Rustom Antia
Modelling Immune memory and the turnover of memory cells.
We will develop and test a theoretical framework to describe the longevity of immune memory, and very recent experimental tests of the assumptions of this theoretical framework.
A Tale of Two Futures: HIV and Antiretroviral Therapy in San Francisco
S. M. Blower, H. B. Gershengorn, R. M. Grant Science, 287: 650 - 654 (2000).
The effect of antiretroviral therapy (ART) in preventing human immunodeficiency virus (HIV) infections and averting acquired immunodeficiency syndrome (AIDS) deaths in the San Francisco gay community over the next 10 years was predicted. A transmission model was coupled with a statistical approach that enabled inclusion of a high degree of uncertainty in the potential treatment effects of ART (in terms of infectivity and survival), increase in risky behavior, and rate of emergence of drug resistance. Increasing the usage of ART in San Francisco would decrease the AIDS death rate and could substantially reduce the incidence rate.
Lindsay Cowell
The nucleotide-replacement spectrum under somatic hypermutation exhibits microsequence dependence that is strand-symmetric and distinct from that under germline mutation.
Somatic mutation is a fundamental component of acquired immunity. Although its molecular basis remains undetermined, the sequence specificity with which mutations are introduced has provided clues to the mechanism. We have analyzed data representing over 1700 unselected mutations in V-gene introns and non-productively rearranged V genes to identify the sequence specificity of the mutation spectrum---the distribution of resultant mucleotides. In other words, we sought to determine what effects the neighboring bases have on what a given base mutates to. We find that both neighboring bases have a significant effect on the mutation spectrum. Their influences are complicated but much of the effect can be characterized as enhancing homogeneity of the mutated DNA sequence. In contrast to what has been reported for the sequence specificity of the ``targeting'' mechanism, that of the spectrum is notably symmetric under complementation, indicating little if any strand bias. We compared the spectrum to that found previously for germline mutations as revealed by analyzing pseudogene sequences. We find that the influences of nearest neighbors are quite different in the two datasets. Altogether, our findings suggest that the mechanism of somatic hypermutation is complex, involving two or more stages: introduction of mis-pairs and their subsequent resolution, each with distinct sequence specificity and strand bias.
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Vitaly Ganusov
The effect of heterogeneity on the evolution of parasite virulence
Microparasites generally evolve in response to the immune system of vertebrate hosts. Earlier models have examined parasite evolution by determining the growth rate of the parasite at which its transmission is maximized. These earlier studies considered this problem for acute infections of hosts with a single parasite strain (which cannot escape from the immune response), and assumed that there was no heterogeneity in the parameters describing the interaction of the parasite and the host. In this case transmission was maximized for the parasite with an intermediate rate of growth $r$ that corresponds to the parasite being just controlled by the immune response prior to its reaching a lethal density $D$. We extend the earlier work by examining the influence of heterogeneity in host parameters on the optimal growth rate of the parasite and its virulence. Our results suggest that: (i) an increase in heterogeneity initially leads to the decrease in the optimal growth rate of the parasite with subsequent increase as the variance is elevated to very high levels, (ii) the total transmission of the pathogen from an infected host decreases with an increase of the heterogeneity, and (iii) that the virulence as measured by the case mortality rate (a fraction of hosts who die when they are exposed to the pathogen) equals zero in homogeneous population and increases with increasing heterogeneity.
Byron Goldstein
Modeling Peptide-MHC Complex/T Cell Receptor Dynamics in the Immunological Synapse
The activation of a T cell begins with the formation of an ``immunological synapse,'' a region of contact between a T cell and an antigen presenting cell (APC). Shortly after its formation, two well-defined regions within the immunological synapse are observed, an inner region where T cell receptors (TCR) on the T cell and peptide-MHC complexes on the APC interact and an outer annulus where adhesion bonds collect. We present a model of the dynamics of TCR-peptide-MHC complex interactions in the contact area, and use the model to assess the roles of serial engagement, TCR oligomerization, and kinetic proofreading in T cell activation.
Patient Specificity and the difference in the half-life of productively infected T-cells.
