### Workshop 6: Disease Models: Host-pathogen Interactions: Abstracts and Lecture Materials

CTL Action During HIV-1 is Determined via Interactions with Several Cell Types
Seema Bajaria, Department of Microbiology and Immunology, University of Michigan Medical School

During HIV-1 infection, interactions between immune cells and virus yield three distinct disease stages: high viral levels in acute infection, immune control in the chronic stage, and AIDS, when CD4+ T cells fall to extremely low levels. The immune system consists of many players that have key roles during infection. In particular, CD8+ T cells are important for killing of virally infected cells as well as inhibition of cellular infection and viral production. Activated CD8+ T cells, or cytotoxic T cells (CTLs) have unique functions during HIV-1, most of which are thought to be compromised during HIV-1 disease progression. Controversy exists regarding priming of CTLs, and our work attempts to address the dynamics occurring during HIV-1 infection. To explore the influence of CD8+ T cells as determinants in disease progression and issues relating to their priming and activation, we develop a two-compartment ordinary differential equation model describing cellular interactions that occur during HIV-1 infection. We track CD4+ T cells, CD8+ T cells, dendritic cells, infected cells, and virus, each circulating between blood and lymphatic tissues. Using parameter estimates from literature, we simulate commonly observed disease patterns. Our results indicate that CD4+ T cells as well as dendritic cells likely play a significant role in successful activation of CD8+ T cells into CTLs. Model simulations correlate with clinical data confirming a quantitative relationship between CD4+ T cells and CD8+ T-cell effectiveness.

Patterns of KIR/HLA Association in HIV and HCV Infection
Mary Carrington, Ph.D., Laboratory of Genomic Diversity, Basic Research Program, SAIC-Frederick, Inc., NCI Frederick

Natural killer (NK) cells are a unique group of lymphocytes involved in surveillance and killing of foreign or infected cells through a mechanism involving recognition of HLA molecules by an extremely diverse set of receptors on the NK cell surface. A major group of these receptors are the killer immunoglobin-like receptors (KIRs) that are encoded by genes mapping to chromosome 19q13.4. These receptors regulate inhibition and activation of NK cell responses through recognition of HLA class I molecules on target cells. Given their receptor-ligand relationship, we have hypothesized that KIR may be involved in many of the diseases for which an HLA influence has been identified. In this regard, we performed KIR genotyping in several AIDS cohorts and have shown that one activating KIR allele, KIR3DS1, in combination with the HLA-B alleles encoding its possible HLA ligand, HLA-Bw4-80Ile, results in delayed progression to AIDS, suggesting a synergistic interaction between the two loci. We have also performed KIR genotyping in a cohort of individuals with HCV infection. We show that genes encoding the inhibitory NK cell receptor KIR2DL3 and its HLA-Cw group1 ligand, which transmit relatively weak inhibitory signals, influence resolution of hepatitis C virus (HCV) infection. This effect was observed in Caucasians and African Americans with expected low infectious doses of HCV, but not in those with high-dose exposure, in whom the innate immune response is likely overwhelmed. Data from both of these infectious diseases indicate that net activation of NK cells is beneficial in the anti-viral immune response.

The Damage-Framework of Microbial Pathogenesis and the Weapon Potential of a Microbe
Arturo Casadevall, Albert Einstein College of Medicine

In recognition of the need for a general theory of microbial pathogenesis that takes into account the contributions of both the host and the microbe we have developed the 'damage-response framework' of microbial pathogenesis. The 'damage-response' framework is based on three assumptions which we believe are universally agreed: 1) that microbial pathogenesis results from the interaction of two entities which are the microbe and the host; 2) that the host-relevant outcome of the interaction is the amount of damage incurred by the host as a consequence of the host-microbe interaction; and 3) that host damage can be initiated by the host response to a microbial determinant, a microbial determinant, or both. When damage is plotted as a function of the host response, a basic parabolic curve is generated whereby damage occurs primarily in situations of weak or strong immune responses. In most host-microbe interactions occurring in the setting of weak host responses, damage is primarily microbe mediated and/or the result of limitations of a critical aspect of the host response. In host-microbe interactions occurring in the setting of strong host responses, damage is primarily host-mediated. Considering various microbial disease syndromes and assuming that damage is a function of the host response allows the classification of host microbe interactions into six basic types. Based on knowledge of the disease syndromes that occur in patients, damage-response curves can be used to classify host-microbe interactions according to the amount of host damage as a function of the host immune response; whereas plotting damage as a function of time yields the basic states of microbial pathogenesis: pathogenesis: commensalisms, colonization, persistence and disease. The damage-response framework is useful because it considers all types of host-microbe interactions as continuous in the context of potentially quantifiable parameters. Furthermore, the damage-response framework simplifies the lexicon of microbial pathogenesis, predicts new types of microbial interactions and suggests new approaches to vaccine design. Using the principles of microbial pathogenesis we have also developed a formula for the weapon potential of a microbe, which allows one to compute this parameter from the principles of microbial pathogenesis.

