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Syk/Zap70 family kinases are essential for signaling via multichain immune-recognition receptors such as tetrameric (αβγ2) FcεRI. Syk activation is generally attributed to cis binding of its tandem SH2 domains to dual phosphotyrosines within FcεRIγ-ITAMs (immunoreceptor tyrosine-based activation motifs). However, the mechanistic details of Syk docking on γ homodimers are unresolved. Here, we estimate that multivalent interactions for WT Syk improve cis-oriented binding by three orders of magnitude. We applied molecular dynamics (MD), hybrid MD/worm-like chain polymer modeling, and live cell imaging to evaluate relative binding and signaling output for all possible cis and trans Syk–FcεRIγ configurations. Syk binding is likely modulated during signaling by autophosphorylation on Y130 in interdomain A, since a Y130E phosphomimetic form of Syk is predicted to lead to reduced helicity of interdomain A and alter Syk’s bias for cis binding. Experiments in reconstituted γ-KO cells, whose γ subunits are linked by disulfide bonds, as well as in cells expressing monomeric ITAM or hemITAM γ-chimeras, support model predictions that short distances between γ ITAM pairs are required for trans docking. We propose that the full range of docking configurations improves signaling efficiency by expanding the combinatorial possibilities for Syk recruitment, particularly under conditions of incomplete ITAM phosphorylation.

Syk/Zap70 family kinases are essential for signaling via multichain immune-recognition receptors such as the tetrameric (αβγ2) FcεRI The simplest model assumes that Syk activation occurs throughcisbinding of its tandem SH2 domains to dual phosphotyrosines within immunoreceptor tyrosine-based activation motifs of individual γ chains. In this model, Syk activity is modulated by phosphorylation occurring between adjacent Syk molecules docked on γ homodimers and by Lyn molecules bound to FcεRIβ. However, the mechanistic details of Syk docking on γ homodimers are not fully resolved, particularly the possibility oftransbinding orientations and the impact of Y130 autophosphorylation within Syk interdomain A. Analytical modeling shows that multivalent interactions lead to increased WT Sykcis-oriented binding by three orders of magnitude. Molecular dynamics (MD) simulations show increased inter-SH2 flexibility in a Y130E phosphomimetic form of Syk, associated with reduced overall helicity of interdomain A. Hybrid MD/worm-like chain polymer models show that the Y130E substitution reducescisbinding of Syk. We report computational models and estimates of relative binding for all possiblecisandtrans2:2 Syk:FcεRIγ complexes. Calcium imaging experiments confirm model predictions thatcisbinding of WT Syk is strongly preferred for efficient signaling, whiletransconformations trigger weak but measurable responses.

Sugar recognition at the membrane is critical in various physiological processes. Many aspects of sugar-membrane interaction are still unknown. We take an integrated approach by combining conventional molecular-dynamics simulations with enhanced sampling methods and analytical models to understand the thermodynamics and kinetics of a di-mannose molecule in a phospholipid bilayer system. We observe that di-mannose has a slight preference to localize at the water-phospholipid interface. Using umbrella sampling, we show the free energy bias for this preferred location to be just −0.42 kcal/mol, which explains the coexistence of attraction and exclusion mechanisms of sugar-membrane interaction. Accurate estimation of absolute entropy change of water molecules with a two-phase model indicates that the small energy bias is the result of a favorable entropy change of water molecules. Then, we incorporate results from molecular-dynamics simulation in two different ways to an analytical diffusion-reaction model to obtain association and dissociation constants for di-mannose interaction with membrane. Finally, we verify our approach by predicting concentration dependence of di-mannose recognition at the membrane that is consistent with experiment. In conclusion, we provide a combined approach for the thermodynamics and kinetics of a weak ligand-binding system, which has broad implications across many different fields.

Many receptor systems initiate cell signaling through ligand-induced receptor aggregation. For bivalent ligands binding to mono- or bivalent receptors, a plot of the equilibrium concentration of receptors in aggregates against the log of the free ligand concentration, the cross-linking curve, is symmetric and bell shaped. However, steady state cellular responses initiated through receptor cross-linking may have a different dependence on ligand concentration than the aggregated receptors that initiate and maintain these responses. The authors illustrate by considering the activation of the protein kinase Syk that rapidly occurs after high affinity receptors for IgE, FcεRI, are aggregated on the surface of mast cells and basophils. Using a mathematical model of Syk activation the authors investigate two effects, one straightforward and one less so, that result in Syk activation not qualitatively following the cross-linking curve. Model predictions show that if the mechanism by which Syk is fully activated involves the transphosphorylation of Syk by Syk, then Syk activation curves can be either bell shaped or double humped, depending on the cellular concentrations of Syk and FcεRI. The model also predicts that the Syk activation curve can be non-symmetric with respect to the ligand concentration. The cell can exhibit differential Syk activation at two different ligand concentrations that produce identical distributions of receptor aggregates that form and dissociate at the same rates. The authors discuss how, even though it is only receptor aggregates that trigger responses, differences in total ligand concentration can lead to subtle kinetic effects that yield qualitative differences in the levels of Syk activation.

