Heterogeneity of epidermal growth factor binding kinetics on individual cells

The ability to sense the environment is heterogeneously distributed in cell populations

Channel capacity of signaling networks quantifies their fidelity in sensing extracellular inputs. Low estimates of channel capacities for several mammalian signaling networks suggest that cells can barely detect the presence/absence of environmental signals. However, given the extensive heterogeneity and temporal stability of cell state variables, we hypothesize that the sensing ability itself may depend on the state of the cells. In this work, we present an information-theoretic framework to quantify the distribution of sensing abilities from single-cell data. Using data on two mammalian pathways, we show that sensing abilities are widely distributed in the population and most cells achieve better resolution of inputs compared to an 'average cell'. We verify these predictions using live-cell imaging data on the IGFR/FoxO pathway. Importantly, we identify cell state variables that correlate with cells' sensing abilities. This information-theoretic framework will significantly improve our understanding of how cells sense in their environment.

The ability to sense the environment is heterogeneously distributed in cell populations

Channel capacity of signaling networks quantifies their fidelity in sensing extracellular inputs. Low estimates of channel capacities for several mammalian signaling networks suggest that cells can barely detect the presence/absence of environmental signals. However, given the extensive heterogeneity and temporal stability of cell state variables, we hypothesize that the sensing ability itself may depend on the state of the cells. In this work, we present an information theoretic framework to quantify the distribution of sensing abilities from single cell data. Using data on two mammalian pathways, we show that sensing abilities are widely distributed in the population and most cells achieve better resolution of inputs compared to an " average cell ". We verify these predictions using live cell imaging data on the IGFR/FoxO pathway. Importantly, we identify cell state variables that correlate with cells' sensing abilities. This information theoretic framework will significantly improve our understanding of how cells sense in their environment.

Maximum Entropy Framework for Predictive Inference of Cell Population Heterogeneity and Responses in Signaling Networks

Predictive models of signaling networks are essential for understanding cell population heterogeneity and designing rational interventions in disease. However, using computational models to predict heterogeneity of signaling dynamics is often challenging because of the extensive variability of biochemical parameters across cell populations. Here, we describe a maximum entropy-based framework for inference of heterogeneity in dynamics of signaling networks (MERIDIAN). MERIDIAN estimates the joint probability distribution over signaling network parameters that is consistent with experimentally measured cell-to-cell variability of biochemical species. We apply the developed approach to investigate the response heterogeneity in the EGFR/Akt signaling network. Our analysis demonstrates that a significant fraction of cells exhibits high phosphorylated Akt (pAkt) levels hours after EGF stimulation. Our findings also suggest that cells with high EGFR levels predominantly contribute to the subpopulation of cells with high pAkt activity. We also discuss how MERIDIAN can be extended to accommodate various experimental measurements.

Simultaneous topographic and recognition imaging of epidermal growth factor receptor (EGFR) on single human breast cancer cells

Epidermal growth factor receptor (EGFR) plays an important role in signaling pathway of the development of breast cancer cells. Since EGFR overexpresses in most breast cancer cells, it is regarded as a biomarker molecule of breast cancer cells. Here we demonstrated a new AFM technique-topography and recognition (TREC) imaging-to simultaneously obtain highly sensitive and specific molecular recognition images and high-resolution topographic images of EGFR on single breast cancer cells.

Systematic identifiability testing for unambiguous mechanistic modeling--application to JAK-STAT, MAP kinase, and NF-kappaB signaling pathway models

Background

When creating mechanistic mathematical models for biological signaling processes it is tempting to include as many known biochemical interactions into one large model as possible. For the JAK-STAT, MAP kinase, and NF-κB pathways a lot of biological insight is available, and as a consequence, large mathematical models have emerged. For large models the question arises whether unknown model parameters can uniquely be determined by parameter estimation from measured data. Systematic approaches to answering this question are indispensable since the uniqueness of model parameter values is essential for predictive mechanistic modeling.

Results

We propose an eigenvalue based method for efficiently testing identifiability of large ordinary differential models and compare this approach to three existing ones. The methods are benchmarked by applying them to models of the signaling pathways mentioned above. In all cases the eigenvalue method proposed here and the orthogonal method find the largest set of identifiable parameters, thus clearly outperforming the other approaches. The identifiability analysis shows that the pathway models are not identifiable, even under the strong assumption that all system state variables are measurable. We demonstrate how the results of the identifiability analysis can be used for model simplification.

Conclusion

While it has undoubtedly contributed to recent advances in systems biology, mechanistic modeling by itself does not guarantee unambiguous descriptions of biological processes. We show that some recent signal transduction pathway models have reached a level of detail that is not warranted. Rigorous identifiability tests reveal that even if highly idealized experiments could be carried out to measure all state variables of these signaling pathways, some unknown parameters could still not be estimated. The identifiability tests therefore show that the level of detail of the investigated models is too high in principle, not just because too little experimental information is available. We demonstrate how the proposed method can be combined with biological insight, however, to simplify these models.

