Hester Korthals Altes, Hopital Pitie-Salpetriere
Title: Models of HIV infection in which CD4 cells are both helpers and targets
Infection with HIV is characterised by very diverse disease progression patterns across patients, associated with different viral setpoints. Progression is a multifactorial process, but an important role has been attributed to the HIV-specific CD4 and CD8 T cell response. We have formulated a theoretical framework that catches the essential features of HIV infection, in order to explore the conditions under which different viral setpoints may be explained by differences in initial conditions on CD4 and CD8 T cell responses and virus inoculum. We have assumed that HIV-specific CD4 cells are both targets for infection and mediators of a mono- or polyclonal immune response, with clones differing from each other in their functional avidity for antigen. Importantly, competition between cells within clones allows the coexistence of multiple clones at viral setpoint, contrary to previous models. We found that for certain parameter conditions, multiple steady states are possible, each characterized by different numbers of T helper clones controlling infection ("n-stability"). Which state is reached depends on the balance between initial numbers of CD4 helper cells of each clone and virus inoculum. Conditions for "n-stability" occurring are investigated in terms of the effector mechanism of the clones involved (lytic or non-lytic).
Sebastian Bonhoeffer, ETH Zurich
Title: Key factors contributing to virus load variation
While the steady state virus load in HIV-1 infected patients is remarkably stable within an individual infected patient, it displays variation over several orders of magnitude between patients. Compiling a large body of published data we analyze the extent and origin of the variation of virus load. Based on robust population biological models we identify key host and virus factors responsible for the observed variation. Importantly the models suggest that differences between patients in the rate at which susceptible, activated CD4 cells are generated may be the main factor contributing to differences in viral load.
Carson Chow, University of Pittsburgh
Title: Modeling the acute inflammatory response
The acute inflammatory response is a cascade of cellular and molecular events that takes place in the body after injury or an infection. This response which involves the immune and endocrine systems, aims to eliminate damaging agents and restore the body back to equilibrium. The clinical manifestation is called systemic inflammatory response syndrome (SIRS) or sepsis in the case of infection. Sepsis can lead to major organ failure and death. Although much has been learned about the molecular and cellular pathways of sepsis, this knowledge has not translated into many effective treatments. A better understanding of the global dynamical behavior of the acute inflammatory response may be necessary. As a result, I will present recent results of our efforts to develop a mathematical model of systemic inflammation.
Miles Davenport,University of New South Wales
Title: CD4 cell turnover as a driver of HIV-1 viral phenotype switch
HIV-1 infection of CD4 T cells is mediated by interactions both with CD4 molecules and with various chemokine co-receptors. In early HIV infection, the virus utilizes predominantly the CCR5 co-receptor (R5 virus). In late disease, this viral tropism shifts to the use of the CXCR4 receptor (X4 virus) in approximately 50% of patients. There are several proposals to explain this shift, including increased virulence of X4 virus.
CCR5 and CXCR4 are predominantly expressed on memory and naove cells respectively. In uninfected individuals, memory cells divide approximately 10 times as often as naove cells, suggesting that a tropism for these (CCR5 +?ve) memory cells may be advantageous. With disease progression and declining CD4 T cell numbers, naove cell division rates approach those of memory cells, making infection of naove (CXCR4 +?ve) cells equally productive.
We have developed a model that includes naove and memory cells, X4 and R5 virus, and an empirically based relationship between CD4 cell numbers and cell turnover. The results qualitatively resemble the observed features of infection including slow CD4 depletion, and a late shift of virus from CCR5 to CXCR4 viral tropism.