The accessory protein MD2 has been implicated in LPS-mediated activation of the innate immune system by functioning as a co-receptor with TLR4 for LPS binding at the cell surface. Epithelial cells that play a role in primary immune response, such as in the lung or gut, often express TLR4, but are dependent on circulating soluble MD2 (sMD2) to bind TLR4 to assemble the functional receptor. In this study, we show that sMD2 incubation with HEK293 epithelial cells transfected with TLR4 increases the cell surface levels of TLR4 in the absence of LPS. Dose response studies reveal that a threshold sMD2 concentration (approximately 450 nM) stimulates maximal TLR4 levels on the cell surface, whereas higher concentrations of sMD2 (approximately 1800 nM) reduce these enhanced TLR4 levels. We show evidence that MD2 multimer formation is increased at these higher concentrations of sMD2 and that addition of LPS to sMD2-stimulated cells masks the enhanced TLR4 cell surface levels, most likely due to the LPS-induced downregulation of TLR4 by endocytosis following receptor stimulation. All together, these results support a model in which sMD2 binds to TLR4 and increases TLR4 levels at the cell surface by preventing TLR4 turnover through the endocytic pathway. Thus, sMD2 may prime epithelial cells for enhanced immunoresponsive function prior to LPS exposure.

The high affinity interleukin-2 receptor is composed of three cell surface subunits, IL-2Ralpha, IL-2Rbeta, and IL-2Rgamma. Functional forms of the IL-2 receptor exist, however, that enlist only two of the three subunits. On activated T-cells, the alpha- and beta-subunits combine as a preformed heterodimer (the pseudo-high affinity receptor) that serves to capture IL-2. On a subpopulation of natural killer cells, the beta- and gamma-subunits interact in a ligand-dependent manner to form the intermediate affinity receptor site. Previously, we have demonstrated the feasibility of employing coiled-coil molecular recognition for the solution assembly of a heteromeric IL-2 receptor complex. In that study, although the receptor was functional, the coiled-coil complex was a trimer rather than the desired heterodimer. We have now redesigned the hydrophobic heptad sequences of the coiled-coils to generate soluble forms of both the pseudo-high affinity and the intermediate affinity heterodimeric IL-2 receptors. The properties of these complexes were examined and their relevance to the physiological IL-2 receptor mechanism is discussed.

Alefacept is a chimeric protein combining CD58 immunoglobulin-like domain 1 with human IgG1 Fc. Alefacept mediates adhesion by bridging CD2 on T cells to activating Fc receptors on effector cells, but the equilibrium binding parameters have not been determined. Alefacept mediated T cell killing by NK cells and adhesion between CD2- and CD16-expressing cells at an optimum concentration of 100 nM. We introduce novel measurements with supported planer bilayers, from which key two-dimensional and three-dimensional parameters can be determined by data fitting. Alefacept competitively inhibited cell bilayer adhesion mediated by the CD2-CD58 interaction. Alefacept mediated maximal adhesion of CD2(+) T cells to CD16B, an Fc receptor, in planar bilayers at 500 nM. A mechanistic model for alefacept-mediated cell-bilayer adhesion allowed fitting of the data and determination of two-dimensional binding parameters. These included the density of bonds in the adhesion area, which grew to maintain a consistent average bond density of 200 molecules/microm(2) and two-dimensional association constants of 3.1 and 630 microm(2) for bivalently and monovalently bound forms of alefacept, respectively. The maximum number of CD16 bound and the fit value of 4,350 CD2 per cell are much lower than the 40,000 CD2 per cell measured with anti-CD2 Fab. These results suggest that additional information is needed to correctly predict Alefacept-mediated bridge formation.

A recent workshop discussed the recognition of multiple distinct ligands by individual T cell and B cell receptors and the implications of this discovery for lymphocyte biology. The workshop recommends general use of the term polyspecificity because it emphasizes two fundamental aspects, the inherent specificity of receptor recognition and the ability to recognize multiple ligands. Many different examples of polyspecificity and the structural mechanisms were discussed, and the group concluded that polyspecificity is a general, inherent feature of TCR and antibody recognition. This review summarizes the relevance of polyspecificity for lymphocyte development, activation and disease processes.

Cells may discriminate among ligands with different dwell times for receptor binding through a mechanism called kinetic proofreading in which the formation of an activated receptor complex requires a progression of events that is aborted if the ligand dissociates before completion. This mechanism explains how, at equivalent levels of receptor occupancy, a rapidly dissociating ligand can be less effective than a more slowly dissociating analog at generating distal cellular responses. Simple mathematical models predict that kinetic proofreading is limited to the initial complex; once the signal passes to second messengers, the dwell time no longer regulates the signal. This suggests that an assay for kinetic proofreading might be used to determine which activation events occur within the initial signaling complex. In signaling through the high affinity IgE receptor FcεRI, the transmembrane adaptor called linker for activation of T cells (LAT) is thought to nucleate a distinct secondary complex. Experiments in which the concentrations of two ligands with different dwell times are adjusted to equalize the level of LAT phosphorylation in rat basophilic leukemia 2H3 cells show that Erk2 phosphorylation, intracellular Ca2+, and degranulation exhibit kinetic proofreading downstream of LAT phosphorylation. These results suggest that ligand-bound FcεRI and LAT form a complex that is required for effective signal transmission.

