Exploring higher-order EGFR oligomerisation and phosphorylation--a combined experimental and theoretical approach

Mathematical Modeling and Inference of Epidermal Growth Factor-Induced Mitogen-Activated Protein Kinase Cell Signaling Pathways

The mitogen-activated protein kinase (MAPK) pathway is an important intracellular signaling cascade that plays a key role in various cellular processes. Understanding the regulatory mechanisms of this pathway is essential for developing effective interventions and targeted therapies for related diseases. Recent advances in single-cell proteomic technologies have provided unprecedented opportunities to investigate the heterogeneity and noise within complex, multi-signaling networks across diverse cells and cell types. Mathematical modeling has become a powerful interdisciplinary tool that bridges mathematics and experimental biology, providing valuable insights into these intricate cellular processes. In addition, statistical methods have been developed to infer pathway topologies and estimate unknown parameters within dynamic models. This review presents a comprehensive analysis of how mathematical modeling of the MAPK pathway deepens our understanding of its regulatory mechanisms, enhances the prediction of system behavior, and informs experimental research, with a particular focus on recent advances in modeling and inference using single-cell proteomic data.

Drug-resistant EGFR mutations promote lung cancer by stabilizing interfaces in ligand-free kinase-active EGFR oligomers

The Epidermal Growth Factor Receptor (EGFR) is frequently found to be mutated in non-small cell lung cancer. Oncogenic EGFR has been successfully targeted by tyrosine kinase inhibitors, but acquired drug resistance eventually overcomes the efficacy of these treatments. Attempts to surmount this therapeutic challenge are hindered by a poor understanding of how and why cancer mutations specifically amplify ligand-independent EGFR auto-phosphorylation signals to enhance cell survival and how this amplification is related to ligand-dependent cell proliferation. Here we show that drug-resistant EGFR mutations manipulate the assembly of ligand-free, kinase-active oligomers to promote and stabilize the assembly of oligomer-obligate active dimer sub-units and circumvent the need for ligand binding. We reveal the structure and assembly mechanisms of these ligand-free, kinase-active oligomers, uncovering oncogenic functions for hitherto orphan transmembrane and kinase interfaces, and for the ectodomain tethered conformation of EGFR. Importantly, we find that the active dimer sub-units within ligand-free oligomers are the high affinity binding sites competent to bind physiological ligand concentrations and thus drive tumor growth, revealing a link with tumor proliferation. Our findings provide a framework for future drug discovery directed at tackling oncogenic EGFR mutations by disabling oligomer-assembling interactions.

Extracellular domain mutations of the EGF receptor differentially modulate high-affinity and low-affinity responses to EGF receptor ligands

The EGF receptor is mutated in a number of cancers. In most cases, the mutations occur in the intracellular tyrosine kinase domain. However, in glioblastomas, many of the mutations are in the extracellular ligand binding domain. To determine what changes in receptor function are induced by such extracellular domain mutations, we analyzed the binding and biological response to the seven different EGF receptor ligands in three common glioblastoma mutants-R84K, A265V, and G574V. Our data indicate that all three mutations significantly increase the binding affinity of all seven ligands. In addition, the mutations increase the potency of all ligands for stimulating receptor autophosphorylation, phospholipase Cγ, Akt, and MAP kinase activity. In all mutants, the rank order of ligand potency seen at the wild-type receptor was retained, suggesting that the receptors still discriminate among the different ligands. However, the low-affinity ligands, EPR and EPG, did show larger than average enhancements of potency for stimulating Akt and MAPK but not receptor autophosphorylation and phospholipase Cγ activation. Relative to the wild-type receptor, these changes lead to an increase in the responsiveness of these mutants to physiological concentrations of ligands and an alteration in the ratio of activation of the different pathways. This may contribute to their oncogenic potential. In the context of recent findings, our data also suggest that so-called "high"-affinity biological responses arise from activation by isolated receptor dimers, whereas "low"-affinity biological responses require clustering of receptors which occurs at higher concentrations of ligand.

Surface-Patterned DNA Origami Rulers Reveal Nanoscale Distance Dependency of the Epidermal Growth Factor Receptor Activation

The nanoscale arrangement of ligands can have a major effect on the activation of membrane receptor proteins and thus cellular communication mechanisms. Here we report on the technological development and use of tailored DNA origami-based molecular rulers to fabricate "Multiscale Origami Structures As Interface for Cells" (MOSAIC), to enable the systematic investigation of the effect of the nanoscale spacing of epidermal growth factor (EGF) ligands on the activation of the EGF receptor (EGFR). MOSAIC-based analyses revealed that EGF distances of about 30-40 nm led to the highest response in EGFR activation of adherent MCF7 and Hela cells. Our study emphasizes the significance of DNA-based platforms for the detailed investigation of the molecular mechanisms of cellular signaling cascades.

Distinct interactions stabilize EGFR dimers and higher-order oligomers in cell membranes

The epidermal growth factor receptor (EGFR) is a receptor tyrosine kinase with important roles in many cellular processes as well as in cancer and other diseases. EGF binding promotes EGFR dimerization and autophosphorylation through interactions that are well understood structurally. How these dimers relate to higher-order EGFR oligomers seen in cell membranes, however, remains unclear. Here, we used single-particle tracking (SPT) and Förster resonance energy transfer imaging to examine how each domain of EGFR contributes to receptor oligomerization and the rate of receptor diffusion in the cell membrane. Although the extracellular region of EGFR is sufficient to drive receptor dimerization, we find that the EGF-induced EGFR slowdown seen by SPT requires higher-order oligomerization-mediated in part by the intracellular tyrosine kinase domain when it adopts an active conformation. Our data thus provide important insight into the interactions required for higher-order EGFR assemblies involved in EGF signaling.

Quantitative modeling of EGF receptor ligand discrimination via internalization proofreading

The epidermal growth factor receptor (EGFR) is a central regulator of cell physiology that is stimulated by multiple distinct ligands. Although ligands bind to EGFR while the receptor is exposed on the plasma membrane, EGFR incorporation into endosomes following receptor internalization is an important aspect of EGFR signaling, with EGFR internalization behavior dependent upon the type of ligand bound. We develop quantitative modeling for EGFR recruitment to and internalization from clathrin domains, focusing on how internalization competes with ligand unbinding from EGFR. We develop two model versions: a kinetic model with EGFR behavior described as transitions between discrete states and a spatial model with EGFR diffusion to circular clathrin domains. We find that a combination of spatial and kinetic proofreading leads to enhanced EGFR internalization ratios in comparison to unbinding differences between ligand types. Various stages of the EGFR internalization process, including recruitment to and internalization from clathrin domains, modulate the internalization differences between receptors bound to different ligands. Our results indicate that following ligand binding, EGFR may encounter multiple clathrin domains before successful recruitment and internalization. The quantitative modeling we have developed describes competition between EGFR internalization and ligand unbinding and the resulting proofreading.

