, we predicted and subsequently verified experimentally macrophage-CD8 T cell cooperativity and the participation of virus-specific CD8⁺ T cells with an early effector transcriptome profile in the host adaptation to chronic infection. Thus, the linking of gene expression changes with immune cell kinetics provides novel insights into the complex immune processes within infected tissues.

Integrative Computational Modeling of the Lymph Node Stromal Cell Landscape

Adaptive immune responses develop in secondary lymphoid organs such as lymph nodes (LNs) in a well-coordinated series of interactions between migrating immune cells and resident stromal cells. Although many processes that occur in LNs are well understood from an immunological point of view, our understanding of the fundamental organization and mechanisms that drive these processes is still incomplete. The aim of systems biology approaches is to unravel the complexity of biological systems and describe emergent properties that arise from interactions between individual constituents of the system. The immune system is greater than the sum of its parts, as is the case with any sufficiently complex system. Here, we review recent work and developments of computational LN models with focus on the structure and organization of the stromal cells. We explore various mathematical studies of intranodal T cell motility and migration, their interactions with the LN-resident stromal cells, and computational models of functional chemokine gradient fields and lymph flow dynamics. Lastly, we discuss briefly the importance of hybrid and multi-scale modeling approaches in immunology and the technical challenges involved.

Interplay between reaction and diffusion processes in governing the dynamics of virus infections

Spreading of viral infection in the tissues such as lymph nodes or spleen depends on virus multiplication in the host cells, their transport and on the immune response. Reaction-diffusion systems of equations with delays in cell proliferation and death by apoptosis represent an appropriate model to study this process. The properties of the cells of the immune system and the initial viral load determine the spatiotemporal regimes of infection spreading. Infection can be completely eliminated or it can persist at some level together with a certain chronic immune response in a spatially uniform or oscillatory mode. Finally, the immune cells can be completely exhausted leading to a high viral load persistence in the tissue. It has been found experimentally, that virus proteins can affect the immune cell migration. Our study shows that both the motility of immune cells and the virus infection spreading represented by the diffusion rate coefficients are relevant control parameters determining the fate of virus-host interaction.

Modelling of Experimental Infections

This chapter aims to give a clear idea of how mathematical analysis for experimental systems could help in the process of data assimilation, parameter estimation and hypothesis testing.

Hybrid approach to model the spatial regulation of T cell responses

BACKGROUND

Moving from the molecular and cellular level to a multi-scale systems understanding of immune responses requires the development of novel approaches to integrate knowledge and data from different biological levels into mechanism-based integrative mathematical models. The aim of our study is to present a methodology for a hybrid modelling of immunological processes in their spatial context.

METHODS

A two-level hybrid mathematical model of immune cell migration and interaction integrating cellular and organ levels of regulation for a 2D spatial consideration of idealized secondary lymphoid organs is developed. It considers the population dynamics of antigen-presenting cells, CD4 + and CD8 + T lymphocytes in naive-, proliferation- and differentiated states. Cell division is assumed to be asymmetric and regulated by the extracellular concentration of interleukin-2 (IL-2) and type I interferon (IFN), together controlling the balance between proliferation and differentiation. The cytokine dynamics is described by reaction-diffusion PDEs whereas the intracellular regulation is modelled with a system of ODEs.

RESULTS

The mathematical model has been developed, calibrated and numerically implemented to study various scenarios in the regulation of T cell immune responses to infection, in particular the change in the diffusion coefficient of type I IFN as compared to IL-2. We have shown that a hybrid modelling approach provides an efficient tool to describe and analyze the interplay between spatio-temporal processes in the emergence of abnormal immune response dynamics.

DISCUSSION

Virus persistence in humans is often associated with an exhaustion of T lymphocytes. Many factors can contribute to the development of exhaustion. One of them is associated with a shift from a normal clonal expansion pathway to an altered one characterized by an early terminal differentiation of T cells. We propose that an altered T cell differentiation and proliferation sequence can naturally result from a spatial separation of the signaling events delivered via TCR, IL-2 and type I IFN receptors. Indeed, the spatial overlap of the concentration fields of extracellular IL-2 and IFN in lymph nodes changes dynamically due to different migration patterns of APCs and CD4 + T cells secreting them.