Work done in collaboration with Arturo Casadevall and Liise-anne Pirofski.

References

1. Casadevall, A., & Pirofski,,L. (1999). Host-pathogen interactions: redefining the basic concepts of virulence and pathogenicity. Infect. Immun., 67, 3703-3713.
2. Casadevall, A., & Pirofski, L. (2000). Host-Pathogen Interactions: The basic concepts of microbial commensalism, colonization, infection, and disease. Infect. Immun., 68, 6511-6518.
3. Casadevall, A., & Pirofski, L. (2001). Host-pathogen interactions: the attributes of virulence. J. Infect. Dis., 184, 337-344.
4. Pirofski, L., & Casadevall, A. (2002). The meaning of microbial exposure, infection, colonisation, and disease in clinical practice. Lancet Infect. Dis., 2, 628.
5. Casadevall, A., & Pirofski, L. (2003). The damage-response framework of microbial pathogenesis. Nature Microbiol. Rev., 1, 17-24.
6. Casadevall, A., & Pirofski, L. (in press). The weapon potential of a microbe. Trends Microbiol.

Why does Mycobacterium tuberculosis use multiple mechanisms to inhibit antigen presentation?
Stewart Chang, Bioinformatics Program, The University of Michigan

Sandro Cinti, Department of Infectious Diseases, University of Michigan Hospitals

Pathogenic Mechanism of HIV
Miles W. Cloyd, Ph.D., Department of Microbiology and Immunology, University of Texas Medical Branch

HIV infection causes an acquired immunodeficiency, principally because it causes depletion of CD4 lymphocytes. The mechanism by which the virus depletes these cells however, is not clearly understood. Many studies demonstrate that uninfected CD4 cells are the cells predominantly depleted. The most plausible mechanism, which is backed by in vivo data, involves the consequences of HIV contact with resting CD4 lymphocytes, which are cells which do not support replication of HIV. HIV binding to and signaling through CD4 and chemokine receptor molecules on resting CD4 lymphocytes and other cell types (which extensively occurs as the rare productively infected cells migrate among other cells within the lymphoid tissues) induces up regulation L-selection and Fas. When these resting HIV-signaled CD4 cells return to the blood, they home very rapidly back to the peripheral lymph nodes and axial bone marrow. Thus, the disappearance of CD4 cells from the blood in HIV-infected individuals appears to be due to them leaving the blood. Approximately one third of these cells that are HIV induced to home to lymph nodes are subsequently induced into apoptosis during the process of trans-endothelial migration, during which they receive secondary signals through various homing receptors. These cells are not making HIV, which explain the observation that CD4 cells not making HIV are the predominate cells dying in the lymph nodes of HIV+ subjects. Mathematical modeling of this process yielded an accurate picture of the rate of depletion of CD4 cells over an eight to ten year period. This is unique mechanism of pathogenesis for a virus, and if correct, leads to the possibility that HIV might not cause depletion of CD4 lymphocytes if it used some other receptor to infect cells.

Victor DiRita, Department of Microbiology and Immunology, University of Michigan Medical School

The immune response to Mycobacterium tuberculosis is dynamic and evolves from primary to chronic infection
JoAnne L. Flynn, Ph.D. Department of Molecular Genetics and Biochemistry, University of Pittsburgh School of Medicine

The immune response to Mycobacterium tuberculosis was studied in a murine model, focusing on the lungs and lung draining lymph nodes, over the course of 7 months. Bacterial numbers peak by week 4 post-infection and are then maintained at apparently steady levels in the lungs. The immune response, as measured by T cell infiltration and cytokine production, also peaks at 4 weeks post-infection, and then contracts. However, there are additional bursts of activation of the T cell response in the lungs over the next 6 months. Proliferation and apoptosis were also followed. The immune response may respond to small changes in bacterial numbers within the lungs by increasing to try to prevent reactivation. The effector functions of T cells were also studied. CD4 T cells are the primary producers of IFN-gamma early in infection, while CD8 T cells are cytotoxic for the first 6 weeks. In chronic infection, CD8 T cells are no longer cytotoxic, but begin to produce substantial amounts of IFN-g. The mechanisms responsible for modulation of CD8 T cell effector function remain unknown.

Modeling the dynamics of HIV disease: simpler is not always better
Zvi Grossman, Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel-Aviv University, Israel

The ability of simple mathematical models of cellular and viral dynamics in HIV infected people, and in SIV infected monkeys, to fit available kinetic data has often been over-interpreted. A common pitfall is a failure to properly differentiate between systemic and microscopic parameters, overlooking issues such as heterogeneity and non-uniformity, spatial as well as temporal, of the cellular and molecular constituents at the microscopic level. Another common pitfall is fitting a model to a limited set of data rather than to all the relevant available data. It is common also to make unjustified extrapolations from observed correlations to cause-and-effect relationships.