An integrated mechanistic and data-driven computational model predicts cell responses to high- and low-affinity EGFR ligands

The biophysical properties of ligand binding heavily influence the ability of receptors to specify cell fates. Understanding the rules by which ligand binding kinetics impact cell phenotype is challenging, however, because of the coupled information transfers that occur from receptors to downstream signaling effectors and from effectors to phenotypes. Here, we address that issue by developing an integrated mechanistic and data-driven computational modeling platform to predict cell responses to different ligands for the epidermal growth factor receptor (EGFR). Experimental data for model training and validation were generated using MCF7 human breast cancer cells treated with the high- and low-affinity ligands epidermal growth factor (EGF) and epiregulin (EREG), respectively. The integrated model captures the unintuitive, concentration-dependent abilities of EGF and EREG to drive signals and phenotypes differently, even at similar levels of receptor occupancy. For example, the model correctly predicts the dominance of EREG over EGF in driving a cell differentiation phenotype through AKT signaling at intermediate and saturating ligand concentrations and the ability of EGF and EREG to drive a broadly concentration-sensitive migration phenotype through cooperative ERK and AKT signaling. Parameter sensitivity analysis identifies EGFR endocytosis, which is differentially regulated by EGF and EREG, as one of the most important determinants of the alternative phenotypes driven by different ligands. The integrated model provides a new platform to predict how phenotypes are controlled by the earliest biophysical rate processes in signal transduction and may eventually be leveraged to understand receptor signaling system performance depends on cell context.

One-sentence summary

Integrated kinetic and data-driven EGFR signaling model identifies the specific signaling mechanisms that dictate cell responses to EGFR activation by different ligands.

Distinct interactions stabilize EGFR dimers and higher-order oligomers in cell membranes

The epidermal growth factor receptor (EGFR) is a receptor tyrosine kinase (RTK) with important roles in many cellular processes as well as cancer and other diseases. EGF binding promotes EGFR dimerization and autophosphorylation through interactions that are well understood structurally. However, it is not clear how these dimers relate to higher-order EGFR oligomers detected at the cell surface. We used single-particle tracking (SPT) and Förster resonance energy transfer (FRET) imaging to examine how each domain within EGFR contributes to receptor dimerization and the rate of its diffusion in the cell membrane. We show that the EGFR extracellular region is sufficient to drive receptor dimerization, but that the EGF-induced EGFR slow-down seen by SPT requires formation of higher order oligomers, mediated in part by the intracellular tyrosine kinase domain - but only when in its active conformation. Our data thus provide important insight into higher-order EGFR interactions required for EGF signaling.

Refinement of Singer-Nicolson fluid-mosaic model by microscopy imaging: Lipid rafts and actin-induced membrane compartmentalization

This year celebrates the 50th anniversary of the Singer-Nicolson fluid mosaic model for biological membranes. The next level of sophistication we have achieved for understanding plasma membrane (PM) structures, dynamics, and functions during these 50 years includes the PM interactions with cortical actin filaments and the partial demixing of membrane constituent molecules in the PM, particularly raft domains. Here, first, we summarize our current knowledge of these two structures and emphasize that they are interrelated. Second, we review the structure, molecular dynamics, and function of raft domains, with main focuses on raftophilic glycosylphosphatidylinositol-anchored proteins (GPI-APs) and their signal transduction mechanisms. We pay special attention to the results obtained by single-molecule imaging techniques and other advanced microscopy methods. We also clarify the limitations of present optical microscopy methods for visualizing raft domains, but emphasize that single-molecule imaging techniques can "detect" raft domains associated with molecules of interest in the PM.

The dependence of EGFR oligomerization on environment and structure: A camera-based N&B study

Number and brightness (N&B) analysis is a fluorescence spectroscopy technique to quantify oligomerization of the mobile fraction of proteins. Accurate results, however, rely on a good knowledge of nonfluorescent states of the fluorescent labels, especially of fluorescent proteins, which are widely used in biology. Fluorescent proteins have been characterized for confocal, but not camera-based, N&B, which allows, in principle, faster measurements over larger areas. Here, we calibrate camera-based N&B implemented on a total internal reflection fluorescence microscope for various fluorescent proteins by determining their propensity to be fluorescent. We then apply camera-based N&B in live CHO-K1 cells to determine the oligomerization state of the epidermal growth factor receptor (EGFR), a transmembrane receptor tyrosine kinase that is a crucial regulator of cell proliferation and survival with implications in many cancers. EGFR oligomerization in resting cells and its regulation by the plasma membrane microenvironment are still under debate. Therefore, we investigate the effects of extrinsic factors, including membrane organization, cytoskeletal structure, and ligand stimulation, and intrinsic factors, including mutations in various EGFR domains, on the receptor's oligomerization. Our results demonstrate that EGFR oligomerization increases with removal of cholesterol or sphingolipids or the disruption of GM3-EGFR interactions, indicating raft association. However, oligomerization is not significantly influenced by the cytoskeleton. Mutations in either I706/V948 residues or E685/E687/E690 residues in the kinase and juxtamembrane domains, respectively, lead to a decrease in oligomerization, indicating their necessity for EGFR dimerization. Finally, EGFR phosphorylation is oligomerization dependent, involving the extracellular domain (550-580 residues). Coupled with biochemical investigations, camera-based N&B indicates that EGFR oligomerization and phosphorylation are the outcomes of several molecular interactions involving the lipid content and structure of the cell membrane and multiple residues in the kinase, juxtamembrane, and extracellular domains.

NF-kB in Signaling Patterns and Its Temporal Dynamics Encode/Decode Human Diseases

Defects in signaling pathways are the root cause of many disorders. These malformations come in a wide variety of types, and their causes are also very diverse. Some of these flaws can be brought on by pathogenic organisms and viruses, many of which can obstruct signaling processes. Other illnesses are linked to malfunctions in the way that cell signaling pathways work. When thinking about how errors in signaling pathways might cause disease, the idea of signalosome remodeling is helpful. The signalosome may be conveniently divided into two types of defects: phenotypic remodeling and genotypic remodeling. The majority of significant illnesses that affect people, including high blood pressure, heart disease, diabetes, and many types of mental illness, appear to be caused by minute phenotypic changes in signaling pathways. Such phenotypic remodeling modifies cell behavior and subverts normal cellular processes, resulting in illness. There has not been much progress in creating efficient therapies since it has been challenging to definitively confirm this connection between signalosome remodeling and illness. The considerable redundancy included into cell signaling systems presents several potential for developing novel treatments for various disease conditions. One of the most important pathways, NF-κB, controls several aspects of innate and adaptive immune responses, is a key modulator of inflammatory reactions, and has been widely studied both from experimental and theoretical perspectives. NF-κB contributes to the control of inflammasomes and stimulates the expression of a number of pro-inflammatory genes, including those that produce cytokines and chemokines. Additionally, NF-κB is essential for controlling innate immune cells and inflammatory T cells' survival, activation, and differentiation. As a result, aberrant NF-κB activation plays a role in the pathogenesis of several inflammatory illnesses. The activation and function of NF-κB in relation to inflammatory illnesses was covered here, and the advancement of treatment approaches based on NF-κB inhibition will be highlighted. This review presents the temporal behavior of NF-κB and its potential relevance in different human diseases which will be helpful not only for theoretical but also for experimental perspectives.