Patrick W. Nelson, John E. Mittler, and Alan S. Perelson
Fits of mathematical models for HIV drug treatment dynamics to the decline in HIV-1 RNA following antiretroviral therapies have yielded estimates for the life span of productively infected cells of about 1.5 days. Subsequent models have extended the analysis to account for imperfect viral suppression and the presence of an intracellular delay (the eclipse phase of the viral life cycle). The interactions between these factors, however, have not previously been explored. Here we show that if drug is not completely efficacious that the addition of an intracellular delay will decrease the estimated lifespan of virus producing cells (while increasing the expected lifespan of a cell that has just been infected). When we fit this model to published data on the decline of HIV-1 RNA following treatment with the protease inhibitor ritonavir, the estimated death rate of virus producing cells increased from 0.5 day$^{-1}$ to 0.89 $^{-1}$ day as the efficacy parameter was reduced from 100\% to 80\%. For efficacies in this range, the estimated half-lives of the virus producing stage range from 0.8 to 1.4 days, while the estimated viral generation times range from 2.1 to 3.3 days.
Sergei Pilyugin
Estimating birth and death of immune cell populations using cell cycle based models.
We use age structured cell cycle models to estimate birth/death rates in a population of immune cells from the kinetics of age distribution of cells in the population. Our model generalizes the approach of Smith and Martin in using a two stage cell cycle model to interprete the FLM curves. We developed this model to quantify the CFSE dye dilution assays for a marked population of immune cells.
Effect of HAART on Incidence of HIV-Associated Nephropathy
Elissa J. Schwartz, Jonathan A. Winston, and Paul E. Klotman
Mount Sinai Medical Center, New York, NY
HIV-Associated Nephropathy (HIV AN) is the third leading cause of end stage renal disease in Blacks between the ages of 20-64. The disease is a late manifestation of HIV-1 infection. After the onset of HIV AN, patients progress rapidly to renal failure and survive only 1-2 years. Treatments for HIV AN include angiotensin-converting enzyme inhibitors or antiretroviral therapy, but controlled studies to determine the optimal therapy have been difficult due to the small number of patients and the necessity for a biopsy to confirm the HIV AN diagnosis. We sought to gain insight into the best therapeutic regimen from the epidemiology of HIV AN. Since the introduction of highly active antiretroviral therapy (HAART) in 1995, AIDS mortality has decreased and the progression to AIDS has declined. The net result has been a slowing of the overall growth rate of AIDS. Each year since 1995, the number of new cases of HIV AN has also decreased. This suggests that HAART may have reduced the incidence of HIV AN as well. Using a simple mathematical model of HIV AN population dynamics, we examined whether the introduction of HAART explains the decrease in HIV AN incidence. The results of the model suggest that HAART caused both a reduction in the AIDS growth rate and a decrease in the incidence of HIV AN in AIDS patients. This indicates that HAART is likely to be effective therapy for patients at risk for the development of HIV AN.
Effect of Thymectomy on Human Peripheral T Cell Pools
G. Sempowski, J. Thomasch, M. Gooding, L. Hale, L. Edwards, E. Ciafaloni, D. Sanders, J. Massey, D. Douek, R. Koup and B. Haynes.
The human thymus is required for establishment of the T cell pool in fetal life, but postnatal thymectomy does not lead to immune deficiency in humans. We have studied the effect of thymectomy on peripheral blood (PB) T cell pool in 10 patients undergoing thymectomy for myasthenia gravis(MG) using surface marker analysis for naive (CD45RA+,CD62L+) and memory (CD45R0+) T cells and signal joint T cell receptor excision circle (sjTREC) analysis. We found thymectomy decreased CD4 and CD8 sjTREC and naive T cell levels in 5/10 patients, all of whom had active thymopoiesis in their thymus at the time of thymectomy. In contrast, of 5 patients in whom sjTREC levels did not fall post-tymectomy, only 1 of 5 had active thymopoiesis present. In 36 thymectomized MG patients studied once at varying times after tymectomy (1 day to 41 years), we found that time after thymectomy was a significant variable in determining PB T cells sjTREC level independent of age. In contrast to the effect on naive T cells, thymectomy induced rises in memory CD4 and/or CD8 T cells in 9 of 10 patients. Total T cell levels rose post-thymectomy in 6/10 patients. Taken together, these data demonstrate selective effects of thymectomy on human naive and memory PB T cell pools. In presence of active thymopoiesis, thymectomy gradually decreased naive T cell levels, whereas thymectomy induced rises in memory PB T cell levels, regardless of the degree of active thymopoieses present at the time of thymectomy. Thus, the human thymus has dual regulatory effects on naive and memory T cell pools. (NIH CA28936, AI44758, AG16826, and CA09058)
Modeling T Cell Dynamics Following Antiretroviral Therapy
N. Defranoux, H. Struemper, T. Paterson.
Entelos Inc., 4040 Campbell St., Menlo Park, CA 94025
Mathematical modeling is a powerful tool for unraveling the complex interplay between HIV and its host immune system. To facilitate the study of HIV pathogenesis and therapies using a single, large-scale model, we have developed a comprehensive representation of the T cell dynamics relevant to HIV.

