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During an early period of the Coronavirus Disease 2019 (COVID-19) pandemic, the Navajo Nation, much like New York City, experienced a relatively high rate of disease transmission. Yet, between January and October 2020, it experienced only a single period of growth in new COVID-19 cases, which ended when cases peaked in May 2020. The daily number of new cases slowly decayed in the summer of 2020 until late September 2020. In contrast, the surrounding states of Arizona, Colorado, New Mexico, and Utah all experienced at least two periods of growth in the same time frame, with second surges beginning in late May to early June. To investigate the causes of this difference, we used a compartmental model accounting for distinct periods of non-pharmaceutical interventions (NPIs) (e.g., behaviors that limit disease transmission) to analyze the epidemic in each of the five regions. We used Bayesian inference to estimate region-specific model parameters from regional surveillance data (daily reports of new COVID-19 cases) and to quantify uncertainty in parameter estimates and model predictions. Our results suggest that NPIs in the Navajo Nation were sustained over the period of interest, whereas in the surrounding states, NPIs were relaxed, which allowed for subsequent surges in cases. Our region-specific model parameterizations allow us to quantify the impacts of NPIs on disease incidence in the regions of interest.

To increase situational awareness and support evidence-based policy-making, we formulated two types of mathematical models for COVID-19 transmission within a regional population. One is a fitting function that can be calibrated to reproduce an epidemic curve with two timescales (e.g., fast growth and slow decay). The other is a compartmental model that accounts for quarantine, self-isolation, social distancing, a non-exponentially distributed incubation period, asymptomatic individuals, and mild and severe forms of symptomatic disease. Using Bayesian inference, we have been calibrating our models daily for consistency with new reports of confirmed cases from the 15 most populous metropolitan statistical areas in the United States and quantifying uncertainty in parameter estimates and predictions of future case reports. This online learning approach allows for early identification of new trends despite considerable variability in case reporting. We infer new significant upward trends for five of the metropolitan areas starting between 19-April-2020 and 12-June-2020.

Although many persons in the United States have acquired immunity to COVID-19, either through vaccination or infection with SARS-CoV-2, COVID-19 will pose an ongoing threat to non-immune persons so long as disease transmission continues. We can estimate when sustained disease transmission will end in a population by calculating the population-specific basic reproduction number ℛ0, the expected number of secondary cases generated by an infected person in the absence of any interventions. The value of ℛ0 relates to a herd immunity threshold (HIT), which is given by 1 − 1/ℛ0. When the immune fraction of a population exceeds this threshold, sustained disease transmission becomes exponentially unlikely (barring mutations allowing SARS-CoV-2 to escape immunity). Here, we report state-level ℛ0 estimates obtained using Bayesian inference. Maximum a posteriori estimates range from 7.1 for New Jersey to 2.3 for Wyoming, indicating that disease transmission varies considerably across states and that reaching herd immunity will be more difficult in some states than others. ℛ0 estimates were obtained from compartmental models via the next-generation matrix approach after each model was parameterized using regional daily confirmed case reports of COVID-19 from 21-January-2020 to 21-June-2020. Our ℛ0 estimates characterize infectiousness of ancestral strains, but they can be used to determine HITs for a distinct, currently dominant circulating strain, such as SARS-CoV-2 variant Delta (lineage B.1.617.2), if the relative infectiousness of the strain can be ascertained. On the basis of Delta-adjusted HITs, vaccination data, and seroprevalence survey data, we find that no state has achieved herd immunity as of 20-September-2021.Significance StatementCOVID-19 will continue to threaten non-immune persons in the presence of ongoing disease transmission. We can estimate when sustained disease transmission will end by calculating the population-specific basic reproduction number ℛ0, which relates to a herd immunity threshold (HIT), given by 1 − 1/ℛ0. When the immune fraction of a population exceeds this threshold, sustained disease transmission becomes exponentially unlikely. Here, we report state-level ℛ0 estimates indicating that disease transmission varies considerably across states. Our ℛ0 estimates can also be used to determine HITs for the Delta variant of COVID-19. On the basis of Delta-adjusted HITs, vaccination data, and serological survey results, we find that no state has yet achieved herd immunity.

To characterize Coronavirus Disease 2019 (COVID-19) transmission dynamics in each of the 15 most populous metropolitan statistical areas (MSAs) in the United States (US) from January 2020 to September 2021, we extended a previously reported compartmental model accounting for effects of multiple distinct periods of social distancing by adding consideration of vaccination and Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) variants Alpha (lineage B.1.1.7) and Delta (lineage B.1.617.2). For each MSA, we found region-specific parameterizations of the model using daily reports of new COVID-19 cases available from January 21, 2020 to August 24, 2021. In the process, we obtained estimates of the relative infectiousness of Alpha and Delta as well as their takeover times in each MSA. We find that 14-d ahead forecasts are reasonably accurate; these forecasts are being updated daily. Projections made on August 24, 2021 suggest that 5 of the 15 MSAs have already achieved herd immunity.