Multivalent Ligand-Nanoparticle Conjugates Amplify Reactive Oxygen Species Second Messenger Generation and Enhance Epidermal Growth Factor Receptor Phosphorylation

The epidermal growth factor (EGF) receptor (EGFR) is heterogeneously distributed on the cellular surface and enriched in clusters with diameters of tens of nanometers. Multivalent presentation of EGF ligand on nanoparticles (NPs) provides an approach for controlling and amplifying the local activation of EGFR in these clusters. Reactive oxygen species (ROS) have been indicated to play a role in the regulation of EGFR activation as second messengers, but the effect of nanoconjugation on EGF-mediated ROS formation and ROS-induced EGFR activation is not well established. The goal of this manuscript is to characterize the multivalent enhancement of EGF-induced ROS formation and to test its effect on EGFR phosphorylation in breast cancer cell models using gold (Au) NPs with a diameter of 81 ± 1 nm functionalized with two different EGF ligand densities (12 ± 7 EGF/NP (NP-EGF12) and 87 ± 6 EGF/NP (NP-EGF87)). In the EGFR overexpressing cell lines MDA-MB-231 and MDA-MB-468, NP-EGF87 achieved a measurable multivalent enhancement of ROS that peaked at concentrations c ROSmax ≤ 25 pM and that were EGFR and nicotinamide adenine dinucleotide phosphate oxidase (NOX) dependent. NP-EGF12 failed to generate comparable ROS levels as NP-EGF87 in the investigated NP input concentration range (0-100 pM). In cells with nearly identical numbers of bound NP-EGF87 and NP-EGF12, the ROS levels for NP-EGF87 were systematically higher, indicating that the multivalent enhancement is exclusively related not only to avidity but also to a stronger stimulation per NP. Importantly, the increase in EGF-induced ROS formation associated with EGF nanoconjugation at c ROSmax resulted in a measurable gain in EGFR phosphorylation, confirming that ROS generation contributes to the multivalent enhancement of EGFR activation in response to NP-EGF87.

Critical roles for EGFR and EGFR-HER2 clusters in EGF binding of SW620 human carcinoma cells

Epidermal growth factor (EGF) signalling regulates normal epithelial and other cell growth, with EGF receptor (EGFR) overexpression reported in many cancers. However, the role of EGFR clusters in cancer and their dependence on EGF binding is unclear. We present novel single-molecule total internal reflection fluorescence microscopy of (i) EGF and EGFR in living cancer cells, (ii) the action of anti-cancer drugs that separately target EGFR and human EGFR2 (HER2) on these cells and (iii) EGFR–HER2 interactions. We selected human epithelial SW620 carcinoma cells for their low level of native EGFR expression, for stable transfection with fluorescent protein labelled EGFR, and imaged these using single-molecule localization microscopy to quantify receptor architectures and dynamics upon EGF binding. Prior to EGF binding, we observe pre-formed EGFR clusters. Unexpectedly, clusters likely contain both EGFR and HER2, consistent with co-diffusion of EGFR and HER2 observed in a different model CHO-K1 cell line, whose stoichiometry increases following EGF binding. We observe a mean EGFR : EGF stoichiometry of approximately 4 : 1 for plasma membrane-colocalized EGFR–EGF that we can explain using novel time-dependent kinetics modelling, indicating preferential ligand binding to monomers. Our results may inform future cancer drug developments.

Competitive binding of STATs to receptor phospho-Tyr motifs accounts for altered cytokine responses

Cytokines elicit pleiotropic and non-redundant activities despite strong overlap in their usage of receptors, JAKs and STATs molecules. We use IL-6 and IL-27 to ask how two cytokines activating the same signaling pathway have different biological roles. We found that IL-27 induces more sustained STAT1 phosphorylation than IL-6, with the two cytokines inducing comparable levels of STAT3 phosphorylation. Mathematical and statistical modeling of IL-6 and IL-27 signaling identified STAT3 binding to GP130, and STAT1 binding to IL-27Rα, as the main dynamical processes contributing to sustained pSTAT1 levels by IL-27. Mutation of Tyr613 on IL-27Rα decreased IL-27-induced STAT1 phosphorylation by 80% but had limited effect on STAT3 phosphorgylation. Strong receptor/STAT coupling by IL-27 initiated a unique gene expression program, which required sustained STAT1 phosphorylation and IRF1 expression and was enriched in classical Interferon Stimulated Genes. Interestingly, the STAT/receptor coupling exhibited by IL-6/IL-27 was altered in patients with systemic lupus erythematosus (SLE). IL-6/IL-27 induced a more potent STAT1 activation in SLE patients than in healthy controls, which correlated with higher STAT1 expression in these patients. Partial inhibition of JAK activation by sub-saturating doses of Tofacitinib specifically lowered the levels of STAT1 activation by IL-6. Our data show that receptor and STATs concentrations critically contribute to shape cytokine responses and generate functional pleiotropy in health and disease.

Dissecting biological activities of fibroblast growth factor receptors by the coiled-coil-mediated oligomerization of FGF1

Fibroblast growth factor receptors (FGFRs) are integral membrane proteins involved in various biological processes including proliferation, migration and apoptosis. There are a number of regulatory mechanisms of FGFR signaling, which tightly control the specificity and duration of transmitted signals. The effect of the FGFRs spatial distribution in the plasma membrane on receptor-dependent functions is still largely unknown. We have demonstrated that oligomerization of FGF1 with coiled-coil motifs largely improves FGF1 affinity for FGFRs and heparin. Set of developed FGF1 oligomers evoked prolonged activation of FGFR1 and receptor-downstream signaling pathways, as compared to the wild type FGF1. The majority of obtained oligomeric FGF1 variants showed increased stability, enhanced mitogenic activity and largely improved internalization via FGFR1-dependent endocytosis. Importantly, FGF1 oligomers with the highest oligomeric state exhibited reduced ability to stimulate FGFR-dependent glucose uptake, while at the same time remained hyperactive in the induction of cell proliferation. Our data implicate that oligomerization of FGF1 alters the biological activity of the FGF/GFR1 signaling system. Furthermore, developed FGF1 oligomers, due to improved stability and proliferative potential, can be applied in the regenerative medicine or as drug delivery vehicles in the ADC approach against FGFR1-overproducing cancers.