Rob De Boer, Utrecht University
Title: Decline in TRECs with age and HIV infection
When the TCR is formed in the thymus, fragments of DNA are excised from the T~cell progenitor chromosome. These TCR rearrangement excision circles (TRECs) are stable, are not replicated in cell division and are therefore most frequent in naive T~cells that have recently left the thymus. During life, the average TREC content of periferal naive T~cells decreases about 50-fold in humans. It is generally believed that the age dependent decrease in the production of naive T~cells by the thymus is sufficient to explain the decrease in the TREC content. Here, we demonstrate that this decrease in thymic production is required, but it is not sufficient to explain the TREC data. Only if the decrease in thymic output is compensated by homeostasis can one explain the decrease in the TREC content. TREC content is decreased in HIV-infected patients, which was taken as evidence for decreased thymic production. Since HIV-infected patients have increased division rates in their naive and memory T cell pools, and because the TREC content changes on a relatively fast time scale, we argue that the abberant TREC content in HIV-infected patients is no evidence for decreased thymic production.
Christoph Fraser, Imperial College, London, UK
Title: Modeling HIV infection with a non-mass action term
Devising a theory of HIV dynamics that is simultaneously consistent with the rapid turnover of virus and T cells as well as with the long-term pattern of progression to AIDS has proved challenging. We derive a simple mathematical model that we show fits well to patient data gathered from the Amsterdam seroconverters cohort, whose 20 year time-span covers the pre-treatment, the AZT monotherapy and the HAART eras. Starting from a multi-factorial model that allows for multiple modes of viral pathogenesis, we find in the best-fitting model that long-term T-cell dynamics in both treated and untreated infection can be explained simply. Best-fit parameter estimates, obtained by Markov chain Monte-Carlo simulation, provide evidence for a non-linear, non-mass-action relation between viral load and CD4 T-cell destruction. We discuss some plausible biological mechanisms that could generate this relation, focussing on both its functional form and the quantitative details of the parameter estimates in relation to empirical observation. Finally, we conclude by discussing how this method can be used to quantify the relative contribution of pathogenic mechanisms, such as T-cell activation, immune escape or viral evolution to overall patient survival.
David Gammack, University of Michigan
Title: The Dynamics of Granuloma Formation in the Lung
Mycobacterium tuberculosis (Mtb) is an aerosol-transmitted bacteria that can cause tuberculosis (TB). It is estimated that 1/3 of the world population is infected leading to 1.5 million deaths per year. Infection rarely leads to active disease as the host immune response is effective in containing the pathogen resulting in a clinically latent infection. The immune response to Mtb infection is unique: the formation of multi-cellular spheroids (granulomas) consisting of bacteria, macrophages and other inflammatory cells. The dual role of macrophages as a key cell in the immune response and as the host for Mtb is important for different disease outcomes. Reactivation of latent infection is observed in roughly 10% of the population and typically occurs if immunity is compromised e.g. through HIV infection or aging.
We develop a spatio-temporal model of the immune response to Mtb infection in the lung. This allows us to investigate how macrophages initially respond to infection. The model consists of coupled reaction-diffusion-advection equations governing populations of bacteria and macrophages in various stages of activation/infection. Additionally we include a chemoattractant that recruits macrophages to infection sites. Using this model we define regions in parameter space such that infection is: cleared, controlled or uncontrolled.
Suman Ganguli, University of Michigan
Title: Granuloma Formation
Essential to understanding the immune response to infection with Mycobacterium tuberculosis is understanding the process of granuloma formation. Granuloma are multicellular lesions that form in the lung in response to infection. Successful granuloma formation can contain infection, leading to clinical latency. We have developed a spatio-temporal model of granuloma formation using a metapopulation approach that we use to explore the dynamics of this process. We discretize the spatial domain within the lung into a two-dimensional lattice of compartments. Granuloma formation involves the movement and interactions of various cell types, including bacteria, macrophages, T cells, cytokines, and chemokines. Our model includes subpopulations of these cell types for each of the compartments in the lattice. The interactions of these subpopulations within each compartment and their spatial movement between compartments is modeled with coupled systems of ordinary differential equations. By using this model to simulate granuloma formation under various conditions, we identify key parameter values and the spatio-temporal organization of cell types associated with successful granuloma formation. We also explore what conditions contribute to the breakdown of a granuloma, corresponding to reactivation of latent infection.