I shall overview the major outstanding issues in the area of HIV-infection dynamics and the attempts that have been made, with various degrees of success and acceptance, to use mathematical and conceptual modeling to help resolve these issues

Mechanisms of chronic fungal infection: the interplay between innate and adaptive immunity
Amy C. Herring, PhD, University of Michigan

Host defense against fungal infection is dependent on the interplay between the cells and early signals of innate immunity and T cells. The development of T1 cell-mediated immunity is essential for clearance of fungal pathogens. During states of chronic infection, the host response is often described as unresponsive, anergic, or dysregulated. However, the immunologic mechanisms underlying chronic fungal infections in otherwise healthy individuals remain unknown. We have developed several in vivo animal models to study the chronicity of Cryptococcus neoformans infection in the lung. In our first model, neutralization of TNF at the time of infection results in non-protective immunity to C. neoformans. The immune deviation induced by a transient TNF deficiency results in chronic inflammation and fungal infection. Our second model involves immunization of animals with C. neoformans-pulsed immature dendritic cells (imDC) prior to the pulmonary infection. imDC-recipient mice fail to clear the cryptococcal infection from the lungs and develop a non-protective immune response. Our studies suggest that interruption of critical early signals may underlie susceptibility to chronic fungal infection in immunocompetent individuals. We believe the timing of cytokine signals is more important than the simple presence of a cytokine during infection in determining whether a protective immune response develops. Our findings also demonstrate that immature dendritic cells pulsed with fungal antigen can promote non-protective immunity resulting in chronic pulmonary infection. The delayed induction of key early mediators due to virulence factors, immunotherapy, or secondary infections may promote fungal infection by inducing an ineffective cellular immune response (T2 vs. T1) and/or by immature dendritic cell induction of regulatory T cells.

A mathematial foundation for PathSim, a rule-based spatial model of immune response to viral pathogens
Reinhard Laubenbacher, Virginia Bioinformatics Institute, Virginia Tech

The focus of this talk is a 3-dimensional, stochastic, rule-based model of immune response to viral pathogens. In its present form, the PathSim model focuses on Epstein-Barr virus (EBV) infection of the Waldeyer's tonsilar ring. A multi-scale anatomical viewer helps to visualize infection model dynamics. Rule-based models are well-suited for the simulation of dynamics resulting from a large number of spatially distributed, interacting entities, such as virions and immune cells. One of their shortcomings, however, is the relative lack of mathematical tools available to analyze model dynamics and, in particular, to formulate and solve optimal control problems.

We will describe a research program to develop a mathematical foundation for PathSim. It's goal is to approximate the stochastic simulation by a deterministic model, represented as a discrete dynamical system over a finite field. Optimal control of such systems has been studied in several engineering contexts and is also applicable here. As an illustration, we discuss an optimal control theory problem for polynomial systems in the context of in vitro virus competition.

Agent-Based Simulation of Host-Virus Interactions: Application to Epstein-Barr Virus
Reinhard Laubenbacher, Virginia Bioinformatics Institute, Virginia Tech

PathSim (PathogenSimulation) is a systems biology modeling tool designed for the exploration of human host responses to viral pathogens. It is based on two key components, a multi-scale anatomical viewer and an agent-based simulation engine. Although our engine will eventually be generic, our first implementation involves Epstein-Barr virus (EBV) infection of the Waldeyer's tonsilar ring. In this model, the anatomy is represented as a collection of tissues, each with its own properties that determine both 3D visual rendering and agent behavior during simulation. Agents represent the active and potentially mobile elements within the simulation such as virions (EBV) and immune cells (B and T lymphocytes). Agents are localized at mesh points representing a small region within a tissue. Each mesh point is assigned to a class that further refines its properties. Vertices that form a 3-D mesh controlling the local motion of agents connect the mesh points. In order to account for agent transport via blood and lymph fluids a simple model of the circulatory and lymphatic systems is also represented in the simulation.

The simulation engine is constructed as a discrete-time, cellular automaton. At each time step agent motion, activation, aging, and interaction are controlled by a set of stochastic state transition rules. These rules are based on our current understanding of host responses to EBV. The simulation results to date demonstrate qualitative agreement with data reported in the literature for the acute phase of EBV infection, acute infectious mononucleosis. A comparison to the standard model is included.

Work done in collaboration with J. McGee, K. Lee, R. Laubenbacher, and K.A. Duca.