The regulation of T-cell-mediated immune responses depends on the phosphorylation of immunoreceptor tyrosine-based activation motifs (ITAMs) on T-cell receptors. Although many details of the signaling cascades are well understood, the initial mechanism and regulation of ITAM phosphorylation remains unknown. We used molecular dynamics simulations to study the influence of different compositions of lipid bilayers on the membrane association of the CD3ϵ cytoplasmic tails of the T-cell receptors. Our results show that binding of CD3ϵ to membranes is modulated by both the presence of negatively charged lipids and the lipid order of the membrane. Free-energy calculations reveal that the protein-membrane interaction is favored by the presence of nearby basic residues and the ITAM tyrosines. Phosphorylation minimizes membrane association, rendering the ITAM motif more accessible to binding partners. In systems mimicking biological membranes, the CD3ϵ chain localization is modulated by different facilitator lipids (e.g., gangliosides or phosphoinositols), revealing a plausible regulatory effect on activation through the regulation of lipid composition in cell membranes.

We consider a model of early events in signaling by the epidermal growth factor (EGF) receptor (EGFR). The model includes EGF, EGFR, the adapter proteins Grb2 and Shc, and the guanine nucleotide exchange factor Sos, which is activated through EGFinduced formation of EGFR‐Grb2‐Sos and EGFR‐Shc‐Grb2‐Sos assemblies at the plasma membrane. The protein interactions involved in signaling can potentially generate a diversity of protein complexes and phosphoforms; however, this diversity has been largely ignored in models of EGFR signaling. Here, we develop a model that accounts more fully for potential molecular diversity by specifying rules for protein interactions and then using these rules to generate a reaction network that includes all chemical species and reactions implied by the protein interactions. We obtain a model that predicts the dynamics of 356 molecular species, which are connected through 3749 unidirectional reactions. This network model is compared with a previously developed model that includes only 18 chemical species but incorporates the same scope of protein interactions. The predictions of this model are reproduced by the network model, which also yields new predictions. For example, the network model predicts distinct temporal patterns of autophosphorylation for different tyrosine residues of EGFR. A comparison of the two models suggests experiments that could lead to mechanistic insights about competition among adapter proteins for EGFR binding sites and the role of EGFR monomers in signal transduction. © 2005 Elsevier Ireland Ltd. All rights reserved.

There is a fundamental difference in complexity between signaling initiated by ligands on the surface of one cell binding to receptors on the surface of another cell and ligands in solution binding to these receptors. The fact that two cells must approach each other and form a number of intercellular bonds of different types, all within the restricted geometry of the intercellular contact region, introduces the possibility of complex spatio-temporal dynamics of surface receptors that is not present otherwise. Mathematical modelling of these dynamics is in its early stages. However, useful tools have emerged. The purpose of this paper is to describe some of these mathematical tools, indicating their strengths and shortcomings, and suggest some directions for future theoretical studies.

CD8 + T cells recognize peptides of eight to nine amino acid residues long in the context of MHC class I molecules on the surface of antigen-presenting cells (APCs). This recognition event is highly sensitive, as evidenced by the fact that T cells can be activated by cognate peptide/MHC complex (pMHC) at extremely low densities (1-50 molecules). High sensitivity is particularly valuable for detection of antigens at low density, such as those derived from tumor cells and intracellular pathogens, which can down-modulate cognate pMHCs from the surface of APCs to evade recognition by the adaptive immune system. T cell activation is only triggered in response to interactions between the T cell receptor (TCR) and the pMHC ligand that reach a specific half-life threshold. However, interactions with excessively long half-lives result in impaired T cell activation. Thus, efficient T cell activation by pMHC on the surface of APCs requires an optimal dwell time of TCR-pMHC interaction. Here, we show that, although this is a requirement at low cognate pMHC density on the APC surface, at high epitope density there is no impairment of T cell activation by extended TCR-pMHC dwell times. This observation was predicted by mathematical simulations for T cell activation by pMHC at different densities and supported by experiments performed on APCs selected for varied expression of cognate pMHC. According to these results, effective T cell activation depends on a complex interplay between inherent TCR-pMHC binding kinetics and the epitope density on the APC.

The process of signalling through receptors of the immune system involves highly connected networks of interacting components. Understanding the often counter-intuitive behaviour of these networks requires the development of mathematical and computational models. Here, we focus on the application of these models to understand signalling through immune receptors that are involved in antigen recognition. Simple models, which ignore the details of the signalling machinery, have provided considerable insight into how ligand–receptor binding properties affect signalling outcomes. Detailed models, which include specific molecular components and interactions beyond the ligand and receptor, are difficult to develop but have already provided new mechanistic understanding and uncovered relationships that are difficult to detect by experimental observation alone. They offer hope that models might eventually predict the full spectrum of signalling behaviour.

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.

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.

