Membrane-mediated regulation of the intrinsically disordered CD3ϵ cytoplasmic tail of the TCR.

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.

Estimating the probability of polyreactive antibodies 4E10 and 2F5 disabling a gp41 trimer after T cell-HIV adhesion.

A few broadly neutralizing antibodies, isolated from HIV-1 infected individuals, recognize epitopes in the membrane proximal external region (MPER) of gp41 that are transiently exposed during viral entry. The best characterized, 4E10 and 2F5, are polyreactive, binding to the viral membrane and their epitopes in the MPER. We present a model to calculate, for any antibody concentration, the probability that during the pre-hairpin intermediate, the transient period when the epitopes are first exposed, a bound antibody will disable a trivalent gp41 before fusion is complete. When 4E10 or 2F5 bind to the MPER, a conformational change is induced that results in a stably bound complex. The model predicts that for these antibodies to be effective at neutralization, the time to disable an epitope must be shorter than the time the antibody remains bound in this conformation, about five minutes or less for 4E10 and 2F5. We investigate the role of avidity in neutralization and show that 2F5 IgG, but not 4E10, is much more effective at neutralization than its Fab fragment. We attribute this to 2F5 interacting more stably than 4E10 with the viral membrane. We use the model to elucidate the parameters that determine the ability of these antibodies to disable epitopes and propose an extension of the model to analyze neutralization data. The extended model predicts the dependencies of IC50 for neutralization on the rate constants that characterize antibody binding, the rate of fusion of gp41, and the number of gp41 bridging the virus and target cell at the start of the pre-hairpin intermediate. Analysis of neutralization experiments indicate that only a small number of gp41 bridges must be disabled to prevent fusion. However, the model cannot determine the exact number from neutralization experiments alone.

Taste of sugar at the membrane: thermodynamics and kinetics of the interaction of a disaccharide with lipid bilayers.

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.

Quantifying intramolecular binding in multivalent interactions: a structure-based synergistic study on Grb2-Sos1 complex.

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.

A detailed mathematical model predicts that serial engagement of IgE-Fc epsilon RI complexes can enhance Syk activation in mast cells.

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 FcepsilonRI 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 membrane proteins by cytosolic cross-linkers: theory and simulation of the LAT-Grb2-SOS1 system.

Ligand-induced receptor aggregation is a well-known mechanism for initiating intracellular signals but oligomerization of distal signaling molecules may also be required for signal propagation. Formation of complexes containing oligomers of the transmembrane adaptor protein, linker for the activation of T cells (LAT), has been identified as critical in mast cell and T cell activation mediated by immune response receptors. Cross-linking of LAT arises from the formation of a 2:1 complex between the adaptor Grb2 and the nucleotide exchange factor SOS1, which bridges two LAT molecules through the interaction of the Grb2 SH2 domain with a phosphotyrosine on LAT. We model this oligomerization and find that the valence of LAT for Grb2, which ranges from zero to three, is critical in determining the nature and extent of aggregation. A dramatic rise in oligomerization can occur when the valence switches from two to three. For valence three, an equilibrium theory predicts the possibility of forming a gel-like phase. This prediction is confirmed by stochastic simulations, which make additional predictions about the size of the gel and the kinetics of LAT oligomerization. We discuss the model predictions in light of recent experiments on RBL-2H3 and Jurkat E6.1 cells and suggest that the gel phase has been observed in activated mast cells.

Soluble MD2 increases TLR4 levels on the epithelial cell surface.

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.

Combinatorial diversity of Syk recruitment driven by its multivalent engagement with FcεRIγ.

Syk/Zap70 family kinases are essential for signaling via multichain immune-recognition receptors such as tetrameric (αßγ2) 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.

Kinetic proofreading model.

Kinetic proofreading is an intrinsic property of the cell signaling process. It arises as a consequence of the multiple interactions that occur after a ligand triggers a receptor to initiate a ignaling cascade and it ensures that false signals do not propagate to completion. In order for an active signaling complex to form after a ligand binds to a cell surface receptor, a sequence of binding and phosphorylation events must occur that are rapidly reversed if the ligand dissociates from the receptor. This gives rise to a mechanism by which cells can discriminate among ligands that bind to the same receptor but form ligand-receptor complexes with different lifetimes. We review experiments designed to test for kinetic proofreading and models that exhibit kinetic proofreading.

A network model of early events in epidermal growth factor receptor signaling that accounts for combinatorial complexity.

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 EGF-induced 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.

Modeling the early signaling events mediated by FcepsilonRI.

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.

A mechanistic model of early FcεRI signaling: lipid rafts and the question of protection from dephosphorylation.

We present a model of the early events in mast cell signaling mediated by FcεRI where the plasma membrane is composed of many small ordered lipid domains (rafts), surrounded by a non-order region of lipids consisting of the remaining plasma membrane. The model treats the rafts as transient structures that constantly form and breakup, but that maintain a fixed average number per cell. The rafts have a high propensity for harboring Lyn kinase, aggregated, but not unaggregated receptors, and the linker for the activation of T cells (LAT). Phosphatase activity in the rafts is substantially reduced compared to the nonraft region. We use the model to analyze published experiments on the rat basophilic leukemia (RBL)-2H3 cell line that seem to contradict the notion that rafts offer protection. In these experiments IgE was cross-linked with a multivalent antigen and then excess monovalent hapten was added to break-up cross-links. The dephosphorylation of the unaggregated receptor (nonraft associated) and of LAT (raft associated) were then monitored in time and found to decay at similar rates, leading to the conclusion that rafts offer no protection from dephosphorylation. In the model, because the rafts are transient, a protein that is protected while in a raft will be subject to dephosphorylation when the raft breaks up and the protein finds itself in the nonraft region of the membrane. We show that the model is consistent with the receptor and LAT dephosphorylation experiments while still allowing rafts to enhance signaling by providing substantial protection from phosphatases.

