Aggregation of FcεRI on mast cells and basophils leads to autophosphorylation and increased activity of the cytosolic protein tyrosine kinase Syk. We investigated the roles of the Src kinase Lyn, the immunoreceptor tyrosine-based activation motifs (ITAMs) on the β and γ subunits of FcεRI, and Syk itself in the activation of Syk. Our approach was to build a detailed mathematical model of reactions involving FcεRI, Lyn, Syk, and a bivalent ligand that aggregates FcεRI. We applied the model to experiments in which covalently cross-linked IgE dimers stimulate rat basophilic leukemia cells. The model makes it possible to test the consistency of mechanistic assumptions with data that alone provide limited mechanistic insight. For example, the model helps sort out mechanisms that jointly control dephosphorylation of receptor subunits. In addition, interpreted in the context of the model, experimentally observed differences between the β- and γ-chains with respect to levels of phosphorylation and rates of dephosphorylation indicate that most cellular Syk, but only a small fraction of Lyn, is available to interact with receptors. We also show that although the β ITAM acts to amplify signaling in experimental systems where its role has been investigated, there are conditions under which the β ITAM will act as an inhibitor.

To assess the roles of serial engagement and kinetic proofreading in T cell receptor (TCR) internalization, we have developed a mathematical model of this process. Our determination of TCR down-regulation for an array of TCR mutants, interpreted in the context of the model, has provided new information about peptide-induced TCR internalization. The amount of TCR down-regulation increases to a maximum value and then declines as a function of the half-life of the bond between the TCR and peptide-major histocompatibility complex (pMHC). The model shows that this behavior, which reflects competition between serial engagement and kinetic proofreading, arises only if it is postulated that activated TCRs remain marked for internalization after dissociation from pMHC. The model also predicts that because of kinetic proofreading, the range of TCR-pMHC-binding half-lives required for T cell activation depends on the concentrations and localization of intracellular signaling molecules. We show here that kinetic proofreading provides an explanation for the different requirements for activation observed in naïve and memory T cells.

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To investigate the role of receptor aggregation in EGF binding, we construct a mathematical model describing receptor dimerization (and higher levels of aggregation) that permits an analysis of the influence of receptor aggregation on ligand binding. We answer two questions: (a) Can Scatchard plots of EGF binding data be analyzed productively in terms of two noninteracting receptor populations with different affinities if EGF induced receptor aggregation occurs? No. If two affinities characterize aggregated and monomeric EGF receptors, we show that the Scatchard plot should have curvature characteristic of positively cooperative binding, the opposite of that observed. Thus, the interpretation that the high affinity population represents aggregated receptors and the low affinity population nonaggregated receptors is wrong. If the two populations are interpreted without reference to receptor aggregation, an important determinant of Scatchard plot shape is ignored. (b) Can a model for EGF receptor aggregation and EGF binding be consistent with the "negative curvature" (i.e., curvature characteristic of negatively cooperative binding) observed in most Scatchard plots of EGF binding data? Yes. In addition, the restrictions on the model parameters required to obtain negatively curved Scatchard plots provide new information about binding and aggregation. In particular, EGF binding to aggregated receptors must be negatively cooperative, i.e., binding to a receptor in a dimer (or higher oligomer) having one receptor already bound occurs with lower affinity than the initial binding event. A third question we consider is whether the model we present can be used to detect the presence of mechanisms other than receptor aggregation that are contributing to Scatchard plot curvature. For the membrane and cell binding data we analyzed, the best least squares fits of the model to each of the four data sets deviate systematically from the data, indicating that additional factors are also important in shaping the binding curves. Because we have controlled experimentally for many sources of receptor heterogeneity, we have limited the potential explanations for residual Scatchard plot curvature.

In many situations, cell-cell adhesion is mediated by multiple ligand-receptor pairs. For example, the interaction between T cells and antigen-presenting cells of the immune system is mediated not only by T cell receptors and their ligands (peptide-major histocompatibility complex) but also by binding of intracellular adhesion molecules. Interestingly, these binding pairs have different resting lengths. Fluorescent labeling reveals segregation of the longer adhesion molecules from the shorter T cell receptors in this case. Here, we explore the thermal equilibrium of a general cell-cell interaction mediated by two ligand-receptor pairs to examine competition between the elasticity of the cell wall, nonspecific intercellular repulsion, and bond formation, leading to segregation of bonds of different lengths at equilibrium. We make detailed predictions concerning the relationship between physical properties of the membrane and ligand-receptor pairs and equilibrium pattern formation, and suggest experiments to refine our understanding of the system. We demonstrate our model by application to the T cell/antigen-presenting-cell system and outline applications to natural killer cell adhesion.