David Gordon, Australian National University
Title: The transmission ecology of Escherichia coli between its primary and secondary habitats
Escherichia coli is one of the most popular species for the study of gene expression and regulation, biochemistry and cell physiology. Despite the wealth of knowledge generated from this work, little is known about this species ecology or natural history. Enteric bacteria such as E. coli are found in two quite different environments: the gastro-intestinal tract of the host; and soil water and sediments. The factors influencing the fate of E. coli cells moving between these two habitats will be the focus of this presentation. The transmission of E. coli from the external environment to its successful establishment in the host is influenced by many factors, including host diet, gastro-intestinal tract morphology, and body size. Some of these same factors also explain the genetic make-up of E. coli in a particular host population. Selection also plays a significant role in determining the fate of E. coli moving from the host to the external environment. These factors determine both the geographic distribution of E. coli and the genetic structure of E. coli populations at smaller spatial scales. It seems clear that even among the commensal E. coli different strains have divergent life history strategies.
Tom Kepler, Duke University Medical Center
Title: Cytokine subversion by B. anthracis
The bacterium Bacillus anthracis is the causative of agent of anthrax; it is not parasitic, but predaceous?it depends critically on the host?s death. As a result, the bacterium has not evolved to a modest level of virulence, as is often the case with parasitic microorganisms, but has become extraordinarily virulent, with death often following rapidly following the first appearance of symptoms.
The B. anthracis toxin lethal factor (LF) enters host macrophages and induces the abnormal synthesis and secretion of tumor necrosis factor (TNF) and interleukin 1 (IL-1). At very high concentrations, TNF and IL-1 mediate shock and cell death, but at lower concentrations, these cytokines are pivotal actors in immune regulation, co-stimulating lymphocytes and effector cells, activating chemotaxis, and inducing several other short-term tissue-remodeling events.
We have developed a microsimulation model of B. anthracis-macrophage interactions to elucidate the complex roles of these proinflammatory cytokines in anthrax pathogenesis. Our contention is that B. anthracis subverts the cytokine regulatory system?and thus the normal transient reorganization of the immune system itself?to enhance its own replication and ensure the death of the host. It does not evade immunity, but turns it inside-out.
Steve Kleinstein, Princeton University
Title: Germinal Centers, Somatic Hypermutation and Affinity Maturation
Numerous in vivo and in vitro studies have elucidated the basic molecular mechanisms that underlie many aspects of immune response dynamics. However, in most cases it is not well understood how these mechanisms fit together. This is particularly true for the germinal center reaction (an important component of many immune responses). After providing an overview of germinal centers in the lymph nodes and spleen, this talk will review progress towards the next generation of detailed, comprehensive and validated mathematical models of the germinal center. This will include attempts to explain the key mutant paradox, the dynamic evolution of germinal center structure, as well as new methods to estimate the somatic hypermutation rate directly from clonal tree data (which depict the ancestral relationships between cells).
Bruce Levin, Emory University
Title: The Within-Host Population Dynamics of Systemic Bacterial Infections and Their Treatment with Antibiotics
The general motivation for our investigations of the within-host dynamics of bacterial infections is to understand the mechanisms responsible for the pathogenesis of bacterial infections in mammalian host and the conditions under which these infections will be controlled by the host?s constitutive (non-specific) defenses and/or successfully treated with antibiotics. Towards these ends we have been constructing and analyzing (primarily by tacky numerical methods the properties) of mathematical models of the population dynamics of bacterial infections in mammalian hosts. But we have also been doing some real work, in vitro and in vivo (in mouseo) experiments with potentially lethal E. coli K1 infections. The aspects of this investigations that we will report at this meeting are; (1) the reasons for the failure of antibiotic treatment in the absence of resistance, (ii) the conditions under which acquired (evolved within the host) antibiotic resistance can be anticipated, and (iii) the conditions under which acquired resistance will lead to treatment failure. At the meeting BRL will present the latest results of investigations. Yes, you can interpret that to mean that they do not yet know the answers to the questions they are addressing, but hope to by the time of the meeting. (Research with Renata Zappala)
Ramit Mehr, Bar-Ilan University
Title: The Dynamics of Germinal Centre Selection as measured by Graph-Theoretical Analysis of Mutational Lineage Trees
We have developed a rigorous graph-theoretical algorithm for quantifying the shape properties of mutational lineage trees. We show that information about the dynamics of hypermutation and antigen-driven clonal selection during the humoral immune response is contained in the shape of mutational lineage trees deduced from the responding clones. Age- and tissue- related differences in the selection process can be studied using this method. Thus, tree shape analysis can be used as a means of elucidating humoral immune response dynamics in various situations.