Modeling and simulation of aggregation of membrane protein LAT with molecular variability in the number of binding sites for cytosolic Grb2-SOS1-Grb2.

The linker for activation of T cells (LAT), the linker for activation of B cells (LAB), and the linker for activation of X cells (LAX) form a family of transmembrane adaptor proteins widely expressed in lymphocytes. These scaffolding proteins have multiple binding motifs that, when phosphorylated, bind the SH2 domain of the cytosolic adaptor Grb2. Thus, the valence of LAT, LAB and LAX for Grb2 is variable, depending on the strength of receptor activation that initiates phosphorylation. During signaling, the LAT population will exhibit a time-varying distribution of Grb2 valences from zero to three. In the cytosol, Grb2 forms 1:1 and 2:1 complexes with the guanine nucleotide exchange factor SOS1. The 2:1 complex can bridge two LAT molecules when each Grb2, through their SH2 domains, binds to a phosphorylated site on a separate LAT. In T cells and mast cells, after receptor engagement, receptor phosphoyrlation is rapidly followed by LAT phosphorylation and aggregation. In mast cells, aggregates containing more than one hundred LAT molecules have been detected. Previously we considered a homogeneous population of trivalent LAT molecules and showed that for a range of Grb2, SOS1 and LAT concentrations, an equilibrium theory for LAT aggregation predicts the formation of a gel-like phase comprising a very large aggregate (superaggregate). We now extend this theory to investigate the effects of a distribution of Grb2 valence in the LAT population on the formation of LAT aggregates and superaggregate and use stochastic simulations to calculate the fraction of the total LAT population in the superaggregate.

A biophysical model of cell adhesion mediated by immunoadhesin drugs and antibodies.

A promising direction in drug development is to exploit the ability of natural killer cells to kill antibody-labeled target cells. Monoclonal antibodies and drugs designed to elicit this effect typically bind cell-surface epitopes that are overexpressed on target cells but also present on other cells. Thus it is important to understand adhesion of cells by antibodies and similar molecules. We present an equilibrium model of such adhesion, incorporating heterogeneity in target cell epitope density, nonspecific adhesion forces, and epitope immobility. We compare with experiments on the adhesion of Jurkat T cells to bilayers containing the relevant natural killer cell receptor, with adhesion mediated by the drug alefacept. We show that a model in which all target cell epitopes are mobile and available is inconsistent with the data, suggesting that more complex mechanisms are at work. We hypothesize that the immobile epitope fraction may change with cell adhesion, and we find that such a model is more consistent with the data, although discrepancies remain. We also quantitatively describe the parameter space in which binding occurs. Our model elaborates substantially on previous work, and our results offer guidance for the refinement of therapeutic immunoadhesins. Furthermore, our comparison with data from Jurkat T cells also points toward mechanisms relating epitope immobility to cell adhesion.

Guidelines for visualizing and annotating rule-based models.

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 (FcεRI) 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.

Shaping the response: the role of FcεRI and Syk expression levels in mast cell signaling.

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.

Binding mechanisms of PEGylated ligands reveal multiple effects of the PEG scaffold.

A series of synthetic ligands consisting of poly(ethylene glycol) (PEG), capped on one or both ends with the hapten 2,4-dinitrophenyl (DNP), were previously shown to be potent inhibitors of cellular activation in RBL mast cells stimulated by a multivalent antigen [Baird, E. J., Holowka, D., Coates, G. W., and Baird, B. (2003) Biochemistry 42, 12739-12748]. In this study, we systematically investigated the effect of increasing length of the PEG scaffold on the binding of these monovalent and bivalent ligands to anti-DNP IgE in solution. Our analysis reveals evidence for an energetically favorable interaction between two monovalent ligands bound to the same receptor, when the PEG molecular mass exceeds approximately 5 kDa. Additionally, for ligands with much higher molecular masses (>10 kDa PEG), the binding of a single ligand apparently leads to a steric exclusion of the second binding site by the bulky PEG scaffold. These results are further corroborated by data from an alternate fluorescence-based assay that we developed to quantify the capacity of these ligands to displace a small hapten bound to IgE. This new assay monitors the displacement of a small, receptor-bound hapten by a competitive monovalent ligand and thus quantifies the competitive inhibition offered by a monovalent ligand. We also show that, for bivalent ligands, inhibitory capacity is correlated with the capacity to form effective intramolecular cross-links with IgE.

Kinetic proofreading of ligand-FcepsilonRI interactions may persist beyond LAT phosphorylation.

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 FcepsilonRI, 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 Ca(2+), and degranulation exhibit kinetic proofreading downstream of LAT phosphorylation. These results suggest that ligand-bound FcepsilonRI and LAT form a complex that is required for effective signal transmission.