Molecular Targeting of Epidermal Growth Factor Receptor (EGFR) and Vascular Endothelial Growth Factor Receptor (VEGFR)

Epidermal growth factor receptor (EGFR) and vascular endothelial growth factor receptor (VEGFR) are two extensively studied membrane-bound receptor tyrosine kinase proteins that are frequently overexpressed in many cancers. As a result, these receptor families constitute attractive targets for imaging and therapeutic applications in the detection and treatment of cancer. This review explores the dynamic structure and structure-function relationships of these two growth factor receptors and their significance as it relates to theranostics of cancer, followed by some of the common inhibition modalities frequently employed to target EGFR and VEGFR, such as tyrosine kinase inhibitors (TKIs), antibodies, nanobodies, and peptides. A summary of the recent advances in molecular imaging techniques, including positron emission tomography (PET), single-photon emission computerized tomography (SPECT), computed tomography (CT), magnetic resonance imaging (MRI), and optical imaging (OI), and in particular, near-IR fluorescence imaging using tetrapyrrolic-based fluorophores, concludes this review.

Structural Basis for Vascular Endothelial Growth Factor Receptor Activation and Implications for Disease Therapy

Vascular endothelial growth factors (VEGFs) bind to membrane receptors on a wide variety of cells to regulate diverse biological responses. The VEGF-A family member promotes vasculogenesis and angiogenesis, processes which are essential for vascular development and physiology. As angiogenesis can be subverted in many disease states, including tumour development and progression, there is much interest in understanding the mechanistic basis for how VEGF-A regulates cell and tissue function. VEGF-A binds with high affinity to two VEGF receptor tyrosine kinases (VEGFR1, VEGFR2) and with lower affinity to co-receptors called neuropilin-1 and neuropilin-2 (NRP1, NRP2). Here, we use a structural viewpoint to summarise our current knowledge of VEGF-VEGFR activation and signal transduction. As targeting VEGF-VEGFR activation holds much therapeutic promise, we examine the structural basis for anti-angiogenic therapy using small-molecule compounds such as tyrosine kinase inhibitors that block VEGFR activation and downstream signalling. This review provides a rational basis towards reconciling VEGF and VEGFR structure and function in developing new therapeutics for a diverse range of ailments.

Conserved roles for receptor tyrosine kinase extracellular regions in regulating receptor and pathway activity

Receptor Tyrosine Kinases (RTKs) comprise a diverse group of cell-surface receptors that mediate key signaling events during animal development and are frequently activated in cancer. We show here that deletion of the extracellular regions of 10 RTKs representing 7 RTK classes or their substitution with the dimeric immunoglobulin Fc region results in constitutive receptor phosphorylation but fails to result in phosphorylation of downstream signaling effectors Erk or Akt. Conversely, substitution of RTK extracellular regions with the extracellular region of the Epidermal Growth Factor Receptor (EGFR) results in increases in effector phosphorylation in response to EGF. These results indicate that the activation signal generated by the EGFR extracellular region is capable of activating at least seven different RTK classes. Failure of phosphorylated Fc-RTK chimeras or RTKs with deleted extracellular regions to stimulate phosphorylation of downstream effectors indicates that either dimerization and receptor phosphorylation per se are insufficient to activate signaling or constitutive dimerization leads to pathway inhibition.

Homo-Oligomerisation in Signal Transduction: Dynamics, Homeostasis, Ultrasensitivity, Bistability

Homo-oligomerisation of proteins is a ubiquitous phenomenon whose exact role remains unclear in many cases. To identify novel functions, this paper provides an exploration of general dynamical mathematical models of homo-oligomerisation. Simulation and analysis of these models show that homo-oligomerisation on its own allows for a remarkable variety of complex dynamic and steady state regulatory behaviour such as transient overshoots or homeostatic control of monomer concentration. If post-translational modifications are considered, however, conventional mass action kinetics lead to thermodynamic inconsistencies due to asymmetric combinatorial expansion of reaction routes. Introducing a conservation principle to balance rate equations re-establishes thermodynamic consistency. Using such balanced models it is shown that oligomerisation can lead to bistability by enabling pseudo-multisite modification and kinetic pseudo-cooperativity via multi-enzyme regulation, thereby constituting a novel motif for bistable modification reactions. Due to these potential signal processing capabilities, homo-oligomerisation could play far more versatile roles in signal transduction than previously appreciated.

Bayesian inference using qualitative observations of underlying continuous variables

MOTIVATION

Recent work has demonstrated the feasibility of using non-numerical, qualitative data to parameterize mathematical models. However, uncertainty quantification (UQ) of such parameterized models has remained challenging because of a lack of a statistical interpretation of the objective functions used in optimization.

RESULTS

We formulated likelihood functions suitable for performing Bayesian UQ using qualitative observations of underlying continuous variables or a combination of qualitative and quantitative data. To demonstrate the resulting UQ capabilities, we analyzed a published model for immunoglobulin E (IgE) receptor signaling using synthetic qualitative and quantitative datasets. Remarkably, estimates of parameter values derived from the qualitative data were nearly as consistent with the assumed ground-truth parameter values as estimates derived from the lower throughput quantitative data. These results provide further motivation for leveraging qualitative data in biological modeling.

AVAILABILITY AND IMPLEMENTATION

The likelihood functions presented here are implemented in a new release of PyBioNetFit, an open-source application for analyzing Systems Biology Markup Language- and BioNetGen Language-formatted models, available online at www.github.com/lanl/PyBNF.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Dissecting Particle Uptake Heterogeneity in a Cell Population Using Bayesian Analysis

Individual cells in a solution display variable uptake of nanomaterials, peptides, and nutrients. Such variability reflects their heterogeneity in endocytic capacity. In a recent work, we have shown that the endocytic capacity of a cell depends on its size and surface density of endocytic components (transporters). We also demonstrated that in MDA-MB-231 breast cancer cells, the cell-surface transporter density (n) may decay with cell radius (r) following the power rule n ∼ r^α, where α ≈ -1. In this work, we investigate how n and r may independently contribute to the endocytic heterogeneity of a cell population. Our analysis indicates that the smaller cells display more heterogeneity because of the higher stochastic variations in n. By contrast, the larger cells display a more uniform uptake, reflecting less-stochastic variations in n. We provide analyses of these dependencies by establishing a stochastic model. Our analysis reveals that the exponent α in the above relationship is not a constant; rather, it is a random variable whose distribution depends on cell size r. Using Bayesian analysis, we characterize the cell-size-dependent distributions of α that accurately capture the particle uptake heterogeneity of MDA-MB-231 cells.

Receptor tyrosine kinase activation: From the ligand perspective

Receptor tyrosine kinases (RTKs) are single-span transmembrane receptors in which relatively conserved intracellular kinase domains are coupled to divergent extracellular modules. The extracellular domains initiate receptor signaling upon binding to either soluble or membrane-embedded ligands. The diversity of extracellular domain structures allows for coupling of many unique signaling inputs to intracellular tyrosine phosphorylation. The combinatorial power of this receptor system is further increased by the fact that multiple ligands can typically interact with the same receptor. Such ligands often act as biased agonists and initiate distinct signaling responses via activation of the same receptor. Mechanisms behind such biased agonism are largely unknown for RTKs, especially at the level of receptor-ligand complex structure. Using recent progress in understanding the structures of active RTK signaling units, we discuss selected mechanisms by which ligands couple receptor activation to distinct signaling outputs.

