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Proteins in cell signaling networks tend to interact promiscuously through low-affinity interactions. Consequently, evaluating the physiological importance of mapped interactions can be difficult. Attempts to do so have tended to focus on single, measurable physicochemical factors, such as affinity or abundance. For example, interaction importance has been assessed on the basis of the relative affinities of binding partners for a protein of interest, such as a receptor. However, multiple factors can be expected to simultaneously influence the recruitment of proteins to a receptor (and the potential of these proteins to contribute to receptor signaling), including affinity, abundance, and competition, which is a network property. Here, we demonstrate that measurements of protein copy numbers and binding affinities can be integrated within the framework of a mechanistic, computational model that accounts for mass action and competition. We use cell line-specific models to rank the relative importance of protein-protein interactions in the epidermal growth factor receptor (EGFR) signaling network for 11 different cell lines. Each model accounts for experimentally characterized interactions of six autophosphorylation sites in EGFR with proteins containing a Src homology 2 and/or phosphotyrosine-binding domain. We measure importance as the predicted maximal extent of recruitment of a protein to EGFR following ligand-stimulated activation of EGFR signaling. We find that interactions ranked highly by this metric include experimentally detected interactions. Proteins with high importance rank in multiple cell lines include proteins with recognized, well-characterized roles in EGFR signaling, such as GRB2 and SHC1, as well as a protein with a less well-defined role, YES1. Our results reveal potential cell line-specific differences in recruitment.

The Epidermal Growth Factor Receptor (EGFR) plays an important role in both physiological and cancer-related processes. Ligand-binding to EGFR leads to phosphorylation of several tyrosine residues in the cytoplasmic tail of the receptor. Once phosphorylated, each of those residues will serve as docking sites for particular signaling proteins, such as Shc1 and Grb2, that propagate the signal and ultimately lead to different cellular responses. Upon ligand binding, phosphorylation of EGFR increases rapidly, but is followed by a significant decrease after 30 seconds. This response has been difficult to explain. While groups have incorporated mechanisms such as endocytosis or negative feedback loops into their mathematical models to explain this behavior, these predictions have not completely recapitulated the behavior and/or remain to be experimentally tested. We have built a computational model of EGFR signaling to allow us assess the contribution of the different proposed mechanisms on the observed behavior. To test the model, we used Single-Molecule Pull-down (SiMPull) to determine the phosphorylation state of thousands of individual receptors. This unique data reveals the fraction of receptors phosphorylated at specific tyrosine residues as a function of time after activation. To fit the data, we needed to include a novel mechanism to explain the overshoot in EGFR phosphorylation in which increased Shc1-Grb2 interaction reduces Grb2 availability to bind to the phospho-sites in the receptor, consequently leaving those sites more accessible to phosphatases. Our results indicate that the ligand-induced interaction between Shc1 and Grb2 is primarily responsible for the early overshoot observed in EGFR phosphorylation. The increased association of phosphorylated Shc1 with Grb2 has been demonstrated in vitro. Experiments to test this prediction in cells are underway.

We use flow cytometry to characterize equilibrium binding of a fluorophore-labeled trivalent model antigen to bivalent IgE-FcεRI complexes on RBL cells. We find that flow cytometric measurements are consistent with an equilibrium model for ligand-receptor binding in which binding sites are assumed to be equivalent and ligand-induced receptor aggregates are assumed to be acyclic. However, this model predicts extensive receptor aggregation at antigen concentrations that yield strong cellular secretory responses, which is inconsistent with the expectation that large receptor aggregates should inhibit such responses. To investigate possible explanations for this discrepancy, we evaluate four rule-based models for interaction of a trivalent ligand with a bivalent cell-surface receptor that relax simplifying assumptions of the equilibrium model. These models are simulated using a rule-based kinetic Monte Carlo approach to investigate the kinetics of ligand-induced receptor aggregation and to study how the kinetics and equilibria of ligand-receptor interaction are affected by steric constraints on receptor aggregate configurations and by the formation of cyclic receptor aggregates. The results suggest that formation of linear chains of cyclic receptor dimers may be important for generating secretory signals. Steric effects that limit receptor aggregation and transient formation of small receptor aggregates may also be important.