CONCLUSIONS

The proposed hybrid mathematical model of the immune response represents a novel analytical tool to examine challenging issues in the spatio-temporal regulation of cell growth and differentiation, in particular the effect of timing and location of activation signals.

Spatiotemporal Dynamics of Virus Infection Spreading in Tissues

Virus spreading in tissues is determined by virus transport, virus multiplication in host cells and the virus-induced immune response. Cytotoxic T cells remove infected cells with a rate determined by the infection level. The intensity of the immune response has a bell-shaped dependence on the concentration of virus, i.e., it increases at low and decays at high infection levels. A combination of these effects and a time delay in the immune response determine the development of virus infection in tissues like spleen or lymph nodes. The mathematical model described in this work consists of reaction-diffusion equations with a delay. It shows that the different regimes of infection spreading like the establishment of a low level infection, a high level infection or a transition between both are determined by the initial virus load and by the intensity of the immune response. The dynamics of the model solutions include simple and composed waves, and periodic and aperiodic oscillations. The results of analytical and numerical studies of the model provide a systematic basis for a quantitative understanding and interpretation of the determinants of the infection process in target organs and tissues from the image-derived data as well as of the spatiotemporal mechanisms of viral disease pathogenesis, and have direct implications for a biopsy-based medical testing of the chronic infection processes caused by viruses, e.g. HIV, HCV and HBV.

Topological Small-World Organization of the Fibroblastic Reticular Cell Network Determines Lymph Node Functionality

Fibroblastic reticular cells (FRCs) form the cellular scaffold of lymph nodes (LNs) and establish distinct microenvironmental niches to provide key molecules that drive innate and adaptive immune responses and control immune regulatory processes. Here, we have used a graph theory-based systems biology approach to determine topological properties and robustness of the LN FRC network in mice. We found that the FRC network exhibits an imprinted small-world topology that is fully regenerated within 4 wk after complete FRC ablation. Moreover, in silico perturbation analysis and in vivo validation revealed that LNs can tolerate a loss of approximately 50% of their FRCs without substantial impairment of immune cell recruitment, intranodal T cell migration, and dendritic cell-mediated activation of antiviral CD8+ T cells. Overall, our study reveals the high topological robustness of the FRC network and the critical role of the network integrity for the activation of adaptive immune responses.

Asymmetry of Cell Division in CFSE-Based Lymphocyte Proliferation Analysis

Flow cytometry-based analysis of lymphocyte division using carboxyfluorescein succinimidyl ester (CFSE) dye dilution permits acquisition of data describing cellular proliferation and differentiation. For example, CFSE histogram data enable quantitative insight into cellular turnover rates by applying mathematical models and parameter estimation techniques. Several mathematical models have been developed using different types of deterministic or stochastic approaches. However, analysis of CFSE proliferation assays is based on the premise that the label is halved in the two daughter cells. Importantly, asymmetry of protein distribution in lymphocyte division is a basic biological feature of cell division with the degree of the asymmetry depending on various factors. Here, we review the recent literature on asymmetric lymphocyte division and CFSE-based lymphocyte proliferation analysis. We suggest that division- and label-structured mathematical models describing CFSE-based cell proliferation should take into account asymmetry and time-lag in cell proliferation. Utilization of improved modeling algorithms will permit straightforward quantification of essential parameters describing the performance of activated lymphocytes.

RNAtips: Analysis of temperature-induced changes of RNA secondary structure

Although multiple biological phenomena are related to temperature (e.g. elevation of body temperature due to an illness, adaptation to environmental temperature conditions, biology of coldblooded versus warm-blooded organisms), the molecular mechanisms of these processes remain to be understood. Perturbations of secondary RNA structures may play an important role in an organism’s reaction to temperature change—in all organisms from viruses and bacteria to humans. Here, we present RNAtips (temperature-induced perturbation of structure) web server, which can be used to predict regions of RNA secondary structures that are likely to undergo structural alterations prompted by temperature change. The server can also be used to: (i) detect those regions in two homologous RNA sequences that undergo different structural perturbations due to temperature change and (ii) test whether these differences are specific to the particular nucleotide substitutions distinguishing the sequences. The RNAtips web server is freely accessible without any login requirement at http://rnatips.org.