Membrane receptor activation mechanisms and transmembrane peptide tools to elucidate them

Single-pass membrane receptors contain extracellular domains that respond to external stimuli and transmit information to intracellular domains through a single transmembrane (TM) α-helix. Because membrane receptors have various roles in homeostasis, signaling malfunctions of these receptors can cause disease. Despite their importance, there is still much to be understood mechanistically about how single-pass receptors are activated. In general, single-pass receptors respond to extracellular stimuli via alterations in their oligomeric state. The details of this process are still the focus of intense study, and several lines of evidence indicate that the TM domain (TMD) of the receptor plays a central role. We discuss three major mechanistic hypotheses for receptor activation: ligand-induced dimerization, ligand-induced rotation, and receptor clustering. Recent observations suggest that receptors can use a combination of these activation mechanisms and that technical limitations can bias interpretation. Short peptides derived from receptor TMDs, which can be identified by screening or rationally developed on the basis of the structure or sequence of their targets, have provided critical insights into receptor function. Here, we explore recent evidence that, depending on the target receptor, TMD peptides cannot only inhibit but also activate target receptors and can accommodate novel, bifunctional designs. Furthermore, we call for more sharing of negative results to inform the TMD peptide field, which is rapidly transforming into a suite of unique tools with the potential for future therapeutics.

In-cell structural dynamics of an EGF receptor during ligand-induced dimer-oligomer transition

The epidermal growth factor receptor (EGFR) is a membrane protein that regulates cell proliferation, differentiation and survival, and is a drug target for cancer therapy. Ligand-induced activation of the EGFR kinase is generally regarded to require ligand-bound-dimers, while phosphorylation and down-stream signalling is modulated by oligomers. Recent work has unveiled changes in EGFR dynamics from ligand-induced dimerization in membranes extracted from cells, however, less is known about the changes in EGFR dynamics that accompany the ligand-induced oligomerization in a live cell environment. Here, we determine the dynamics of a c-terminal GFP tag attached to EGFR in the unliganded dimer and in the liganded oligomers. By means of the single-frequency polarized phasor ellipse approach we extracted two correlation times on the sub-nanosecond and super-nanosecond timescales, respectively. EGF binding to the EGFR-GFP dimer lengthened the sub-nanosecond correlation time (from 0.1 to 1.3 ns) and shortened the super-nanosecond correlation time (from 210 to 56 ns) of the c-terminal GFP probe. The sub-nanosecond depolarization processes were assigned to electronic energy migration between proximal GFPs in the EGFR dimer or oligomer, while the super-nanosecond correlation times were assigned to nanosecond fluctuations of the GFP probe in the EGFR complex. Accordingly, these results show that ligand binding increased the average separation between the c-terminal tags and increased their rotational mobility. We propose that the dynamics are linked to an inhibitory function of the c-terminal tail in the un-liganded dimer and to the requirement of facile stochastic switching between kinase activation and cytoplasmic adaptor/effector binding in the active oligomers.

Pleione: A tool for statistical and multi-objective calibration of Rule-based models

Mathematical models based on Ordinary Differential Equations (ODEs) are frequently used to describe and simulate biological systems. Nevertheless, such models are often difficult to understand. Unlike ODE models, Rule-Based Models (RBMs) utilise formal language to describe reactions as a cumulative number of statements that are easier to understand and correct. They are also gaining popularity because of their conciseness and simulation flexibility. However, RBMs generally lack tools to perform further analysis that requires simulation. This situation arises because exact and approximate simulations are computationally intensive. Translating RBMs into ODEs is commonly used to reduce simulation time, but this technique may be prohibitive due to combinatorial explosion. Here, we present the software called Pleione to calibrate RBMs. Parameter calibration is essential given the incomplete experimental determination of reaction rates and the goal of using models to reproduce experimental data. The software distributes stochastic simulations and calculations and incorporates equivalence tests to determine the fitness of RBMs compared with data. The primary features of Pleione were thoroughly tested on a model of gene regulation in Escherichia coli. Pleione yielded satisfactory results regarding calculation time and error reduction for multiple simulators, models, parameter search strategies, and computing infrastructures.

PyBioNetFit and the Biological Property Specification Language

In systems biology modeling, important steps include model parameterization, uncertainty quantification, and evaluation of agreement with experimental observations. To help modelers perform these steps, we developed the software PyBioNetFit, which in addition supports checking models against known system properties and solving design problems. PyBioNetFit introduces Biological Property Specification Language (BPSL) for the formal declaration of system properties. BPSL allows qualitative data to be used alone or in combination with quantitative data. PyBioNetFit performs parameterization with parallelized metaheuristic optimization algorithms that work directly with existing model definition standards: BioNetGen Language (BNGL) and Systems Biology Markup Language (SBML). We demonstrate PyBioNetFit's capabilities by solving various example problems, including the challenging problem of parameterizing a 153-parameter model of cell cycle control in yeast based on both quantitative and qualitative data. We demonstrate the model checking and design applications of PyBioNetFit and BPSL by analyzing a model of targeted drug interventions in autophagy signaling.

Characterizing Large-Scale Receptor Clustering on the Single Cell Level: A Comparative Plasmon Coupling and Fluorescence Superresolution Microscopy Study

Spatial clustering of cell membrane receptors has been indicated to play a regulatory role in signal initiation, and the distribution of receptors on the cell surface may represent a potential biomarker. To realize its potential for diagnostic purposes, scalable assays capable of mapping spatial receptor heterogeneity with high throughput are needed. In this work, we use gold nanoparticle (NP) labels with an average diameter of 72.17 ± 2.16 nm as bright markers for large-scale epidermal growth factor receptor (EGFR) clustering in hyperspectral plasmon coupling microscopy and compare the obtained clustering maps with those obtained through fluorescence superresolution microscopy (direct stochastic optical reconstruction microscopy, dSTORM). Our dSTORM experiments reveal average EGFR cluster sizes of 172 ± 99 and 150 ± 90 nm for MDA-MB-468 and HeLa, respectively. The cluster sizes decrease after EGFR activation. Hyperspectral imaging of the NP labels shows that differences in the EGFR cluster sizes are accompanied by differences in the average separations between electromagnetically coupled NPs. Because of the distance dependence of plasmon coupling, changes in the average interparticle separation result in significant spectral shifts. For the experimental conditions investigated in this work, hyperspectral plasmon coupling microscopy of NP labels identified the same trends in large-scale EGFR clustering as dSTORM, but the NP imaging approach provided the information in a fraction of the time. Both dSTORM and hyperspectral plasmon coupling microscopy confirm the cortical actin network as one structural component that determines the average size of EGFR clusters.