Interactive Visualization of Pathism Simulation Output Using Information-Rich Virtual Environments
Reinhard Laubenbacher, Virginia Bioinformatics Institute, Virginia Tech

In the life sciences, the development of rigorous models and databases of biological phenomena provides major benefits for biological research, drug design, and education. A grand goal in biology is to produce integrated information-rich biological databases that capture the complexity of reality. A common class of such databases can be characterized as integrating diverse information including: spatial representations of physical systems and phenomena, abstract data such as gene expression data and annotations, temporal dimension for time series, multiple levels of scale (from anatomical to cellular to molecular), and multiple runs of simulation output, and experimental results.

However, the current major shortcoming is the lack of effective user interfaces and visualizations for information-rich databases that enable biologists to gain insight. The true utility of the databases will come to fruition when biologists are able to explore and navigate them and relate effects between space, abstract data, and time across levels of scale. Current virtual environments and information visualizations lack the usability and support for such complex information-rich databases.

PathSim is an example of an information-rich model with associated databases. The main goal of PathSim is to model a variety of viral agents in human and animal hosts, from initial infection to viral clearance. PathSim allows an end-user to explore the physiology and dynamics of infections and immune system response. As an interface to this system, we are constructing and evaluating information-rich virtual environments (IRVEs) for the PathSim project. This interface framework can also be applied to other similar information-rich databases in the life sciences that share these characteristics.

An IRVE combines the capabilities of virtual environments and information visualization to support integrated exploration of both spatial and embedded abstract data. Biologists can view the simulated physical structures of the model in a 3D virtual environment, interact with visually embedded abstract data, navigate across levels of scale, choose data for display, and control simulation run management all within an integrated environment. For example, a user might decide to examine the effect of titer on the course of infection. Within the IRVE, the user deposits virions in the locations to be infected. After the simulation commences, the user revisits the IRVE to view signaling events initiated by virus deposition at the molecular level. Later, the user examines how fast the virus is spreading, killing cells, or recruiting immune cells to the vicinity. All activities are viewable in the virtual environment, with interactive links and data export to a suite of analytic tools also possible.

This work is discovering critical new methods for display and interaction in multi-scale IRVEs that are usable and useful for biologists. The system user interface operates on a wide range of hardware, from standard desktop displays to high-performance immersive CAVEs. The system will eventually be public and open for use in other applications.

Work done in collaboration with N.F. Polys, D. Bowman, K.A. Duca, R. Laubenbacher, and C. North.

Immune Response to HTLV-I Infection of T Cells and Backward Bifurcation
Michael Y. Li, Department of Mathematical and Statistical Sciences, University of Alberta

Human T-cell Leukemia Virus Type I (HTLV-I) is a retrovirus that preferentially infects CD 4+ helper T cells. In contrast to the notorious HIV-I, HTLV-I infects mainly through cell-to-cell contact. While reverse transcription process adopted by retroviruses has a high mutation rate, the HTLV-I infection has a remarkably low genetic variability. To explain this phenomenon, immunologists hypothesized that the HTLV-I infection has two modes/stages of transmission: horizontal transmission through cell-to-cell contact, and a vertical transmission thorough mitotic division of infected cells. We propose a mathematical model to verify this hypothesis. Among interesting dynamical behaviours we show the occurrence of a backward bifurcation. This is a joint work with Horacio Gomez-Acevedo.

Gene Expression Analysis of Host-Defense in Arabidopsis
Jun Lu, Center for Bioinformatics and Computational Biology, Duke University

This talk is about the mechanisms of plant host defense in Arabidopsis. I will give a background introduction on host defense systems in plants, and in particular, systematic acquired resistance (SAR). The activation of SAR by avirulent pathogens involves up-regulation of many pathogenesis-related genes, which further confer resistance to a broad spectrum of other pathogens. We use microarrays to identify genes involved in SAR, and to search for expression patterns that are distinct between virulent and avirulent pathogen infection.

Work done in collaboration with Jun Lu, John Tomfohr, Natalie Weaver, Dong Wang, Xiannian Dong, and Thomas Kepler.

Dendritic Cell Trafficking and Antigen Presentation in the Human Immune Response to Mycobacterium Tuberculosis
Simeone Marino, Department of Microbiology and Immunology, University of Michigan Medical School

Mycobacterium tuberculosis (Mtb) is an extraordinarily successful human pathogen, one of the major causes of death by infectious disease worldwide. A key issue for the study of tuberculosis is to understand why individuals infected with Mtb experience different clinical outcomes. To better understand the dynamics of Mtb infection and immunity, we coupled non-human primate (NHP) experiments with a mathematical model we previously developed that qualitatively and quantitatively captures important processes of cellular priming and activation. These processes occur between the lung and the nearest draining lymph node (DLN) where the key cells mediating this process are the dendritic cells (DC). We are able to reproduce typical disease progression scenarios including primary infection, latency or clearance.

The NHP experiments consist of bacteria and cell numbers from tissues of seventeen adult cynomolgus macaques (Macacca fascicularis) that were infected with M. tuberculosis strain Erdman (~25 CFU/animal via bronchoscope).

