Dynamical conditions for the containment of HIV infection by CD8+ T Cells — A variable structure control approach

In the study of the Human Immunodeficiency Virus (HIV) infection dynamics, the reproductive ratio is a well-known tool which provides a steady-state condition to determine the outcome of the infection. This paper assesses the control of HIV by the immune response. Dynamical conditions for the containment of HIV infection by the HIV-specific CD8+ T cell response are evaluated using a model of HIV dynamics in vivo in which HIV-infected cells are killed before they start producing new virion. The reachability paradigm from Variable Structure Control (VSC) theory is used to formulate a dynamical condition for immunity. Simulation results show that this reachability condition effectively monitors the immunological requirements to contain HIV. This work also suggests that the cytolytic killing mechanism of CD8+ T cells operates as a boundary layer control to contain HIV infection. Together, the findings indicate that in contrast to the reproductive ratio, the proposed VSC approach delivers a framework to assess the effects of nonlinear dynamics and uncertainty as well as providing a means to investigate immunotherapy strategies

A Study of the Synergies Between Control Mechanisms in the Immune System and the Variable Structure Control Paradigm

This thesis argues that variable structure control theory finds application in immunology. The immune system maintains a healthy state by using feedback to switch on and off immune responses. Experimental and mathematical work has analysed the dynamics of the immune response of T cells, relatively little attention has been paid to examine the underlying control paradigm. Besides, in modelling and simulation studies, it is necessary to evaluate the impact of uncertainty and perturbations on immunological dynamics. This is important to deliver robust predictions and insights. These facts motivate considering variable structure control techniques to investigate the control strategy and robustness of the immune system in the context of immunity to infection and tolerance. The results indicate that the dynamic response of T cells following foreign or self-antigen stimulation behaves as a naturally occurring switched control law. Further, the reachability analysis from sliding mode control highlights dynamical conditions to assess the performance and robustness of the T cell response dynamics. Additionally, this approach delivers dynamical conditions for the containment of Human Immunodeficiency Virus (HIV) infection by the HIV-specific CD8+ T cell response and antiretroviral therapy by enforcing a sliding mode on a manifold associated with the infection-free steady-state. This condition for immunity reveals particular patterns for early diagnosis of eventual success, marginal and failure cases of antiretroviral therapy. Together, the findings in this thesis evidence that variable structure control theory presents a useful framework to study health and disease dynamics as well as to monitor the performance of treatment regimes

Prediction of the Containment of HIV Infection by Antiretroviral Therapy - a Variable Structure Control Approach

It is demonstrated that the reachability paradigm from variable structure control theory is a suitable framework to monitor and predict the progression of the human immunodeficiency virus (HIV) infection following initiation of antiretroviral therapy (ART). A manifold is selected which characterises the infection-free steady-state. A model of HIV infection together with an associated reachability analysis is used to formulate a dynamical condition for the containment of HIV infection on the manifold. This condition is tested using data from two different HIV clinical trials which contain measurements of the CD4+ T cell count and HIV load in the peripheral blood collected from HIV infected individuals for the six month period following initiation of ART. The biological rates of the model are estimated using the multi-point identification method and data points collected in the initial period of the trial. Using the parameter estimates and the numerical solutions of the model, the predictions of the reachability analysis are shown to be consistent with the clinical diagnosis at the conclusion of the trial. The methodology captures the dynamical characteristics of eventual successful, failed and marginal outcomes. The findings evidence that the reachability analysis is an appropriate tool to monitor and develop personalised antiretroviral treatment

Early estimation of the number of hidden HIV infected subjects: An extended Kalman filter approach