Resolving the conformational dynamics of ErbB growth factor receptor dimers

The combinatorial dimerization of the ErbB growth factor receptors (ErbB¹- ErbB⁴) are critical for their function. Here, we have characterized the conformational dynamics of ErbB transmembrane homo-dimers and hetero-dimers by using a coarse-grain simulation framework. All dimers, except ErbB^4-4 and ErbB^1-4, exhibit at least two conformations. The reported NMR structures correspond to one of these conformations, representing the N-terminal active state in ErbB^1-1 (RH2), ErbB^2-2 (RH1) and ErbB^4-4 (RH) homo-dimers and the LH dimer in ErbB^3-3 homo-dimer, validating the computational approach. Further, we predict a right-handed ErbB^3-3 dimer conformer that warrants experimental testing. The five hetero-dimers that have not yet been experimentally resolved display prominent right-handed dimers associating by the SmXXXSm motif. Our results provide insights into the constitutive signaling of ErbB⁴ after cleavage of the extracellular region. The presence of the inactive-like dimer conformers leading to symmetric kinase domains gives clues on the autoinhibition of the receptor dimers. The dimer states characterized here represent an important step towards understanding the combinatorial cross associations in the ErbB family.

Mapping Tyrosine Kinase Receptor Dimerization to Receptor Expression and Ligand Affinities

Tyrosine kinase receptor (RTK) ligation and dimerization is a key mechanism for translating external cell stimuli into internal signaling events. This process is critical to several key cell and physiological processes, such as in angiogenesis and embryogenesis, among others. While modulating RTK activation is a promising therapeutic target, RTK signaling axes have been shown to involve complicated interactions between ligands and receptors both within and across different protein families. In angiogenesis, for example, several signaling protein families, including vascular endothelial growth factors and platelet-derived growth factors, exhibit significant cross-family interactions that can influence pathway activation. Computational approaches can provide key insight to detangle these signaling pathways but have been limited by the sparse knowledge of these cross-family interactions. Here, we present a framework for studying known and potential non-canonical interactions. We constructed generalized models of RTK ligation and dimerization for systems of two, three and four receptor types and different degrees of cross-family ligation. Across each model, we developed parameter-space maps that fully determine relative pathway activation for any set of ligand-receptor binding constants, ligand concentrations and receptor concentrations. Therefore, our generalized models serve as a powerful reference tool for predicting not only known ligand: Receptor axes but also how unknown interactions could alter signaling dimerization patterns. Accordingly, it will drive the exploration of cross-family interactions and help guide therapeutic developments across processes like cancer and cardiovascular diseases, which depend on RTK-mediated signaling.

A Step-by-Step Guide to Using BioNetFit

BioNetFit is a software tool designed for solving parameter identification problems that arise in the development of rule-based models. It solves these problems through curve fitting (i.e., nonlinear regression). BioNetFit is compatible with deterministic and stochastic simulators that accept BioNetGen language (BNGL)-formatted files as inputs, such as those available within the BioNetGen framework. BioNetFit can be used on a laptop or stand-alone multicore workstation as well as on many Linux clusters, such as those that use the Slurm Workload Manager to schedule jobs. BioNetFit implements a metaheuristic population-based global optimization procedure, an evolutionary algorithm (EA), to minimize a user-defined objective function, such as a residual sum of squares (RSS) function. BioNetFit also implements a bootstrapping procedure for determining confidence intervals for parameter estimates. Here, we provide step-by-step instructions for using BioNetFit to estimate the values of parameters of a BNGL-encoded model and to define bootstrap confidence intervals. The process entails the use of several plain-text files, which are processed by BioNetFit and BioNetGen. In general, these files include (1) one or more EXP files, which each contains (experimental) data to be used in parameter identification/bootstrapping; (2) a BNGL file containing a model section, which defines a (rule-based) model, and an actions section, which defines simulation protocols that generate GDAT and/or SCAN files with model predictions corresponding to the data in the EXP file(s); and (3) a CONF file that configures the fitting/bootstrapping job and that defines algorithmic parameter settings.

The architecture of EGFR's basal complexes reveals autoinhibition mechanisms in dimers and oligomers

Our current understanding of epidermal growth factor receptor (EGFR) autoinhibition is based on X-ray structural data of monomer and dimer receptor fragments and does not explain how mutations achieve ligand-independent phosphorylation. Using a repertoire of imaging technologies and simulations we reveal an extracellular head-to-head interaction through which ligand-free receptor polymer chains of various lengths assemble. The architecture of the head-to-head interaction prevents kinase-mediated dimerisation. The latter, afforded by mutation or intracellular treatments, splits the autoinhibited head-to-head polymers to form stalk-to-stalk flexible non-extended dimers structurally coupled across the plasma membrane to active asymmetric tyrosine kinase dimers, and extended dimers coupled to inactive symmetric kinase dimers. Contrary to the previously proposed main autoinhibitory function of the inactive symmetric kinase dimer, our data suggest that only dysregulated species bear populations of symmetric and asymmetric kinase dimers that coexist in equilibrium at the plasma membrane under the modulation of the C-terminal domain.

Preassembled GPCR signaling complexes mediate distinct cellular responses to ultralow ligand concentrations

G protein-coupled receptors (GPCRs) are the largest class of cell surface signaling proteins, participate in nearly all physiological processes, and are the targets of 30% of marketed drugs. Typically, nanomolar to micromolar concentrations of ligand are used to activate GPCRs in experimental systems. We detected GPCR responses to a wide range of ligand concentrations, from attomolar to millimolar, by measuring GPCR-stimulated production of cyclic adenosine monophosphate (cAMP) with high spatial and temporal resolution. Mathematical modeling showed that femtomolar concentrations of ligand activated, on average, 40% of the cells in a population provided that a cell was activated by one to two binding events. Furthermore, activation of the endogenous β2-adrenergic receptor (β2AR) and muscarinic acetylcholine M3 receptor (M3R) by femtomolar concentrations of ligand in cell lines and human cardiac fibroblasts caused sustained increases in nuclear translocation of extracellular signal-regulated kinase (ERK) and cytosolic protein kinase C (PKC) activity, respectively. These responses were spatially and temporally distinct from those that occurred in response to higher concentrations of ligand and resulted in a distinct cellular proteomic profile. This highly sensitive signaling depended on the GPCRs forming preassembled, higher-order signaling complexes at the plasma membrane. Recognizing that GPCRs respond to ultralow concentrations of neurotransmitters and hormones challenges established paradigms of drug action and provides a previously unappreciated aspect of GPCR activation that is quite distinct from that typically observed with higher ligand concentrations.