To characterize Coronavirus Disease 2019 (COVID-19) transmission dynamics in each of the metropolitan statistical areas (MSAs) surrounding Dallas, Houston, New York City, and Phoenix in 2020 and 2021, we extended a previously reported compartmental model accounting for effects of multiple distinct periods of non-pharmaceutical interventions by adding consideration of vaccination and Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) variants Alpha (lineage B.1.1.7) and Delta (lineage B.1.617.2). For each MSA, we found region-specific parameterizations of the model using daily reports of new COVID-19 cases available from January 21, 2020 to October 31, 2021. In the process, we obtained estimates of the relative infectiousness of Alpha and Delta as well as their takeoff times in each MSA (the times at which sustained transmission began). The estimated infectiousness of Alpha ranged from 1.1x to 1.6x that of viral strains circulating in 2020 and early 2021. The estimated relative infectiousness of Delta was higher in all cases, ranging from 1.6x to 2.2x. The estimated Alpha takeoff times ranged from February 16 (for New York City, which was evidently impacted much earlier than the other regions) to April 2, 2021. The estimated Delta takeoff times were more tightly clustered, ranging from June 15 to June 24, 2021. Estimated takeoff times are consistent with genomic surveillance data.One-Sentence SummaryUsing a compartmental model parameterized to reproduce available reports of new Coronavirus Disease 2019 (COVID-19) cases, we quantified the impacts of vaccination and Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) variants Alpha (lineage B.1.1.7) and Delta (lineage B.1.617.2) on regional epidemics in the metropolitan statistical areas (MSAs) surrounding Dallas, Houston, New York City, and Phoenix.

Summary Bayesian inference in biological modeling commonly relies on Markov chain Monte Carlo (MCMC) sampling of a multidimensional and non-Gaussian posterior distribution that is not analytically tractable. Here, we present the implementation of a practical MCMC method in the open-source software package PyBioNetFit (PyBNF), which is designed to support parameterization of mathematical models for biological systems. The new MCMC method, am, incorporates an adaptive move proposal distribution. For warm starts, sampling can be initiated at a specified location in parameter space and with a multivariate Gaussian proposal distribution defined initially by a specified covariance matrix. Multiple chains can be generated in parallel using a computer cluster. We demonstrate that am can be used to successfully solve real-world Bayesian inference problems, including forecasting of new Coronavirus Disease 2019 case detection with Bayesian quantification of forecast uncertainty. Availability and implementation PyBNF version 1.1.9, the first stable release with am, is available at PyPI and can be installed using the pip package-management system on platforms that have a working installation of Python 3. PyBNF relies on libRoadRunner and BioNetGen for simulations (e.g. numerical integration of ordinary differential equations defined in SBML or BNGL files) and Dask.Distributed for task scheduling on Linux computer clusters. The Python source code can be freely downloaded/cloned from GitHub and used and modified under terms of the BSD-3 license (https://github.com/lanl/pybnf). Online documentation covering installation/usage is available (https://pybnf.readthedocs.io/en/latest/). A tutorial video is available on YouTube (https://www.youtube.com/watch?v=2aRqpqFOiS4&t=63s). Supplementary information Supplementary data are available at Bioinformatics online.

To increase situational awareness and support evidence-based policy-making, we formulated two types of mathematical models for COVID-19 transmission within a regional population. One is a fitting function that can be calibrated to reproduce an epidemic curve with two timescales (e.g., fast growth and slow decay). The other is a compartmental model that accounts for quarantine, self-isolation, social distancing, a non-exponentially distributed incubation period, asymptomatic individuals, and mild and severe forms of symptomatic disease. Using Bayesian inference, we have been calibrating our models daily for consistency with new reports of confirmed cases from the 15 most populous metropolitan statistical areas in the United States and quantifying uncertainty in parameter estimates and predictions of future case reports. This online learning approach allows for early identification of new trends despite considerable variability in case reporting. We infer new significant upward trends for five of the metropolitan areas starting between 19-April-2020 and 12-June-2020., 48 pages, 10 figures, 4 Appendix figures, 3 tables, 1 Appendix figure, 1 Appendix text

Background: Pancreatic ductal adenocarcinoma (PDA) is a lethal cancer with complex genomes and dense fibrotic stroma. This study was designed to identify clinically relevant somatic aberrations in pancreatic cancer genomes of patients with primary and metastatic disease enrolled and treated in two clinical trials. Methods: Tumour nuclei were flow sorted prior to whole genome copy number variant (CNV) analysis. Targeted or whole exome sequencing was performed on most samples. We profiled biopsies from 68 patients enrolled in two Stand Up to Cancer (SU2C)-sponsored clinical trials. These included 38 resected chemoradiation naïve tumours (SU2C 20206-003) and metastases from 30 patients who progressed on prior therapies (SU2C 20206-001). Patient outcomes including progression-free survival (PFS) and overall survival (OS) were observed. Results: We defined: (a) CDKN2A homozygous deletions that included the adjacent MTAP gene, only its’ 3′ region, or excluded MTAP; (b) SMAD4 homozygous deletions that included ME2; (c) a pancreas-specific MYC super-enhancer region; (d) DNA repair-deficient genomes; and (e) copy number aberrations present in PDA patients with long-term (⩾ 40 months) and short-term (⩽ 12 months) survival after surgical resection. Conclusions: We provide a clinically relevant framework for genomic drivers of PDA and for advancing novel treatments.