Pathogenesis and treatment of HIV infection: the cellular, the immune system and the neuroendocrine systems perspective

Infections with HIV represent a great challenge for the development of strategies for an effective cure. The spectrum of diseases associated with HIV ranges from opportunistic infections and cancers to systemic physiological disorders like encephalopathy and neurocognitive impairment. A major progress in controlling HIV infection has been achieved by highly active antiretroviral therapy (HAART). However, HAART does neither eliminate the virus reservoirs in form of latently infected cells nor does it completely reconstitute immune reactivity and physiological status. Furthermore, the failure of the STEP vaccine trial and the only marginal efficacies of the RV144 trial together suggest that the causal relationships between the complex sets of viral and immunological processes that contribute to protection or disease pathogenesis are still poorly understood. Here, we provide an up-to-date overview of HIV-host interactions at the cellular, the immune system and the neuroendocrine systems level. Only by integrating this multi-level knowledge one will be able to handle the systems complexity and develop new methodologies of analysis and prediction for a functional restoration of the immune system and the health of the infected host.

A global "imaging'' view on systems approaches in immunology

The immune system exhibits an enormous complexity. High throughput methods such as the "-omic'' technologies generate vast amounts of data that facilitate dissection of immunological processes at ever finer resolution. Using high-resolution data-driven systems analysis, causal relationships between complex molecular processes and particular immunological phenotypes can be constructed. However, processes in tissues, organs, and the organism itself (so-called higher level processes) also control and regulate the molecular (lower level) processes. Reverse systems engineering approaches, which focus on the examination of the structure, dynamics and control of the immune system, can help to understand the construction principles of the immune system. Such integrative mechanistic models can properly describe, explain, and predict the behavior of the immune system in health and disease by combining both higher and lower level processes. Moving from molecular and cellular levels to a multiscale systems understanding requires the development of methodologies that integrate data from different biological levels into multiscale mechanistic models. In particular, 3D imaging techniques and 4D modeling of the spatiotemporal dynamics of immune processes within lymphoid tissues are central for such integrative approaches. Both dynamic and global organ imaging technologies will be instrumental in facilitating comprehensive multiscale systems immunology analyses as discussed in this review.

A new model for the estimation of cell proliferation dynamics using CFSE data

CFSE analysis of a proliferating cell population is a popular tool for the study of cell division and divisionlinked changes in cell behavior. Recently Banks et al. (2011), Luzyanina et al. (2009), Luzyanina et al. (2007), a partial differential equation (PDE) model to describe lymphocyte dynamics in a CFSE proliferation assay was proposed. We present a significant revision of this model which improves the physiological understanding of several parameters. Namely, the parameter used previously as a heuristic explanation for the dilution of CFSE dye by cell division is replaced with a more physical component, cellular autofluorescence. The rate at which label decays is also quantified using a Gompertz decay process. We then demonstrate a revised method of fitting the model to the commonly used histogram representation of the data. It is shown that these improvements result in a model with a strong physiological basis which is fully capable of replicating the behavior observed in the data.

Fitness ranking of individual mutants drives patterns of epistatic interactions in HIV-1

Fitness interactions between mutations, referred to as epistasis, can strongly impact evolution. For RNA viruses and retroviruses with their high mutation rates, epistasis may be particularly important to overcome fitness losses due to the accumulation of deleterious mutations and thus could influence the frequency of mutants in a viral population. As human immunodeficiency virus type 1 (HIV-1) resistance to azidothymidine (AZT) requires selection of sequential mutations, it is a good system to study the impact of epistasis. Here we present a thorough analysis of a classical AZT-resistance pathway (the 41–215 cluster) of HIV-1 variants by fitness measurements in single round infection assays covering physiological drug concentrations ex vivo. The sign and value of epistasis varied and did not predict the epistatic effect on the mutant frequency. This complex behavior is explained by the fitness ranking of the variants that strongly depends on environmental factors, i.e., the presence and absence of drugs and the host cells used. Although some interactions compensate fitness losses, the observed small effect on the relative mutant frequencies suggests that epistasis might be inefficient as a buffering mechanism for fitness losses in vivo. While the use of epistasis-based hypotheses to make general assumptions on the evolutionary dynamics of viral populations is appealing, our data caution their interpretation without further knowledge on the characteristics of the viral mutant spectrum under different environmental conditions.

