Mathematical modeling of endogenous and exogenously administered T cell recirculation in mouse and its application to pharmacokinetic studies of cell therapies.

Introduction: In vivo T cell migration has been of interest to scientists for the past 60 years. T cell kinetics are important in the understanding of the immune response to infectious agents. More recently, adoptive T cell therapies have proven to be a most promising approach to treating a wide range of diseases, including autoimmune and cancer diseases, whereby the characterization of cellular kinetics represents an important step towards the prediction of therapeutic efficacy. Methods: Here, we developed a physiologically-based pharmacokinetic (PBPK) model that describes endogenous T cell homeostasis and the kinetics of exogenously administered T cells in mouse. Parameter calibration was performed using a nonlinear fixed-effects modeling approach based on published data on T cell kinetics and steady-state levels in different tissues of mice. The Partial Rank Correlation Coefficient (PRCC) method was used to perform a global sensitivity assessment. To estimate the impact of kinetic parameters on exogenously administered T cell dynamics, a local sensitivity analysis was conducted. Results: We simulated the model to analyze cellular kinetics following various T cell doses and frequencies of CCR7+ T cells in the population of infused lymphocytes. The model predicted the effects of T cell numbers and of population composition of infused T cells on the resultant concentration of T cells in various organs. For example, a higher percentage of CCR7+ T cells among exogenously administered T lymphocytes led to an augmented accumulation of T cells in the spleen. The model predicted a linear dependence of T cell dynamics on the dose of adoptively transferred T cells. Discussion: The mathematical model of T cell migration presented here can be integrated into a multi-scale model of the immune system and be used in a preclinical setting for predicting the distribution of genetically modified T lymphocytes in various organs, following adoptive T cell therapies.

Anti-PD-L1 Immunotherapy of Chronic Virus Infection Improves Virus Control without Augmenting Tissue Damage by Fibrosis.

Immunotherapy with checkpoint inhibitors, albeit commonly used against tumors, is still at its infancy against chronic virus infections. It relies on the reinvigoration of exhausted T lymphocytes to eliminate virus-infected cells. Since T cell exhaustion is a physiological process to reduce immunopathology, the reinvigoration of these cells might be associated with an augmentation of pathological changes. To test this possibility, we here analyzed in the model system of chronic lymphocytic choriomeningitis virus (LCMV)-infected mice whether treatment with the checkpoint inhibitor anti-PD-L1 antibody would increase CD8 T cell-dependent fibrosis. We show that pre-existing spleen fibrosis did not worsen under conditions that increase CD8 T cell functionality and reduce virus loads suggesting that the CD8 T cell functionality increase remained below its pathogenicity threshold. These promising findings should further encourage immunotherapeutic trials against chronic virus infections.

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.

Mathematical Analysis of the Effectiveness of Screening for Intracranial Aneurysms in First-Degree Relatives of Persons with Subarachnoid Hemorrhage.

OBJECTIVE: Population screening for aneurysms in patients with risk factors and preventive surgical treatment are beneficial according to numerous studies. One of the most significant risk factors is heredity, namely, the presence of first-degree relatives (FDR) with aneurysmal subarachnoid hemorrhage (aSAH). Nevertheless, there are still no generally accepted approaches or evidence bases regarding the benefits of the aneurysm screening strategy. METHODS: Mathematical modeling of the dynamics of aneurysm development in the population was carried out using an algorithm implementing a discrete Markov's chain. To implement the model, all probabilities of events and distributions are taken from available literature sources. Three-dimensional time of flight noncontrast magnetic resonance angiography was chosen as a screening method. Patients underwent preventive surgical treatment if an aneurysm was detected. RESULTS: Screening and preventive treatment in the general population reduces the prevalence of aneurysms by 1.74% (3.44% in the FDR group) and the prevalence of aSAH by 14.36% (37.48% in the FDR group). Mortality due to aSAH was reduced by 14.44%. The number of disabilities also decreases. The occurrence of deep disability was reduced by 20.2% in the FDR group. Economic analysis of the part of the population consisting of FDRs showed annual savings of ies also decr CONCLUSIONS: The mathematical model demonstrated that screening and preventive treatment of cerebral aneurysms can reduce aSAH-associated morbidity and mortality. In the FDR group, there was decrease in the prevalence of aSAH and decrease in associated mortality. Screening for cerebral aneurysms is cost-effective.

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.

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.

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.

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.

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.

Sensitivity of SARS-CoV-2 Life Cycle to IFN Effects and ACE2 Binding Unveiled with a Stochastic Model.

Mathematical modelling of infection processes in cells is of fundamental interest. It helps to understand the SARS-CoV-2 dynamics in detail and can be useful to define the vulnerability steps targeted by antiviral treatments. We previously developed a deterministic mathematical model of the SARS-CoV-2 life cycle in a single cell. Despite answering many questions, it certainly cannot accurately account for the stochastic nature of an infection process caused by natural fluctuation in reaction kinetics and the small abundance of participating components in a single cell. In the present work, this deterministic model is transformed into a stochastic one based on a Markov Chain Monte Carlo (MCMC) method. This model is employed to compute statistical characteristics of the SARS-CoV-2 life cycle including the probability for a non-degenerate infection process. Varying parameters of the model enables us to unveil the inhibitory effects of IFN and the effects of the ACE2 binding affinity. The simulation results show that the type I IFN response has a very strong effect on inhibition of the total viral progeny whereas the effect of a 10-fold variation of the binding rate to ACE2 turns out to be negligible for the probability of infection and viral production.

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.

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.

Modeling of the HIV-1 Life Cycle in Productively Infected Cells to Predict Novel Therapeutic Targets.

There are many studies that model the within-host population dynamics of Human Immunodeficiency Virus Type 1 (HIV-1) infection. However, the within-infected-cell replication of HIV-1 remains to be not comprehensively addressed. There exist rather few quantitative models describing the regulation of the HIV-1 life cycle at the intracellular level. In treatment of HIV-1 infection, there remain issues related to side-effects and drug-resistance that require further search "...for new and better drugs, ideally targeting multiple independent steps in the HIV-1 replication cycle" (as highlighted recently by Teldury et al., The Future of HIV-1 Therapeutics, 2015). High-resolution mathematical models of HIV-1 growth in infected cells provide an additional analytical tool in identifying novel drug targets. We formulate a high-dimensional model describing the biochemical reactions underlying the replication of HIV-1 in target cells. The model considers a nonlinear regulation of the transcription of HIV-1 mediated by Tat and the Rev-dependent transport of fully spliced and singly spliced transcripts from the nucleus to the cytoplasm. The model is calibrated using available information on the kinetics of various stages of HIV-1 replication. The sensitivity analysis of the model is performed to rank the biochemical processes of HIV-1 replication with respect to their impact on the net production of virions by one actively infected cell. The ranking of the sensitivity factors provides a quantitative basis for identifying novel targets for antiviral therapy. Our analysis suggests that HIV-1 assembly depending on Gag and Tat-Rev regulation of transcription and mRNA distribution present two most critical stages in HIV-1 replication that can be targeted to effectively control virus production. These processes are not covered by current antiretroviral treatments.

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-ß-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.

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.

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

[This corrects the article DOI: 10.3389/fimmu.2019.01213.].

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.