David Michael, Australian National University
Title: Population Ecology and Genetics of Escherichia coli
Escherichia coli is one of the most popular species for the study of gene expression and regulation, biochemistry and cell physiology. Despite the wealth of knowledge generated from this work, little is known about this species ecology or natural history. Enteric bacteria such as E. coli are found in two quite different environments: the gastro-intestinal tract of the host; and soil water and sediments. The factors influencing the fate of E. coli cells moving between these two habitats will be the focus of this presentation. The transmission of E. coli from the external environment to its successful establishment in the host is influenced by many factors, including host diet, gastro-intestinal tract morphology, and body size. Some of these same factors also explain the genetic make-up of E. coli in a particular host population. Selection also plays a significant role in determining the fate of E. coli moving from the host to the external environment. These factors determine both the geographic distribution of E. coli and the genetic structure of E. coli populations at smaller spatial scales. It seems clear that even among the commensal E. coli that different strains have divergent life history strategies.
Patrick Nelson, University of Michigan
Title: A new model of HIV infection with time varying virus production and infected cell death rates
Models using DDEs are more consistent with the biology and provide different estimates for certain kinetic parameters. We will show the differences we have found when comparing these models to existing patient data. We then will discuss advances in the modeling by incorporating structured dynamics that allow one to consider varying death and production rates. These models are able to better predict experimental data and are providing the framework for the study of genetic variations, such as changes in the nef and rev gene expressions, and how these changes relate to viral pathogenesis. These models we feel are more robust and allow us to focus on the mechanisms of viral infection, from primary infection through mutation.
Avidan Neumann, Bar-Ilan University
Title: Second Hepatitis C Compartment Indicated By Biral Dynamics During Liver Transplantation
Authors: H. Dahari, M. Garcia-Retortillo, X. Forns, A.U. Neumann
Background: An important question in understanding and treating Hepatitis C Virus (HCV) infection is the putative existence of a second compartment of HCV replication besides the liver. In principle, the existence of a second compartment could be indicated if HCV decline during the anhepatic phase (AHP) of liver transplantation (LT) is not a single exponential. However, the duration of the physiological AHP is too short to allow such analysis. We use here a mathematical model of viral dynamics to enable a more detailed analysis of HCV kinetics during LT.
Methods: We analyzed HCV kinetics in 20 patients undergoing LT for HCV-related cirrhosis. Viral load (Cobas Monitor V2, Roche) was measured at the beginning and at the end of AHP, and at 4, 8, 12, 16, 24, 48, 72, 96 and 120 hours after graft reperfusion. A mathematical model was developed by duplicating the equations for target cells, infected cells and free virus from a previous model (Neumann et al, Science 98) to allow for a liver compartment (T1, I1, V1) and for a putative second compartment (T2, I2, V2) with diffusion of virus between the two compartments. LT procedure was simulated by assuming steady state for both compartments before LT, thereafter setting T1=0 and I1=0 at the beginning of the anhepatic phase and allowing the new liver to become infected (T1=10^12) and produce virus after an arbitrary time-delay (tp) post-reperfusion.
