Bioinformatics Advance Access originally published online on March 6, 2007
Bioinformatics 2007 23(11):1371-1377; doi:10.1093/bioinformatics/btm044
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Simulating Epstein-Barr virus infection with C-ImmSim
1Istituto Applicazioni del Calcolo (IAC) "M. Picone"-CNR, Viale del Policlinico, 137, 00161 – Rome, Italy, 2Virginia Bioinformatics Institute, Washington St., MC 0477, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061 and 3Department of Pathology Jaharis Building, Tufts University School of Medicine, 150 Harrison Ave., Boston, MA 02111, USA
*To whom correspondence should be addressed.
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ABSTRACT |
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 TOP ABSTRACT 1 INTRODUCTION2 SYSTEM AND METHODS3 IMPLEMENTATION4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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Motivation: Epstein-Barr virus (EBV) infects greater than 90% of humans benignly for life but can be associated with tumors. It is a uniquely human pathogen that is amenable to quantitative analysis; however, there is no applicable animal model. Computer models may provide a virtual environment to perform experiments not possible in human volunteers.
Results: We report the application of a relatively simple stochastic cellular automaton (C-ImmSim) to the modeling of EBV infection. Infected B-cell dynamics in the acute and chronic phases of infection correspond well to clinical data including the establishment of a long term persistent infection (up to 10 years) that is absolutely dependent on access of latently infected B cells to the peripheral pool where they are not subject to immunosurveillance. In the absence of this compartment the infection is cleared.
Availability: The latest version 6 of C-ImmSim is available under the GNU General Public License and is downloadable from www.iac.cnr.it/~filippo/cimmsim.html
Contact: david.thorley-lawson{at}tufts.edu
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1 INTRODUCTION |
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TOPABSTRACT1 INTRODUCTION2 SYSTEM AND METHODS3 IMPLEMENTATION4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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Epstein-Barr virus is a
-herpesvirus that infects greater than 90% of humans by the time they are adults (Reviewed in Rickinson and Kieff, 2001; Thorley-Lawson, 2001). Once established, the virus persists latently for life and is usually benign making it a model pathogen for studying persistent infection (Thorley-Lawson, 2001; Thorley-Lawson and Babcock, 1999). Occasionally, however, EBV infection is associated with important human cancers (Rickinson and Kieff, 2001; Thorley-Lawson, 2001). Through the application of quantitative experimental techniques, a conceptual model of how EBV establishes and maintains persistent infection has been developed (Thorley-Lawson, 2001; Thorley-Lawson and Babcock, 1999; Thorley-Lawson and Gross, 2004). Briefly, EBV infects B cells in the Waldeyer's ring (tonsils and adenoids) using a defined set of nine latent proteins to first activate the cells to become proliferating lymphoblasts and subsequently allowing them to differentiate into memory cells (Babcock et al., 1998; 2000). The latently infected memory cells then enter the peripheral circulation where they exit the cell cycle (Miyashita et al., 1997), turn off viral protein expression (Hochberg et al., 2004a) and are maintained at stable levels as normal memory cells, thus making them invisible to the immune system and non-pathogenic to the host. It is assumed that the memory compartment is the site of and essential for long-term persistent infection by EBV, however definitive proof of this is lacking. Occasionally these cells re-enter Waldeyer's ring and terminally differentiate into plasma cells, the signal for viral reactivation (Laichalk and Thorley-Lawson, 2005) allowing the virus to be shed into saliva to infect new hosts and new B cells to begin the cycle of infection again. Neoplastic disease is thought to arise when the normal progression of an infected, proliferating lymphoblastoid cell into a resting memory cell is blocked leading to constitutive expression of viral growth promoting genes (Thorley-Lawson and Gross, 2004). In essence, this is a one-way circuit. The progression is from virus to latently infected cells expressing latent proteins to latently infected cells expressing no proteins to lytic reactivation to viral replication to virus. This circuit is brought under control by the immune response [CTLs to latently and lytically infected cells and antibody to virus (Rickinson and Kieff, 2001)] whose function is to control the number of infected cells and not the states of viral infection. The result is that persistent infection by EBV appears to be a steady-state equilibrium between host and virus with continuous shedding of infectious virus into the saliva, stable levels of infected cells in the blood and lymph nodes and a constitutively active antiviral immune response. While this model explains all the major features of EBV biology, definitive proof is lacking and there are many unanswered questions related to the dynamics of this system making other interpretations possible. Currently there are no generally applicable animal models for EBV to answer these questions. Computer simulations potentially provide an alternative approach to this issue however, no such models addressing the issue of EBV persistence have been described to date. In the present article, we adapted a discrete mathematical model of the immune response to a generic pathogen to investigate and further validate the proposed dynamics of persistent EBV infection.
