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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.

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.

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.

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.

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.

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.

The Epidermal Growth Factor Receptor (EGFR/ErbB1/HER1) plays an important role in both physiological and cancer-related processes. To study the factors that influence receptor phosphorylation, we have coupled Single Molecule Pull-down (SiMPull) measurements with rule-based modeling of EGFR signaling. Using SiMPull, we quantified the phosphorylation state of thousands of individual receptors. These measurements enabled the first direct detection of multisite phosphorylation on full-length EGFR and revealed that the extent of phosphorylation varies by tyrosine site and is dependent on the relative abundance of signaling partners that limit access by tyrosine phosphatases. We also evaluated the impact of oncogenic mutations and ligands with varying affinity on phosphorylation kinetics. Simulations highlight the importance of dimer lifetimes on EGFR phosphorylation and signaling output.

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.

The high-affinity receptor for IgE expressed on the surface of mast cells and basophils interacts with antigens, via bound IgE antibody, and triggers secretion of inflammatory mediators that contribute to allergic reactions. To understand how past inputs (memory) influence future inflammatory responses in mast cells, a microfluidic device was used to precisely control exposure of cells to alternating stimulatory and non-stimulatory inputs. We determined that the response to subsequent stimulation depends on the interval of signaling quiescence. For shorter intervals of signaling quiescence, the second response is blunted relative to the first response, whereas longer intervals of quiescence induce an enhanced second response. Through an iterative process of computational modeling and experimental tests, we found that these memory-like phenomena arise from a confluence of rapid, short-lived positive signals driven by the protein tyrosine kinase Syk; slow, long-lived negative signals driven by the lipid phosphatase Ship1; and slower degradation of Ship1 co-factors. This work advances our understanding of mast cell signaling and represents a generalizable approach for investigating the dynamics of signaling systems.

Rule-based modeling languages, such as the Kappa and BioNetGen languages (BNGL), are powerful frameworks for modeling the dynamics of complex biochemical reaction networks. Each language is distributed with a distinct software suite and modelers may wish to take advantage of both toolsets. This paper introduces a practical application called TRuML that translates models written in either Kappa or BNGL into the other language. While similar in many respects, key differences between the two languages makes translation sufficiently complex that automation becomes a useful tool. TRuML accommodates the languages’ complexities and produces a semantically equivalent model in the alternate language of the input model when possible and an approximate model in certain other cases. Here, we discuss a number of these complexities and provide examples of equivalent models in both Kappa and BNGL.CCS CONCEPTS• Applied computing → Systems biology; • Computing methodologies → Simulation languages

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

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 post-translational 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).

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). Supplementary information Supplementary data are available at Bioinformatics online.

We formulated a computational model for a MAPK signaling cascade downstream of the EGF receptor to investigate how interlinked positive and negative feedback loops process EGF signals into ERK pulses of constant amplitude but dose-dependent duration and frequency. A positive feedback loop involving RAS and SOS, which leads to bistability and allows for switch-like responses to inputs, is nested within a negative feedback loop that encompasses RAS and RAF, MEK, and ERK that inhibits SOS via phosphorylation. This negative feedback, operating on a longer time scale, changes switch-like behavior into oscillations having a period of 1 hour or longer. Two auxiliary negative feedback loops, from ERK to MEK and RAF, placed downstream of the positive feedback, shape the temporal ERK activity profile but are dispensable for oscillations. Thus, the positive feedback introduces a hierarchy among negative feedback loops, such that the effect of a negative feedback depends on its position with respect to the positive feedback loop. Furthermore, a combination of the fast positive feedback involving slow-diffusing membrane components with slower negative feedbacks involving faster diffusing cytoplasmic components leads to local excitation/global inhibition dynamics, which allows the MAPK cascade to transmit paracrine EGF signals into spatially non-uniform ERK activity pulses.

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 RBLrαKO 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.

