Denise E. Kirschner

A Methodology For Performing Global Uncertainty And Sensitivity Analysis In Systems Biology

Accuracy of results from mathematical and computer models of biological systems is often complicated by the presence of uncertainties in experimental data that are used to estimate parameter values. Current mathematical modeling approaches typically use either single-parameter or local sensitivity analyses. However, these methods do not accurately assess uncertainty and sensitivity in the system as, by default, they hold all other parameters fixed at baseline values. Using techniques described within we demonstrate how a multi-dimensional parameter space can be studied globally so all uncertainties can be identified. Further, uncertainty and sensitivity analysis techniques can help to identify and ultimately control uncertainties. In this work we develop methods for applying existing analytical tools to perform analyses on a variety of mathematical and computer models. We compare two specific types of global sensitivity analysis indexes that have proven to be among the most robust and efficient. Through familiar and new examples of mathematical and computer models, we provide a complete methodology for performing these analyses, in both deterministic and stochastic settings, and propose novel techniques to handle problems encountered during these types of analyses.

Dynamics of HIV infection of CD4 T cells

We examine a model for the interaction of HIV with CD4+ T cells that considers four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. Using this model we show that many of the puzzling quantitative features of HIV infection can be explained simply. We also consider effects of AZT on viral growth and T-cell population dynamics. The model exhibits two steady states, an uninfected state in which no virus is present and an endemically infected state, in which virus and infected T cells are present. We show that if N, the number of infectious virions produced per actively infected T cell, is less a critical value, Ncrit, then the uninfected state is the only steady state in the nonnegative orthant, and this state is stable. For N > Ncrit, the uninfected state is unstable, and the endemically infected state can be either stable, or unstable and surrounded by a stable limit cycle. Using numerical bifurcation techniques we map out the parameter regimes of these various behaviors. oscillatory behavior seems to lie outside the region of biologically realistic parameter values. When the endemically infected state is stable, it is characterized by a reduced number of T cells compared with the uninfected state. Thus T-cell depletion occurs through the establishment of a new steady state. The dynamics of the establishment of this new steady state are examined both numerically and via the quasi-steady-state approximation. We develop approximations for the dynamics at early times in which the free virus rapidly binds to T cells, during an intermediate time scale in which the virus grows exponentially, and a third time scale on which viral growth slows and the endemically infected steady state is approached. Using the quasi-steady-state approximation the model can be simplified to two ordinary differential equations the summarize much of the dynamical behavior. We compute the level of T cells in the endemically infected state and show how that level varies with the parameters in the model. The model predicts that different viral strains, characterized by generating differing numbers of infective virions within infected T cells, can cause different amounts of T-cell depletion and generate depletion at different rates. Two versions of the model are studied. In one the source of T cells from precursors is constant, whereas in the other the source of T cells decreases with viral load, mimicking the infection and killing of T-cell precursors.(ABSTRACT TRUNCATED AT 400 WORDS)

A Model to Predict Cell-Mediated Immune Regulatory Mechanisms During Human Infection with Mycobacterium tuberculosis

A key issue for the study of tuberculosis infection (TB) is to understand why individuals infected with Mycobacterium tuberculosis experience different clinical outcomes. Elaborating the immune mechanisms that determine whether an infected individual will suffer active TB or latent infection can aid in developing treatment and prevention strategies. To better understand the dynamics of M. tuberculosis infection and immunity, we have developed a virtual human model that qualitatively and quantitatively characterizes the cellular and cytokine control network operational during TB infection. Using this model, we identify key regulatory elements in the host response. In particular, factors affecting cell functions, such as macrophage activation and bactericidal capabilities, and effector T cell functions such as cytotoxicity and cytokine production can each be determinative. The model indicates, however, that even if latency is achieved, it may come at the expense of tissue damage if the response is not properly regulated. A balance in Th1 and Th2 immune responses governed by IFN-γ, IL-10, and IL-4 facilitate this down-regulation. These results are further explored through virtual deletion and depletion experiments.