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2 SYSTEM AND METHODS |
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TOPABSTRACT1 INTRODUCTION2 SYSTEM AND METHODS3 IMPLEMENTATION4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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2.1 Quantitation of infected cells in the peripheral circulation
Blood samples were drawn by venipuncture at the AIM clinic of University of Massachusetts-Amherst and processed as described previously (Hochberg et al., 2004a). The absolute number of virus infected cells was then measured using a limiting dilution assay where virus infected cells were detected by DNA-PCR as described previously (Babcock et al., 1998).
2.2 Basic model
The core model is based on a special class of cellular automata (Celada and Seiden, 1992; Seiden and Celada, 1992) and includes the most significant immune cells and features (Bernaschi and Castiglione, 2001). The physical space represented approximates one cubic millimeter of a peripheral lymph node, but is two dimensional. We believe this is reasonable because the essential features of the lymphoepithelium of the Waldeyer's ring (germinal centers, mantle zone, lymphocyte homing from HEV and draining into efferent lymphatics) are those of a lymph node distributed around the oropharynx except antigen is delivered by the epithelium rather than the afferent lymphatic. The model incorporates, at its current stage (C-ImmSim—www.iac.cnr.it/~filippo/cimmsim.html) the principal core facts of today's immunological knowledge, e.g. the diversity of specific elements, human leukocyte antigen (HLA) restriction, clonal selection by antigen affinity, thymic education of T cells, antigen processing and presentation (both the cytosolic and endocytic pathways are implemented), cell–cell cooperation, homeostasis of cells created by the bone marrow, hyper-mutation of antibodies, maturation of the cellular and humoral response and memory. Less relevant in the current EBV model are thymic selection, representation of a large repertoire, affinity maturation and antibody hypermutation.
Major classes of cells of the lymphoid lineage (B and T lymphocytes) and some of the myeloid lineage (macrophages and dendritic cells) are represented. Note however that even though the importance of natural killer cells in viral infection has been documented they are omitted in the current model. In addition to leukocytes, the model represents antibodies (of the IgM type only), immunocomplexes and a few cytokines such as interleukin-2 and, following the danger theory of Matzinger, a generic damage signal (Matzinger, 1998). Damage is used to implement the idea that a signal is necessary to activate the clonal response of the immune system. The damage arises from necrotic cell death, Ab/Ag complexes, toxins and injected adjuvant and in turn can activate antigen-processing cells.
Leukocytes form three general classes (granulocytes; lymphocytes and monocytes) which are present in different ratios in blood, tissues and various organs. The absolute numbers and relative proportions of cells used in the present simulation are based on an average human leukocyte formula [which gives the count in the blood (Goldsby, 2000)], with the notable omission of granulocytes. In our virtual lymph node, we consider a concentration of about 2700 leukocytes in a microliter. The lymphocytes are divided into 260 B cells, 1310 T cells (further subdivided into 880 T helper cells and 430 cytotoxic T cells) while the monocytes are divided into 350 macrophages and 350 dendritic cells.