The Epidermal Growth Factor Receptor (EGFR) plays an important role in both physiological and cancer-related processes. Ligand-binding to EGFR leads to phosphorylation of several tyrosine residues in the cytoplasmic tail of the receptor. Once phosphorylated, each of those residues will serve as docking sites for particular signaling proteins, such as Shc1 and Grb2, that propagate the signal and ultimately lead to different cellular responses. Upon ligand binding, phosphorylation of EGFR increases rapidly, but is followed by a significant decrease after 30 seconds. This response has been difficult to explain. While groups have incorporated mechanisms such as endocytosis or negative feedback loops into their mathematical models to explain this behavior, these predictions have not completely recapitulated the behavior and/or remain to be experimentally tested. We have built a computational model of EGFR signaling to allow us assess the contribution of the different proposed mechanisms on the observed behavior. To test the model, we used Single-Molecule Pull-down (SiMPull) to determine the phosphorylation state of thousands of individual receptors. This unique data reveals the fraction of receptors phosphorylated at specific tyrosine residues as a function of time after activation. To fit the data, we needed to include a novel mechanism to explain the overshoot in EGFR phosphorylation in which increased Shc1-Grb2 interaction reduces Grb2 availability to bind to the phospho-sites in the receptor, consequently leaving those sites more accessible to phosphatases. Our results indicate that the ligand-induced interaction between Shc1 and Grb2 is primarily responsible for the early overshoot observed in EGFR phosphorylation. The increased association of phosphorylated Shc1 with Grb2 has been demonstrated in vitro. Experiments to test this prediction in cells are underway.

BCR signaling regulates the activities and fates of B cells. BCR signaling encompasses two feedback loops emanating from Lyn and Fyn, which are Src family protein tyrosine kinases (SFKs). Positive feedback arises from SFK-mediated trans phosphorylation of BCR and receptor-bound Lyn and Fyn, which increases the kinase activities of Lyn and Fyn. Negative feedback arises from SFK-mediated cis phosphorylation of the transmembrane adapter protein PAG1, which recruits the cytosolic protein tyrosine kinase Csk to the plasma membrane, where it acts to decrease the kinase activities of Lyn and Fyn. To study the effects of the positive and negative feedback loops on the dynamical stability of BCR signaling and the relative contributions of Lyn and Fyn to BCR signaling, we consider in this study a rule-based model for early events in BCR signaling that encompasses membrane-proximal interactions of six proteins, as follows: BCR, Lyn, Fyn, Csk, PAG1, and Syk, a cytosolic protein tyrosine kinase that is activated as a result of SFK-mediated phosphorylation of BCR. The model is consistent with known effects of Lyn and Fyn deletions. We find that BCR signaling can generate a single pulse or oscillations of Syk activation depending on the strength of Ag signal and the relative levels of Lyn and Fyn. We also show that bistability can arise in Lyn- or Csk-deficient cells.

The pathogen Brucella melitensis secretes a Toll/interleukin-1 receptor (TIR) domain containing protein that abrogates host innate immune responses. In this study, we have characterized the biochemical interactions of Brucella TIR-like protein TcpB with host innate immune adaptor proteins. Using protein-fragment complementation assays based on Gaussia luciferase and green fluorescent protein, we find that TcpB interacts directly with MyD88 and that this interaction is significantly stronger than the interaction of TcpB with TIRAP, the only other adaptor protein that detectably interacts with TcpB. Surprisingly, the TcpB-MyD88 interaction depends on the death domain (DD) of MyD88, and TcpB does not interact with the isolated TIR domain of MyD88. TcpB disrupts MyD88(DD)-MyD88(DD), MyD88(DD)-MyD88(TIR) and MyD88(DD)-MyD88 interactions but not MyD88-MyD88 or MyD88(TIR)-MyD88(TIR) interactions. Structural models consistent with these results suggest how TcpB might inhibit TLR signaling by targeting MyD88 via a DD-TIR domain interface.

We use flow cytometry to characterize equilibrium binding of a fluorophore-labeled trivalent model antigen to bivalent IgE-FcεRI complexes on RBL cells. We find that flow cytometric measurements are consistent with an equilibrium model for ligand-receptor binding in which binding sites are assumed to be equivalent and ligand-induced receptor aggregates are assumed to be acyclic. However, this model predicts extensive receptor aggregation at antigen concentrations that yield strong cellular secretory responses, which is inconsistent with the expectation that large receptor aggregates should inhibit such responses. To investigate possible explanations for this discrepancy, we evaluate four rule-based models for interaction of a trivalent ligand with a bivalent cell-surface receptor that relax simplifying assumptions of the equilibrium model. These models are simulated using a rule-based kinetic Monte Carlo approach to investigate the kinetics of ligand-induced receptor aggregation and to study how the kinetics and equilibria of ligand-receptor interaction are affected by steric constraints on receptor aggregate configurations and by the formation of cyclic receptor aggregates. The results suggest that formation of linear chains of cyclic receptor dimers may be important for generating secretory signals. Steric effects that limit receptor aggregation and transient formation of small receptor aggregates may also be important.

