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.

Evaluation of FluSight influenza forecasting in the 2021-22 and 2022-23 seasons with a new target laboratory-confirmed influenza hospitalizations

Accurate forecasts can enable more effective public health responses during seasonal influenza epidemics. Forecasting teams were asked to provide national and jurisdiction-specific probabilistic predictions of weekly confirmed influenza hospital admissions for one through four weeks ahead for the 2021-22 and 2022-23 influenza seasons. Across both seasons, 26 teams submitted forecasts, with the submitting teams varying between seasons. Forecast skill was evaluated using the Weighted Interval Score (WIS), relative WIS, and coverage. Six out of 23 models outperformed the baseline model across forecast weeks and locations in 2021-22 and 12 out of 18 models in 2022-23. Averaging across all forecast targets, the FluSight ensemble was the 2nd most accurate model measured by WIS in 2021-22 and the 5th most accurate in the 2022-23 season. Forecast skill and 95% coverage for the FluSight ensemble and most component models degraded over longer forecast horizons and during periods of rapid change. Current influenza forecasting efforts help inform situational awareness, but research is needed to address limitations, including decreased performance during periods of changing epidemic dynamics.

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.

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 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.

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.

Parameter Estimation and Uncertainty Quantification for Systems Biology Models

Mathematical models can provide quantitative insights into immunoreceptor signaling, and other biological processes, but require parameterization and uncertainty quantification before reliable predictions become possible. We review currently available methods and software tools to address these problems. We consider gradient-based and gradient-free methods for point estimation of parameter values, and methods of profile likelihood, bootstrapping, and Bayesian inference for uncertainty quantification. We consider recent and potential future applications of these methods to systems-level modeling of immune-related phenomena.

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, N_c, 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.

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 K_D 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.

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.

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.

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

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

SPATKIN: a simulator for rule-based modeling of biomolecular site dynamics on surfaces

Summary

Rule-based modeling is a powerful approach for studying biomolecular site dynamics. Here, we present SPATKIN, a general-purpose simulator for rule-based modeling in two spatial dimensions. The simulation algorithm is a lattice-based method that tracks Brownian motion of individual molecules and the stochastic firing of rule-defined reaction events. Because rules are used as event generators, the algorithm is network-free, meaning that it does not require to generate the complete reaction network implied by rules prior to simulation. In a simulation, each molecule (or complex of molecules) is taken to occupy a single lattice site that cannot be shared with another molecule (or complex). SPATKIN is capable of simulating a wide array of membrane-associated processes, including adsorption, desorption and crowding. Models are specified using an extension of the BioNetGen language, which allows to account for spatial features of the simulated process.

Availability and implementation

The C ++ source code for SPATKIN is distributed freely under the terms of the GNU GPLv3 license. The source code can be compiled for execution on popular platforms (Windows, Mac and Linux). An installer for 64-bit Windows and a macOS app are available. The source code and precompiled binaries are available at the SPATKIN Web site (http://pmbm.ippt.pan.pl/software/spatkin).

Contact

spatkin.simulator@gmail.com.

Supplementary information

Supplementary data are available at Bioinformatics online.

Using Equation-Free Computation to Accelerate Network-Free Stochastic Simulation of Chemical Kinetics

The chemical kinetics of many complex systems can be concisely represented by reaction rules, which can be used to generate reaction events via a kinetic Monte Carlo method that has been termed network-free simulation. Here, we demonstrate accelerated network-free simulation through a novel approach to equation-free computation. In this process, variables are introduced that approximately capture system state. Derivatives of these variables are estimated using short bursts of exact stochastic simulation and finite differencing. The variables are then projected forward in time via a numerical integration scheme, after which a new exact stochastic simulation is initialized and the whole process repeats. The projection step increases efficiency by bypassing the firing of numerous individual reaction events. As we show, the projected variables may be defined as populations of building blocks of chemical species. The maximal number of connected molecules included in these building blocks determines the degree of approximation. Equation-free acceleration of network-free simulation is found to be both accurate and efficient.