By changing a parameter in the simulation we can scale-up the system in multiples of a cubic millimeter of a generic peripheral lymph node, the only limit of our system being the computational limits of currently available computers (e.g. the simulations performed for this study consider 40 cubic millimeters of simulation space, representing about ninety thousands leukocytes). Specificity refers to the physical shape of each cellular entity that can be recognized by their paratopes (complementary shapes of peptides and receptors). Each entity, except for plasma cells, has at least one receptor (or paratope/epitope, depending on whether they are cellular or molecular entities) which is its primary identifier, i.e. specificity. The specificity determinant of the plasma cell is the paratope of the antibody produced by that cell. The specificity determinant is identified by a binary string. All cells have MHC class I receptors. Macrophages, dendritic cells and B cells are implicitly assumed to carry a complete sample of class II MHC receptors. B cells also have MHC class I receptors. In addition to B cells, T helper cells and cytotoxic T cells are endowed with receptors used for binding antigen. The B-cell receptor binds antigen which can then be endocytosed. The T cell receptors only bind antigen in MHC/peptide complexes. For example CD8 cells recognize their cognate antigen on infected cells and kill them. The plasma cells have no specific receptor; however, they do produce antibodies with the same receptor as the B cell from which they originate.
Cellular and molecular entities move randomly on the lattice and interact with a probability given by the molecular affinity of their receptors. In the model, this probability of interaction increases with the number of matching bits in the corresponding bit-string comparison (i.e. zeros match ones and vice versa). The immune response to antigens shows up in terms of production of antibodies that bind the antigenic molecular shell and/or stimulation of cytotoxic cells able to recognize and destroy virus-bearing infected cells. The physical space is mapped onto a bi-dimensional triangular lattice (six neighbors) with periodic boundary conditions. The 2D lattice approximates 3D behavior by adjustment of the encounter and interaction probabilities to reflect the 3D collapsed onto the 2D lattice. All interactions among cells and molecules take place within a lattice site in a single time step, so that there is no correlation among entities residing on different sites. Since the time step is 8 h, a very detailed description of cell tracking is not required in our model. A random diffusion process at the end of each time step introduces spatial correlations among the entities.
The simulation is carried out by iterating the following steps: Step 1: New cells are generated from bone marrow and thymus selection of immature CD4/CD8 T lymphocytes. Step 2: Entities interact in random order to avoid any bias toward a particular interaction. Step 3: Cells and molecules randomly diffuse. However, at this stage, we do not take into account any real estimate of the cell mobility coefficient. To prevent unrealistic accumulations of cells in one lattice site, diffusion is constrained by the cell density of the destination lattice site. For this purpose, we assume that the whole lattice represents 109 cubic micrometers and that all cells are perfect spheres with an average diameter of 10 µm. Under these assumptions, the probability for diffusion to a neighboring lattice site chosen at random is set equal to 1 minus the ratio between the current number of cells occupying the destination site and the maximum number of cells that can occupy one lattice site (about 8000 in a 16 x 16 lattice). Step 4: Stimulated cells duplicate. Clone division is performed at a rate of one division each time step and five divisions per stimulated cell (since one time step equals 6–8 h a stimulated cell takes 1.5 days for duplication). During division, cells cannot interact with other entities. Division of T cells is constrained by the availability of IL-2 at the same lattice site. This requirement, together with the very short lifetime of the IL-2, mimics the paracrine and autocrine action of cytokines. Without an antigenic stimulus, the population of cells is at equilibrium, that is, the turnover is constant. Deviations from the equilibrium are triggered by the presence of antigens.
Time is defined with respect to the mitotic cycle of actual cells (between 6 and 8 h). Since we allow a cell to create a single copy of itself per time step, one day of real time corresponds to 3–4 time steps of simulation. Figure 1 shows a block diagram of the various compartments of the simulated immune system. In particular, the model includes lymphocyte generation from the bone marrow and a circulation in which latently infected cells enter and exit. Antigen presentation and setting of the humoral and cellular response is localized in the (portion of the) lymph node represented by the lattice using biological information derived from a variety of different systems, but not specifically EBV.