We investigate the ability of algorithms developed for reverse engineering of transcriptional regulatory networks to reconstruct metabolic networks from high-throughput metabolite profiling data. For this, we generate synthetic metabolic profiles for benchmarking purposes based on a well-established model for red blood cell metabolism. A variety of data sets is generated, accounting for different properties of real metabolic networks, such as experimental noise, metabolite correlations, and temporal dynamics. These data sets are made available online. We apply ARACNE, a mainstream transcriptional networks reverse engineering algorithm, to these data sets and observe performance comparable to that obtained in the transcriptional domain, for which the algorithm was originally designed., 14 pages, 3 figures. Presented at the DIMACS Workshop on Dialogue on Reverse Engineering Assessment and Methods (DREAM), Sep 2006

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.

Summary: Rule-based models are analyzed with specialized simulators, such as those provided by the BioNetGen and NFsim open-source software packages. Here, we present BioNetFit, a general-purpose fitting tool that is compatible with BioNetGen and NFsim. BioNetFit is designed to take advantage of distributed computing resources. This feature facilitates fitting (i.e. optimization of parameter values for consistency with data) when simulations are computationally expensive. Availability and implementation: BioNetFit can be used on stand-alone Mac, Windows/Cygwin, and Linux platforms and on Linux-based clusters running SLURM, Torque/PBS, or SGE. The BioNetFit source code (Perl) is freely available (http://bionetfit.nau.edu). Supplementary information: Supplementary data are available at Bioinformatics online. Contact: bionetgen.help@gmail.com

We consider a model of early events in signaling by the epidermal growth factor (EGF) receptor (EGFR). The model includes EGF, EGFR, the adapter proteins Grb2 and Shc, and the guanine nucleotide exchange factor Sos, which is activated through EGFinduced formation of EGFR‐Grb2‐Sos and EGFR‐Shc‐Grb2‐Sos assemblies at the plasma membrane. The protein interactions involved in signaling can potentially generate a diversity of protein complexes and phosphoforms; however, this diversity has been largely ignored in models of EGFR signaling. Here, we develop a model that accounts more fully for potential molecular diversity by specifying rules for protein interactions and then using these rules to generate a reaction network that includes all chemical species and reactions implied by the protein interactions. We obtain a model that predicts the dynamics of 356 molecular species, which are connected through 3749 unidirectional reactions. This network model is compared with a previously developed model that includes only 18 chemical species but incorporates the same scope of protein interactions. The predictions of this model are reproduced by the network model, which also yields new predictions. For example, the network model predicts distinct temporal patterns of autophosphorylation for different tyrosine residues of EGFR. A comparison of the two models suggests experiments that could lead to mechanistic insights about competition among adapter proteins for EGFR binding sites and the role of EGFR monomers in signal transduction. © 2005 Elsevier Ireland Ltd. All rights reserved.

The process of signalling through receptors of the immune system involves highly connected networks of interacting components. Understanding the often counter-intuitive behaviour of these networks requires the development of mathematical and computational models. Here, we focus on the application of these models to understand signalling through immune receptors that are involved in antigen recognition. Simple models, which ignore the details of the signalling machinery, have provided considerable insight into how ligand–receptor binding properties affect signalling outcomes. Detailed models, which include specific molecular components and interactions beyond the ligand and receptor, are difficult to develop but have already provided new mechanistic understanding and uncovered relationships that are difficult to detect by experimental observation alone. They offer hope that models might eventually predict the full spectrum of signalling behaviour.

We consider the design of a type of repressible gene circuit that is common in bacteria. In this type of circuit, a regulator protein acts to coordinately repress the expression of effector genes when a signal molecule with which it interacts is present. The regulator protein can also independently influence the expression of its own gene, such that regulator gene expression is repressible (like effector genes), constitutive, or inducible. Thus, a signal-directed change in the activity of the regulator protein can result in one of three patterns of coupled regulator and effector gene expression: direct coupling, in which regulator and effector gene expression change in the same direction; uncoupling, in which regulator gene expression remains constant while effector gene expression changes; or inverse coupling, in which regulator and effector gene expression change in opposite directions. We have investigated the functional consequences of each form of coupling using a mathematical model to compare alternative circuits on the basis of engineering-inspired criteria for functional effectiveness. The results depend on whether the regulator protein acts as a repressor or activator of transcription at the promoters of effector genes. In the case of repressor control of effector gene expression, direct coupling is optimal among the three forms of coupling, whereas in the case of activator control, inverse coupling is optimal. Results also depend on the sensitivity of effector gene expression to changes in the level of a signal molecule; the optimal form of coupling can be physically realized only for circuits with sufficiently small sensitivity. These theoretical results provide a rationale for autoregulation of regulator genes in repressible gene circuits and lead to testable predictions, which we have compared with data available in the literature and electronic databases.