In the last decades several epidemic emergencies have been affecting the world, influ encing the social relationships, the economics and the habits. In particular, starting in the early 0 80, the Acquired Immunodeficiency Syndrome, AIDS, is representing one of the most worrying sanitary emergency, that has caused up to now more than 25 million of dead patients. The infection is caused by the Human Immunodeficiency Virus, HIV, that may be transmitted by body fluids; therefore with wise behaviours the epidemic spread could rapidly be contained. This sanitary emergency is peculiar for the long incubation time: it can reach even 10 years, a long period in which the individual can unconsciously infect other subjects. The identification of the number of infected unaware people, mandatory to define suitable containment measures, is here obtained by using the extended Kalman filter applied to a noisy model in which, reasonably, only the number of infected diagnosed patients is available. Numerical simulations and real data analysis support the effective ness of the approac

Control theory helps to resolve the measles paradox

Measles virus (MV) is a highly contagious respiratory morbillivirus that results in many disabilities and deaths. A crucial challenge in studying MV infection is to understand the so-called ‘measles paradox’—the progression of the infection to severe immunosuppression before clearance of acute viremia, which is also observed in canine distemper virus (CDV) infection. However, a lack of models that match in vivo data has restricted our understanding of this complex and counter-intuitive phenomenon. Recently, progress was made in the development of a model that fits data from acute measles infection in rhesus macaques. This progress motivates our investigations to gain additional insights from this model into the control mechanisms underlying the paradox. In this paper, we investigated analytical conditions determining the control and robustness of viral clearance for MV and CDV, to untangle complex feedback mechanisms underlying the dynamics of acute infections in their natural hosts. We applied control theory to this model to help resolve the measles paradox. We showed that immunosuppression is important to control and clear the virus. We also showed under which conditions T-cell killing becomes the primary mechanism for immunosuppression and viral clearance. Furthermore, we characterized robustness properties of T-cell immunity to explain similarities and differences in the control of MV and CDV. Together, our results are consistent with experimental data, advance understanding of control mechanisms of viral clearance across morbilliviruses, and will help inform the development of effective treatments. Further the analysis methods and results have the potential to advance understanding of immune system responses to a range of viral infections such as COVID-19

Mathematical Modeling of Virus Dynamics in Immunology

A simplified dynamical model of immune response to uncomplicated influenza virus infection is presented, which focuses on the control of the infection by the innate and adaptive immunity. Innate immunity is represented by interferon-induced resistance to infection of respiratory epithelial cells and by removal of infected cells by effector cells. Adaptive immunity is represented by virus-specific antibodies. Similar in spirit to the recent model of Bocharov & Romanyukha (Bocharov and Romanyukha, 1994), the model is constructed as a system of 10 ordinary differential equations with 27 parameters. In the first part, parameter values for the model are obtained either from published experimental data or by estimation based on fitting available data about the time course of IAV infection in a naïve host. Sensitivity analysis is performed on the model parameters. To account for the variability and speed of adaptation, a variable is introduced that quantifies the antigenic compatibility between the virus and the antibodies. It is found that for small initial viral load the disease progresses through an asymptomatic course, for intermediate value it takes a typical course with constant duration and severity of infection but variable onset, and for large initial viral load the disease becomes severe. The absence of antibody response leads to recurrence of disease and appearance of a chronic state with nontrivial constant viral load. In the second part, an ensemble model of immune response is developed, which consists of multiple ODE models that are identical in form but differ in parameter values. A probabilistic measure of goodness of fit of the ODE model is used to derive an a posteriori probability density on the space of parameter values. This probability density is sampled using the Metropolis Monte Carlo method and sampling is enhanced using parallel tempering algorithm. The ensemble model is employed to compute probabilistic estimates on trajectory of the immune response, duration of disease, maximum damage, likelihood of rebound in the disease and the probability of occurrence of superspreaders. The effectiveness of using antiviral drug to treat the infection is addressed and optimal treatment scenarios are discussed

Mathematische Analyse des rezeptorvermittelten Immunzelltods bei angeborener antiviraler Immunität