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.

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.

In systems biology, qualitative data are often generated, but rarely used to parameterize models. We demonstrate an approach in which qualitative and quantitative data can be combined for parameter identification. In this approach, qualitative data are converted into inequality constraints imposed on the outputs of the model. These inequalities are used along with quantitative data points to construct a single scalar objective function that accounts for both datasets. To illustrate the approach, we estimate parameters for a simple model describing Raf activation. We then apply the technique to a more elaborate model characterizing cell cycle regulation in yeast. We incorporate both quantitative time courses (561 data points) and qualitative phenotypes of 119 mutant yeast strains (1647 inequalities) to perform automated identification of 153 model parameters. We quantify parameter uncertainty using a profile likelihood approach. Our results indicate the value of combining qualitative and quantitative data to parameterize systems biology models.

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.

Background: The choice of a regimen in metastatic pancreatic cancer patients following progression on 1st line therapy is empiric and outcomes are unsatisfactory. This phase II study was performed to evaluate the efficacy of therapy selected by immunohistochemistry (IHC) in these patients following progression after one or more therapies. Methods: Eligible patients underwent a percutaneous biopsy of a metastatic lesion and treatment selection was determined by IHC. The study required 35 evaluable patients (power of 86%) for detecting a true 1-year survival rate of >20%. Results: A tumor biopsy was performed in 48 of 49 accrued patients. Study therapy was not given (n=13) either due to insufficient tumor on biopsy (n=8) or due to worsening cancer related symptoms after biopsy (n=5). The demographics of evaluable patients (n=35) are male/female (59%/41%), with age range 34–78 years (median 63 years). Patients had 1–6 prior regimens (median of 2). The most common IHC targets were topoisomerase 1 or 2, thymidylate synthase, excision repair cross-complementation group 1 protein (ERCC1), and osteonectin secreted protein acidic and rich in cysteine (SPARC). Commercially available treatment regimens prescribed included FOLFIRI, FOLFOX, irinotecan, and doxorubicin. The response (RECIST) was 9%, the median survival was 5.6 months (94% CI, 3.8–8.2), and the 1-year survival was 20% (95% CI, 7–33%). Conclusions: In all patients, IHC assays resulted in identification of at least two targets for therapy and a non-cross resistant regimen could be prescribed for therapy with evidence of some benefit. An IHC based treatment strategy is feasible and needs validation in larger studies.

Pancreatic cancer is characterized by a desmoplastic reaction that creates a dense fibroinflammatory microenvironment, promoting hypoxia and limiting cancer drug delivery due to decreased blood perfusion. Here, we describe a novel tumor–stroma interaction that may help explain the prevalence of desmoplasia in this cancer. Specifically, we found that activation of hypoxia-inducible factor-1α (HIF-1α) by tumor hypoxia strongly activates secretion of the sonic hedgehog (SHH) ligand by cancer cells, which in turn causes stromal fibroblasts to increase fibrous tissue deposition. In support of this finding, elevated levels of HIF-1α and SHH in pancreatic tumors were determined to be markers of decreased patient survival. Repeated cycles of hypoxia and desmoplasia amplified each other in a feed forward loop that made tumors more aggressive and resistant to therapy. This loop could be blocked by HIF-1α inhibition, which was sufficient to block SHH production and hedgehog signaling. Taken together, our findings suggest that increased HIF-1α produced by hypoxic tumors triggers the desmoplasic reaction in pancreatic cancer, which is then amplified by a feed forward loop involving cycles of decreased blood flow and increased hypoxia. Our findings strengthen the rationale for testing HIF inhibitors and may therefore represent a novel therapeutic option for pancreatic cancer. Cancer Res; 73(11); 3235–47. ©2013 AACR.

Increased extracellular matrix (ECM) deposition is a characteristic observed in many solid tumors. Increased levels of one ECM component—namely, hyaluronan (HA)—leads to reduced elasticity of tumor tissue and increased interstitial fluid pressure. Multiple initial reports showed that the addition of hyaluronidase (HYAL) to chemotherapeutic regimens could greatly improve efficacy. Unfortunately, the bovine HYAL used in those studies was limited therapeutically by immunologic responses to treatment. Newly developed recombinant human HYAL has recently been introduced into clinical trials. In this article, we describe the role of HA in cancer, methods of targeting HA, and clinical studies performed to date, and we propose that targeting HA could now be an effective treatment option for patients with many different types of solid tumors. Cancer Discovery; 1(4): 291–96. ©2011 AACR.