New insights into RAS biology reinvigorate interest in mathematical modeling of RAS signaling

RAS is the most frequently mutated gene across human cancers, but developing inhibitors of mutant RAS has proven to be challenging. Given the difficulties of targeting RAS directly, drugs that impact the other components of pathways where mutant RAS operates may potentially be effective. However, the system-level features, including different localizations of RAS isoforms, competition between downstream effectors, and interlocking feedback and feed-forward loops, must be understood to fully grasp the opportunities and limitations of inhibiting specific targets. Mathematical modeling can help us discern the system-level impacts of these features in normal and cancer cells. New technologies enable the acquisition of experimental data that will facilitate development of realistic models of oncogenic RAS behavior. In light of the wealth of empirical data accumulated over decades of study and the advancement of experimental methods for gathering new data, modelers now have the opportunity to advance progress toward realization of targeted treatment for mutant RAS-driven cancers.

A phase 2 trial of personalized cytotoxic therapy based on tumor immunohistochemistry in previously treated metastatic pancreatic cancer patients

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.

Differential mast cell outcomes are sensitive to FcεRI-Syk binding kinetics

Cross-linking of immunoglobulin E-bound FcεRI triggers multiple cellular responses, including degranulation and cytokine production. Signaling is dependent on recruitment of Syk via docking of its dual SH2 domains to phosphorylated tyrosines within the FcεRI immunoreceptor tyrosine-based activation motifs. Using single-molecule imaging in live cells, we directly visualized and quantified the binding of individual mNeonGreen-tagged Syk molecules as they associated with the plasma membrane after FcεRI activation. We found that Syk colocalizes transiently to FcεRI and that Syk-FcεRI binding dynamics are independent of receptor aggregate size. Substitution of glutamic acid for tyrosine between the Syk SH2 domains (Syk-Y130E) led to an increased Syk-FcεRI off-rate, loss of site-specific Syk autophosphorylation, and impaired downstream signaling. Genome edited cells expressing only Syk-Y130E were deficient in antigen-stimulated calcium release, degranulation, and production of some cytokines (TNF-a, IL-3) but not others (MCP-1, IL-4). We propose that kinetic discrimination along the FcεRI signaling pathway occurs at the level of Syk-FcεRI interactions, with key outcomes dependent upon sufficiently long-lived Syk binding events.

Allergen Valency, Dose, and FcεRI Occupancy Set Thresholds for Secretory Responses to Pen a 1 and Motivate Design of Hypoallergens

Ag-mediated crosslinking of IgE-FcεRI complexes activates mast cells and basophils, initiating the allergic response. Of 34 donors recruited having self-reported shrimp allergy, only 35% had significant levels of shrimp-specific IgE in serum and measurable basophil secretory responses to rPen a 1 (shrimp tropomyosin). We report that degranulation is linked to the number of FcεRI occupied with allergen-specific IgE, as well as the dose and valency of Pen a 1. Using clustered regularly interspaced palindromic repeat-based gene editing, human RBL^rαKO cells were created that exclusively express the human FcεRIα subunit. Pen a 1-specific IgE was affinity purified from shrimp-positive plasma. Cells primed with a range of Pen a 1-specific IgE and challenged with Pen a 1 showed a bell-shaped dose response for secretion, with optimal Pen a 1 doses of 0.1-10 ng/ml. Mathematical modeling provided estimates of receptor aggregation kinetics based on FcεRI occupancy with IgE and allergen dose. Maximal degranulation was elicited when ∼2700 IgE-FcεRI complexes were occupied with specific IgE and challenged with Pen a 1 (IgE epitope valency of ≥8), although measurable responses were achieved when only a few hundred FcεRI were occupied. Prolonged periods of pepsin-mediated Pen a 1 proteolysis, which simulates gastric digestion, were required to diminish secretory responses. Recombinant fragments (60-79 aa), which together span the entire length of tropomyosin, were weak secretagogues. These fragments have reduced dimerization capacity, compete with intact Pen a 1 for binding to IgE-FcεRI complexes, and represent a starting point for the design of promising hypoallergens for immunotherapy.