The main result of this work is that delays in either DC migration to the DLN or T-cell trafficking to the site of infection can alter the outcome of Mtb infection, defining progression to primary disease or latent infection and reactivated tuberculosis. Our results also support the idea that the development of a new generation of treatment against Mtb should optimally elicit a fast DC turnover at the site of infection, as well as strong activation of DCs for maximal antigen presentation and production of key cytokines. This will induce the most protective T cell response.

Simeone Marino, Santosh Pawar, Craig L. Fuller, Todd A. Reinhart, JoAnne L. Flynn, and Denise E. Kirschner.

Two-Photon Imaging of Lymphocyte Trafficking and Antigen Presentation
Mark J. Miller, Departments of Physiology and Biophysics, University of California, Irvine

The adaptive immune response is initiated by physical contact between antigen-bearing dendritic cells (DCs) and antigen-specific naive T cells. These contacts occur deep within the highly specialized anatomy of secondary lymphoid tissues, such as the lymph nodes. A fundamental description of T cell priming dynamics in vivo has relevance to vaccine development and will advance our understanding of how immune responses are regulated during infection, cancer, and autoimmunity. Using two-photon microscopy we resolved the real-time behavior of endogenous DCs and CD4+ T cells in lymph node explants during a robust T cell response. Our results suggest that naive CD4+ T cells encounter DCs at random and not by following chemokine gradients emitted by DCs. In contrast, DCs enhance T cell repertoire scanning by vigorously deploying long agile dendrites, thereby increasing the available surface area for T cell interactions. Initial cognate T cell/DC interactions are remarkably dynamic and often involve serial contacts with DCs. As T cells activate they progress through several distinct phases of behavior from relatively immotile clusters containing a few cells to large groups of cells displaying dynamic swarming behavior. Quantitative analysis of our imaging data suggests that random motility is a natural property of lymphocytes and that stochastic, multi-agent based models may best describe lymphocyte trafficking and behavior in situ.

Work done in collaboration with Mark J. Miller, Ian Parker, and Michael D. Cahalan.

Bacterial and host response to intracellular infection
Mary O'Riordan, Department of Microbiology and Immunology, University of Michigan School of Medicine

Some remarks on backward bifurcations and the role of coinfection in multi-disease dynamics
Sergei Pilyugin, University of Florida

Host/Pathogen Interactions at Multiple Levels during HIV-1 Infection and AIDS
Todd A. Reinhart, Sc.D.,Department of Infectious Diseases & Microbiology, Graduate School of Public Health, University of Pittsburgh

The interactions between HIV-1 and the host occur at multiple levels and have generally been studied at all such levels. This spectrum spans from the associations of individual proteins, through cell/cell interactions, on up to the interactions of infected individuals within populations. Increased understanding of such interactions has led to intervention strategies - implemented or proposed - at each level including such diverse strategies as viral reverse transcriptase inhibitors and community outreach programs. Our interests have focused on the effects of HIV-1 infection on host function at the cellular and tissue levels, using infection of nonhuman primates with the related simian immunodeficiency virus (SIV) as a model system. Our ultimate goal is to identify new targets for therapeutic intervention, and we have approached this issue in two major ways. First, we have studied the effects of expression of a pathogenesis-associated viral protein named "Nef" on cell surface protein expression. Nef is not essential for viral replication in vitro, but contributes to high-level viral replication in vivo and the subsequent development of AIDS, although it has no known enzymatic function. In searching for cellular binding partners of Nef, we identified a critical component of the T cell signaling complex, TCR , as a Nef partner. SIV Nef bound TCR on two independent sites and reduced the surface expression levels of the TCR signaling complex, thereby likely inhibiting the ability of an infected cell to exert its function as an immune cell. Second, we have studied the effects of in vivo infection with SIV on the immune environments within lymphoid tissues. We have used gene expression profiling approaches such as cDNA arrays, in situ hybridization, and real-time RT-PCR to identify genes differentially expressed in tissues from rhesus macaques infected with pathogenic SIV. These approaches have revealed a number of alterations to immune environments in lymphoid, lung, and intestinal tissues during the progression of SIV-associated disease. The changes we have identified and which are likely to be important in this disease include: (1) up-regulation of chemokines, which control constitutive and inflammatory cell trafficking; (2) altered tissue compositions of dendritic cells, which are potent antigen presenting cells controlling the nature and strength of immune responses; and (3) up-regulation of members of a group of receptors within the innate immune system, Toll-like receptors, which control rapidly-induced inflammatory responses. These approaches have their respective strengths and limitations, but combined together can provide insight into the roles that these alterations to immune function play in the progression of disease, and thereby identify targets for new therapeutic intervention strategies.

Funding Sources: National Institutes of Health; National Heart, Lung, and Blood Institute.