Receptor tyrosine kinases (RTKs) typically contain multiple autophosphorylation sites in their cytoplasmic domains. Once activated, these autophosphorylation sites can recruit downstream signaling proteins containing Src homology 2 (SH2) and phosphotyrosine-binding (PTB) domains, which recognize phosphotyrosine-containing short linear motifs (SLiMs). These domains and SLiMs have polyspecific or promiscuous binding activities. Thus, multiple signaling proteins may compete for binding to a common SLiM and vice versa. To investigate the effects of competition on RTK signaling, we used a rule-based modeling approach to develop and analyze models for ligand-induced recruitment of SH2/PTB domain-containing proteins to autophosphorylation sites in the insulin-like growth factor 1 (IGF1) receptor (IGF1R). Models were parameterized using published datasets reporting protein copy numbers and site-specific binding affinities. Simulations were facilitated by a novel application of model restructuration, to reduce redundancy in rule-derived equations. We compare predictions obtained via numerical simulation of the model to those obtained through simple prediction methods, such as through an analytical approximation, or ranking by copy number and/or KD value, and find that the simple methods are unable to recapitulate the predictions of numerical simulations. We created 45 cell line-specific models that demonstrate how early events in IGF1R signaling depend on the protein abundance profile of a cell. Simulations, facilitated by model restructuration, identified pairs of IGF1R binding partners that are recruited in anti-correlated and correlated fashions, despite no inclusion of cooperativity in our models. This work shows that the outcome of competition depends on the physicochemical parameters that characterize pairwise interactions, as well as network properties, including network connectivity and the relative abundances of competitors., Author summary Cells rely on networks of interacting biomolecules to sense and respond to environmental perturbations and signals. However, it is unclear how information is processed to generate appropriate and specific responses to signals, especially given that these networks tend to share many components. For example, receptors that detect distinct ligands and regulate distinct cellular activities commonly interact with overlapping sets of downstream signaling proteins. Here, to investigate the downstream signaling of a well-studied receptor tyrosine kinase (RTK), the insulin-like growth factor 1 (IGF1) receptor (IGF1R), we formulated and analyzed 45 cell line-specific mathematical models, which account for recruitment of 18 different binding partners to six sites of receptor autophosphorylation in IGF1R. The models were parameterized using available protein copy number and site-specific affinity measurements, and restructured to allow for network generation. We find that recruitment is influenced by the protein abundance profile of a cell, with different patterns of recruitment in different cell lines. Furthermore, in a given cell line, we find that pairs of IGF1R binding partners may be recruited in a correlated or anti-correlated fashion. We demonstrate that the simulations of the model have greater predictive power than protein copy number and/or binding affinity data, and that even a simple analytical model cannot reproduce the predicted recruitment ranking obtained via simulations. These findings represent testable predictions and indicate that the outputs of IGF1R signaling depend on cell line-specific properties in addition to the properties that are intrinsic to the biomolecules involved.

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.

Background Halogen bonding has recently come to play as a target for lead optimization in rational drug design. However, most docking program don’t account for halogen bonding in their scoring functions and are not able to utilize this new approach. In this study a new and improved halogen bonding scoring function (XBSF) is presented along with its implementation in the AutoDock Vina molecular docking software. This new improved program is termed as AutoDock VinaXB, where XB stands for the halogen bonding parameters that were added. Results XBSF scoring function is derived based on the X···A distance and C–X···A angle of interacting atoms. The distance term was further corrected to account for the polar flattening effect of halogens. A total of 106 protein-halogenated ligand complexes were tested and compared in terms of binding affinity and docking poses using Vina and VinaXB. VinaXB performed superior to Vina in the majority of instances. VinaXB was closer to native pose both above and below 2 Å deviation categories almost twice as frequently as Vina. Conclusions Implementation of XBSF into AutoDock Vina has been shown to improve the accuracy of the docking result with regards to halogenated ligands. AutoDock VinaXB addresses the issues of halogen bonds that were previously being scored unfavorably due to repulsion factors, thus effectively lowering the output RMSD values. Electronic supplementary material The online version of this article (doi:10.1186/s13321-016-0139-1) contains supplementary material, which is available to authorized users.

Summary: 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

Intrapulmonary chemoreceptors (IPC) are neurons that sense tonic and phasic CO2 stimuli in the lungs of birds and diapsid reptiles. IPC are different from most other vertebrate respiratory CO2 receptors because: (1) they are stimulated by low PCO2 and inhibited by high PCO2, (2) they have extremely rapid response characteristics, (3) their CO2 sensitivity is nearly abolished by intracellular inhibitors of carbonic anhydrase, and (4) their CO2 sensitivity is strongly depressed by inhibiting Na+/H+ antiport exchange. Experimental evidence suggests that IPC respond to intracellular pH, not CO2 directly, and that intracellular pH and IPC discharge are determined by a kinetic balance between CO2 hydration/dehydration rates, transmembrane acid/base exchange rates, and intracellular buffering. We review experimental evidence for and against various mechanisms of IPC CO2 chemotransduction, present a conceptual and mathematical model of the proposed mechanisms, and compare this model to CO2 transduction in other respiratory chemoreceptors.