The equilibria that allow bacterial persistence in human hosts

We propose that microbes that have developed persistent relationships with human hosts have evolved cross-signalling mechanisms that permit homeostasis that conforms to Nash equilibria and, more specifically, to evolutionarily stable strategies. This implies that a group of highly diverse organisms has evolved within the changing contexts of variation in effective human population size and lifespan, shaping the equilibria achieved, and creating relationships resembling climax communities. We propose that such ecosystems contain nested communities in which equilibrium at one level contributes to homeostasis at another. The model can aid prediction of equilibrium states in the context of further change: widespread immunodeficiency, changing population densities, or extinctions.

Microenvironments in Tuberculous Granulomas Are Delineated by Distinct Populations of Macrophage Subsets and Expression of Nitric Oxide Synthase and Arginase Isoforms

Macrophages in granulomas are both antimycobacterial effector and host cell for Mycobacterium tuberculosis, yet basic aspects of macrophage diversity and function within the complex structures of granulomas remain poorly understood. To address this, we examined myeloid cell phenotypes and expression of enzymes correlated with host defense in macaque and human granulomas. Macaque granulomas had upregulated inducible and endothelial NO synthase (iNOS and eNOS) and arginase (Arg1 and Arg2) expression and enzyme activity compared with nongranulomatous tissue. Immunohistochemical analysis indicated macrophages adjacent to uninvolved normal tissue were more likely to express CD163, whereas epithelioid macrophages in regions where bacteria reside strongly expressed CD11c, CD68, and HAM56. Calprotectin-positive neutrophils were abundant in regions adjacent to caseum. iNOS, eNOS, Arg1, and Arg2 proteins were identified in macrophages and localized similarly in granulomas across species, with greater eNOS expression and ratio of iNOS/Arg1 expression in epithelioid macrophages as compared with cells in the lymphocyte cuff. iNOS, Arg1, and Arg2 expression in neutrophils was also identified. The combination of phenotypic and functional markers support that macrophages with anti-inflammatory phenotypes localized to outer regions of granulomas, whereas the inner regions were more likely to contain macrophages with proinflammatory, presumably bactericidal, phenotypes. Together, these data support the concept that granulomas have organized microenvironments that balance antimicrobial anti-inflammatory responses to limit pathology in the lungs.

A model for treatment strategy in the chemotherapy of aids

Mathematical models are developed for the chemotherapy of AIDS. The models are systems of differential equations describing the interaction of the HIV infected immune system with AZT chemotherapy. The models produce the three types of qualitative clinical behavior: an uninfected steady state, an infected steady state (latency) and a progression to AIDS state. The effect of treatment is to perturb the system from progression to AIDS back to latency. Simulation of treatment schedules is provided for the consideration of treatment regimes. The following issues of chemotherapy are addressed: (i) daily frequency of treatment, (ii) early versus late initiation of treatment and (iii) intermittent treatment with intervals of no treatment. The simulations suggest the following properties of AZT chemotherapy: (i) the daily period of treatment does not affect the outcome of the treatment, (ii) treatment should not begin until after the final decline of T cells begins (not until the T cell population falls below approximately 300 mm-3) and then, it should be administered immediately and (iii) a possible strategy for treatment which may cope with side effects and/or resistance, is to treat intermittently with chemotherapy followed by interruptions in the treatment during which either a different drug or no treatment is administered. These properties are revealed in the simulations, as the model equations incorporate AZT chemotherapy as a weakly effective treatment process. We incorporate into the model the fact that AZT treatment does not eliminate HIV, but only restrains its progress. The mathematical model, although greatly simplified as a description of an extremely complex process, offers a means to pose hypotheses concerning treatment protocols, simulate alternative strategies and guide the qualitative understanding of AIDS chemotherapy.