Understanding control mechanisms of TB granuloma formation with an agent-based model
Jose Segovia-Juarez, Department of Microbiology and Immunology, University of Michigan Medical School

Avoiding Cytolysis: Evasion, Resistance and Repair
Jaroslav Stark, Department of Mathematics, Imperial College London

Cytotoxic killing of target cells by CD8 T cells and natural killer cells is one of the main mechanisms for the immune control of intracellular pathogens and tumours. The basis for this cell killing is the controlled release of perforin and granzyme granules at the immune cell-target cell interface, which together serve to puncture the cell membrane and activate the apoptotic program in the target cell. Both pathogens and tumours can sometimes evolve to escape immune killing. Research in this area has focused on mechanisms for evasion. However, an al-ternative strategy for a target cell is to boost defences rather than (or in addition to) avoiding detection. This has recently been highlighted by the discovery that certain tumour cells express a specific stoichiometric inhibitor of granzyme B known as PI-9. A variety of other cell types also express PI-9, including endothelial, mesothelial, and dendritic cells, as well as cytotoxic T cells themselves. We use a simple mathematical model to provide insight into the different roles of evasion and resistance in the evolution of escape mechanisms to avoid cytotoxicity. Finally, we suggest experiments to validate the hypotheses of the model, and discuss the implications for immunotherapy against intracellular pathogens and tumours.

Work done in collaboration with Jaroslav Stark, Cliburn Chan, Andrew J. T. George.

Optimal Control of Disease Processes
Robert F. Stengel, Princeton University, School of Engineering and Applied Science

Mathematical modeling of immune system response to pathogenic assault can greatly aid the management of infected individuals, but considerable development must occur before the biology and mathematics can be merged to provide tools for treatment. Given a model for a disease process, it remains to be seen how established methods of control system design can suggest therapeutic protocols that could be applied in a clinical setting.

We examine means for specifying optimal therapeutic protocols given a satisfactory immune system model. For illustration, the presentation is based on three models that represent humoral response to extracellular bacteria, cellular response to the human-immunodeficiency virus (HIV), and control of cancer by anti-tumor viruses. Therapy is based upon both open- and closed-loop optimal control strategies that take into account uncertainty in system models, measurements, and environment. We note that though observability of the dynamic state is a critical issue for closed-loop control, effective control can be provided by incomplete or "noisy" measurements. Immune system models possess classical attributes of dynamic stability or instability; for example, our humoral response model is stable, while the HIV model is not. In either case, effective therapies can be specified, although the HIV infection is never cured, requiring continued treatment to keep the condition in remission.

Assessment of Treatment Effects on HIV Pathogenesis Under Haart by State Space Models
Wai-Yuan Tan, Department of Mathematical Sciences, The University of Memphis and St. Jude Children's Research Hospital

To monitor the progression of therapy in HIV-infected individuals treated with anti-viral drugs, it is critical to estimate and assess the efficiency of the drugs and to estimate the number of infectious and non-infectious HIV under treatment. In this paper we have developed a method to estimate these parameters and the state variables to assess effects of drugs on HIV pathogenesis. As an illustration, we have applied the method to some clinical and laboratory data of an AIDS patient treated with various anti-viral drugs. For this individual, we have estimated the numbers of infectious HIV virus and non-infectious HIV virus per $ml$ of blood over time, and the rates for measuring effects of drugs. These estimates show that the HAART protocol has effectively controlled the number of infectious HIV virus to below $400/ml$ copies although the total number of HIV copies was very high in some intervals.

Work done in collaboration with Wai-Yuan Tan, Ping Zhang, Xiao-Ping Xiong, and Pat Flynn.

Noncytolytic CD8+ T cell-Mediated Suppression and HIV-1 Escape
Georgia D. Tomaras, Ph.D. Department of Experimental Surgery, Duke University

CD8+ T cells play an important role in controlling virus replication in both acute and chronic HIV infection. There is substantial interest in further deciphering the contributions of noncytolytic CD8+ T cells in reducing virus replication as part of the host's protective immune response. It is commonly known that HIV can escape potent immune pressures such as cytotoxic T lymphocytes and neutralizing antibodies. It has recently become evident that virus can escape from noncytolytic suppression illustrating the ability of this antiviral activity to exert significant immune pressure in vivo. The molecules involved in this antiviral response and their precise mechanisms remain elusive. Studies of HIV variants harboring escape mutations are likely to provide new insights into the identities of noncytolytic CD8+ suppression.

Pathway-level View of Gene Expression
John Tomfohr, Duke University

Gene expression microarray experiments provide a snapshot of the expression levels of thousands of genes in a sample. The challenge is to interpret this data--for example, to identify key genes associated with some condition and to form hypotheses about their relation to that condition. While a large amount of work has focused on identifying significantly differently expressed individual genes, it is sometimes valuable to look at expression data at the level of groups of functionally related genes, such as those belonging to the same pathway or complex. This can reveal higher level features not as apparent from the variations in the individual genes alone. We present an approach to analyzing gene expression at a multi-gene level using a collection of about 400 predefined pathways and complexes. Gene expression levels are translated into pathway expression levels after a screening process that removes pathways for which the data show weak evidence of correlation between member genes. The method will be demonstrated using expression profiles from a study on diabetes and another on the immune response to inhaled LPS in mice.