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Memory cells are eliminated by the simulation with a probability that is a function of both the cell's age (a) and its half-life (
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to the half-life of the lymphocyte each time it interacts successfully with another cell or phagocytes an antigen as in the case of B cells: ' = + where is proportional to the match between the binding sites of the two interacting entities. The proportionality constant for as well as the parameter C in the above definition of p(a, ) are chosen to have a reasonable first and secondary response to a generic inactive antigen. (Although this procedure may seem risky, it is noteworthy that it is the only way we can proceed given the generality of the concept of memory, the great variability of the immune response and persistence of memory to generic pathogens and, last but not least, the lack of a complete understanding of the origin of memory and its biological mechanisms.) The overall result of this process is that a few cells increase their half-life considerably and live longer than any other cell. Moreover, in this way we obtain an expansion of the memory compartment that is somehow proportional (in a non-linear way) to the magnitude of the infection and consequent duration of the immune response. In other words, in the case of a chronic infection, the pool of memory cells is virtually lifelong, while at the same time, the actual lifespan of any individual lymphocyte is finite. In addition to the core features described above, new rules that are necessary to simulate the dynamics of EBV infection have been added. Of particular importance is the successful reproduction of both acute and persistent phases of the EBV infection. EBV's infectivity rate of B lymphocytes is high and near unity. We define the activation rate of EBV as the probability that at each time step a latent B cell enters the lytic phase. EBV infects only B cells in our simulation. Infected B cells proceed through a latently infected state, the so-called latent state, and then to an active viral replication state, called the lytic state. While in the latent state the virus does not replicate inside host cells, in the lytic state the virus replicates at a certain rate. Lytic B cells are not stimulated by T helpers, but it is largely irrelevant, as they do not survive for very long. When the amount of virus in a lytic cell reaches a threshold level, the cell bursts and releases its viral content. Newly budded virions infect other B lymphocytes, starting the infection cycle again.
2.3 Parameter estimation
The core model has a long history in simulating different immune system pathologies. Effectively, most parameters have been determined in previous studies and represent typical behaviors. Other parameters have been set by examining the biological literature. A complete list of parameters is available at the following URL: http://www.iac.cnr.it/~filippo/cimmsimparameters/index.html. To simulate EBV the following new parameters were added to the core model:
- The probability that a naive B cell encountering a virus makes the transition to the latent state within the virtual lymph node is set to near unity.
- The probability that a latent B cell becomes lytic is based on values in (Laichalk and Thorley-Lawson, 2005).
- The viral growth inside a lytic B follows an exponential growth emt with m = 0.35.
- A lytic B cell that is filled with newly assembled viruses bursts when the number of viruses reaches 103. Of these, just 5% are considered infectious to account for the fact that most virus is trapped on the surface of nearby cells, yet only one virus is needed to start an infection.
- The growth rate m and the burst size are chosen to fix at one day on average, the time it takes a lytic B cell to burst once it starts viral replication.
- Latently infected B cells arrive from the blood compartment at about one cell every three days on average. This rate is lower than the actual estimated return rate.
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3 IMPLEMENTATION |
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TOPABSTRACT1 INTRODUCTION2 SYSTEM AND METHODS3 IMPLEMENTATION4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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3.1 Infected B cell production peaks at about one month post-infection and then declines into persistence
The infected B cell count in one cubic millimeter of simulated lymph node tissue is shown in Figure 2. The simulation exhibits a peak in the number of infected B cells about one month post-infection and subsequently decays. The peak of infection coincides well with the published incubation period of EBV, which is estimated to be approximately 32–47 days (Hoagland, 1964) suggesting it is probably reasonable to assume that clinical symptoms arise about the time of peak infection. After approximately 300 days, the number of latently infected B cells reaches a nadir. Subsequently, due to the small volume and corresponding small number of infected cells, the actual number of infected cells oscillates stochastically. This effect is dampened, as expected, when an average of ten simulations of 40 cubic millimeters of lymphoid tissue is analyzed. A persistent phase, defined by the presence of latently infected B cells was observed that lasted for the duration of the simulation, more than 10 years of simulated time. Latently and lytically infected cells behave with similar kinetics in both the acute and persistent phases.