We present a detailed mathematical model of the phosphorylation and dephosphorylation events that occur upon ligand-induced receptor aggregation, for a transfectant expressing FcepsilonRI, Lyn, Syk and endogenous phosphatases that dephosphorylate exposed phosphotyrosines on FcepsilonRI and Syk. Through model simulations we show how changing the ligand concentration, and consequently the concentration of receptor aggregates, can change the nature of a cellular response as well as its amplitude. We illustrate the value of the model in analyzing experimental data by using it to show that the intrinsic rate of dephosphorylation of the FcepsilonRI gamma immunoreceptor tyrosine-based activation motif (ITAM) in rat basophilic leukemia (RBL) cells is much faster than the observed rate, provided that all of the cytosolic Syk is available to receptors.

Interleukin-2 is the primary T cell growth factor secreted by activated T cells. IL-2 is an alpha-helical cytokine that binds to a multisubunit receptor expressed on the surface of a variety of cell types. IL-2Ralpha, IL-2Rbeta, and IL-2Rgammac receptor subunits expressed on the surface of cells may aggregate to form distinct binding sites of differing affinities. IL-2Rgammac was the last receptor subunit to be identified. It has since been shown to be shared by at least five other cytokine receptors. In this study, we have probed the role of IL-2Rgammac in the assembly of IL-2R complexes and in ligand binding. We demonstrate that in the absence of ligand IL-2Rgammac does not possess detectable affinity for IL-2Ralpha, IL-2Rbeta, or the pseudo-high-affinity binding site composed of preformed IL-2Ralpha/beta. We also demonstrate that IL-2Rgammac possesses an IL-2-dependent affinity for IL-2Rbeta and IL-2Ralpha/beta. We performed a detailed biosensor analysis to examine the interaction of soluble IL-2Rgammac with IL-2-bound IL-2Rbeta and IL-2-bound IL-2Ralpha/beta. The kinetic and equilibrium constants for sIL-2Rgammac binding to these two different liganded complexes were similar, indicating that IL-2Ralpha does not play a role in recruitment of IL-2Rgammac. We also determined that the binding of IL-2 to the isolated IL-2Rgammac was very weak (approximate K(D) = 0.7 mM). The experimental methodologies and principles derived from these studies can be extended to at least five other cytokines that share IL-2Rgammac as a receptor subunit.

Cholera toxin entry into mammalian cells is mediated by binding of the pentameric B subunit (CTB) to ganglioside GM(1) in the cell membrane. We used flow cytometry to quantitatively measure in real time the interactions of fluorescently labeled pentameric cholera toxin B-subunit (FITC-CTB) with its ganglioside receptor on microsphere-supported phospholipid membranes. A model that describes the multiple steps of this mode of recognition was developed to guide our flow cytometric experiments and extract relevant equilibrium and kinetic rate constants. In contrast to previous studies, our approach takes into account receptor cross-linking, an important feature for multivalent interactions. From equilibrium measurements, we determined an equilibrium binding constant for a single subunit of FITC-CTB binding monovalently to GM(1) presented in bilayers of approximately 8 x 10(7) M(-1) while that for binding to soluble GM(1)-pentasaccharide was found to be approximately 4 x 10(6) M(-1). From kinetic measurements, we determined the rate constant for dissociation of a single site of FITC-CTB from microsphere-supported bilayers to be (3.21 +/- 0.03) x 10(-3) s(-1), and the rate of association of a site on FITC-CTB in solution to a GM(1) in the bilayer to be (2.8 +/- 0.4) x 10(4) M(-1) s(-1). These values yield a lower estimate for the equilibrium binding constant of approximately 1 x 10(7) M(-1). We determined the equilibrium surface cross-linking constant [(1.1 +/- 0.1) x 10(-12) cm(2)] and from this value and the value for the rate constant for dissociation derived a value of approximately 3.5 x 10(-15) cm(2) s(-1) for the forward rate constant for cross-linking. We also compared the interaction of the receptor binding B-subunit with that of the whole toxin (A- and B-subunits). Our results show that the whole toxin binds with approximately 100-fold higher avidity than the pentameric B-subunit alone which is most likely due to the additional interaction of the A(2)-subunit with the membrane surface. Interaction of cholera toxin B-subunit and whole cholera toxin with gangliosides other than GM(1) revealed specific binding only to GD1(b) and asialo-GM(1). These interactions, however, are marked by low avidity and require high receptor concentrations to be observed.

In the context of cell signaling, kinetic proofreading was introduced to explain how cells can discriminate among ligands based on a kinetic parameter, the ligand-receptor dissociation rate constant. In the kinetic proofreading model of cell signaling, responses occur only when a bound receptor undergoes a complete series of modifications. If the ligand dissociates prematurely, the receptor returns to its basal state and signaling is frustrated. We extend the model to deal with systems where aggregation of receptors is essential to signal transduction, and present a version of the model for systems where signaling depends on an extrinsic kinase. We also investigate the kinetics of signaling molecules, “messengers,” that are generated by aggregated receptors but do not remain associated with the receptor complex. We show that the extended model predicts modes of signaling that exhibit kinetic discrimination for some range of parameters but for other parameter values show little or no discrimination and thus escape kinetic proofreading. We compare model predictions with experimental data.