Work done in collaboration with John Tomfohr, Jun Lu, and Thomas B. Kepler.

A Mathematical Approach to Modeling Structure and Conformation of Bacterial Consortia
Jorge X. Velasco-Hernandez, Mathematics Department, Instituto Mexicano del Petroleo

I present work being developed at the IMP on three aspects of biofilm formation: spatial structure and its relation to coexistence of multispecies biofilms, the role of mutations in the exitence of colonial biofilms and the interaction between biofilms and the fluid environment in which they thrive. The results are preliminary and comments and criticisms are very wellcome.

The Role of Quorum Sensing in Bacterial Wound Infections
John Ward, Department of Mathematical Sciences, Loughborough University

Many species of bacteria incorporate a sophisticated cell-cell signalling mechanism, called quorum sensing (QS), to regulate their behaviour in a cell density dependent manner. Whilst infecting an open wound or burn, the opportunistic pathogen {\it Pseudomonas aeruginosa} employs QS to initially subdue its virulence characteristics, "fooling" the immune response, whilst the population multiplies. Hence, when they do become virulent their greater numbers are more likely to overwhelm the immune system, leading to septicaemia and perhaps death. Here, the QS process involves the dimerising of a cell-signalling molecule (QSM) and a cognate protein, which enhances both QSM and virulence factor production; consequently, up regulation of virulence factor production is induced at high QSM concentrations, reflecting high population density.

We present a spatio-temporal model of bacterial growth and QS in an infected burn wound situation incorporating the known microbiology; the QS core of the model will be discussed in light of experimental work using liquid cultures, from which parameter estimates are obtained. Using asymptotic and numerical techniques the conflicting effects of QSM production in the infected regions and loss (via diffusion and degradation in the surrounding tissues) are studied. Regimes in which substantial up-regulation (and therefore virulence) can occur and on what timescale are determined in terms of the model parameters. Therapeutic implications will also be discussed.

Work done in collaboration with Adrian Koerber, John King, Paul Williams, Julie Croft, and Liz Sockett.

Stochastic Fluctuations in HIV-1 Tat Transactivation May Lead to Proviral Latency
Leor S. Weinberger, University of California, Berkeley

The human immunodeficiency virus type I (HIV-1) proviral latent reservoir is considered the most significant obstacle facing HIV-1 eradication from the patient. The exact mechanism by which this reservoir is established remains a topic of much research. Bacteriophage l is known to utilize stochastic molecular fluctuations (SMF) in viral protein levels (C1 and Cro) to influence its lifecycle decision between lytic and lysogenic states and recently SMF in yeast transcriptional and translational pathways have been observed to lead to clonal population variability, even in the absence of chromatin remodeling. SMF have yet to be demonstrated or implicated in higher eukaryotes or mammalian systems. Here we present the first evidence that an HIV-1 positive feedback regulatory pathway, implicated in the establishment of proviral latency (the HIV-1 Tat transactivation loop) may utilize such stochastic molecular fluctuations.

Work done in collaboration with Leor S. Weinberger, Adam P. Arkin, and David V. Schaffer

Patterns of Immunodominance in CMV Infection
Dominik Wodarz, University of California, Irvine

I will present a mathematical model which describes the interactions between CMV infection and the immune systen. The model aims to explain the phenomenon of "CTL inflation" which has been obseved in experimental data from mice infected with CMV.

Lack of Good Correlation of Serum CC-chemokine Levels with HIV-1 Disease Stage and Response to Treatment
Ping Ye, Department of Microbiology and Immunology, The University of Michigan Medical School

Three CC-chemokines, MIP-1α (CCL3), MIP-1β (CCL4), and RANTES (CCL5) are natural ligands for the HIV-1 co-receptor CCR5. To determine correlations between CC-chemokines and HIV-1 disease stage or response to treatment, we examined serum levels of MIP-1α, MIP-1β, and RANTES in sixty HIV-1 infected patients during eighteen months on highly active anti-retroviral therapy (HAART). Our results demonstrate that serum levels of MIP-1α and RANTES were elevated in HIV-1 infected individ-uals as compared with healthy controls. No significant difference has been found between four clinical stages of HIV-1 infection in serum levels of three CC-chemokines. Longitudinal HAART analyses re-veal there was a pronounced decline in serum MIP-1α levels over time. No difference in this decline was exhibited between HAART responders and non-responders. These findings indicate that production of MIP-1α and RANTES changes during HIV-1 infection and treatment; however, serum levels of CC-chemokines should not be used as a biomarker for HIV-1 disease stage or response to treatment.