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

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

AVAILABILITY AND IMPLEMENTATION

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

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

CONTACT

bionetgen.help@gmail.com.

Use of mechanistic models to integrate and analyze multiple proteomic datasets

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

Enhanced dimerization drives ligand-independent activity of mutant epidermal growth factor receptor in lung cancer

Epidermal growth factor receptor kinase mutations drive oncogenesis, but the molecular mechanism of pathological signal initiation is poorly understood. Using high-resolution microscopy methods, the authors reveal that these kinase mutations induce structural changes in the receptor ectodomain that lead to enhanced, ligand-independent dimerization.

Mutations within the epidermal growth factor receptor (EGFR/erbB1/Her1) are often associated with tumorigenesis. In particular, a number of EGFR mutants that demonstrate ligand-independent signaling are common in non–small cell lung cancer (NSCLC), including kinase domain mutations L858R (also called L834R) and exon 19 deletions (e.g., ΔL747-P753insS), which collectively make up nearly 90% of mutations in NSCLC. The molecular mechanisms by which these mutations confer constitutive activity remain unresolved. Using multiple subdiffraction-limit imaging modalities, we reveal the altered receptor structure and interaction kinetics of NSCLC-associated EGFR mutants. We applied two-color single quantum dot tracking to quantify receptor dimerization kinetics on living cells and show that, in contrast to wild-type EGFR, mutants are capable of forming stable, ligand-independent dimers. Two-color superresolution localization microscopy confirmed ligand-independent aggregation of EGFR mutants. Live-cell Förster resonance energy transfer measurements revealed that the L858R kinase mutation alters ectodomain structure such that unliganded mutant EGFR adopts an extended, dimerization-competent conformation. Finally, mutation of the putative dimerization arm confirmed a critical role for ectodomain engagement in ligand-independent signaling. These data support a model in which dysregulated activity of NSCLC-associated kinase mutants is driven by coordinated interactions involving both the kinase and extracellular domains that lead to enhanced dimerization.

Modeling for (physical) biologists: an introduction to the rule-based approach

Models that capture the chemical kinetics of cellular regulatory networks can be specified in terms of rules for biomolecular interactions. A rule defines a generalized reaction, meaning a reaction that permits multiple reactants, each capable of participating in a characteristic transformation and each possessing certain, specified properties, which may be local, such as the state of a particular site or domain of a protein. In other words, a rule defines a transformation and the properties that reactants must possess to participate in the transformation. A rule also provides a rate law. A rule-based approach to modeling enables consideration of mechanistic details at the level of functional sites of biomolecules and provides a facile and visual means for constructing computational models, which can be analyzed to study how system-level behaviors emerge from component interactions.

Modeling biomolecular site dynamics in immunoreceptor signaling systems

The immune system plays a central role in human health. The activities of immune cells, whether defending an organism from disease or triggering a pathological condition such as autoimmunity, are driven by the molecular machinery of cellular signaling systems. Decades of experimentation have elucidated many of the biomolecules and interactions involved in immune signaling and regulation, and recently developed technologies have led to new types of quantitative, systems-level data. To integrate such information and develop nontrivial insights into the immune system, computational modeling is needed, and it is essential for modeling methods to keep pace with experimental advances. In this chapter, we focus on the dynamic, site-specific, and context-dependent nature of interactions in immunoreceptor signaling (i.e., the biomolecular site dynamics of immunoreceptor signaling), the challenges associated with capturing these details in computational models, and how these challenges have been met through use of rule-based modeling approaches.