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In Figure 3, data from five acute infectious mononucleosis patients (taken from (Hochberg et al., 2004b) has been superimposed on the simulated infection. Due to the different number of lymphocytes in the simulation as compared to the blood drawn from patients, we have normalized the clinical data such that the number of infected B cells at first clinic visit reflected the peak value in the simulation. At this stage, we are interested in the dynamics of decay, and this adjustment does not alter our understanding of that behavior. Similarly most patients cannot usually recall specifically when or how they were exposed to EBV therefore we have assumed that the first measurement occurs at the peak in infected B cells i.e. around 35 days post-infection. Given these caveats the simulated dynamics of EBV infection as it passes from acute into persistent infection agrees well with the measurements of infected B cell numbers in the actual patients. As noted above, 35 days is consistent with published data that patients enter the clinic 35–47 days. In extensive time course studies of EBV levels in acute infectious mononucleosis, we have never observed an increase in infected B-cell numbers in our patient time courses (Hochberg et al., 2004b and unpublished data), so it appears that patients seek treatment at or soon after the peak of infection. In reality, though patients differ considerably in their tolerance for discomfort. Consequently, some may enter the clinic at the peak of infection and some shortly thereafter. Therefore we also tried assigning the day of initial visit to the clinic at days 30, 32, 35, 40, 45 and 50 post-infection and found that all assignments match the simulated data well.
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3.2 Escaping immune surveillance in the blood compartment is critical to the establishment of persistence
We have demonstrated that the simulation can approximate the kinetics of virus infected cells during both acute and persistent infection. Furthermore persistence was seen for all simulations and for all values of parameters examined. This was not true however in the absence of a blood compartment where the latently infected cells could be shielded from immune surveillance. Using the original model, which lacks a blood compartment, only acute infection was observed. Simulations using ODE models also showed a very rough approximation of the acute phase, but again persistent infection was not established (not shown). Both virus and infected B cells were always cleared. To solve this problem we tried setting a very low reactivation rate for the latent virus in order to stretch out the persistence period due to long-lived memory B lymphocytes. However, this change only delayed the clearing of the infection not in lifelong persistence. A second attempt to obtain persistence involved implementing a higher reactivation rate for EBV replication in order to have a rapid turnover of infected cells. This produced a chronic infection but at the cost of an unrealistically high number of infected B cells in the persistent phase (close to 80–90% of the B-cell compartment) compared to what is seen in vivo. A realistic level of latently infected B cells is about 1% of the peak value two months post-infection and 0.1% of the same value after one year (Hochberg et al., 2004b and unpublished data). We concluded that it was impossible to achieve a lifelong, low level, persistent infection with the features represented in the original model.
We therefore decided to modify the topology of the model. Since the lattice space is a torus, the system is closed and latently infected B cells cannot escape immune surveillance and ultimate destruction. Realistically, that scenario does not parallel EBV infection where latently infected B cells escape from the tonsils into the circulation. We corrected this inadequacy by building another compartment to represent the blood (see Fig. 1). Infected B cells leave the virtual lymph node where they escape detection in the blood reservoir. Latently infected B cells reenter the simulation space at a low rate, approximately one every three days. This rate of return, adjusted for the volume of the lymph node compared to that of the Waldeyer's ring, may be slightly less than the actual rate. When a blood compartment was incorporated a persistent phase, defined by the presence of latently infected B cells, was seen for all simulations and all values of parameters examined (Fig. 4). Therefore the simulation suggests that the blood compartment is essential for maintenance of a persistent infection by EBV.
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3.3 Virus production, antibody responses and immune complex formation reflect normal immune responses to EBV infection
We also examined the kinetics of EBV and EBV-specific antibody production and immune complex formation using average parameters reported in the literature. Not surprisingly, the simulated results are typical of a robust immune response. The dynamics of virion production is essentially parallel to those of infected cells, but peaks slightly earlier and decays more rapidly to relatively low levels (Fig. 5). Again assuming that AIM patients arrive in the clinic at around days 35–50, the leveling out of virus production in the simulation is consistent with the observation that, unlike infected cells, the levels of virus shedding in patients does not drop dramatically over time as the infection resolves (Hadinoto and Thorley-Lawson, unpublished data). At any given time, most virus was actively replicating within infected B cells and not freely diffusing. Lytic bursts of infected cells gave rise to the spikes visible in Figure 5. (Due to the small size of the simulation, the noise level is high.) Free virus quickly infected neighboring cells or was captured by antibodies, leading to the formation of immune complexes. EBV-specific antibody titers were higher during the first four weeks of disease, as is common in most viral infections. They were reduced to very low levels during persistence (Fig. 6).