A systems immunology approach to plasmacytoid dendritic cell function in cytopathic virus infections

Plasmacytoid dendritic cell (pDC)-mediated protection against cytopathic virus infection involves various molecular, cellular, tissue-scale, and organism-scale events. In order to better understand such multiscale interactions, we have implemented a systems immunology approach focusing on the analysis of the structure, dynamics and operating principles of virus-host interactions which constrain the initial spread of the pathogen. Using high-resolution experimental data sets coming from the well-described mouse hepatitis virus (MHV) model, we first calibrated basic modules including MHV infection of its primary target cells, i.e. pDCs and macrophages (Mphis). These basic building blocks were used to generate and validate an integrative mathematical model for in vivo infection dynamics. Parameter estimation for the system indicated that on a per capita basis, one infected pDC secretes sufficient type I IFN to protect 10(3) to 10(4) Mphis from cytopathic viral infection. This extremely high protective capacity of pDCs secures the spleen's capability to function as a 'sink' for the virus produced in peripheral organs such as the liver. Furthermore, our results suggest that the pDC population in spleen ensures a robust protection against virus variants which substantially down-modulate IFN secretion. However, the ability of pDCs to protect against severe disease caused by virus variants exhibiting an enhanced liver tropism and higher replication rates appears to be rather limited. Taken together, this systems immunology analysis suggests that antiviral therapy against cytopathic viruses should primarily limit viral replication within peripheral target organs.

Distributed parameter identification for a label-structured cell population dynamics model using CFSE histogram time-series data

In this work we address the problem of the robust identification of unknown parameters of a cell population dynamics model from experimental data on the kinetics of cells labelled with a fluorescence marker defining the division age of the cell. The model is formulated by a first order hyperbolic PDE for the distribution of cells with respect to the structure variable x (or z) being the intensity level (or the log(10)-transformed intensity level) of the marker. The parameters of the model are the rate functions of cell division, death, label decay and the label dilution factor. We develop a computational approach to the identification of the model parameters with a particular focus on the cell birth rate alpha(z) as a function of the marker intensity, assuming the other model parameters are scalars to be estimated. To solve the inverse problem numerically, we parameterize alpha(z) and apply a maximum likelihood approach. The parametrization is based on cubic Hermite splines defined on a coarse mesh with either equally spaced a priori fixed nodes or nodes to be determined in the parameter estimation procedure. Ill-posedness of the inverse problem is indicated by multiple minima. To treat the ill-posed problem, we apply Tikhonov regularization with the regularization parameter determined by the discrepancy principle. We show that the solution of the regularized parameter estimation problem is consistent with the data set with an accuracy within the noise level in the measurements.

[Parvovirus B-19 infections in pregnant women in day care facilities: health economic analysis of prohibition to employ seronegative women]

German protective legislation during pregnancy and maternity prohibit employing pregnant women if occupational activities endanger the health of either the mother-to-be or the fetus. This applies for parvovirus B19 seronegative women caring for children <6 years. Here we present a cost-effectiveness analysis from the view of the society for the prohibition to employ B19-seronegative women in day care. Prohibition of employment starting at the first day of pregnancy may prevent 1.4 cases of fetal death (mortality) and 1.7 cases of hydrops fetalis (morbidity) per year resulting in costs of 30 million <euro> (22 million <euro>/live birth). The incidence of B19 infection, the elevated occupational risk and the fetal death rate were varied in sensitivity analyses. This resulted in 0.2-3.1 fetal deaths prevented per year and costs between 10 million <euro> and 150 million <euro> per live birth. Indeed, the protective effect is assumed to be even lower since 30% of fetal deaths occur after infection during the first 8 weeks of pregnancy. During that time prohibition of employment is often unrealistic since the majority of women are not aware of pregnancy. In conclusion a small number of fetal lives can be saved by prohibiting employment in contrast to the extremely high costs. The regulations for maternal protection should be revised.

Numerical modelling of label-structured cell population growth using CFSE distribution data

Background

The flow cytometry analysis of CFSE-labelled cells is currently one of the most informative experimental techniques for studying cell proliferation in immunology. The quantitative interpretation and understanding of such heterogenous cell population data requires the development of distributed parameter mathematical models and computational techniques for data assimilation.

Methods and Results

The mathematical modelling of label-structured cell population dynamics leads to a hyperbolic partial differential equation in one space variable. The model contains fundamental parameters of cell turnover and label dilution that need to be estimated from the flow cytometry data on the kinetics of the CFSE label distribution. To this end a maximum likelihood approach is used. The Lax-Wendroff method is used to solve the corresponding initial-boundary value problem for the model equation. By fitting two original experimental data sets with the model we show its biological consistency and potential for quantitative characterization of the cell division and death rates, treated as continuous functions of the CFSE expression level.