Ping Ye, Powel Kazanjian, Steven L. Kunkel, and Denise E. Kirschner.

#### Poster Presentations

Predicting differential responses to structured treatment interruptions during HAART
Seema Bajaria, Department of Microbiology and Immunology, University of Michigan Medical School

Highly active antiretroviral therapy (HAART) has been used clinically in various administration schemes for several years. However, due to the development of drug resistance, evolution of viral strains, serious side effects, and poor patient compliance, the combination of drugs used in HAART fails to effectively contain virus long term in a high proportion of patients. Our group and others have suggested a change to the usual regimen of continuous HAART through structured treatment interruptions (STIs). STIs may provide similar clinical benefits as continuous treatment such as reduced viral loads and reestablishment of CD4+ T cells while allowing patients drug holidays. We explore the use of STIs using a previously published model that accurately represents CD4+ T-cell counts and viral loads during both untreated HIV-1 infection and HAART therapy. We simulate the effects of different STI regimens including weekly and monthly interruptions together with variations in treatment initiation time. We predict that differential responses to STIs as observed in conflicting clinical trial data are impacted by the duration of the interruption, stage of infection at initiation of treatment, strength of the immune system in suppressing virus, or pre-therapy CD4+ T-cell count or virus load. Our results indicate that dynamics occurring below the limit of detection (LOD) are influenced by these factors, and contribute to reemergence or suppression of virus during interruptions. Simulations predict that short-term viral suppression with varying interruption strategies does not guarantee long-term clinical benefit.

Growth on 2 Nutrients in the Chemostat
Patrick De Leenheer, DIMACS/Rutgers

We will analyze the dynamics of a single species growing on 2 substrates in a chemostat. It is assumed that uptake and growth are decoupled. The main result is that if a nontrivial steady state exists, it is globally asymptotically stable. Since our analysis requires the use of results from the theory of monotone systems, it is appropriate to review some of its features.

Infrastructure for Host-Immune Response Modeling
Judy Quong, Georgetown University, Lombardi Cancer Center

We have developed a systems toolbox to describe the network interactions of immune resopnse. This includes a database to store descriptions of biomolecules (genes, proteins, metabolites) and pathways invovled in pathogen-induced host response. Also included is a Java-based set of tools that utilizes fuzzy logic, genetic algorithsma, and statistical tools such as singular value decomposition and principal component analysis. These components are an integral part of a 'systems biology' infrastructure to study the network interactions invovled in the host immune response.

Work done in collaboration with Judy N. Quong, Pauline Gu, James R. Kercher, Carl Melius, Bahrad Sokhansanj, and Andrew A. Quong.

The Balance of Activation, Killing Mechanisms and Iron Homeostasis in Determining M. Tuberculosis Survival within Macrophages
Christian Ray, Microbiology and Immunology, University of Michigan

We have developed a mathematical model to predict the outcome of macrophage infection with Mycobacterium tuberculosis relative to the biochemical state of the macrophage. The model consists of two physical scales. One captures biochemical macrophage activation of iNOS-derived nitric oxide coupled to regulation of intracellular iron. The second physical level represents the intracellular population of mycobacteria responsive to, and influencing, the macrophage state. Using this dual-level model we examine context-dependent responses to different macrophage activation states. We applied statistical sensitivity analyses to elucidate important model features in each context. Controlled comparisons between wild-type and various knockout cases allowed us to test the influence of particular interactions on bacterial load. We draw conclusions about the nature of the interaction between M. tuberculosis and its host macrophage with these results and suggest future experiments to test our predictions.

Systems Modeling of Host-Pathogen Interaction Functional Genomics
Bahrad A. Sokhansanj, Chemical, Biological, and Nuclear Sciences Division, Lawrence Livermore National Laboratory, University of California

One of the most important challenges of interpreting large genomic and proteomic data sets is developing pathway and gene network regulation models based on integrating multiple data sets from different experimental platforms and taken under different experimental conditions. This is particularly important for bacterial pathogenesis, which involves the regulation a large number of complex cellular processes, such as toxin production, metabolism, and DNA repair among many others. Using the "informed systems" approach, multiple pathway model hypotheses based on past experiments inform the interpretation of new data sets, which are used to identify the most plausible hypotheses and integrate them to produce new models for the complex biological system being studied. We propose a linear fuzzy rule-based modeling framework, which has advantages of scalability, resolution, and tolerance for poorly quantitative data over conventional fuzzy logic, Boolean, or differential equation-based methods. For the purpose of demonstrating our approach, we are developing a model based on published microarray data for Mycoplasma tuberculosis expression within the mouse (Talaat, et al., PNAS, 101, 4602-4607, 2004), integrating it with other data for M. tuberculosis gene expression measured under different experimental conditions outside the host.