Systems biology of persistent infection: tuberculosis as a case study

The human immune response does an excellent job of clearing most of the pathogens that we encounter throughout our lives. However, some pathogens persist for the lifetime of the host. Despite many years of research, scientists have yet to determine the basis of persistence of most pathogens, and have therefore struggled to develop reliable prevention and treatment strategies. Systems biology provides a new and integrative tool that will help to achieve these goals. In this article, we use Mycobacterium tuberculosis as an example of how systems-biology approaches have begun to make strides in uncovering important facets of the host–pathogen interaction.

Contribution of CD8+ T Cells to Control of Mycobacterium tuberculosis Infection

Tuberculosis is the number one cause of death due to infectious disease in the world today. Understanding the dynamics of the immune response is crucial to elaborating differences between individuals who contain infection vs those who suffer active disease. Key cells in an adaptive immune response to intracellular pathogens include CD8+ T cells. Once stimulated, these cells provide a number of different effector functions, each aimed at clearing or containing the pathogen. To explore the role of CD8+ T cells in an integrative way, we synthesize both published and unpublished data to build and test a mathematical model of the immune response to Mycobacterium tuberculosis in the lung. The model is then used to perform a series of simulations mimicking experimental situations. Selective deletion of CD8+ T cell subsets suggests a differential contribution for CD8+ T cell effectors that are cytotoxic as compared with those that produce IFN-γ. We also determined the minimum levels of effector memory cells of each T cell subset (CD4+ and CD8+) in providing effective protection following vaccination.

Reevaluation of T Cell Receptor Excision Circles as a Measure of Human Recent Thymic Emigrants

The human thymus exports newly generated T cells to the periphery. As no markers have been identified for these recent thymic emigrants (RTE), it is presently impossible to measure human thymic output. T cell receptor excision circles (TREC) have been recently used to assess thymic output during both health and disease. Using a mathematical model, we quantify age-dependent changes both in the number of RTE generated per day and in TREC concentration during an 80-year lifespan. Through analyses, we demonstrate that RTE and peripheral T cell division have the same potential to affect TREC concentration at any age in healthy people. T cell death also influences TREC concentration, but to a lesser extent. During aging, our results indicate that thymic involution primarily induces an age-dependent decline in TREC concentrations within both CD4+ and CD8+ T cell populations. We further apply this model for studying TREC concentration during HIV-1 infection. Our analyses reveal that a decrease in thymic output is the major contributor to the decline in TREC concentration within CD4+ T cells, whereas both increased peripheral T cell division and decreased thymic output induce the decline in TREC concentration within CD8+ T cells. Therefore, we suggest that T cell turnover should be examined together with TREC concentration as a measure of RTE. If peripheral T cell division remains relatively unchanged, then TREC concentration indeed reflects thymic output.

Tumor Necrosis Factor Blockade in Chronic Murine Tuberculosis Enhances Granulomatous Inflammation and Disorganizes Granulomas in the Lungs

ABSTRACT Tumor necrosis factor (TNF) is a prototypic proinflammatory cytokine that contributes significantly to the development of immunopathology in various disease states. A complication of TNF blockade therapy, which is used increasingly for the treatment of chronic inflammatory diseases, is the reactivation of latent tuberculosis. This study used a low-dose aerogenic model of murine tuberculosis to analyze the effect of TNF neutralization on disease progression in mice with chronic tuberculous infections. Histological, immunohistochemical, and flow cytometric analyses of Mycobacterium tuberculosis-infected lung tissues revealed that the neutralization of TNF results in marked disorganization of the tuberculous granuloma, as demonstrated by the dissolution of the previously described B-cell-macrophage unit in granulomatous tissues as well as by increased inflammatory cell infiltration. Quantitative gene expression studies using laser capture microdissected granulomatous lung tissues revealed that TNF blockade in mice chronically infected with M. tuberculosis leads to the enhanced expression of specific proinflammatory molecules. Collectively, these studies have provided evidence suggesting that in the chronic phase of M. tuberculosis infection, TNF is essential for maintaining the structure of the tuberculous granuloma and may regulate the granulomatous response by exerting an anti-inflammatory effect through modulation of the expression of proinflammatory mediators.