Conclusion

Once the initial distribution of the proliferating cell population with respect to the CFSE intensity is given, the distributed parameter modelling allows one to work directly with the histograms of the CFSE fluorescence without the need to specify the marker ranges. The label-structured model and the elaborated computational approach establish a quantitative basis for more informative interpretation of the flow cytometry CFSE systems.

Maintenance of HIV-specific central and effector memory CD4 and CD8 T cells requires antigen persistence

The HIV-specific central and effector CD4 and CD8 memory T cell populations disappear from the peripheral blood of infected individuals under highly active antiretroviral therapy (HAART) with a mean half-life of 6.0 and 7.7 months, respectively. By contrast, cytomegalovirus (CMV)-specific responses are stable or increase. The striking quantitative differences between T cell memory to two persistent viral infections are instructive as to how antigen dosage contributes to the maintenance of antigen-specific memory T cell responses in humans.

Computational analysis of CFSE proliferation assay

CFSE based tracking of the lymphocyte proliferation using flow cytometry is a powerful experimental technique in immunology allowing for the tracing of labelled cell populations over time in terms of the number of divisions cells undergone. Interpretation and understanding of such population data can be greatly improved through the use of mathematical modelling. We apply a heterogenous linear compartmental model, described by a system of ordinary differential equations similar to those proposed by Kendall. This model allows division number-dependent rates of cell proliferation and death and describes the rate of changes in the numbers of cells having undergone j divisions. The experimental data set that we specifically analyze specifies the following characteristics of the kinetics of PHA-induced human T lymphocyte proliferation assay in vitro: (1) the total number of live cells, (2) the total number of dead but not disintegrated cells and (3) the number of cells divided j times. Following the maximum likelihood approach for data fitting, we estimate the model parameters which, in particular, present the CTL birth- and death rate "functions". It is the first study of CFSE labelling data which convincingly shows that the lymphocyte proliferation and death both in vitro and in vivo are division number dependent. For the first time, the confidence in the estimated parameter values is analyzed by comparing three major methods: the technique based on the variance-covariance matrix, the profile-likelihood-based approach and the bootstrap technique. We compare results and performance of these methods with respect to their robustness and computational cost. We show that for evaluating mathematical models of differing complexity the information-theoretic approach, based upon indicators measuring the information loss for a particular model (Kullback-Leibler information), provides a consistent basis. We specifically discuss methodological and computational difficulties in parameter identification with CFSE data, e.g. the loss of confidence in the parameter estimates starting around the sixth division. Overall, our study suggests that the heterogeneity inherent in cell kinetics should be explicitly incorporated into the structure of mathematical models.

A genetic-algorithm approach to simulating human immunodeficiency virus evolution reveals the strong impact of multiply infected cells and recombination

It has been previously shown that the majority of human immunodeficiency virus type 1 (HIV-1)-infected splenocytes can harbour multiple, divergent proviruses with a copy number ranging from one to eight. This implies that, besides point mutations, recombination should be considered as an important mechanism in the evolution of HIV within an infected host. To explore in detail the possible contributions of multi-infection and recombination to HIV evolution, the effects of major microscopic parameters of HIV replication (i.e. the point-mutation rate, the crossover number, the recombination rate and the provirus copy number) on macroscopic characteristics (such as the Hamming distance and the abundance of n-point mutants) have been simulated in silico. Simulations predict that multiple provirus copies per infected cell and recombination act in synergy to speed up the development of sequence diversity. Point mutations can be fixed for some time without fitness selection. The time needed for the selection of multiple mutations with increased fitness is highly variable, supporting the view that stochastic processes may contribute substantially to the kinetics of HIV variation in vivo.

A mathematical approach for optimizing dendritic cell-based immunotherapy

Adoptive dendritic cell (DC)-based immunotherapy represents a promising approach to overcome peripheral tolerance against autologous tumor antigens and to maintain protective antitumor immunity. The translation of successful preclinical studies, however, appears to be hampered by new complexities associated with the clinical situation. Mathematical modeling provides the means for qualitative and quantitative analysis, predictions for complex dynamic systems in immunology, and for the design and improvement of therapeutic approaches. We present here a workable computational methodology for developing meaningful data- and hypothesis-driven mathematical models for DC-based immunotherapy with a particular focus on numerical parameter estimation and sensitivity analysis.