Computational analysis of an autophagy/translation switch based on mutual inhibition of MTORC1 and ULK1

We constructed a mechanistic, computational model for regulation of (macro)autophagy and protein synthesis (at the level of translation). The model was formulated to study the system-level consequences of interactions among the following proteins: two key components of MTOR complex 1 (MTORC1), namely the protein kinase MTOR (mechanistic target of rapamycin) and the scaffold protein RPTOR; the autophagy-initiating protein kinase ULK1; and the multimeric energy-sensing AMP-activated protein kinase (AMPK). Inputs of the model include intrinsic AMPK kinase activity, which is taken as an adjustable surrogate parameter for cellular energy level or AMP:ATP ratio, and rapamycin dose, which controls MTORC1 activity. Outputs of the model include the phosphorylation level of the translational repressor EIF4EBP1, a substrate of MTORC1, and the phosphorylation level of AMBRA1 (activating molecule in BECN1-regulated autophagy), a substrate of ULK1 critical for autophagosome formation. The model incorporates reciprocal regulation of mTORC1 and ULK1 by AMPK, mutual inhibition of MTORC1 and ULK1, and ULK1-mediated negative feedback regulation of AMPK. Through analysis of the model, we find that these processes may be responsible, depending on conditions, for graded responses to stress inputs, for bistable switching between autophagy and protein synthesis, or relaxation oscillations, comprising alternating periods of autophagy and protein synthesis. A sensitivity analysis indicates that the prediction of oscillatory behavior is robust to changes of the parameter values of the model. The model provides testable predictions about the behavior of the AMPK-MTORC1-ULK1 network, which plays a central role in maintaining cellular energy and nutrient homeostasis.

Phosphorylation site dynamics of early T-cell receptor signaling

In adaptive immune responses, T-cell receptor (TCR) signaling impacts multiple cellular processes and results in T-cell differentiation, proliferation, and cytokine production. Although individual protein-protein interactions and phosphorylation events have been studied extensively, we lack a systems-level understanding of how these components cooperate to control signaling dynamics, especially during the crucial first seconds of stimulation. Here, we used quantitative proteomics to characterize reshaping of the T-cell phosphoproteome in response to TCR/CD28 co-stimulation, and found that diverse dynamic patterns emerge within seconds. We detected phosphorylation dynamics as early as 5 s and observed widespread regulation of key TCR signaling proteins by 30 s. Development of a computational model pointed to the presence of novel regulatory mechanisms controlling phosphorylation of sites with central roles in TCR signaling. The model was used to generate predictions suggesting unexpected roles for the phosphatase PTPN6 (SHP-1) and shortcut recruitment of the actin regulator WAS. Predictions were validated experimentally. This integration of proteomics and modeling illustrates a novel, generalizable framework for solidifying quantitative understanding of a signaling network and for elucidating missing links.

Optimal aggregation of FcεRI with a structurally defined trivalent ligand overrides negative regulation driven by phosphatases

To investigate why responses of mast cells to antigen-induced IgE receptor (FcεRI) aggregation depend nonlinearly on antigen dose, we characterized a new artificial ligand, DF3, through complementary modeling and experimentation. This ligand is a stable trimer of peptides derived from bacteriophage T4 fibritin, each conjugated to a hapten (DNP). We found low and high doses of DF3 at which degranulation of mast cells sensitized with DNP-specific IgE is minimal, but ligand-induced receptor aggregation is comparable to aggregation at an intermediate dose, optimal for degranulation. This finding makes DF3 an ideal reagent for studying the balance of negative and positive signaling in the FcεRI pathway. We find that the lipid phosphatase SHIP and the protein tyrosine phosphatase SHP-1 negatively regulate mast cell degranulation over all doses considered. In contrast, SHP-2 promotes degranulation. With high DF3 doses, relatively rapid recruitment of SHIP to the plasma membrane may explain the reduced degranulation response. Our results demonstrate that optimal secretory responses of mast cells depend on the formation of receptor aggregates that promote sufficient positive signaling by Syk to override phosphatase-mediated negative regulatory signals.

