Impacts of Vaccination and Severe Acute Respiratory Syndrome Coronavirus 2 Variants Alpha and Delta on Coronavirus Disease 2019 Transmission Dynamics in Four Metropolitan Areas of the United States.

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 1.4x 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 2.1x. The estimated Alpha takeoff times ranged from February 1 to February 28, 2021. The estimated Delta takeoff times ranged from June 2 to June 26, 2021. Estimated takeoff times are consistent with genomic surveillance data.

Impacts of vaccination and Severe Acute Respiratory Syndrome Coronavirus 2 variants Alpha and Delta on Coronavirus Disease 2019 transmission dynamics in four metropolitan areas of the United States.

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 1.4x 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 2.1x. The estimated Alpha takeoff times ranged from February 1 to February 28, 2021. The estimated Delta takeoff times ranged from June 2 to June 26, 2021. Estimated takeoff times are consistent with genomic surveillance data. One-Sentence Summary: Using 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.

Differential contagiousness of respiratory disease across the United States.

The initial contagiousness of a communicable disease within a given population is quantified by the basic reproduction number, R0. This number depends on both pathogen and population properties. On the basis of compartmental models that reproduce Coronavirus Disease 2019 (COVID-19) surveillance data, we used Bayesian inference and the next-generation matrix approach to estimate region-specific R0 values for 280 of 384 metropolitan statistical areas (MSAs) in the United States (US), which account for 95% of the US population living in urban areas and 82% of the total population. We focused on MSA populations after finding that these populations were more uniformly impacted by COVID-19 than state populations. Our maximum a posteriori (MAP) estimates for R0 range from 1.9 to 7.7 and quantify the relative susceptibilities of regional populations to spread of respiratory diseases. ONE-SENTENCE SUMMARY: Initial contagiousness of Coronavirus Disease 2019 varied over a 4-fold range across urban areas of the United States.

Quantification of early nonpharmaceutical interventions aimed at slowing transmission of Coronavirus Disease 2019 in the Navajo Nation and surrounding states (Arizona, Colorado, New Mexico, and Utah).

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. Here, we investigated these differences in disease transmission dynamics with the objective of quantifying the contributions of non-pharmaceutical interventions (NPIs) (e.g., behaviors that limit disease transmission). We considered a compartmental model accounting for distinct periods of NPIs 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.

Quantification of early nonpharmaceutical interventions aimed at slowing transmission of Coronavirus Disease 2019 in the Navajo Nation and surrounding states (Arizona, Colorado, New Mexico, and Utah).

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.

Bayesian Inference of State-Level COVID-19 Basic Reproduction Numbers across the United States.

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 the 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 found that no state had achieved herd immunity as of 20 September 2021.

Implementation of a practical Markov chain Monte Carlo sampling algorithm in PyBioNetFit.

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.

Bayesian Inference of State-Level COVID-19 Basic Reproduction Numbers across the United States.

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 ℛ 0 , the expected number of secondary cases generated by an infected person in the absence of any interventions. The value of ℛ 0 relates to a herd immunity threshold (HIT), which is given by 1 - 1/ℛ 0 . 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 ℛ 0 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. ℛ 0 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 ℛ 0 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 STATEMENT: COVID-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 ℛ 0 , which relates to a herd immunity threshold (HIT), given by 1 - 1/ℛ 0 . When the immune fraction of a population exceeds this threshold, sustained disease transmission becomes exponentially unlikely. Here, we report state-level ℛ 0 estimates indicating that disease transmission varies considerably across states. Our ℛ 0 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.

Daily Forecasting of Regional Epidemics of Coronavirus Disease with Bayesian Uncertainty Quantification, United States.

To increase situational awareness and support evidence-based policymaking, we formulated a mathematical model for coronavirus disease transmission within a regional population. This compartmental model accounts for quarantine, self-isolation, social distancing, a nonexponentially distributed incubation period, asymptomatic persons, and mild and severe forms of symptomatic disease. We used Bayesian inference to calibrate region-specific models for consistency with daily reports of confirmed cases in the 15 most populous metropolitan statistical areas in the United States. We also quantified uncertainty in parameter estimates and forecasts. This online learning approach enables early identification of new trends despite considerable variability in case reporting.

Daily Forecasting of New Cases for Regional Epidemics of Coronavirus Disease 2019 with Bayesian Uncertainty Quantification.

To increase situational awareness and support evidence-based policy-making, we formulated a mathematical model for COVID-19 transmission within a regional population. This compartmental model 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 region-specific 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. ARTICLE SUMMARY LINE: We report models for regional COVID-19 epidemics and use of Bayesian inference to quantify uncertainty in daily predictions of expected reporting of new cases, enabling identification of new trends in surveillance data.

Daily Forecasting of New Cases for Regional Epidemics of Coronavirus Disease 2019 with Bayesian Uncertainty Quantification.

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.

Systems biology markup language (SBML) level 3 package: multistate, multicomponent and multicompartment species, version 1, release 2.

Rule-based modeling is an approach that permits constructing reaction networks based on the specification of rules for molecular interactions and transformations. These rules can encompass details such as the interacting sub-molecular domains and the states and binding status of the involved components. Conceptually, fine-grained spatial information such as locations can also be provided. Through "wildcards" representing component states, entire families of molecule complexes sharing certain properties can be specified as patterns. This can significantly simplify the definition of models involving species with multiple components, multiple states, and multiple compartments. The systems biology markup language (SBML) Level 3 Multi Package Version 1 extends the SBML Level 3 Version 1 core with the "type" concept in the Species and Compartment classes. Therefore, reaction rules may contain species that can be patterns and exist in multiple locations. Multiple software tools such as Simmune and BioNetGen support this standard that thus also becomes a medium for exchanging rule-based models. This document provides the specification for Release 2 of Version 1 of the SBML Level 3 Multi package. No design changes have been made to the description of models between Release 1 and Release 2; changes are restricted to the correction of errata and the addition of clarifications.