Determining control parameters for dendritic cell-cytotoxic T lymphocyte interaction

Dendritic cells (DC) are potent immunostimulatory cells facilitating antigen transport to lymphoid tissues and providing efficient stimulation of T cells. A series of experimental studies in mice demonstrated that cytotoxic T lymphocytes (CTL) can be efficiently induced by adoptive transfer of antigen-presenting DC. However, the success of DC-based immunotherapeutic treatment of human cancer, for example, is still limited because the details of the regulation and kinetics of the DC-CTL interaction are not yet completely understood. Using a combination of experimental mouse studies, mathematical modeling, and nonlinear parameter estimation, we analyzed the population dynamics of DC-induced CTL responses. The model integrates a predator-prey-type interaction of DC and CTL with the non-linear compartmental dynamics of T cells. We found that T cell receptor avidity, the half-life of DC, and the rate of CTL-mediated DC-elimination are the major control parameters for optimal DC-induced CTL responses. For induction of high avidity CTL, the number of adoptively transferred DC was of minor importance once a minimal threshold of approximately 200 cells per spleen had been reached. Taken together, our study indicates that the availability of high avidity T cells in the recipient in combination with the optimal application regimen is of prime importance for successful DC-based immunotherapy.

The non-clonal and transitory nature of HIV in vivo

From a posteriori analyses of genetic variation, recombination can only be identified when the parental genomes are distinct. For viruses like HIV-1, this requires the producer cell to be infected by more than one virus. Using fluorescence in situ hybridisation, the provirus copy numbers in splenocytes from two HIV-1 patients were determined. More than 75% of infected splenocytes harboured two or more proviruses, range 1-8, with a mean of approximately 3-4 per cell. Sequencing of amplified DNA from single laser micro-dissected cells showed an extraordinary degree of diversity while numerous recombinants were evident. Given the dynamics of HIV-1 turnover in vivo and a recombination rate of approximately 3 cross-overs per cycle, some genomes from a fifteen year old infection may have undergone as many cross-overs as bases in the genome. Thus, recombination profoundly influences HIV evolution and gives it a non-clonal and transitory nature in vivo.

Underwhelming the immune response: effect of slow virus growth on CD8+-T-lymphocyte responses

The speed of virus replication has typically been seen as an advantage for a virus in overcoming the ability of the immune system to control its population growth. Under some circumstances, the converse may also be true: more slowly replicating viruses may evoke weaker cellular immune responses and therefore enhance their likelihood of persistence. Using the model of lymphocytic choriomeningitis virus (LCMV) infection in mice, we provide evidence that slowly replicating strains induce weaker cytotoxic-T-lymphocyte (CTL) responses than a more rapidly replicating strain. Conceptually, we show a "bell-shaped" relationship between the LCMV growth rate and the peak CTL response. Quantitative analysis of human hepatitis C virus infections suggests that a reduction in virus growth rate between patients during the incubation period is associated with a spectrum of disease outcomes, from fulminant hepatitis at the highest rate of viral replication through acute resolving to chronic persistence at the lowest rate. A mathematical model for virus-CTL population dynamics (analogous to predator [CTL]-prey [virus] interactions) is applied in the clinical data-driven analysis of acute hepatitis B virus infection. The speed of viral replication, through its stimulus of host CTL responses, represents an important factor influencing the pathogenesis and duration of virus persistence within the human host. Viruses with lower growth rates may persist in the host because they "sneak through" immune surveillance.

The non-clonal and transitory nature of HIV in vivo

From a posteriori analyses of genetic variation, recombination can only be identified when the parental genomes are distinct. For viruses like HIV-1, this requires the producer cell to be infected by more than one virus. Using fluorescence in situ hybridisation, the provirus copy numbers in splenocytes from two HIV-1 patients were determined. More than 75% of infected splenocytes harboured two or more proviruses, range 1-8, with a mean of approximately 3-4 per cell. Sequencing of amplified DNA from single laser micro-dissected cells showed an extraordinary degree of diversity while numerous recombinants were evident. Given the dynamics of HIV-1 turnover in vivo and a recombination rate of approximately 3 cross-overs per cycle, some genomes from a fifteen year old infection may have undergone as many cross-overs as bases in the genome. Thus, recombination profoundly influences HIV evolution and gives it a non-clonal and transitory nature in vivo.