The rate of leukocyte recruitment to and detachment from the vasculature contributes to cellular tethering, rolling, firm adherence, and migration across an endothelium layer. The molecular rates depend on the type and number of bound integrin or selectin adhesion molecules, shear force acting on the bound adhesion molecules, and affinity state of integrins. Although little is known of the effect that the number of adhesion molecules has on leukocyte recruitment, it has been shown that firm adhesion for cells in suspension may be mediated by small numbers of bound adhesion molecules. We studied the disaggregation of aggregates composed of B78H1 cells transfected with human vascular cell adhesion molecule-1 (VCAM-1) and human monoblastoid U937 cells expressing Very Late Antigen-4 (VLA-4). Aggregate disaggregation rates were obtained and compared to dissociation rates for soluble rhVCAM-1 ligand and monoblastoid U937 cells. Under conditions without shear stress, it was found that average cellular disaggregation rates were a factor of 1.3 +/- 0.4 times slower than molecular dissociation rates for the 1 mM Mn(2+) and 1 mM Mn(2+) + 1 mM Ca(2+) conditions. A simple mathematical model was used to predict how much smaller the dissociation constant would be if the number of bonds holding an aggregate varied from one bond to N bonds under conditions without shear stress. The average number of adhesion bonds holding the cell aggregates together was found to be 1.5 +/- 0.7. This suggests that a few bonds were needed to form cellular aggregates and that increased aggregation was related to integrin affinity changes and not due to clustering or increased bond numbers.

Aggregation of cell surface receptors is a ubiquitous means of initiating signal transduction in many cellular systems. In this manuscript, we describe a combined theoretical and experimental approach based on multiparameter flow cytometry for measuring the time course of ligand induced aggregation of IgE–FceRI on RBL cells. By fluorescently labeling both the ligand and surface IgE (sIgE), we have developed an assay that permits us to simultaneously measure both occupancy of sIgE combining sites and association of antigen with the cell surface. This allows for a direct calculation of the degree of receptor aggregation present on the cell. By employing new mixing technologies developed for flow cytometry, we are able to look at aggregation in the sub second time domain. To extend our work, we have synthesized a new set of chemically well defined ligands (of valences 1–3) to use as probes in our studies. We show that the magnitude of the cellular response is dramatically increased as the valence of our ligand is raised from two to three.

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.

Antigen-antibody systems provide the flexibility of varying the kinetics and affinity of molecular interaction and studying the resulting effect on adhesion. In a parallel-plate flow chamber, we measured the extent and rate of adhesion of rat basophilic leukemia cells preincubated with anti-dinitrophenyl IgE clones SPE-7 or H1 26.82 to dinitrophenyl-coated polyacrylamide gel substrates in a linear shear field. Both of these IgEs bind dinitrophenyl, but H1 26.82 has a 10-fold greater on rate and a 30-fold greater affinity. Adhesion was found to be binary; cells either arrested irreversibly or continued at their unencumbered hydrodynamic velocity. Under identical conditions, more adhesion was seen with the higher affinity (higher on rate) IgE clone. At some shear rates, adhesion was robust with H1 26.82, but negligible with SPE-7. Reduction in receptor number or ligand density reduced the maximum level of adhesion seen at any shear rate, but did not decrease the shear rate at which adhesion was first observed. The spatial pattern of adhesion for both IgE clones is well represented by the first-order kinetic rate constant kad, and we have determined how kad depends on ligand and receptor densities and shear rate. The rate constant kad found with H1 26.82 was approximately fivefold greater than with SPE-7. The dependence of kad on site density and shear rate for SPE-7 is complex: kad increases linearly with antigen site density at low to moderate shear rates, but is insensitive to site density at high shear. kad increases with shear rate at low site density but decreases with shear at high site density. With H1 26.82, the functional dependence of kad with shear rate was similar. Although these data are consistent with the hypothesis that we have sampled both transport and reaction-limited adhesion regimes, they point out deficiencies in current theories describing cell attachment under flow.

The tumor associated stroma has been described in recent years as being complicit in tumor growth in pancreatic cancer. The stroma hosts a variety of components of both cellular and molecular makeup. In normal tissues, the stroma provides nutrients and regulatory signals for proper cellular polarity and function. However, following oncogenic transformation, the stromal compartment is conscripted to provide stimulatory signals and protection to tumor cells. It is these tumor-stromal interactions that are currently of great therapeutic interest. Several key reports have suggested that therapeutic targeting of the tumor-stromal interactions in pancreatic cancer has the potential to offer survival benefit. In this review, we will discuss the tumor-stromal interactions that contribute to tumor growth and progression, and ways in which we might counter these interactions.

New modeling approaches are needed to tackle the complexity of cell signaling systems. An emerging approach is rule-based modeling, in which protein-protein interactions are represented at the level of functional components. By using rules to represent interactions, a modeler can avoid enumerating the reachable chemical species in a system, which is a necessity in traditional modeling approaches. A set of rules can be used to generate a reaction network, or to perform simulations with or without network generation. Although the rule-based approach is a relatively recent development in biology, it is based on concepts that have proven useful in other fields. In this chapter, we discuss innovations of the rule-based modeling approach, relative to traditional approaches for modeling chemical kinetics. These innovations include the use of rules to concisely capture the dynamics of molecular interactions, the view of models as programs, and agent-based computational approaches that can be applied to simulate the chemical kinetics of a system characterized by a large traditional model. These innovations should enable the development of models that can relate the molecular state of a cell to its phenotype, even though vast and complex networks bridge perturbations at the molecular level to fates and activities at the cellular level. In the future, we expect that validated rule-based models will be useful for model-guided studies of cell signaling mechanisms, interpretation of temporal phosphoproteomic data, and cell engineering applications.