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4 DISCUSSION |
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TOPABSTRACT1 INTRODUCTION2 SYSTEM AND METHODS3 IMPLEMENTATION4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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In this article, we present studies using a stochastic cellular automaton to model infection with the human herpesvirus EBV. The simulation produces kinetics of virus-infected cells and virion production in the acute phase that resemble that seen in patients, with peak levels of infection (
35 days) corresponding with the known incubation time of EBV. Importantly it was also possible to establish long-term (at least 10 virtual years) low-level, persistent infection. The most striking property of this persistence was the absolute requirement for the presence of a blood compartment where virus-infected cells were not subject to immunosurveillance. This mimics the known persistence of EBV in peripheral blood resting memory B cells which do not express viral proteins and are therefore similarly not subject to immunosurveillance. In contrast to HIV-1 infection, very few mathematical models of EBV infection have been developed to date and none, that we are aware off, deal directly with EBV persistence. Davenport and colleagues have reported a mathematical model to study the evolution of T-cell responses to infection with a persistent virus like EBV but in our hands their model does not perform well with respect to B-cell dynamics and does not address the dynamics of persistence by the virus in B cells (Davenport et al., 2002). In Wang et al. (2003) the authors construct a mathematical model of human herpes virus 6 (HHV-6). However, the authors of that article were interested in lymphoproliferative diseases and the model was not built to investigate the mechanisms of persistence. These models, not unlike most immune system models, are based on ordinary (or partial) differential equations. This approach has two main limitations: first, they assume sufficiently large population sizes from which the properties of essentially identical entities can be calculated. However, each cell of the immune system has a unique life history that defines its particular interaction with the environment so that averaging over such a population may not be adequate. The typical solution to this problem is to divide the cells into a small number of classes based on only a few characteristics. However, this approach ignores the complexity and special cases characteristic of the immune system. The second limitation is that the equations give only the average behavior of a system. Although there are questions for which knowing the distribution of behaviors is not relevant, there are many more questions that cannot be addressed without this knowledge. In summary, the common pitfall is a failure to address issues such as spatial and temporal heterogeneity and non-uniformity. Our approach handles these issues in a logical way. Since our model is stochastic, we can estimate the distribution of behaviors exhibited by the system, not just the average. It is also easy to modify the complexity of the interactions without introducing any new difficulties in solving the model because non-linearities are not intrinsically difficult to handle in cellular automata. Finally, the automaton is able to represent the components and processes of interest in biological language so that the approximations in the model are more biological in character than mathematical.
Our success in modeling the broad outlines of the dynamics of acute and persistent infection lays the groundwork for the development of better agent-based models to more precisely simulate EBV infection. Clearly, there is a need for simulations that are larger, more sophisticated and incorporate more detail such as anatomically correct representation of the entire Waldeyer's ring. For example, in the current simulation there is a large amount of noise in the output of virus production during the persistent phase. This is due to very small numbers of cells that individually burst large numbers of virions and is an artifact of the small size of the c-ImmSim virtual lymph node. This makes it difficult to analyze and comment on what exactly is going on during persistence. Ultimately the hope is that this will allow realistic simulations of infection by EBV and other human pathogens for which there are no good animal models.
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ACKNOWLEDGEMENTS |
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TOPABSTRACT1 INTRODUCTION2 SYSTEM AND METHODS3 IMPLEMENTATION4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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This work was supported by Public Health Service Grants R01 CA65883, R01 AI18757 and RO1 AI062989 to DT-L. Partial support for FC was provided by EC contract FP6-2004-IST-4, No.028069 (ImmunoGrid). Funding to pay the Open Access publication charges was provided by PHS grant RO1 AI062989.
Conflict of Interest: none declared.
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FOOTNOTES |
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Present address: Department of Biochemistry and Biotechnology, KNUST, Kumasi, Ghana. 
Associate Editor: Jonathan Wren
Received on October 27, 2006; revised on January 15, 2007; accepted on February 3, 2007
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REFERENCES |
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TOPABSTRACT1 INTRODUCTION2 SYSTEM AND METHODS3 IMPLEMENTATION4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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