The model we present includes naive, memory, and effector CD4+ and CD8+ T cells specific for either HIV or a generic set of nonHIV antigens. It tracks and measures thymic production of naive T cells, different forms of HIV-infected CD4+ T cells (pre- and post-integration), cytokine cross-regulation, and concentrations of free HIV particles in the lymph nodes and the peripheral blood. We explicitly address the concept that HIV dynamics are embedded within the context of an immune system that is constantly responding to other antigenic challenges. Thus, exposure to environmental antigens drives the homeostatic balance in the nonHIV-specific part of the model, and when HIV is present, exposure also drives the infection rate. Inoculation with HIV virus activates the HIV-specific part of the model, which in turn affects the nonHIV-specific T cell dynamics in the model.

The model can reproduce the T cell and viral dynamics of a prototypical patient at different stages: uninfected and healthy, experiencing the acute and latent phases of HIV infection, and undergoing antiviral therapy. In particular, this model captures the biphasic decline of viremia following antiretroviral therapy by simulating the interaction of virus-producing CD4+ T cells and HIV-specific CD8+ T cells. The comprehensive representation of the nonHIV-specific T cell dynamics makes this model particularly suitable for studying the restoration of the immune system using different combinations of antiretroviral and immune therapies.

A Mathematical Model of the Human Immune Response to Mycobacterium Tuberculosis Infection
Wigginton, J. and D. Kirschner University of Michigan Medical School
A key issue for the study of tuberculosis (TB) infection is to understand the immunologic mechanisms involved in disease resolution, and those that lead to the development of active disease. An enormous body of literature exists regarding individual elements of both pathogenic mechanisms and the immune response to TB; however, little is known about combined interactions or the balance between these processes. In light of the observation that pathology in {\it Mycobacterium tuberculosis} infection may be due to an imbalance between TH1-type T cell responses that act to clear bacteria, but cause tissue damage, and TH2-type T cell responses that downregulate these potent responses, an understanding of TH1/TH2 T cell cross-regulation may be particularly relevant to any investigation of the pathogenesis of M. tuberculosis infection. To this end, we have developed a mathematical model that qualitatively and quantitatively characterizes aspects of the cytokine control network that is operational during TB infection. We are now using this model to explore the hypothesis that the outcomes of infection with {\it M. tuberculosis} depend on the TH1 or TH2 cytokine profile generated during the immune response to {\it M. tuberculosis}. In addition, we identify key interactions among the immune mechanisms critical to the clinical outcome in tuberculosis and explore the effects of perturbing different factors in this system including expression of cytokines/cytokine receptors, activation, deactivation and recruitment of macrophages, T cell and macrophage effector mechanisms, T cell recruitment and differentiation, as well as bacterial growth and mechanisms of immune evasion.
Title: The effect of different viral strains on thymocyte development during HIV-1 infection
Ping Ye and Denise E Kirschner, University of Michigan, Ann Arbor, MI
The thymus is the central lymphoid organ which provides a specialized microenvironment for thymocyte development. Although the thymus undergoes a gradual involution during aging, substantial thymic output is still detectable in adults. A number of clinical and experimental data have demonstrated that the thymus can be infected by different HIV-1 strains, suggesting thymocyte development may be interrupted by HIV-1. This may contribute to the CD4 T cell depletion that occurs during HIV-1 infection, thus accelerating disease progression to AIDS. As expected, this phenomenon is more evident in pediatric patients in whom the thymus is at its peak of function and is the primary source of newly generated T cells. Several critical factors have been identified as contributing to suppression of thympoiesis including: HIV-1 strain, viral coreceptor expression level on thymocytes, and cellular factors favoring HIV-1 replication. We have developed a mathematical model to illustrate the dynamic interactions between thymocytes and virus to understand how and when HIV-1 causes disruption of thymocyte development. Our hyptothesis is that a viral strain switch from R5 to X4 results in thymic function failure and further depletes the peripheral T cell pool. Through our analysis of the steady states of virus-free and various infection scenarios, our model demonstrates that thymic output alters the peripheral T cell pattern, including CD4 T cellcounts, CD4/CD8 T cell ratios in adults, and is also responsible for both CD4, CD8 T cell depletion observed in a subset of pediatric patients who have a faster disease progression to AIDS.