Kinetic approaches are valuable tools for mechanistic studies of cell function. Flow cytometry is well suited to make sensitive kinetic measurements, but the time required to deliver mixed samples to the point of measurement (10-20 s in a conventional cytometer) limits analysis of rapidly occurring events. To address this limitation, we adapted a syringe-based stopped-flow rapid mixing device to a modified commercial flow cytometer to achieve mixing and measurement of sample in under 1 s. Because such screw-driven mixers are designed to deliver fluid at rates of microliters per millisecond and cytometers accept samples at microliters per second, the syringe mixer was modified with a screw to allow sample delivery at rates as low as 1.8 microliters/s. A custom-made nozzle holder featuring a fast-acting three-way sample delivery valve and a 1.5- microliters dead volume was designed for a Becton Dickinson FACS stream-in-air flow nozzle. Syringe motors and valves are computer controlled, as is the start signal for an adjustable time ramp. A stable sample stream can be established within the sheath stream in less than 1 s, enabling fluorescence measurements of microspheres with coefficients of variation of approximately 5%. Light scatter gating to select particles in the center of the laser beam enables fluorescence measurements at times of under 300 ms. Efficient mixing of reagents is demonstrated by the iodide quenching of microspheres surface labeled with fluorescein isothiocyanate (FITC). The instrument is capable of quantitatively proportioning cells and reagent, thereby allowing precise control of reagent concentration and dilution. Rapid kinetic measurements of intact cells are demonstrated by FITC-formyl peptide binding to cell surface receptors.

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

Macroautophagy (autophagy) is a cellular recycling program essential for homeostasis and survival during cytotoxic stress. This process, which has an emerging role in disease etiology and treatment, is executed in four stages through the coordinated action of more than 30 proteins. An effective strategy for studying complicated cellular processes, such as autophagy, involves the construction and analysis of mathematical or computational models. When developed and refined from experimental knowledge, these models can be used to interrogate signaling pathways, formulate novel hypotheses about systems, and make predictions about cell signaling changes induced by specific interventions. Here, we present the development of a computational model describing autophagic vesicle dynamics in a mammalian system. We used time-resolved, live-cell microscopy to measure the synthesis and turnover of autophagic vesicles in single cells. The stochastically simulated model was consistent with data acquired during conditions of both basal and chemically-induced autophagy. The model was tested by genetic modulation of autophagic machinery and found to accurately predict vesicle dynamics observed experimentally. Furthermore, the model generated an unforeseen prediction about vesicle size that is consistent with both published findings and our experimental observations. Taken together, this model is accurate and useful and can serve as the foundation for future efforts aimed at quantitative characterization of autophagy.

Pancreatic adenocarcinoma (PAC) is among the most lethal malignancies. While research has implicated multiple genes in disease pathogenesis, identification of therapeutic leads has been difficult and the majority of currently available therapies provide only marginal benefit. To address this issue, our goal was to genomically characterize individual PAC patients to understand the range of aberrations that are occurring in each tumor. Because our understanding of PAC tumorigenesis is limited, evaluation of separate cases may reveal aberrations, that are less common but may provide relevant information on the disease, or that may represent viable therapeutic targets for the patient. We used next generation sequencing to assess global somatic events across 3 PAC patients to characterize each patient and to identify potential targets. This study is the first to report whole genome sequencing (WGS) findings in paired tumor/normal samples collected from 3 separate PAC patients. We generated on average 132 billion mappable bases across all patients using WGS, and identified 142 somatic coding events including point mutations, insertion/deletions, and chromosomal copy number variants. We did not identify any significant somatic translocation events. We also performed RNA sequencing on 2 of these patients' tumors for which tumor RNA was available to evaluate expression changes that may be associated with somatic events, and generated over 100 million mapped reads for each patient. We further performed pathway analysis of all sequencing data to identify processes that may be the most heavily impacted from somatic and expression alterations. As expected, the KRAS signaling pathway was the most heavily impacted pathway (P