Results: The model shows that if no second compartment is assumed then a single exponential decline is expected to continue post-reperfusion until viral rebound occurs when the new liver cells are productively infected and start to release virions. Thus, a functional AHP of longer duration than the physiological AHP can be assumed. Indeed, all patients showed a rapid exponential viral decline (mean half-life 2.2 hr) during the physiological AHP followed by similar decline (mean half-life 2.1 hr) during 4-8 hrs after reperfusion. Thereafter, 4 patients had viral rebound and 4 reached undetectable levels. However, 11 patients reached then a viral plateau (mean 3.9 log IU/ml) for 8 to 32 hrs. Interestingly, 1 patient with an unusually long AHP (20 hrs) reached viral plateau of 4 log IU/ml 5 hrs before graft reperfusion. The viral plateau during AHP or after graft reperfusion could be modeled only by assuming a non-liver replication compartment independently giving rise to a viremia level of about 10^4 IU/ml in the blood. Eventually, viral load rebounded with tp=8-120 hrs post-reperfusion in all cases. The time TP constitutes of the delay until the new liver cells are infected and of the intra-cellular delay due to the virus life cycle. Interestingly, the patients with a single exponential decline had significantly shorter TP (mean 11 hrs) as compared to those with a bi-phasic kinetics (47 hrs). Thus, also these patients can have 2 compartments, but because of a shorter time for their new liver to get infected the bi-phasic decline is not observed. In any case, we obtain a maximal estimate of 6 hours for the HCV intra-cellular life cycle. An additional model assuming a second compartment where virus is bound to cell with slow off rate was also tested but the was rejected since the amount of the then estimated bound virus was found to be non-realistically high.
Conclusions: By using mathematical modeling of viral dynamics during LT we find clear evidence for a second replication compartment of HCV in about half of the patients. We estimate that this compartment is responsible for about 2% of the virus found in circulation pre-LT. Moreover, the model shows that a minimum delay of 8 hours is necessary for the new liver cells to become productively infected and release virus to circulation. Further studies of viral quasi-species and compartmentalization are necessary to verify why only part of the patients show viral kinetics indicative of a second replication compartment and to elucidate the cellular identity of this compartment.
Alan Perelson, Los Alamos
Title: An Introduction to Modeling HIV Infection
I will review some of the standard models used to describe HIV infection and treatment, explain how current parameter estimates were arrived at, and point out a large number of areas in which our knowledge is still very incomplete.
Sergei Pilyugin, University of Florida
Title: Dynamics of CD8 immune responses
In the first part, I will discuss the general dynamics of CD8 responses (expansion, contraction, and memory phases) and two important phenomena such as immunodominance and generation of immune memory. I will argue why recent experimental discoveries force us to revise the traditional clonal expansion/contraction models of immune responses and discuss alternative models.
In the second part (if time permits), I will discuss the problem of estimating division and death rates for immune cells in different phases of the response.
Roland Regoes, Emory University
Title: The Role of Target Cells and Specific Immunity in Primary SIV Infection
The virus load in primary HIV infection is characterized by a steep initial increase, a peak after a few weeks after infection, and a postpeak decline to the so-called viral setpoint. It is hypothesized that the postpeak decline could be driven by target cell limitation, or by specific cellular immune responses to the virus, or both. Since the viral setpoint is one of the best correlates of disease progression, an understanding of the factors governing primary HIV infection is crucial for the design of rational treatment and vaccination strategies.
We investigated the factors governing primary SIV infection, analyzing an extensive dataset which contains frequent virus load and immune cell measurements obtained from eight SIV-infected rhesus macaques. Fitting two simple mathematical models to the viral load - one that describes the interaction between the virus and its target cells only, and an extended model which additionally takes into account the inhibitory effect of specific CD8+ T cells - enables us to determine whether specific cellular immune responses play an significant role in primary infection.
Our results show that the postpeak decline in the virus load during primary infection is not due to target cell limitation, but is driven to a large extent by specific CD8+ T cells. The level of specific CD8+ T cells, therefore, is an important determinant of the viral setpoint and thus of disease progression.