Recruitment of the adaptor protein Grb2 to EGFR tetramers

Adaptor protein Grb2 binds phosphotyrosines in the epidermal growth factor (EGF) receptor (EGFR) and thereby links receptor activation to intracellular signaling cascades. Here, we investigated how recruitment of Grb2 to EGFR is affected by the spatial organization and quaternary state of activated EGFR. We used the techniques of image correlation spectroscopy (ICS) and lifetime-detected Förster resonance energy transfer (also known as FLIM-based FRET or FLIM–FRET) to measure ligand-induced receptor clustering and Grb2 binding to activated EGFR in BaF/3 cells. BaF/3 cells were stably transfected with fluorescently labeled forms of Grb2 (Grb2–mRFP) and EGFR (EGFR–eGFP). Following stimulation of the cells with EGF, we detected nanometer-scale association of Grb2–mRFP with EGFR–eGFP clusters, which contained, on average, 4 ± 1 copies of EGFR–eGFP per cluster. In contrast, the pool of EGFR–eGFP without Grb2–mRFP had an average cluster size of 1 ± 0.3 EGFR molecules per punctum. In the absence of EGF, there was no association between EGFR–eGFP and Grb2–mRFP. To interpret these data, we extended our recently developed model for EGFR activation, which considers EGFR oligomerization up to tetramers, to include recruitment of Grb2 to phosphorylated EGFR. The extended model, with adjustment of one new parameter (the ratio of the Grb2 and EGFR copy numbers), is consistent with a cluster size distribution where 2% of EGFR monomers, 5% of EGFR dimers, <1% of EGFR trimers, and 94% of EGFR tetramers are associated with Grb2. Together, our experimental and modeling results further implicate tetrameric EGFR as the key signaling unit and call into question the widely held view that dimeric EGFR is the predominant signaling unit.

An Interaction Library for the FcεRI Signaling Network

Antigen receptors play a central role in adaptive immune responses. Although the molecular networks associated with these receptors have been extensively studied, we currently lack a systems-level understanding of how combinations of non-covalent interactions and post-translational modifications are regulated during signaling to impact cellular decision-making. To fill this knowledge gap, it will be necessary to formalize and piece together information about individual molecular mechanisms to form large-scale computational models of signaling networks. To this end, we have developed an interaction library for signaling by the high-affinity IgE receptor, FcεRI. The library consists of executable rules for protein–protein and protein–lipid interactions. This library extends earlier models for FcεRI signaling and introduces new interactions that have not previously been considered in a model. Thus, this interaction library is a toolkit with which existing models can be expanded and from which new models can be built. As an example, we present models of branching pathways from the adaptor protein Lat, which influence production of the phospholipid PIP₃ at the plasma membrane and the soluble second messenger IP₃. We find that inclusion of a positive feedback loop gives rise to a bistable switch, which may ensure robust responses to stimulation above a threshold level. In addition, the library is visualized to facilitate understanding of network circuitry and identification of network motifs.

Mitochondrial morphological features are associated with fission and fusion events

Mitochondria are dynamic organelles that undergo constant remodeling through the regulation of two opposing processes, mitochondrial fission and fusion. Although several key regulators and physiological stimuli have been identified to control mitochondrial fission and fusion, the role of mitochondrial morphology in the two processes remains to be determined. To address this knowledge gap, we investigated whether morphological features extracted from time-lapse live-cell images of mitochondria could be used to predict mitochondrial fate. That is, we asked if we could predict whether a mitochondrion is likely to participate in a fission or fusion event based on its current shape and local environment. Using live-cell microscopy, image analysis software, and supervised machine learning, we characterized mitochondrial dynamics with single-organelle resolution to identify features of mitochondria that are predictive of fission and fusion events. A random forest (RF) model was trained to correctly classify mitochondria poised for either fission or fusion based on a series of morphological and positional features for each organelle. Of the features we evaluated, mitochondrial perimeter positively correlated with mitochondria about to undergo a fission event. Similarly mitochondrial solidity (compact shape) positively correlated with mitochondria about to undergo a fusion event. Our results indicate that fission and fusion are positively correlated with mitochondrial morphological features; and therefore, mitochondrial fission and fusion may be influenced by the mechanical properties of mitochondrial membranes.