Apoptosis is a series of complex biochemical processes of programmed cell death which occurs in multicellular organisms. This mechanism must be highly regulated and controlled; otherwise, harmful illness such as cancer and autoimmune diseases may occur. Apoptosis is a key mechanism during a typical viral immune response.In the course of an infection, this mechanism eliminates infected cells and by that,limits the resources for viral replication. Recently, regulation of the death recep-tor pathway by cFLIP, a key regulator of signaling complexes downstream of death receptors, was targeted experimentally to study the role of apoptosis in influenza A virus (IAV) infection. By increasing the expression level of cFLIP in transgenic mice, a higher accumulation of Natural Killer (NK) cells and a higher viral load in comparison to wild type(WT) mice were observed. However, the viral load was similar in both mice after 10 days. Infection and functional impairment of NK cells was assumed to be responsible for the observed results. In order to validate this hypothesis, a mathematical model was used to quantify the role of apoptosis medi-ated cell death in NK cells during the viral clearance. The model contains variables and parameters that represent population and interactions between healthy and in-fected epithelial cells, influenza A virions, healthy and infected NK cells. Several simplifications were made in order to better estimate the critical parameters of the model. Simulation results showed that infection of NK cells with a longer lifespan alone cannot explain the observed high viral load. However, by increasing the viral production of infected NK cells, the viral load data was fitted. The lack of caspase3, due to the over-expression of cFLIP, may contribute to higher viral production inNK cells. Furthermore, a shorter lifespan of healthy NK cells was predicted, which may be related to biological exhaustion due to higher infection level. The posteriors and the correlation analysis of the parameters showed that parameters associated with lifespan and the viral production of infected NK cells are linearly correlated.Die Apoptose ist ein komplexer biochemischer Prozess des programmierten Zelltod,die in mehrzelligen Organismen auftritt. Dieser Mechanismus muss eng kontrolliert werden, sonst können schädliche Krankheiten auftreten, so wie z.B. Krebs und Autoimmunerkrankungen. Während einer typischen viralen Immunantwort, werden infizierte Zellen durch Apoptose eliminiert, so dass die Ressourcen für die Virus-replikation begrenzt werden. cFLIP ist ein Inhibitor der Todesrezeptor-gesteuerten Apoptose. Die Regulation des extrinsischen Signalwegs durch cFLIP wurde erforscht um die Rolle der Apoptose während Influenza A Infektionen zu untersuchen. Hierfür wurden transgene Mäuse, die cFLIP in allen hämatopowerten Zellen exprimieren,mit dem Influenza A-Virus infiziert. Diese transgenen Mäuse haben mehr natürliche Killerzellen (NK) und höhere Viruslast aufgewiesen. Die Viruslast nach 10 Tagen waren ähnlich bei transgenen und Wildtyp (WT) Mäusen. Tafrishi argumentierte, dass die infizierten NK-Zellen und ihre Funktionsstörung verantwortlich für die Ergebnissen sind. Hierin wurde ein mathematisches Modell verwendet, um diese Hypothese zu validieren und die Rolle der Apoptose in NK Zellen durch Influenza A-Infektionen zu quantifizieren. Die Modellvariablen und Parameter darstellen die Population und Wechselwirkungen beidem Influenza A-Virus, gesunden und infizierten Epithelzellen und gesunden und infizierten NK-Zellen. Die Simulationsergebnissen demonstrieren, dass infizierte NK-Zellen, die eine längere Lebensdauer haben, nicht der Grund für die erhöhte Viruslast sind. Stattdessen ist eine höhere Virusproduktion von der infizierten NK-Zellen notwendig, um die Viruslast Daten anzupassen.Deshalb kann das Fehlen von Caspase 3, aufgrund der Überexpression von cFLIP,zu einer höheren Virusproduktion in den NK-Zellen beitragen. Darüber hinaus hat die Datenanpassung eine kürzere Lebensdauer der gesunden NK-Zellen vorhergesagt,aufgrund der biologischen Erschöpfung. Korrelationsanalysen der Parameter zeigten,dass die Lebensdauer und die Virusproduktion der infizierten NK-Zellen linear korreliert sind

Tumor Necrosis Factor-Regulated Granuloma Formation in Tuberculosis: Multi-Scale Modeling and Experiments.