Mutations within the epidermal growth factor receptor (EGFR/erbB1/Her1) are often associated with carcinogenesis. Specific mutations common in non-small cell lung cancer (NSCLC), including EGFR-L858R and EGFR-ΔL747-P753, lead to ligand-independent phosphorylation, however the molecular mechanism by which these mutations in the EGFR kinase domain confer constitutive activity remain unknown. Here, using multiple sub-diffraction-limit imaging modalities, we reveal the altered behavior of NSCLC-associated EGFR mutants within the plasma membrane_including altered receptor dimerization, dynamics, and structure_which collectively dysregulate receptor activity. Using multi-color single particle tracking (SPT) and Hidden Markov Model analysis, EGFR mutants are shown to form stable dimers in the absence of ligand and exhibit a slower mobility that is consistent with receptor signaling. These results were confirmed using two-color, single-molecule super-resolution microscopy (dSTORM) to visualize the spatial distribution of receptors. Receptor clustering was quantified by localization-based cross-correlation analysis to show ligand-induced aggregation of EGFR as well as ligand-independent aggregation of EGFR mutants. Since the receptor ectodomain is known to play a critical role in dimerization, live cell FRET measurements between the EGFR N-terminus and the plasma membrane was used to quantify changes in ectodomain structure. We found that unliganded EGFR mutants are more readily found in the extended conformation, similar to the ligand bound wild type receptor. Therefore, mutation within the kinase domain biases the structural equilibrium of the extracellular domain toward a dimer-competent state.Collectively, these data support a model where oncogenic signaling from NSCLC-associated EGFR mutants is a result of productive dimerization between non-ligand bound receptors. Furthermore, because these mutations are found in the kinase domain, this work introduces the concept that oncogenic EGFR signaling may be controlled in part by a form of “inside-out” signaling.

Aggregation of cell surface receptors by multivalent ligand can trigger a variety of cellular responses. A well-studied receptor that responds to aggregation is the high affinity receptor for IgE (FcepsilonRI), which is responsible for initiating allergic reactions. To quantify antigen-induced aggregation of IgE-FcepsilonRI complexes, we have developed a method based on multiparameter flow cytometry to monitor both occupancy of surface IgE combining sites and association of antigen with the cell surface. The number of bound IgE combining sites in excess of the number of bound antigens, the number of bridges between receptors, provides a quantitative measure of IgE-FcepsilonRI aggregation. We demonstrate our method by using it to study the equilibrium binding of a haptenated fluorescent protein, 2,4-dinitrophenol-coupled B-phycoerythrin (DNP25-PE), to fluorescein isothiocyanate-labeled anti-DNP IgE on the surface of rat basophilic leukemia cells. The results, which we analyze with the aid of a mathematical model, indicate how IgE-FcepsilonRI aggregation depends on the total concentrations of DNP25-PE and surface IgE. As expected, we find that maximal aggregation occurs at an optimal antigen concentration. We also find that aggregation varies qualitatively with the total concentration of surface IgE as predicted by an earlier theoretical analysis.

The principle of microscopic reversibility implies detailed balance—the statement that, at thermodynamic equilibrium, each individual reaction is balanced. That is, at equilibrium each individual reaction occurs with equal forward and backward fluxes. A reaction system that satisfies detailed balance does not consume or dissipate free energy at thermodynamic equilibrium (1). Although reaction systems with no closed loops (or acyclic systems) always satisfy detailed balance, most complex reaction schemes involve reaction cycles, and satisfying detailed balance requires that the product of equilibrium constants around a reaction cycle equals one. Colquhoun et al. (2) recently presented methods to impose detailed balance on complex reaction mechanisms, such as ion channel kinetic schemes modeled with finite Markov chains. The methods rely on finding a fundamental cycle basis with respect to a spanning tree of a graph representing the reaction topology. In this comment, we discuss an alternative method that balances the forward and backward fluxes of each reversible reaction and does not require direct consideration of reaction cycles. The method will be discussed for single molecule dynamics and mass-action kinetics. We will also discuss techniques for identifying a minimal reaction network for imposing detailed balance.

Mathematical models based upon the biochemical reactions that effectively define these networks have much promise as a tool for studying cell-signaling networks. Such models could be studied computationally to generate hypotheses that can be tested experimentally. A major obstacle for developing such models is “combinatorial complexity”, i.e. the number of potential states for the network becomes combinatorially large when post-translational modifications and protein-protein complexes are considered. Explicitly stating all potential states and their potential interactions is not feasible for very large networks. Modelers often deal with this problem by limiting the scope of the network considered, limiting the biochemical resolution considered, or imposing non-physiological reaction specifications that dramatically reduce the number of states. These simplifications are generally unsatisfactory. The cost of these common simplifications on predictive ability is not well understood. We have rather developed a rule-based approach for efficiently specifying and simulating reaction networks. This “rule-based” approach enables simulations of mechanistic models of cell signaling networks with resolution and scope far larger than traditional modeling methods. We have built a comprehensive model of IGF1R phosphorylation and SH2/PTB signaling that can account for over 1014 possible non-isomorphic complexes. We have also built a model of ErbB family signaling that spans from the four ErbB receptors through ERK and Akt activation and that can account for over 10150 possible non-isomorphic complexes. We have used these models to investigate how protein promiscuity may modulate signaling and also to investigate how feedback loops expand the range of signals a network may generate. Now that we have demonstrated the ability to develop and simulate such large models, we turn our attention to how oncogenic mutants disrupt these signaling networks.