Rule-based modeling: a computational approach for studying biomolecular site dynamics in cell signaling systems

Rule-based modeling was developed to address the limitations of traditional approaches for modeling chemical kinetics in cell signaling systems. These systems consist of multiple interacting biomolecules (e.g., proteins), which themselves consist of multiple parts (e.g., domains, linear motifs, and sites of phosphorylation). Consequently, biomolecules that mediate information processing generally have the potential to interact in multiple ways, with the number of possible complexes and posttranslational modification states tending to grow exponentially with the number of binary interactions considered. As a result, only large reaction networks capture all possible consequences of the molecular interactions that occur in a cell signaling system, which is problematic because traditional modeling approaches for chemical kinetics (e.g., ordinary differential equations) require explicit network specification. This problem is circumvented through representation of interactions in terms of local rules. With this approach, network specification is implicit and model specification is concise. Concise representation results in a coarse graining of chemical kinetics, which is introduced because all reactions implied by a rule inherit the rate law associated with that rule. Coarse graining can be appropriate if interactions are modular, and the coarseness of a model can be adjusted as needed. Rules can be specified using specialized model-specification languages, and recently developed tools designed for specification of rule-based models allow one to leverage powerful software engineering capabilities. A rule-based model comprises a set of rules, which can be processed by general-purpose simulation and analysis tools to achieve different objectives (e.g., to perform either a deterministic or stochastic simulation).

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

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. Ligand-induced higher-order EGFR oligomerisation or clustering has been reported but it is not clear how EGFR oligomers, as distinct from EGFR dimers, influence signaling outputs. To address this question, we combined measures of receptor clustering (microscopy; image correlation spectroscopy) and phosphorylation (Western blots) with modelling of mass-action chemical kinetics. A stable BaF/3 cell-line that contains a high proportion (>90%) of inactive dimers of EGFR-eGFP but no secreted ligand and no other detectable ErbB receptors was used as the model cell system. EGF at concentrations of greater than 1 nM was found to cluster EGFR-eGFP dimers into higher-order complexes and cause parallel increases in EGFR phosphorylation. The kinetics of EGFR clustering and phosphorylation were both rapid, plateauing within 2 minutes after stimulation with 30 nM EGF. A rule-based model was formulated to interpret the data. This model took into account ligand binding, ligand-induced conformational changes in the cytosolic tail, monomer-dimer-trimer-tetramer transitions via ectodomain- and kinase-mediated interactions, and phosphorylation. The model predicts that cyclic EGFR tetramers are the predominant phosphorylated species, in which activated receptor dimers adopt a cyclic side-by-side orientation, and that receptor kinase activation is stabilised by the intramolecular interactions responsible for cyclic tetramerization.

Single-cell measurements of IgE-mediated FcεRI signaling using an integrated microfluidic platform

Heterogeneity in responses of cells to a stimulus, such as a pathogen or allergen, can potentially play an important role in deciding the fate of the responding cell population and the overall systemic response. Measuring heterogeneous responses requires tools capable of interrogating individual cells. Cell signaling studies commonly do not have single-cell resolution because of the limitations of techniques used such as Westerns, ELISAs, mass spectrometry, and DNA microarrays. Microfluidics devices are increasingly being used to overcome these limitations. Here, we report on a microfluidic platform for cell signaling analysis that combines two orthogonal single-cell measurement technologies: on-chip flow cytometry and optical imaging. The device seamlessly integrates cell culture, stimulation, and preparation with downstream measurements permitting hands-free, automated analysis to minimize experimental variability. The platform was used to interrogate IgE receptor (FcεRI) signaling, which is responsible for triggering allergic reactions, in RBL-2H3 cells. Following on-chip crosslinking of IgE-FcεRI complexes by multivalent antigen, we monitored signaling events including protein phosphorylation, calcium mobilization and the release of inflammatory mediators. The results demonstrate the ability of our platform to produce quantitative measurements on a cell-by-cell basis from just a few hundred cells. Model-based analysis of the Syk phosphorylation data suggests that heterogeneity in Syk phosphorylation can be attributed to protein copy number variations, with the level of Syk phosphorylation being particularly sensitive to the copy number of Lyn.