The serial engagement model provides an attractive and plausible explanation for how a typical antigen presenting cell, exhibiting a low density of peptides recognized by a T cell, can initiate T cell responses. If a single peptide displayed by a major histocompatibility complex (MHC) can bind, sequentially, to different T cell receptors (TCR), then a few peptides can activate many receptors. To date, arguments supporting and questioning the prevalence of serial engagement have centered on the down-regulation of TCR after contact of T cells with antigen presenting cells. Recently, the existence of serial engagement has been challenged by the demonstration that engagement of TCR can down-regulate nonengaged bystander TCR. Here we show that for binding and dissociation rates that characterize interactions between T cell receptors and peptide-MHC, substantial serial engagement occurs. The result is independent of mechanisms and measurements of receptor down-regulation. The conclusion that single peptide-MHC engage many TCR, before diffusing out of the contact region between the antigen-presenting cell and the T cell, is based on a general first passage time calculation for a particle alternating between states in which different diffusion coefficients govern its transport.

Chemical reactions on solid surfaces are ubiquitous in natural and industrial processes. In many situations, the reaction is complicated by diffusion and convection of reactants in the surrounding media. The system as a whole is usually highly nonlinear. Theoretical analysis for this complicated phenomenon is difficult if not entirely impossible. It is highly desired to develop efficient computational tools to simulate this process. The lattice Boltzmann method, based on mesoscopic description of fluid systems, is quite suitable for this purpose. This study will present a lattice Boltzmann scheme for simulating the diffusion-convection systems with surface chemical reactions.

Accurate estimation of biomolecular reaction rates from binding data, when ligands in solution bind to receptors on the surfaces of cells or biosensors, requires an understanding of the contributions of both molecular transport and reaction. Efficient estimation of parameters requires relatively simple models. In this review, we give conditions under which various transport effects are negligible and identify simple binding models that incorporate the effects of transport, when transport cannot be neglected. We consider effects of diffusion of ligands to cell or biosensor surfaces, flow in a BIAcore biosensor, and distribution of receptors in a dextran layer above the sensor surface. We also give conditions under which soluble receptors can be expected to compete effectively with surface-bound receptors.

Optical biosensors, including the BIACORE, provide an increasingly popular method for determining reaction rates of biomolecules. In a flow chamber, with one reactant immobilized on a chip on the sensor surface, a solution containing the other reactant (the analyte) flows through the chamber. The time course of binding of the reactants is monitored. Scientists using the BIACORE to understand biomolecular reactions need to be able to separate intrinsic reaction rates from the effects of transport in the biosensor. For a model to provide a useful basis for such an analysis, it must reflect transport accurately, while remaining simple enough to couple with a routine for estimating reaction rates from BIACORE data. Models have been proposed previously for this purpose, consisting of an ordinary differential equation with 'effective rate coefficients' incorporating reaction and transport parameters. In this paper we investigate both the theoretical basis and numerical accuracy of these and related models.

Multivalent DNP-BSA is commonly used to cross-link anti-DNP IgE bound to FcεRI to stimulate cellular responses, although key features of the binding process are unknown. Fluorescence quenching can be used to study the kinetics of DNP-BSA binding to FITC-IgE. We observe that DNP-BSA binds more slowly to IgE than does an equimolar amount of a monovalent DNP ligand, suggesting that the average effective number of DNP groups per BSA is less than one. The binding data are well described by a transient hapten exposure model in which most of the DNP groups are unavailable for binding but have some probability of becoming exposed and available for binding during the time of the binding measurement. Additional experiments indicate that, for suboptimal to optimal concentrations of DNP-BSA, most of the FITC fluorescence quenching on the cell surface is due to cross-linking events. With these concentrations at 15°C, the kinetics of FITC fluorescence quenching by DNP-BSA correlates with the kinetics of DNP-BSA-stimulated tyrosine phosphorylation of FcεRI. At 35°C, the phosphorylation kinetics are biphasic during the time period in which cross-linking continues to increase. Our results establish a quantitative relationship between the timecourse for cross-linking by multivalent Ag and FcεRI-mediated signaling, and they provide the means to predict the kinetics of cross-linking under a wide variety of conditions.

Using defined oligomers of IgE, our group previously studied the quantitative relationship between the aggregation of the high affinity receptors for IgE (FcɛRI) and the earliest signals initiated by such aggregation: the phosphorylation of tyrosines on the receptor. Notably, at certain doses of the oligomers such phosphorylation reached a plateau level well before the aggregation of the receptors had reached a maximum. These findings and others led us to propose that aggregates of the receptor were competing for a limited amount of the critical kinase—thought to be Lyn in this system. This paper describes a test of this proposal. We incubated cells with two distinguishable IgEs and examined the effect of aggregating one or the other or both types on the phosphorylation. When receptors binding antigen-specific IgE were aggregated with polyvalent antigen, they became rapidly phosphorylated as expected. Remarkably, however, FcɛRI that had already been phosphorylated by the binding of dimers of IgE, became dephosphorylated simultaneously. Furthermore, when the antigen-driven aggregates were dissociated with hapten, the phosphorylation pattern reverted to that seen prior to the addition of antigen: as the antigen-driven aggregates became dephosphorylated, the receptors stably aggregated by the bound oligomers became rapidly rephosphorylated. Dephosphorylation of oligomer-driven aggregates was also partially reversed during the “spontaneous” dephosphorylation of the antigen-driven receptors seen at longer times after addition of antigen. Thus signal transduction in this system is in part regulated by the shuttling of limited amounts of the kinase that initiates the cascade of phosphorylations.