Epidermal growth factor receptor: Structure-function informing the design of anticancer therapeutics

Research on the epidermal growth factor (EGF) family and the family of receptors (EGFR) has progressed rapidly in recent times. New crystal structures of the ectodomains with different ligands, the activation of the kinase domain through oligomerisation and the use of fluorescence techniques have revealed profound conformational changes on ligand binding. The control of cell signaling from the EGFR-family is complex, with heterodimerisation, ligand affinity and signaling cross-talk influencing cellular outcomes. Analysis of tissue homeostasis indicates that the control of pro-ligand processing is likely to be as important as receptor activation events. Several members of the EGFR-family are overexpressed and/or mutated in cancer cells. The perturbation of EGFR-family signaling drives the malignant phenotype of many cancers and both inhibitors and antagonists of signaling from these receptors have already produced therapeutic benefits for patients. The design of affibodies, antibodies, small molecule inhibitors and even immunotherapeutic drugs targeting the EGFR-family has yielded promising new approaches to improving outcomes for cancer patients. In this review, we describe recent discoveries which have increased our understanding of the structure and dynamics of signaling from the EGFR-family, the roles of ligand processing and receptor cross-talk. We discuss the relevance of these studies to the development of strategies for designing more effective targeted treatments for cancer patients.

Fluorescence-based approaches for monitoring membrane receptor oligomerization

Membrane protein structures are highly under-represented relative to water-soluble protein structures in the protein databank. This is especially the case because membrane proteins represent more than 30% of proteins encoded in the human genome yet contribute to less than 10% of currently known structures (Torres et al. in Trends Biol Sci 28:137-144, 2003). Obtaining high-resolution structures of membrane proteins by traditional methods such as NMR and x-ray crystallography is challenging, because membrane proteins are difficult to solubilise, purify and crystallize. Consequently, development of methods to examine protein structure in situ is highly desirable. Fluorescence is highly sensitive to protein structure and dynamics (Lakowicz in Principles of fluorescence spectroscopy, Springer, New York, 2007). This is mainly because of the time a fluorescence probe molecule spends in the excited state. Judicious choice and placement of fluorescent molecule(s) within a protein(s) enables the experimentalist to obtain information at a specific site(s) in the protein (complex) of interest. Moreover, the inherent multi-dimensional nature of fluorescence signals across wavelength, orientation, space and time enables the design of experiments that give direct information on protein structure and dynamics in a biological setting. The purpose of this review is to introduce the reader to approaches to determine oligomeric state or quaternary structure at the cell membrane surface with the ultimate goal of linking the oligomeric state to the biological function. In the first section, we present a brief overview of available methods for determining oligomeric state and compare their advantages and disadvantages. In the second section, we highlight some of the methods developed in our laboratory to address contemporary questions in membrane protein oligomerization. In the third section, we outline our approach to determine the link between protein oligomerization and biological activity.

Linear Chains of HER2 Receptors Found in the Plasma Membrane Using Liquid-Phase Electron Microscopy

The spatial distribution of the human epidermal growth factor 2 (HER2) receptor in the plasma membrane of SKBR3 and HCC1954 breast cancer cells was studied. The receptor was labeled with quantum dot nanoparticles, and fixed whole cells were imaged in their native liquid state with environmental scanning electron microscopy using scanning transmission electron microscopy detection. The locations of individual HER2 positions were determined in a total plasma membrane area of 991 μm² for several SKBR3 cells and 1062 μm² for HCC1954 cells. Some of the HER2 receptors were arranged in a linear chain with interlabel distances of 40 ± 7 and 32 ± 10 nm in SKBR3 and HCC1954 cells, respectively. The finding was tested against randomly occurring linear chains of six or more positions, from which it was concluded that the experimental finding is significant and did not arise from random label distributions. Because the measured interlabel distance in the HER2 chains is similar to the 36-nm helix-repetition distance of actin filaments, it is proposed that a linking mechanism between HER2 and actin filaments leads to linearly aligned oligomers.

Phosphorylated EGFR Dimers Are Not Sufficient to Activate Ras

Growth factor binding to EGFR drives conformational changes that promote homodimerization and transphosphorylation, followed by adaptor recruitment, oligomerization, and signaling through Ras. Whether specific receptor conformations and oligomerization states are necessary for efficient activation of Ras is unclear. We therefore evaluated the sufficiency of a phosphorylated EGFR dimer to activate Ras without growth factor by developing a chemical-genetic strategy to crosslink and "trap" full-length EGFR homodimers on cells. Trapped dimers become phosphorylated and recruit adaptor proteins at stoichiometry equivalent to that of EGF-stimulated receptors. Surprisingly, these phosphorylated dimers do not activate Ras, Erk, or Akt. In the absence of EGF, phosphorylated dimers do not further oligomerize or reorganize on cell membranes. These results suggest that a phosphorylated EGFR dimer loaded with core signaling adapters is not sufficient to activate Ras and that EGFR ligands contribute to conformational changes or receptor dynamics necessary for oligomerization and efficient signal propagation through the SOS-Ras-MAPK pathway.

Transient Acceleration of Epidermal Growth Factor Receptor Dynamics Produces Higher-Order Signaling Clusters

Cell signaling depends on spatiotemporally regulated molecular interactions. Although the movements of signaling proteins have been analyzed with various technologies, how spatial dynamics influence the molecular interactions that transduce signals is unclear. Here, we developed a single-molecule method to analyze the spatiotemporal coupling between motility, clustering, and signaling. The analysis was performed with the epidermal growth factor receptor (EGFR), which triggers signaling through its dimerization and phosphorylation after association with EGF. Our results show that the few EGFRs isolated in membrane subdomains were released by an EGF-dependent increase in their diffusion area, facilitating molecular associations and producing immobile clusters. Using a two-color single-molecule analysis, we found that the EGF-induced state transition alters the properties of the immobile clusters, allowing them to interact for extended periods with the cytoplasmic protein, GRB2. Our study reveals a novel correlation between this molecular interaction and its mesoscale dynamics, providing the initial signaling node.

The Effect of Nanoparticles on the Cluster Size Distributions of Activated EGFR Measured with Photobleaching Image Correlation Spectroscopy

The epidermal growth factor receptor (EGFR) is an important cell surface receptor in normal physiology and disease. Recent work has shown that EGF-gold nanoparticle conjugates can influence cell behaviour, but the underlying mechanism at the receptor quaternary structural level remains poorly understood.In the present work, the cluster density and cluster size of activated (phosphorylated) EGFR clusters in HeLa cells were determined with photobleaching image correlation spectroscopy. EGFR activation was probed via immunofluorescence-detected phosphorylation of tyrosines (pY-mAb) located in the kinase domain of EGFR (Y845) and at the EGFR cytoplasmic tail (Y1173). Cell activation was probed via nuclear extracellular-regulated kinase (ERK) phosphorylation. The cluster size of activated EGFR was 1.3-2.4 pY-mAb/cluster in unstimulated HeLa cells. EGF or nanorod treatment led to an increase in EGFR oligomers containing multiple phosphotyrosines (>2 phosphotyrosines per EGFR oligomer, average cluster size range = 3-5 pY-mAb/cluster) which paralleled increases in nuclear p-ERK. In contrast, EGF-nanorods decreased the contribution from higher-order phospho-clusters and decreased nuclear p-ERK relative to the nanorod control. These studies provide direct evidence that targeted nanotechnology can manipulate receptor organization and lead to changes in receptor activation and subsequent signalling processes.