The pool of HIV type 1 (HIV-1) on follicular dendritic cells (FDC) is an important reservoir that has the potential to perpetuate infection (1-3). Although antiretroviral therapies that block viral replication have no direct effect on viral clearance, these therapies are associated with loss of HIV-1 from FDC (4-7). Cavert et al. (4) observed that the amount of HIV-1 on FDC, estimated as Ϸ10 11 virions, decreased by up to 5-fold during the first 2 d of potent antiretroviral therapy and by up to more than four orders of magnitude after 6 mo. This clearance of FDC-associated HIV-1 during antiretroviral therapy suggested that HIV-1 might be eradicated from the FDC reservoir, and an estimate of 30 mo to eradication was proposed (4).To evaluate further the prospect of eradicating or substantially reducing FDC-associated HIV-1 through highly active antiretroviral therapy (HAART), we develop and analyze two related mathematical models for the reversible binding of HIV-1 to FDC via ligand-receptor interactions. One model is a deterministic mass-action model that allows us to follow the time course of dissociation for a population of virions initially on FDC when therapy reduces the pool of virus available for binding to FDC. This model is useful for examining early events during treatment. The other model is a stochastic model that allows us to determine the distribution of dissociation times for individual virions. This model is useful for examining late events during treatment and assessing the treatment time required to eliminate HIV-1 on FDC. These models also allow us to determine how physical quantities, such as the surface density of receptors or the valence of a virion, influence the dissociation process.The mathematical models developed here are based on our current understanding of the physical chemistry of antigen trapping by FDC (8). HIV-1 is held on the surface of FDC through interactions with complement receptors (9) and possibly Fc receptors that bind antibodies attached to HIV-1. FDC express complement receptors CR1, CR2, and CR3 (10). These receptors bind proteolytic fragments of complement component C3 (11): CR1 binds C3b; CR2 binds iC3b, C3dg, and C3d; and CR3 binds iC3b. Ligands of CR2 have been detected on plasma virus (12, 13). One mechanism that contributes to C3 deposition on HIV-1 is direct binding of C1q to sites on the HIV-1 transmembrane glycoprotein gp41 (14), which leads to activation of complement via the classical pathway (15). In our models, we focus on interactions of CR2 on FDC with terminal C3 fragments (C3dg and C3d) on HIV-1. By focusing on this subset of interactions involved in binding of HIV-1 to FDC, we obtain a minimal estimate of the treatment time required to eliminate FDC-associated HIV-1. ModelsModels are based on the reaction scheme illustrated in Fig. 1. We treat CR2 as a monovalent cell-surface receptor, which is consistent with the observed stoichiometry of CR2 binding to C3dg (16), and we treat a complement coated virion as a multivalent ligand that expresses a set of...

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In RBL-2H3 rat leukemic mast cells, cross-linking IgE-receptor complexes with anti-IgE antibody leads to degranulation. Receptor cross-linking also stimulates the redistribution of receptors on the cell surface, a process observed here by labeling the anti-IgE with 15 nm protein A-gold particles that are visible by back-scattered electron imaging in the scanning electron microscope. We report that anti-IgE binding stimulates the redistribution of IgE-receptor complexes at 37 degrees C from a dispersed topography to distributions dominated sequentially by short chains, small clusters, and large aggregates of cross-linked receptors. Cells incubated with 1 microgram/ml anti-IgE, a concentration that stimulates maximum net secretion, redistribute receptors into chains and small clusters during a 15 min incubation period. At 3 and 10 micrograms/ml anti-IgE, net secretion is reduced and the majority of receptors redistribute rapidly into clusters and large aggregates. The addition of Fab fragments with the high anti-IgE concentrations, to reduce cross-linking, delays receptor aggregation and enhances secretion. The progression of receptors from small clusters to large aggregates is prevented in cells treated with dihydrocytochalasin B to prevent F-actin assembly. These results establish that characteristic patterns of receptor topography are correlated with receptor activity. In particular, they link the formation of large receptor aggregates to reduced signalling activity. Cytoskeleton-membrane interaction is implicated in the formation or stabilization of the large receptor clusters.