Previous studies in our laboratory established that the symmetrical bivalent ligand, N,N'-bis-[[epsilon-(2,4-dinitrophenyl)amino]caproyl]-L-tyrosyl]-L-cystin e ((DCT)2-cys), stably cross-links anti-2,4-dinitrophenyl-immunoglobulin E (IgE) bound to high affinity receptors Fc epsilonRI on the surface of RBL-2H3 cells, forming mostly cyclic dimers containing two IgE-Fc epsilonRI and two (DCT)2-cys (Posner et al. (1995) J. Immunol. 155, 3601-3609). These cyclic dimers do not trigger Ca2+ or degranulation responses under a variety of conditions. However, we find that the linearly cross-linked IgE-Fc epsilonRI formed at higher concentrations of (DCT)2-cys do trigger degranulation in the presence of cytochalasin D, an inhibitor of actin polymerization. We further investigated stimulation by (DCT)2-cys of the earliest known events in the functional response, i.e., tyrosine phosphorylation of the beta and gamma subunits of Fc epsilonRI. At the higher (DCT)2-cys concentrations corresponding to linear dimers and maximal degranulation, tyrosine phosphorylation of both beta and gamma are observed. At lower (DCT)2-cys concentrations where cross-linking is maximal and cyclic dimers are overwhelmingly dominant, only gamma tyrosine phosphorylation is observed. Cytochalasin D does not affect these phosphorylation patterns, but instead appears to enhance coupling to downstream signaling events. Phosphorylation of Syk occurs at the higher (DCT)2-cys concentrations in parallel with beta phosphorylation but does not occur in its absence at the lower (DCT)2-cys concentrations. These results suggest that cyclic dimers of IgE-Fc epsilonRI are sterically restricted such that they stimulate tyrosine phosphorylation of gamma but not beta, and this is not sufficient for Syk binding and/or activation.

Previously, we demonstrated that aggregates of the high affinity receptor for IgE (FcϵRI), formed by the binding of chemically cross-linked oligomers of IgE, continue to signal early and late cellular responses long after the formation of new aggregates is blocked. In the present work, we explore quantitatively the relationship between aggregation of the receptors and one of the earliest biochemical changes this initiates. We compare the time course of aggregate formation, inferred from studies of the binding of dimers of IgE, and the time course of phosphorylation of tyrosines on receptor subunits when the receptors are aggregated. A simple model does not fit the data. It appears that aggregates formed late in the response are less effective signaling units than those formed initially. We propose new explanations for the persistence of the response and the unusual kinetics.

In this study, we report the use of coiled-coil (leucine zipper) molecular recognition for the solution assembly of stable, high affinity, heteromeric interleukin-2 receptor complexes. Co-expression of interleukin-2 receptor alpha and beta extracellular domains (ectodomains), each fused to seven coiled-coil heptad repeats, resulted in the formation of heteromeric complexes that bound interleukin-2 in a cooperative fashion and with much higher affinity than similar homomeric complexes. The dissociation constants for these solution complexes are within the range of values reported for the comparable cell surface "pseudo high affinity" interleukin-2 receptor. Ligand-induced cross-linking of homomeric or heteromeric receptor subunits is the common signal transmission mechanism employed by hematopoietin receptors. Individual receptor ectodomains, however, often do not bind ligand with measurable affinity. This is the first study to demonstrate the feasibility of coiled-coil mediated preassembly of cytokine receptor complexes.

When bivalent ligands capable of bridging binding sites on two different receptors interact with bivalent receptors, aggregates form. The aggregates can be of two types: chains (open structures containing n receptors, n − 1 doubly bound ligands and 0, 1, or 2 singly bound ligands) and rings (closed structures containing n receptors and n doubly bound ligands). Both types of aggregates have been detected experimentally. In general, to determine the time dependence of the concentration of any particular aggregate requires solving an infinite set of coupled ordinary differential equations (ODEs). Perelson and DeLisi [19] showed that great simplification results if all receptor binding sites are equivalent, i.e., the binding properties of a site on a receptor are independent of the size of the aggregate the receptor is in. If only chains form, the problem reduces to solving two coupled ODEs for the concentrations of singly and doubly bound ligands. From the solutions to these ODEs, the time dependence of the entire aggregate size distribution can be determined. We show that the equivalent site approximation as formulated by Perelson and DeLisi [19] is incompatible with ring formation. We then present a modified equivalent site approximation that is useful if chains of any size can form but rings above a certain size ( k ) cannot. We show how to reduce the resulting infinite set of coupled ODEs to a closed system of at most 4 k + 2 ODEs for the ligand concentrations, the ring concentrations, and the concentrations of all chains up to size k . Although we can only predict the kinetics of aggregate formation for aggregates of size k or less, at equilibrium the modified equivalent site approximation yields the complete aggregate size distribution.