Mutations within the epidermal growth factor receptor (EGFR/erbB1/Her1) are often associated with carcinogenesis. Specific mutations common in non-small cell lung cancer (NSCLC), including EGFR-L858R and EGFR-ΔL747-P753, lead to ligand-independent phosphorylation, however the molecular mechanism by which these mutations in the EGFR kinase domain confer constitutive activity remain unknown. Here, using multiple sub-diffraction-limit imaging modalities, we reveal the altered behavior of NSCLC-associated EGFR mutants within the plasma membrane_including altered receptor dimerization, dynamics, and structure_which collectively dysregulate receptor activity. Using multi-color single particle tracking (SPT) and Hidden Markov Model analysis, EGFR mutants are shown to form stable dimers in the absence of ligand and exhibit a slower mobility that is consistent with receptor signaling. These results were confirmed using two-color, single-molecule super-resolution microscopy (dSTORM) to visualize the spatial distribution of receptors. Receptor clustering was quantified by localization-based cross-correlation analysis to show ligand-induced aggregation of EGFR as well as ligand-independent aggregation of EGFR mutants. Since the receptor ectodomain is known to play a critical role in dimerization, live cell FRET measurements between the EGFR N-terminus and the plasma membrane was used to quantify changes in ectodomain structure. We found that unliganded EGFR mutants are more readily found in the extended conformation, similar to the ligand bound wild type receptor. Therefore, mutation within the kinase domain biases the structural equilibrium of the extracellular domain toward a dimer-competent state.Collectively, these data support a model where oncogenic signaling from NSCLC-associated EGFR mutants is a result of productive dimerization between non-ligand bound receptors. Furthermore, because these mutations are found in the kinase domain, this work introduces the concept that oncogenic EGFR signaling may be controlled in part by a form of “inside-out” signaling.

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

We present a detailed mathematical model of the phosphorylation and dephosphorylation events that occur upon ligand-induced receptor aggregation, for a transfectant expressing FcepsilonRI, Lyn, Syk and endogenous phosphatases that dephosphorylate exposed phosphotyrosines on FcepsilonRI and Syk. Through model simulations we show how changing the ligand concentration, and consequently the concentration of receptor aggregates, can change the nature of a cellular response as well as its amplitude. We illustrate the value of the model in analyzing experimental data by using it to show that the intrinsic rate of dephosphorylation of the FcepsilonRI gamma immunoreceptor tyrosine-based activation motif (ITAM) in rat basophilic leukemia (RBL) cells is much faster than the observed rate, provided that all of the cytosolic Syk is available to receptors.

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.

To investigate why responses of mast cells to antigen-induced IgE receptor (FceRI) 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 FceRI 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.

The q-bio Conference and the associated q-bio Summer School were started in 2007 by a prescient group of researchers based at Los Alamos National Laboratory (LANL) and the University of New Mexico (J. Edwards, J. Faeder, W. Hlavacek, Y. Jiang, I. Nemenman and M. Wall) who envisioned a systems biology community focused on modeling, simulations and targeted experiments to advance the fundamental understanding of biological regulation. Sponsorship for the initial 2007 conference and school came from the Center for Nonlinear Studies at LANL, with additional support from the LANL Institute for Advanced Studies, the New Mexico Consortium, the Molecular Sciences Institute, the Center for the Spatiotemporal Modeling of Cell Signaling, and the University of New Mexico Cancer Center. q-bio is now a well-established international systems biology event in July/August of each year and is currently registering participants for its 8th meeting and summer school (http://q-bio.org/wiki/The_Eighth_q-bio_Conference or http://q-bio.org/wiki/The_Eighth_q-bio_Summer_School).