Ruy Riberio, Los Alamos National Laboratory
Title: Modeling the dynamics of T cells and TREC after treatment of HIV-1
We quantified T-cell proliferation and thymic function, by measuring Ki67 staining and T-cell receptor excision circle (TREC) number, in primary (PHI, n=19) and chronic (CHI, n=14) HIV infection. Following antiretroviral therapy of PHI there is a profound decrease in the number and percentage of Ki67+ T-cells, with no significant increase in TREC/million cells and a transient increase in TREC/ml. In contrast, following antiretroviral therapy of CHI, there is a reduction in the percentage but little change in the total number of Ki67+ CD4+ T-cells associated with increases in both TREC/million cells and TREC/ml. We developed a mathematical model that describes TREC/ml and TREC/million cells and accounts for thymic input, proliferation, death and redistribution of T-cells. This model was used to analyze the experimental data of HIV-1 treatment, by using analytic techniques to study the effect of each parameter on TREC/ml and TREC/million cells. We find that redistribution is consistent with the TREC changes observed during treatment of PHI and that an increase in thymic output is most consistent with the increases in TREC during treatment of CHI. Consideration of TREC/ml in the model gives us added information to understand the behaviour of TREC during therapy.
Hal Smith, Arizona State
Title: Bacterial Wall Attachment In A Flow Reactor: Mixed Culture
A mathematical model of a mixed culture of bacteria in a flow reactor which accounts for the colonization of the reactor surface by microbes is studied both analytically and by numerical simulations. It can be viewed as a model of the colon or of the fouling of a commercial bio-reactor or pipe flow. The primary focus is on coexistence of microbial populations in the reactor.
Bahrad Sokhansanj, Larewnce Livermore National Laboratory
Title: Modeling Yersina Pestis
Recent technological advances in high-throughput data collection provide the ability to study increasingly complex systems of infection and host immune response. However, these new technologies, such as DNA microarrays and 2D gel electrophoresis, generally produce noisy low-resolution measurements. Consequently, a new methodology is needed to develop and test biological models, design more efficient experiments, experimental design, and predict the effect of network perturbation (e.g. genetic engineering, pharmaceuticals, gene therapy). Current models of biological systems either fail to include necessary biological details (i.e. pure Boolean logic models of gene networks) or require large numbers of parameters that are very difficult to accurately measure (i.e. chemical kinetic simulations). We propose that fuzzy logic rule-based models are an effective way to incorporate details of molecular mechanism obtained from microarray and similar experiments into higher-level models of the host-pathogen interaction. Using both preliminary microarray data and information from the literature for the virulence mechanisms and host interaction of Yersinia pestis, the bacterium that causes plague, we illustrate the use of a fuzzy logic-based modeling approach to incorporate additional details that can not be included in contemporary differential equation models.
Jaroslav Stark, University College London
Title: Multiple T Cell Antigen Presenting Cell Encounters and the Role of Anergy
A key step in the function of the whole adaptive immune system is the recognition by the T-cell receptor (TCR) of short peptides presented in the groove of the major histocompatibility complex (MHC) on the surface of anti-gen presenting cells (APC). It appears that APC?s present both foreign and self peptides and that the property that best correlates with T-cell response is the disassociation time of the MHC-peptide-TCR complex. In order to avoid an auto-immune response, it is therefore essential that T cells are ?educated? to distinguish between self peptides and those produced by pathogens. This occurs in the thymus where those T cells with a high response to self peptides are deleted (negative selection). However, due to the stochastic nature of TCR recognition and to the fact that any given T cell will have a large number of encounters with APC?s during its lifetime, some potentially auto-reactive T cells escape such deletion and are exported to the periphery. One of mechanisms that helps to guard against such peripheral auto-reactivity appears to be anergy, whereby T cells exposed to a weak signal enter an unresponsive state in which they fail to react to subsequent agonist signals. We present a simple mathematical analysis of this phenomenon and discuss the implications for the interaction of the immune system with pathogens.
Jorge Velasco-Hernandez, UAM-Iztapalapa
Title: Coevolution and coinfection in a virus-host model
We consider the interaction between two virus strains that coinfect host cells. We explore the effects of cell death and virulence in this context.
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