Binding of nucleoid-associated protein fis to DNA is regulated by DNA breathing dynamics

Physicochemical properties of DNA, such as shape, affect protein-DNA recognition. However, the properties of DNA that are most relevant for predicting the binding sites of particular transcription factors (TFs) or classes of TFs have yet to be fully understood. Here, using a model that accurately captures the melting behavior and breathing dynamics (spontaneous local openings of the double helix) of double-stranded DNA, we simulated the dynamics of known binding sites of the TF and nucleoid-associated protein Fis in Escherichia coli. Our study involves simulations of breathing dynamics, analysis of large published in vitro and genomic datasets, and targeted experimental tests of our predictions. Our simulation results and available in vitro binding data indicate a strong correlation between DNA breathing dynamics and Fis binding. Indeed, we can define an average DNA breathing profile that is characteristic of Fis binding sites. This profile is significantly enriched among the identified in vivo E. coli Fis binding sites. To test our understanding of how Fis binding is influenced by DNA breathing dynamics, we designed base-pair substitutions, mismatch, and methylation modifications of DNA regions that are known to interact (or not interact) with Fis. The goal in each case was to make the local DNA breathing dynamics either closer to or farther from the breathing profile characteristic of a strong Fis binding site. For the modified DNA segments, we found that Fis-DNA binding, as assessed by gel-shift assay, changed in accordance with our expectations. We conclude that Fis binding is associated with DNA breathing dynamics, which in turn may be regulated by various nucleotide modifications.

Cellular transcription factors (TFs) are proteins that regulate gene expression, and thereby cellular activity and fate, by binding to specific DNA segments. The physicochemical determinants of protein-DNA binding specificity are not completely understood. Here, we report that the propensity of transient opening and re-closing of the double helix, resulting from thermal fluctuations, aka “DNA breathing” or “DNA bubbles,” can be associated with binding affinity in the case of Fis, a well-studied nucleoid-associated protein in Escherichia coli. We found that a particular breathing profile is characteristic of high-affinity Fis binding sites and that DNA fragments known to bind Fis in vivo are statistically enriched for this profile. Furthermore, we used simulations of DNA breathing dynamics to guide design of gel-shift experiments aimed at testing the idea that local breathing influences Fis binding. As a result, we show that via nucleotide modifications but without modifying nucleotides that directly contact Fis, we were able to transform a low-affinity Fis binding site into a high-affinity site and vice versa. The nucleotide modifications were designed only based on DNA breathing simulations. Our study suggests that strong Fis-DNA binding depends on DNA breathing - a novel physicochemical characteristic that could be used for prediction and rational design of TF binding sites.

Computational model for autophagic vesicle dynamics in single cells

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.

Improved predictions of transcription factor binding sites using physicochemical features of DNA

Typical approaches for predicting transcription factor binding sites (TFBSs) involve use of a position-specific weight matrix (PWM) to statistically characterize the sequences of the known sites. Recently, an alternative physicochemical approach, called SiteSleuth, was proposed. In this approach, a linear support vector machine (SVM) classifier is trained to distinguish TFBSs from background sequences based on local chemical and structural features of DNA. SiteSleuth appears to generally perform better than PWM-based methods. Here, we improve the SiteSleuth approach by considering both new physicochemical features and algorithmic modifications. New features are derived from Gibbs energies of amino acid-DNA interactions and hydroxyl radical cleavage profiles of DNA. Algorithmic modifications consist of inclusion of a feature selection step, use of a nonlinear kernel in the SVM classifier, and use of a consensus-based post-processing step for predictions. We also considered SVM classification based on letter features alone to distinguish performance gains from use of SVM-based models versus use of physicochemical features. The accuracy of each of the variant methods considered was assessed by cross validation using data available in the RegulonDB database for 54 Escherichia coli TFs, as well as by experimental validation using published ChIP-chip data available for Fis and Lrp.