As part of our SU2C studies we are profiling the genomes of primary localized pancreatic ductal adenocarcinomas (PDAs) obtained from surgical samples collected at the University of Pennsylvania (SU2C-003). A fundamental challenge for the study of PDA genomes in clinical samples is the presence of varied admixtures of reactive stroma, inflammatory cells, and necrosis within the tumor. Furthermore, it is well-established that biopsies frequently contain multiple clonal populations of neoplastic cells that cannot be distinguished on the basis of morphology alone. In order to overcome the limitations of histopatholgy-based methods to study PDA genomes, we are using DNA content-based flow cytometry to identify and purify distinct clonal populations from each surgical sample. These assays are done while collecting up to 6 simultaneous sorting streams thus optimizing the use of each clinical sample. Each sorted diploid, aneuploid, and tetraploid population is interrogated with oligonucleotide CGH arrays. In addition, the epithelial and mesenchymal content of each tumor sample is assessed in flow assays with cytokeratin 19, vimentin, and ZEB1. Our unbiased approach provides clonal analysis of distinct populations in each patient’s tumor regardless of tumor cell content. We have identified a series of novel patient-specific selected aberrations, including homozygous deletions that target regulators of chromatin remodeling (SMYD3, ASXL2), and high-level focal amplicons that include mediators of oncogenic signaling pathways (FNTA, RAB3IP) and cellular metabolism (CTPS). The genes targeted by the somatic aberrations in each patient are overlaid onto a collection of 33 PDA-specific maps, containing 763 genes of interest, developed as part of the Metaminer Oncology initiative. These include signaling pathways of aberrant KRAS, DNA repair, apoptosis, epithelial mesenchymal transition (EMT), inflammation, and other mediators of PDA. We have accumulated clonal genomic data for 15 patients in the first 4 months of this study (December 2011- April 2012) and are currently profiling 3-5 new samples per month. These are providing a unique prospective data set to test hypothesis of the genomic basis of clinical outcomes in patients with localized resectable PDA. This proffered talk is also presented as Poster B19. Citation Format: Michael T. Barrett, Elizabeth Lenkiewicz, Lisa Evers, Tara Holley, Meraj Aziz, Edward Stites, Richard Posner, Amy Kramer, Jeffrey Drebin, Daniel D. Von Hoff. Clonal profiling of prospectively collected primary pancreatic ductal adenocarcinomas. [abstract]. In: Proceedings of the AACR Special Conference on Pancreatic Cancer: Progress and Challenges; Jun 18-21, 2012; Lake Tahoe, NV. Philadelphia (PA): AACR; Cancer Res 2012;72(12 Suppl):Abstract nr PR7.

Background Mathematical/computational models are needed to understand cell signaling networks, which are complex. Signaling proteins contain multiple functional components and multiple sites of post-translational modification. The multiplicity of components and sites of modification ensures that interactions among signaling proteins have the potential to generate myriad protein complexes and post-translational modification states. As a result, the number of chemical species that can be populated in a cell signaling network, and hence the number of equations in an ordinary differential equation model required to capture the dynamics of these species, is prohibitively large. To overcome this problem, the rule-based modeling approach has been developed for representing interactions within signaling networks efficiently and compactly through coarse-graining of the chemical kinetics of molecular interactions. Results Here, we provide a demonstration that the rule-based modeling approach can be used to specify and simulate a large model for ERBB receptor signaling that accounts for site-specific details of protein-protein interactions. The model is considered large because it corresponds to a reaction network containing more reactions than can be practically enumerated. The model encompasses activation of ERK and Akt, and it can be simulated using a network-free simulator, such as NFsim, to generate time courses of phosphorylation for 55 individual serine, threonine, and tyrosine residues. The model is annotated and visualized in the form of an extended contact map. Conclusions With the development of software that implements novel computational methods for calculating the dynamics of large-scale rule-based representations of cellular signaling networks, it is now possible to build and analyze models that include a significant fraction of the protein interactions that comprise a signaling network, with incorporation of the site-specific details of the interactions. Modeling at this level of detail is important for understanding cellular signaling.

The N-methyl-3'-O-anthranoyl (MANT) guanine nucleotide analogs are useful environmentally sensitive fluorescent probes for studying G protein mechanisms. Both MANT-GTP gamma S (mGTP gamma S) and MANT-GTP (mGTP) displayed a magnesium-dependent increase in fluorescence upon binding to bovine brain G(o). A much greater increase in MANT-guanine nucleotide fluorescence was observed with excitation at 280 nm compared with 350 nm, due to energy transfer from tryptophan in G(o). G(o)-bound mGTP gamma S displays a blue-shift in its emission spectrum indicating a nonpolar environment for the G(o)-bound MANT. For the hydrolyzable analog, mGTP, the increase in fluorescence is followed by a decrease as it is hydrolyzed to mGDP. Unexpectedly, dissociation of mGDP was fast (t1/2 1.7 s) by comparison with GDP itself (t1/2 120 s). Binding of mGTP gamma S to G(o) was slow, but mastoparan increased the rate approximately 4-fold. For mGTP, mastoparan increased both the rate of binding and the peak fluorescence, even at saturating mGTP concentrations. Modeling the mGTP fluorescence kinetics in the presence and absence of mastoparan results in two novel conclusions. First, mGTP does not fully activate the G protein, even when bound. Second, mastoparan appears to increase the rate of the G protein conformational activation step, in addition to its known effect on GDP release.