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.

Multisite EGFR phosphorylation is regulated by adaptor protein abundances and dimer lifetimes.

Differential epidermal growth factor receptor (EGFR) phosphorylation is thought to couple receptor activation to distinct signaling pathways. However, the molecular mechanisms responsible for biased signaling are unresolved due to a lack of insight into the phosphorylation patterns of full-length EGFR. We extended a single-molecule pull-down technique previously used to study protein-protein interactions to allow for robust measurement of receptor phosphorylation. We found that EGFR is predominantly phosphorylated at multiple sites, yet phosphorylation at specific tyrosines is variable and only a subset of receptors share phosphorylation at the same site, even with saturating ligand concentrations. We found distinct populations of receptors as soon as 1 min after ligand stimulation, indicating early diversification of function. To understand this heterogeneity, we developed a mathematical model. The model predicted that variations in phosphorylation are dependent on the abundances of signaling partners, while phosphorylation levels are dependent on dimer lifetimes. The predictions were confirmed in studies of cell lines with different expression levels of signaling partners, and in experiments comparing low- and high-affinity ligands and oncogenic EGFR mutants. These results reveal how ligand-regulated receptor dimerization dynamics and adaptor protein concentrations play critical roles in EGFR signaling.

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.

Scaling methods for accelerating kinetic Monte Carlo simulations of chemical reaction networks.

Various kinetic Monte Carlo algorithms become inefficient when some of the population sizes in a system are large, which gives rise to a large number of reaction events per unit time. Here, we present a new acceleration algorithm based on adaptive and heterogeneous scaling of reaction rates and stoichiometric coefficients. The algorithm is conceptually related to the commonly used idea of accelerating a stochastic simulation by considering a subvolume λΩ (0 < λ < 1) within a system of interest, which reduces the number of reaction events per unit time occurring in a simulation by a factor 1/λ at the cost of greater error in unbiased estimates of first moments and biased overestimates of second moments. Our new approach offers two unique benefits. First, scaling is adaptive and heterogeneous, which eliminates the pitfall of overaggressive scaling. Second, there is no need for an a priori classification of populations as discrete or continuous (as in a hybrid method), which is problematic when discreteness of a chemical species changes during a simulation. The method requires specification of only a single algorithmic parameter, Nc, a global critical population size above which populations are effectively scaled down to increase simulation efficiency. The method, which we term partial scaling, is implemented in the open-source BioNetGen software package. We demonstrate that partial scaling can significantly accelerate simulations without significant loss of accuracy for several published models of biological systems. These models characterize activation of the mitogen-activated protein kinase ERK, prion protein aggregation, and T-cell receptor signaling.

Using RuleBuilder to Graphically Define and Visualize BioNetGen-Language Patterns and Reaction Rules.

RuleBuilder is a tool for drawing graphs that can be represented by the BioNetGen language (BNGL), which is used to formulate mathematical, rule-based models of biochemical systems. BNGL provides an intuitive plain text, or string, representation of such systems, which is based on a graphical formalism. Reactions are defined in terms of graph-rewriting rules that specify the necessary intrinsic properties of the reactants, a transformation, and a rate law. Rules also contain contextual constraints that restrict application of the rule. In some cases, the specification of contextual constraints can be verbose, making a rule difficult to read. RuleBuilder is designed to ease the task of reading and writing individual reaction rules or other BNGL patterns required for model formulation. The software assists in the reading of existing models by converting BNGL strings of interest into a graph-based representation composed of nodes and edges. RuleBuilder also enables the user to construct de novo a visual representation of BNGL strings using drawing tools available in its interface. As objects are added to the drawing canvas, the corresponding BNGL string is generated on the fly, and objects are similarly drawn on the fly as BNGL strings are entered into the application. RuleBuilder thus facilitates construction and interpretation of rule-based models.

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.

Prediction of Optimal Drug Schedules for Controlling Autophagy.

The effects of molecularly targeted drug perturbations on cellular activities and fates are difficult to predict using intuition alone because of the complex behaviors of cellular regulatory networks. An approach to overcoming this problem is to develop mathematical models for predicting drug effects. Such an approach beckons for co-development of computational methods for extracting insights useful for guiding therapy selection and optimizing drug scheduling. Here, we present and evaluate a generalizable strategy for identifying drug dosing schedules that minimize the amount of drug needed to achieve sustained suppression or elevation of an important cellular activity/process, the recycling of cytoplasmic contents through (macro)autophagy. Therapeutic targeting of autophagy is currently being evaluated in diverse clinical trials but without the benefit of a control engineering perspective. Using a nonlinear ordinary differential equation (ODE) model that accounts for activating and inhibiting influences among protein and lipid kinases that regulate autophagy (MTORC1, ULK1, AMPK and VPS34) and methods guaranteed to find locally optimal control strategies, we find optimal drug dosing schedules (open-loop controllers) for each of six classes of drugs and drug pairs. Our approach is generalizable to designing monotherapy and multi therapy drug schedules that affect different cell signaling networks of interest.

Modeling cell line-specific recruitment of signaling proteins to the insulin-like growth factor 1 receptor.

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.