In the context of cell signaling, kinetic proofreading was introduced to explain how cells can discriminate among ligands based on a kinetic parameter, the ligand-receptor dissociation rate constant. In the kinetic proofreading model of cell signaling, responses occur only when a bound receptor undergoes a complete series of modifications. If the ligand dissociates prematurely, the receptor returns to its basal state and signaling is frustrated. We extend the model to deal with systems where aggregation of receptors is essential to signal transduction, and present a version of the model for systems where signaling depends on an extrinsic kinase. We also investigate the kinetics of signaling molecules, “messengers,” that are generated by aggregated receptors but do not remain associated with the receptor complex. We show that the extended model predicts modes of signaling that exhibit kinetic discrimination for some range of parameters but for other parameter values show little or no discrimination and thus escape kinetic proofreading. We compare model predictions with experimental data.

In patients infected with human immunodeficiency virus type 1 (HIV-1), a large amount of virus is associated with follicular dendritic cells (FDCs) in lymphoid tissue. To assess the influence of FDCs on viral dynamics during antiretroviral therapy, we have developed a mathematical model for treatment of HIV-1 infection that includes FDCs. Here, we use this model to analyse measurements of HIV-1 dynamics in the blood and lymphoid tissue of a representative patient, who was treated with a combination of HIV-1 reverse transcriptase and protease inhibitors. We show that loss of virus from FDCs during therapy can make a much larger contribution to plasma virus than production of virus by infected cells. This result challenges the notion that long-lived infected cells are a significant source of HIV-1 during drug therapy. Due to release of FDC-associated virus, we find that it is necessary to revise upward previous estimates ofc, the rate at which free virus is cleared, andδ, the rate at which productively infected cells die. Furthermore, we find that potentially infectious virus, present before treatment, is released from FDCs during therapy and that the persistence of this virus can be affected by whether therapy includes reverse transcriptase inhibitors.

This special issue consists of 12 original papers that elaborate on work presented at The Second q-bio Conference on Cellular Information Processing, which was held on the campus of St. John's College in Santa Fe, New Mexico, USA, 6-9 August 2008.

Aggregation of cell surface receptors by multivalent ligand can trigger a variety of cellular responses. A well-studied receptor that responds to aggregation is the high affinity receptor for IgE (FcepsilonRI), which is responsible for initiating allergic reactions. To quantify antigen-induced aggregation of IgE-FcepsilonRI complexes, we have developed a method based on multiparameter flow cytometry to monitor both occupancy of surface IgE combining sites and association of antigen with the cell surface. The number of bound IgE combining sites in excess of the number of bound antigens, the number of bridges between receptors, provides a quantitative measure of IgE-FcepsilonRI aggregation. We demonstrate our method by using it to study the equilibrium binding of a haptenated fluorescent protein, 2,4-dinitrophenol-coupled B-phycoerythrin (DNP25-PE), to fluorescein isothiocyanate-labeled anti-DNP IgE on the surface of rat basophilic leukemia cells. The results, which we analyze with the aid of a mathematical model, indicate how IgE-FcepsilonRI aggregation depends on the total concentrations of DNP25-PE and surface IgE. As expected, we find that maximal aggregation occurs at an optimal antigen concentration. We also find that aggregation varies qualitatively with the total concentration of surface IgE as predicted by an earlier theoretical analysis.

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.

Two forms of extreme coupling have been documented for the regulation of gene expression in repressible systems governed by a regulator protein. The first form, complete uncoupling, is distinguished by a constant level of regulator protein. The second form, perfect coupling, is distinguished by a level of regulator protein that varies coordinately with the level of the regulated enzyme. To determine how these two forms of coupling influence the performance of a system, so that we might predict the conditions under which each evolves through natural selection, we have used a mathematical approach to compare systems with complete uncoupling and perfect coupling. Our comparisons, which are controlled so that alternative systems are free from irrelevant differences, are based on a priori criteria that are related to various aspects of a system’s performance, such as temporal responsiveness. By examining the influence of physical constraints that are related to the subunit structure of regulatory proteins and that limit the cooperativity of regulatory interactions, we have extended an early theory of gene circuitry for repressible systems. We obtain new results and testable predictions that can be summarized as follows. For typical systems with a low gain, performance is better with perfect coupling than with complete uncoupling if the mode of regulation is negative and better with complete uncoupling than with perfect coupling if the mode of regulation is positive. For systems with a high gain, these preferred forms of coupling are prevented by the physical constraints on cooperativity, and other forms of coupling can be expected. Tests of our predictions are illustrated by using data available in the literature.

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.