Environmentally sensitive molecules have many potential cellular applications. We have investigated the utility of a pH sensitive ligand for the formyl peptide receptor, CHO-Met-Leu-Phe-Phe-Lys (SNAFL)-OH (SNAFL-seminaphtho-fluorescein), because in previous studies (Fay et al.: Biochemistry 30:5066-5075, 1991) protonation has been used to explain the quenching when the fluoresceinated formyl pentapeptide ligand binds to this receptor. Moreover, acidification in intracellular compartments is a general mechanism occurring in cells during processing of ligand-receptor complexes. Because the protonated form of SNAFL is excited at 488 nm with emission at 530 nm and the unprotonated form is excited at 568 nm with emission at 650 nm, the ratio of protonated and unprotonated forms can be examined by multiparameter flow cytometry. We found that the receptor-bound ligand is sensitive to both the extracellular and intracellular pH. There is a small increase in the pKa of the ligand upon binding to the receptor consistent with protonation in the binding pocket. Once internalized, spectral changes in the probe consistent with acidification and ligand dissociation from the receptor are observed.

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

Background The system-level dynamics of many molecular interactions, particularly protein-protein interactions, can be conveniently represented using reaction rules, which can be specified using model-specification languages, such as the BioNetGen language (BNGL). A set of rules implicitly defines a (bio)chemical reaction network. The reaction network implied by a set of rules is often very large, and as a result, generation of the network implied by rules tends to be computationally expensive. Moreover, the cost of many commonly used methods for simulating network dynamics is a function of network size. Together these factors have limited application of the rule-based modeling approach. Recently, several methods for simulating rule-based models have been developed that avoid the expensive step of network generation. The cost of these "network-free" simulation methods is independent of the number of reactions implied by rules. Software implementing such methods is now needed for the simulation and analysis of rule-based models of biochemical systems. Results Here, we present a software tool called RuleMonkey, which implements a network-free method for simulation of rule-based models that is similar to Gillespie's method. The method is suitable for rule-based models that can be encoded in BNGL, including models with rules that have global application conditions, such as rules for intramolecular association reactions. In addition, the method is rejection free, unlike other network-free methods that introduce null events, i.e., steps in the simulation procedure that do not change the state of the reaction system being simulated. We verify that RuleMonkey produces correct simulation results, and we compare its performance against DYNSTOC, another BNGL-compliant tool for network-free simulation of rule-based models. We also compare RuleMonkey against problem-specific codes implementing network-free simulation methods. Conclusions RuleMonkey enables the simulation of rule-based models for which the underlying reaction networks are large. It is typically faster than DYNSTOC for benchmark problems that we have examined. RuleMonkey is freely available as a stand-alone application http://public.tgen.org/rulemonkey. It is also available as a simulation engine within GetBonNie, a web-based environment for building, analyzing and sharing rule-based models.

Motivation: Interactions of molecules, such as signaling proteins, with multiple binding sites and/or multiple sites of post-translational covalent modification can be modeled using reaction rules. Rules comprehensively, but implicitly, define the individual chemical species and reactions that molecular interactions can potentially generate. Although rules can be automatically processed to define a biochemical reaction network, the network implied by a set of rules is often too large to generate completely or to simulate using conventional procedures. To address this problem, we present DYNSTOC, a general-purpose tool for simulating rule-based models. Results: DYNSTOC implements a null-event algorithm for simulating chemical reactions in a homogenous reaction compartment. The simulation method does not require that a reaction network be specified explicitly in advance, but rather takes advantage of the availability of the reaction rules in a rule-based specification of a network to determine if a randomly selected set of molecular components participates in a reaction during a time step. DYNSTOC reads reaction rules written in the BioNetGen language which is useful for modeling protein–protein interactions involved in signal transduction. The method of DYNSTOC is closely related to that of StochSim. DYNSTOC differs from StochSim by allowing for model specification in terms of BNGL, which extends the range of protein complexes that can be considered in a model. DYNSTOC enables the simulation of rule-based models that cannot be simulated by conventional methods. We demonstrate the ability of DYNSTOC to simulate models accounting for multisite phosphorylation and multivalent binding processes that are characterized by large numbers of reactions. Availability: DYNSTOC is free for non-commercial use. The C source code, supporting documentation and example input files are available at http://public.tgen.org/dynstoc/. Contact: dynstoc@tgen.org Supplementary information: Supplementary data are available at Bioinformatics online.

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

The epidermal growth factor receptor (EGFR) kinase is generally considered to be activated by either ligand-induced dimerisation or a ligand-induced conformational change within pre-formed dimers. We report the relationship between ligand-induced higher-order EGFR oligomerization and EGFR phosphorylation on the surface of intact cells. We have combined lifetime-detected Forster resonance energy transfer, as a probe of the receptor phosphorylation state and image correlation spectroscopy, to extract the relative association state of activated versus unactivated EGFR, to determine the ratio of the average number of receptors for active (phosphorylated) and inactive clusters. There are at least four times as many receptors in the ligand-induced active clusters than inactive clusters. Contrary to the prevailing view that the EGFR dimer is the predominant, active form, our data determine that higher-order EGFR oligomers are the dominant species associated with the ligand activated EGFR tyrosine kinase.