Mast cells and basophils play major roles in allergic responses of the immediate type (Rivera & Gilfillan, 2006). Allergic individuals produce IgE that is specific for the multivalent foreign molecules (allergens) that trigger their allergic responses. IgE binds with high affinity through its constant region to a monovalent receptor, FcǫRI, that is expressed on the surface of basophils and mast cells and that mediates much of mast cell activation in allergic reactions. Upon exposure to the allergen, the bridging of multiple IgEs by the allergen results in the aggregation of FcǫRI receptors on the cell surface, which in turn triggers a cascade of biochemical reactions that results in the release of preformed mediators from granules together with the synthesis and release of lipid mediators and cytokines. The cytosolic protein tyrosine kinase Syk plays a crucial role in FcǫRI-mediated signaling cascade in mast cells. A clone of the syk gene was first isolated on the basis of partial sequenced information of a 40 kDa kinase from porcine spleen (de Castro, 2011; Taniguchi et al., 1991). The product of this gene was identified as a nonreceptor-type protein tyrosine kinase of 72 kDa (Yang et al., 1994) and was named Spleen Tyrosine Kinase (Syk). Syk has two Src-homology 2 domains (SH2) which are separated by a linker region from the kinase domain (Siraganian et al., 2002). FcǫRI is a tetrameric complex composed of an α-chain that binds IgE to form a long-lived complex, and three subunits, a β-chain and two disulfide-linked γ-chains (Blank et al., 1989) that contain immunoreceptor tyrosine-based activation motifs (ITAMs). The FcǫRI receptor lacks intrinsic enzymatic acitivity and requires non-receptor protein tyrosine kinase activity in propagating cellular signals in allergen-stimulated mast cells and basophils. The unphosphorylated β-chain of the FcǫRI receptor associates weakly with the Src family kinase Lyn, which is anchored to the inner layer of the plasma membrane (Vonakis et al., 1997; 2001). Upon receptor aggregation, Lyn transphosphorylates tyrosines in the β and γ ITAMs. Syk from the cytosol binds with high affinity through its two SH2 domains to the doubly phosphorylated γ ITAM (Benhamou et al., 1993; Hutchcroft et al., 1992). Recent experimental

Numerous signaling proteins use multivalent binding to increase the specificity and affinity of their interactions within the cell. Enhancement arises because the effective binding constant for multivalent binding is larger than the binding constants for each individual interaction. We seek to gain both qualitative and quantitative understanding of the multivalent interactions of an adaptor protein, growth factor receptor bound protein-2 (Grb2), containing two SH3 domains interacting with the nucleotide exchange factor son-of-sevenless 1 (Sos1) containing multiple polyproline motifs separated by flexible unstructured regions. Grb2 mediates the recruitment of Sos1 from the cytosol to the plasma membrane where it activates Ras by inducing the exchange of GDP for GTP. First, using a combination of evolutionary information and binding energy calculations, we predict an additional polyproline motif in Sos1 that binds to the SH3 domains of Grb2. This gives rise to a total of five polyproline motifs in Sos1 that are capable of binding to the two SH3 domains of Grb2. Then, using a hybrid method combining molecular dynamics simulations and polymer models, we estimate the enhancement in local concentration of a polyproline motif on Sos1 near an unbound SH3 domain of Grb2 when its other SH3 domain is bound to a different polyproline motif on Sos1. We show that the local concentration of the Sos1 motifs that a Grb2 SH3 domain experiences is approximately 1000 times greater than the cellular concentration of Sos1. Finally, we calculate the intramolecular equilibrium constants for the crosslinking of Grb2 on Sos1 and use thermodynamic modeling to calculate the stoichiometry. With these equilibrium constants, we are able to predict the distribution of complexes that form at physiological concentrations. We believe this is the first systematic analysis that combines sequence, structure, and thermodynamic analyses to determine the stoichiometry of the complexes that are dominant in the cellular environment., Author Summary Many biochemical interactions are mediated by multivalent binding where signaling proteins use relatively weak promiscuous interactions to increase the strength and specificity of complex formation. For a bivalent adaptor protein binding to a multivalent ligand, the tethering of one of the adaptors binding sites to a motif on a multivalent ligand constrains the adaptors second binding site to a region with a high local concentration of ligand binding motifs. Intramolecular equilibrium constants associated with multivalency are difficult to measure. Typically, polymer models are utilized to estimate the enhancement in local concentration and, when the biomolecular equilibrium constants for the individual sites are known, to obtain intramolecular equilibrium constants. However, flexibility of structured regions in proteins that contain the binding motifs restricts the application of simple polymer models for many systems. Here, we develop a hybrid method combining molecular dynamics simulations and polymer models to estimate the intramolecular equilibrium constants. We apply this method to study the multivalent interactions between the widely expressed adaptor protein growth factor receptor bound protein-2 (Grb2) and the nucleotide exchange factor son of sevenless 1 (Sos1).