Exploring oligomeric state of the serotonin1A receptor utilizing photobleaching image correlation spectroscopy: implications for receptor function

Photobleaching image correlation spectroscopy (pbICS) reveals that membrane cholesterol modulates the oligomeric state of the serotonin_1A receptor.

Maximal aggregation of polynomial dynamical systems

Ordinary differential equations (ODEs) with polynomial derivatives are a fundamental tool for understanding the dynamics of systems across many branches of science, but our ability to gain mechanistic insight and effectively conduct numerical evaluations is critically hindered when dealing with large models. Here we propose an aggregation technique that rests on two notions of equivalence relating ODE variables whenever they have the same solution (backward criterion) or if a self-consistent system can be written for describing the evolution of sums of variables in the same equivalence class (forward criterion). A key feature of our proposal is to encode a polynomial ODE system into a finitary structure akin to a formal chemical reaction network. This enables the development of a discrete algorithm to efficiently compute the largest equivalence, building on approaches rooted in computer science to minimize basic models of computation through iterative partition refinements. The physical interpretability of the aggregation is shown on polynomial ODE systems for biochemical reaction networks, gene regulatory networks, and evolutionary game theory.

EGF and NRG induce phosphorylation of HER3/ERBB3 by EGFR using distinct oligomeric mechanisms

Heteromeric interactions between the catalytically impaired human epidermal growth factor receptor (HER3/ERBB3) and its catalytically active homologs EGFR and HER2 are essential for their signaling. Different ligands can activate these receptor pairs but lead to divergent signaling outcomes through mechanisms that remain largely unknown. We used stochastic optical reconstruction microscopy (STORM) with pair-correlation analysis to show that EGF and neuregulin (NRG) can induce different extents of HER3 clustering that are dependent on the nature of the coexpressed HER receptor. We found that the presence of these clusters correlated with distinct patterns and mechanisms of receptor phosphorylation. NRG induction of HER3 phosphorylation depended on the formation of the asymmetric kinase dimer with EGFR in the absence of detectable higher-order oligomers. Upon EGF stimulation, HER3 paralleled previously observed EGFR behavior and formed large clusters within which HER3 was phosphorylated via a noncanonical mechanism. HER3 phosphorylation by HER2 in the presence of NRG proceeded through still another mechanism and involved the formation of clusters within which receptor phosphorylation depended on asymmetric kinase dimerization. Our results demonstrate that the higher-order organization of HER receptors is an essential feature of their ligand-induced behavior and plays an essential role in lateral cross-activation of the receptors. We also show that HER receptor ligands exert unique effects on signaling by modulating this behavior.

EGFR oligomerization organizes kinase-active dimers into competent signalling platforms

Epidermal growth factor receptor (EGFR) signalling is activated by ligand-induced receptor dimerization. Notably, ligand binding also induces EGFR oligomerization, but the structures and functions of the oligomers are poorly understood. Here, we use fluorophore localization imaging with photobleaching to probe the structure of EGFR oligomers. We find that at physiological epidermal growth factor (EGF) concentrations, EGFR assembles into oligomers, as indicated by pairwise distances of receptor-bound fluorophore-conjugated EGF ligands. The pairwise ligand distances correspond well with the predictions of our structural model of the oligomers constructed from molecular dynamics simulations. The model suggests that oligomerization is mediated extracellularly by unoccupied ligand-binding sites and that oligomerization organizes kinase-active dimers in ways optimal for auto-phosphorylation in trans between neighbouring dimers. We argue that ligand-induced oligomerization is essential to the regulation of EGFR signalling.

Epidermal growth factor receptors have been shown to oligomerise upon binding to their cognate ligands. Here, the authors use biochemical, biophysical and cell biology techniques to analyse the structures of these oligomers, and argue that these formations are required for signalling.

The Dipole Potential Modifies the Clustering and Ligand Binding Affinity of ErbB Proteins and Their Signaling Efficiency

Although activation of the ErbB family of receptor tyrosine kinases (ErbB1-4) is driven by oligomerization mediated by intermolecular interactions between the extracellular, the kinase and the transmembrane domains, the transmembrane domain has been largely neglected in this regard. The largest contributor to the intramembrane electric field, the dipole potential, alters the conformation of transmembrane peptides, but its effect on ErbB proteins is unknown. Here, we show by Förster resonance energy transfer (FRET) and number and brightness (N&B) experiments that the epidermal growth factor (EGF)-induced increase in the homoassociation of ErbB1 and ErbB2 and their heteroassociation are augmented by increasing the dipole potential. These effects were even more pronounced for ErbB2 harboring an activating Val → Glu mutation in the transmembrane domain (NeuT). The signaling capacity of ErbB1 and ErbB2 was also correlated with the dipole potential. Since the dipole potential decreased the affinity of EGF to ErbB1, the augmented growth factor-induced effects at an elevated dipole potential were actually induced at lower receptor occupancy. We conclude that the dipole potential plays a permissive role in the clustering of ErbB receptors and that the effects of lipid rafts on ligand binding and receptor signaling can be partially attributed to the dipole potential.

Molecular basis for multimerization in the activation of the epidermal growth factor receptor

The epidermal growth factor receptor (EGFR) is activated by dimerization, but activation also generates higher-order multimers, whose nature and function are poorly understood. We have characterized ligand-induced dimerization and multimerization of EGFR using single-molecule analysis, and show that multimerization can be blocked by mutations in a specific region of Domain IV of the extracellular module. These mutations reduce autophosphorylation of the C-terminal tail of EGFR and attenuate phosphorylation of phosphatidyl inositol 3-kinase, which is recruited by EGFR. The catalytic activity of EGFR is switched on through allosteric activation of one kinase domain by another, and we show that if this is restricted to dimers, then sites in the tail that are proximal to the kinase domain are phosphorylated in only one subunit. We propose a structural model for EGFR multimerization through self-association of ligand-bound dimers, in which the majority of kinase domains are activated cooperatively, thereby boosting tail phosphorylation.

DOI:http://dx.doi.org/10.7554/eLife.14107.001

BioNetFit: a fitting tool compatible with BioNetGen, NFsim and distributed computing environments

Rule-based models are analyzed with specialized simulators, such as those provided by the BioNetGen and NFsim open-source software packages. Here, we present BioNetFit, a general-purpose fitting tool that is compatible with BioNetGen and NFsim. BioNetFit is designed to take advantage of distributed computing resources. This feature facilitates fitting (i.e. optimization of parameter values for consistency with data) when simulations are computationally expensive.

AVAILABILITY AND IMPLEMENTATION

BioNetFit can be used on stand-alone Mac, Windows/Cygwin, and Linux platforms and on Linux-based clusters running SLURM, Torque/PBS, or SGE. The BioNetFit source code (Perl) is freely available (http://bionetfit.nau.edu).

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

CONTACT

bionetgen.help@gmail.com.

Use of mechanistic models to integrate and analyze multiple proteomic datasets

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.