The development of quantum dot calibration beads and quantitative multicolor bioassays in flow cytometry and microscopy

The use of fluorescence calibration beads has been the hallmark of quantitative flow cytometry. It has enabled the direct comparison of interlaboratory data as well as quality control in clinical flow cytometry. In this article, we describe a simple method for producing color-generalizable calibration beads based on streptavidin functionalized quantum dots. Based on their broad absorption spectra and relatively narrow emission, which is tunable on the basis of dot size, quantum dot calibration beads can be made for any fluorophore that matches their emission color. In an earlier publication, we characterized the spectroscopic properties of commercial streptavidin functionalized dots (Invitrogen). Here we describe the molecular assembly of these dots on biotinylated beads. The law of mass action is used to readily define the site densities of the dots on the beads. The applicability of these beads is tested against the industry standard, namely commercial fluorescein calibration beads. The utility of the calibration beads is also extended to the characterization surface densities of dot-labeled epidermal growth factor ligands as well as quantitative indicators of the binding of dot-labeled virus particles to cells.

Single-molecule analysis of epidermal growth factor binding on the surface of living cells

Global cellular responses induced by epidermal growth factor (EGF) receptor (EGFR) occur immediately with a less than 1% occupancy among tens of thousands of EGFR molecules on single cell surface. Activation of EGFR requires the formation of a signaling dimer of EGFR bound with a single ligand to each molecule. How sufficient numbers of signaling dimers are formed at such low occupancy rate is still not known. Here, we have analyzed the kinetics of EGF binding and the formation of the signaling dimer using single-molecule imaging and mathematical modeling. A small number of EGFR on the cell surface formed dimeric binding sites, which bound EGF two orders of magnitude faster than the monomeric binding sites. There was a positive cooperative binding of EGF to the dimeric binding sites through a newly discovered kinetic intermediate. These two mechanisms facilitate the formation of signaling dimers of EGF/EGFR complexes.

Heterogeneities in EGF receptor density at the cell surface can lead to concave up scatchard plot of EGF binding

The mechanism responsible for the concave up nature of the Scatchard plot of epidermal growth factor (EGF) binding on EGF receptor (EGFR) has been a controversial issue for more than a decade. Past efforts to mechanistically simulate the concave up nature of the Scatchard plot of EGF binding have shown that negative cooperativity in EGF binding on an EGFR dimer or inclusion of some external site or binding event can describe this behavior. However, herein we show that heterogeneity in the density of EGFR due to localization in certain regions of the plasma membrane, which has been experimentally reported, can also lead to concave up shape of the Scatchard plot of the EGF binding on EGFR.

G protein threshold behavior in the human neutrophil oxidant response: measurement of G proteins available for signaling in responding and nonresponding subpopulations

Threshold behavior is an important aspect of signal transduction pathways that allows for responses to be turned on or off. Human neutrophil responses to N-formyl peptides, including oxidant production and release, exhibit threshold behavior with respect to the number of G proteins available for signaling; progressive treatment of neutrophils with pertussis toxin causes the conversion of responding cells to nonresponding cells. To quantify the threshold level of G proteins required for signaling of N-formyl peptide stimulated oxidant production in a neutrophil population, we used a plasma membrane associated G protein quantification assay in conjunction with a sorting flow cytometer and measured differences in the average number of G proteins available for signaling per cell in both the responding and the nonresponding subpopulations after pertussis toxin treatment. Although there appeared to be a threshold separating responding cells and nonresponding cells for a given sample, no discrete threshold was measured across multiple treatment conditions. A mathematical model of the early steps in signaling suggests that cell-to-cell variability in signal parameters, such as numbers of signal components and values of kinetic rate constants, obscures the measurement of a discrete threshold and leads to an apparent decrease in the threshold level of G proteins available for signaling as the total G proteins are decreased.

Preparation and characterization of Alexa Fluor 594-labeled epidermal growth factor for fluorescence resonance energy transfer studies: application to the epidermal growth factor receptor

We have prepared and characterized a new fluorescent derivative of murine epidermal growth factor (EGF), Alexa Fluor 594-labeled EGF (A-EGF), for fluorescence studies of EGF-EGF receptor interactions. We describe the synthesis of this derivative and its physical and biological characterization. The significant overlap between the excitation and the emission spectra of A-EGF makes this probe well suited to fluorescence resonance energy homo-transfer. Using time-resolved fluorescence to examine the oligomeric state of the EGF receptor, we have observed resonance energy homo-transfer of A-EGF bound to EGF receptors in cells, but not of A-EGF bound to EGF receptors in membrane vesicles. Our results, interpreted in the context of recent crystallographic studies of the ligand-binding domains of EGF receptors, suggest that observed fluorescence resonance energy transfer does not result from transfer within receptor dimers, but rather results from transfer within higher-order oligomers. Furthermore, our results support a structural model for oligomerization of EGF receptors in which dimers are positioned head-to-head with respect to the ligand-binding site, consistent with the head-to-head interactions observed between adjacent receptor dimers by X-ray crystallography.

Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors

We present a computational model that offers an integrated quantitative, dynamic, and topological representation of intracellular signal networks, based on known components of epidermal growth factor (EGF) receptor signal pathways. The model provides insight into signal-response relationships between the binding of EGF to its receptor at the cell surface and the activation of downstream proteins in the signaling cascade. It shows that EGF-induced responses are remarkably stable over a 100-fold range of ligand concentration and that the critical parameter in determining signal efficacy is the initial velocity of receptor activation. The predictions of the model agree well with experimental analysis of the effect of EGF on two downstream responses, phosphorylation of ERK-1/2 and expression of the target gene, c-fos.

Real-time kinetics of ligand/cell surface receptor interactions in living cells: binding of epidermal growth factor to the epidermal growth factor receptor

We describe a system for extending stopped-flow analysis to the kinetics of ligand capture and release by cell surface receptors in living cells. While most mammalian cell lines cannot survive the shear forces associated with turbulent stopped-flow mixing, we determined that a murine hematopoietic precursor cell line, 32D, is capable of surviving rapid mixing using flow rates as great as 4.0 mL/s, allowing rapid processes to be quantitated with dead times as short as 10 ms. 32D cells do not express any endogenous epidermal growth factor (EGF) receptor or other ErbB family members and were used to establish monoclonal cell lines stably expressing the EGF receptor. Association of fluorescein-labeled H22Y-murine EGF (F-EGF) to receptor-expressing 32D cells was observed by measuring time-dependent changes in fluorescence anisotropy following rapid mixing. Dissociation of F-EGF from EGF-receptor-expressing 32D cells was measured both by chase experiments using unlabeled mEGF and by experiments in which equilibrium was perturbed by dilution. Comparison of these dissociation experiments showed that little, if any, ligand-induced dissociation occurs in the chase dissociation experiments. Data from a series of association and dissociation experiments, performed at various concentrations of F-EGF in the nanomolar range and at multiple cell densities, were simultaneously analyzed using global analysis techniques and fit to a two independent receptor-class model. Our analysis is consistent with the presence of two distinct receptor populations having association rate constants of k(on1) = 8.6 x 10(6) M(-1) s(-1) and k(on2) = 2.4 x 10(6) M(-1) s(-1) and dissociation rate constants of k(off1) = 0.17 x 10(-2) s(-1) and k(off2) = 0.21 x 10(-2) s(-1). The magnitudes of these parameters suggest that under physiological conditions, in which cells are transiently exposed to nanomolar concentrations of ligand, ligand capture and release may function as the first line of regulation of the EGF receptor-induced signal transduction cascade.

Thermodynamic mixing of molecular states of the epidermal growth factor receptor modulates macroscopic ligand binding affinity

The epidermal growth factor receptor (EGFr), when expressed on the cell surface, has long been known to display two distinct affinities for epidermal growth factor (EGF) binding. In addition, the treatment of cells expressing the EGFr with phorbol esters has been shown to cause a loss of the high-affinity binding capacity of the receptor. In the present study, point mutations that alter acidic or phosphorylation sites have been made in an intracellular domain near Tyr-992 (residues 988-992) of the EGFr. Equilibrium (125)I-EGF binding studies demonstrate that the conversion of Tyr-992 into glutamate induces a 4-fold decrease in the EGFr apparent low-affinity dissociation constant, whereas the mutation of two acidic residues, Asp-988 and Glu-991, or the conversion of Tyr-992 into phenylalanine does not alter EGFr affinity. Phorbol ester treatment of EGFr-expressing Chinese hamster ovary cells results in a loss of high-affinity binding and an increase in the apparent low-affinity dissociation constant of the receptor, similar to the effect of a truncation mutant in which the C-terminal 190 residues are deleted. These results are examined in the context of a new model for regulation of the affinity of the EGFr for EGF in which a cytosolic particle stabilizes the high-affinity conformation of the EGFr and a rapid equilibrium exists between EGFr high-affinity and low-affinity conformations. This model demonstrates that the macroscopic affinities of the EGFr can differ from the affinities of individual EGFr molecules and provides a theoretical framework whereby the measured affinities of the EGFr are modulated by intracellular interactions.

Single-molecule imaging of EGFR signalling on the surface of living cells

The early events in signal transduction from the epidermal growth factor (EGF) receptor (EGFR) are dimerization and autophosphorylation of the receptor, induced by binding of EGF. Here we observe these events in living cells by visualizing single molecules of fluorescent-dye-labelled EGF in the plasma membrane of A431 carcinoma cells. Single-molecule tracking reveals that the predominant mechanism of dimerization involves the formation of a cell-surface complex of one EGF molecule and an EGFR dimer, followed by the direct arrest of a second EGF molecule, indicating that the EGFR dimers were probably preformed before the binding of the second EGF molecule. Single-molecule fluorescence-resonance energy transfer shows that EGF-EGFR complexes indeed form dimers at the molecular level. Use of a monoclonal antibody specific to the phosphorylated (activated) EGFR reveals that the EGFR becomes phosphorylated after dimerization.