Rule-based modeling provides a means to represent cell signaling systems in a way that captures site-specific details of molecular interactions. For rule-based models to be more widely understood and (re)used, conventions for model visualization and annotation are needed. We have developed the concepts of an extended contact map and a model guide for illustrating and annotating rule-based models. An extended contact map represents the scope of a model by providing an illustration of each molecule, molecular component, direct physical interaction, post-translational modification, and enzyme–substrate relationship considered in a model. A map can also illustrate allosteric effects, structural relationships among molecular components, and compartmental locations of molecules. A model guide associates elements of a contact map with annotation and elements of an underlying model, which may be fully or partially specified. A guide can also serve to document the biological knowledge upon which a model is based. We provide examples of a map and guide for a published rule-based model that characterizes early events in IgE receptor (FceRI) signaling. We also provide examples of how to visualize a variety of processes that are common in cell signaling systems but not considered in the example model, such as ubiquitination. An extended contact map and an associated guide can document knowledge of a cell signaling system in a form that is visual as well as executable. As a tool for model annotation, a map and guide can communicate the content of a model clearly and with precision, even for large models.

The term serial engagement was introduced to describe the ability of a single peptide, bound to a MHC molecule, to sequentially interact with TCRs within the contact region between a T cell and an APC. In addition to ligands on surfaces, soluble multivalent ligands can serially engage cell surface receptors with sites on the ligand, binding and dissociating from receptors many times before all ligand sites become free and the ligand leaves the surface. To evaluate the role of serial engagement in Syk activation, we use a detailed mathematical model of the initial signaling cascade that is triggered when FcεRI is aggregated on mast cells by multivalent Ags. Although serial engagement is not required for mast cell signaling, it can influence the recruitment of Syk to the receptor and subsequent Syk phosphorylation. Simulating the response of mast cells to ligands that serially engage receptors at different rates shows that increasing the rate of serial engagement by increasing the rate of dissociation of the ligand–receptor bond decreases Syk phosphorylation. Increasing serial engagement by increasing the rate at which receptors are cross-linked (for example by increasing the forward rate constant for cross-linking or increasing the valence of the ligand) increases Syk phosphorylation. When serial engagement enhances Syk phosphorylation, it does so by partially reversing the effects of kinetic proofreading. Serial engagement rapidly returns receptors that have dissociated from aggregates to new aggregates before the receptors have fully returned to their basal state.

Aggregation of cell surface receptors, with each other or with other membrane proteins, occurs in a variety of experimental systems. The list of systems where receptor aggregation appears to be important in understanding ligand binding and cellular responses is growing rapidly. In this paper we explore the interpretation of equilibrium binding data for aggregating receptor systems. The Scatchard plot is a widely used tool for analyzing equilibrium binding data. The shape of the Scatchard plot is often interpreted in terms of multiple noninteracting receptor populations. Such an analysis does not provide a framework for investigating the role of receptor aggregation and will be misleading if there is a relation between receptor aggregation and ligand binding. We present a general model for the equilibrium binding of a ligand with any number of aggregating receptor populations and derive theoretical expressions for observable Scatchard plot features. These can be used to test particular models and estimate model parameters. We develop particular models and apply the general results in the cases of six aggregating receptor systems where ligand binding and receptor aggregation are related: cross-linking of monovalent cell surface proteins by monoclonal antibodies, cross-linking of cell surface antibodies by bivalent ligand, antibody-induced co-cross-linking of cell surface antibodies and Fcγ receptors, ligand-enhanced aggregation of identical epidermal growth factor receptors, aggregation of heterologous receptors for interleukin 2 to form a high-affinity receptor, and association of receptors, including those for interleukins 5 and 6, with nonbinding accessory proteins that influence receptor affinity or effector function.

The bivalent ligand N,N'-bis[[epsilon-[(2,4- dinitrophenyl)amino]caproyl]-L-tyrosyl]cystine [(DCT)2-Cys] binds and cross-links anti-dinitrophenyl (DNP) immunoglobulin E (IgE)-receptor complexes on the cell surface of rat basophilic leukemia cells. The rate of dissociation of this bound ligand was monitored by using a fluorescence method under two different conditions. In one case the monovalent ligand DCT was added in large excess to prevent the dissociating ligand from rebinding to unoccupied antibody combining sites. Under these conditions, dissociation of the bivalent ligand from IgE-sensitized cells proceeds to completion with kinetics that are well described by two rate constants that are independent of the time of preincubation of the bivalent ligand with the cells. In the second case, dissociation of (DCT)2-Cys from cell-bound anti-DNP IgE was monitored in the presence of a large excess of anti-DNP IgE in solution that acts as a sink to absorb the dissociated ligand. Under these conditions, the bivalent ligand becomes more resistant to dissociation as the preincubation time of the bivalent ligand with the cells is increased. An increasing fraction of the bound ligand does not dissociate on a measurable time scale in the presence of this sink. The results indicate that cell-associated IgE-receptor complexes undergo a time-dependent change that facilitates the reformation of the cross-linked state when one end of the ligand dissociates to break up the existing cross-link. The possible physical basis and functional implications of these results are discussed.