Dendritic cell homeostasis in the regulation of self-reactivity

Dendritic cells (DC) are known for their remarkable ability to induce specific T cell responses. However, the existing views on the role of DC in maintaining tolerance to self-antigens and induction of autoimmunity are somewhat controversial especially when the basic physiology of DC migration, function and homeostasis is considered. This review attempts to provide a comprehensive overview on these topics with particular emphasis on DC homeostasis and presents implications for the generation of pathological autoimmune T cell responses. Furthermore, we advocate the need for a conceptual characterization of the immune system operating in vivo. With particular focus on the contribution of DC, we suggest that a 'spatiotemporal' view of the rules for T cell responses (antigen dose and availability, duration and mode of antigen presentation) permits a better understanding of the relevant factors contributing to the pathogenesis of autoimmune diseases.

Modelling the dynamics of LCMV infection in mice: II. Compartmental structure and immunopathology

In this study, we develop a mathematical model for analysis of the compartmental aspects and immunopathology of lymphocytic choriomeningitis virus (LCMV) infection in mice. We used sets of original and published data on systemic (extrasplenic) virus distribution to estimate the parameters of virus growth and elimination for spleen and other anatomical compartments, such as the liver, kidney, thymus and lung as well as transfer rates between blood and the above organs. A mathematical model quantitatively integrating the virus distribution kinetics in the host, the specific cytotoxic T lymphocyte (CTL) response in spleen and the re-circulation of effector CTL between spleen, blood and liver is advanced to describe the CTL-mediated immunopathology (hepatitis) in mice infected with LCMV. For intravenous and "peripheral" routes of infection we examine the severity of the liver disease, as a function of the virus dose and the host's immune status characterized by the numbers of precursor and/or cytolytic effector CTL. The model is used to predict the efficacy of protection against virus persistence and disease in a localized viral infection as a function of the composition of CTL population. The modelling analysis suggests quantitative demands to CTL memory for maximal protection against a wide range of doses of infection with a primarily peripheral site of virus replication without the risk of favoring immunopathology. It specifies objectives for CTL vaccination to ensure virus elimination with minimal immunopathology vs. vaccination for disease.

Recombination: Multiply infected spleen cells in HIV patients

The genome of the human immunodeficiency virus is highly prone to recombination, although it is not obvious whether recombinants arise infrequently or whether they are constantly being spawned but escape identification because of the massive and rapid turnover of virus particles. Here we use fluorescence in situ hybridization to estimate the number of proviruses harboured by individual splenocytes from two HIV patients, and determine the extent of recombination by sequencing amplified DNA from these cells. We find an average of three or four proviruses per cell and evidence for huge numbers of recombinants and extensive genetic variation. Although this creates problems for phylogenetic analyses, which ignore recombination effects, the intracellular variation may help to broaden immune recognition.

Low level viral persistence after infection with LCMV: a quantitative insight through numerical bifurcation analysis

Many important viruses persist at very low levels in the body in the face of host immunity, and may influence the maintenance of this state of 'infection immunity'. To analyse low level viral persistence in quantitative terms, we use a mathematical model of antiviral cytotoxic T lymphocyte (CTL) response to lymphocytic choriomeningitis virus (LCMV). This model, described by a non-linear system of delay differential equations (DDEs), is studied using numerical bifurcation analysis techniques for DDEs. Domains where low level LCMV coexistence with CTL memory is possible, either as an equilibrium state or an oscillatory pattern, are identified in spaces of the model parameters characterising the interaction between virus and CTL populations. Our analysis suggests that the coexistence of replication competent virus below the conventional detection limit (of about 100 pfu per spleen) in the immune host as an equilibrium state requires the per day relative growth rate of the virus population to decrease at least 5-fold compared to the acute phase of infection. Oscillatory patterns in the dynamics of persisting LCMV and CTL memory, with virus population varying between 1 and 100 pfu per spleen, are possible within quite narrow intervals of the rates of virus growth and precursor CTL population death. Whereas the virus replication rate appears to determine the stability of the low level virus persistence, it does not affect the steady-state level of the viral population, except for very low values.