Tuberculosis is a deadly infectious disease caused by Mycobacterium tuberculosis (Mtb). Multiple immune factors control host responses to Mtb infection, including the formation of granulomas in the lung, which are aggregates of bacteria, infected and uninfected immune cells whose function may reflect success or failure of the host to control infection. One such factor is tumor necrosis factor-α (TNF). TNF has been experimentally characterized to affect macrophage activation, apoptosis, chemokine and cytokine production during Mtb infection. Measurement of TNF concentrations and TNF activities within a granuloma to determine the relevant mechanisms for control of infection are difficult to assess in vivo. Further, processes that control TNF availability and activities within a granuloma remain unknown. We developed a multi-scale computational model that describes the immune response to Mtb in lung over three biological length scales: tissue, cellular and molecular. We used the results of sensitivity analysis as a tool to identify which experiments were needed to measure critical model parameters in an experimental system. This system is a model of a granuloma induced in the lungs of mice following injection of mycobacterial antigen-coated beads. Using these parameters in the model, we identified processes that regulate TNF availability and cellular behaviors and thus influence the outcome of infection within a granuloma. At the level of TNF/TNF receptor dynamics, TNF receptor internalization kinetics were shown to significantly influence TNF concentration dynamics, macrophage and T cell recruitment to site of infection, macrophage activation and apoptosis. These processes play a critical role in control of inflammation and bacterial levels within a granuloma. At the level of intracellular signaling, our analysis elucidated intracellular NF-κB associated signaling molecules and processes that may be new targets for control of infection and inflammation. We also used the model to explain what mechanisms lead to clinically observed differential effects of TNF-neutralizing drugs (generally used to treat inflammatory diseases) on reactivation of tuberculosis. Ultimately, these results can help to elaborate relevant features of the immune response to Mtb infection, identifying new strategies for therapy and prevention of tuberculosis as well as for development of safer anti-TNF drugs to treat inflammatory diseases.Ph.D.Chemical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91477/1/fallahi_1.pd

In vitro expanded human CD4+CD25+ regulatory T cells suppress effector T cell proliferation.

Regulatory T cells (Tregs) have been shown to be critical in the balance between autoimmunity and tolerance and have been implicated in several human autoimmune diseases. However, the small number of Tregs in peripheral blood limits their therapeutic potential. Therefore, we developed a protocol that would allow for the expansion of Tregs while retaining their suppressive activity. We isolated CD4+CD25 hi cells from human peripheral blood and expanded them in vitro in the presence of anti-CD3 and anti-CD28 magnetic Xcyte Dynabeads and high concentrations of exogenous Interleukin (IL)-2. Tregs were effectively expanded up to 200-fold while maintaining surface expression of CD25 and other markers of Tregs: CD62L, HLA-DR, CCR6, and FOXP3. The expanded Tregs suppressed proliferation and cytokine secretion of responder PBMCs in co-cultures stimulated with anti-CD3 or alloantigen. Treg expansion is a critical first step before consideration of Tregs as a therapeutic intervention in patients with autoimmune or graft-versus-host disease

A review of mathematical models of influenza A infections within a host or cell culture: lessons learned and challenges ahead

Most mathematical models used to study the dynamics of influenza A have thus far focused on the between-host population level, with the aim to inform public health decisions regarding issues such as drug and social distancing intervention strategies, antiviral stockpiling or vaccine distribution. Here, we investigate mathematical modeling of influenza infection spread at a different scale; namely that occurring within an individual host or a cell culture. We review the models that have been developed in the last decades and discuss their contributions to our understanding of the dynamics of influenza infections. We review kinetic parameters (e.g., viral clearance rate, lifespan of infected cells) and values obtained through fitting mathematical models, and contrast them with values obtained directly from experiments. We explore the symbiotic role of mathematical models and experimental assays in improving our quantitative understanding of influenza infection dynamics. We also discuss the challenges in developing better, more comprehensive models for the course of influenza infections within a host or cell culture. Finally, we explain the contributions of such modeling efforts to important public health issues, and suggest future modeling studies that can help to address additional questions relevant to public health