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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.

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

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

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.

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

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.

Mathematical models can provide quantitative insight into immunoreceptor signaling, but require parameterization and uncertainty quantification before making reliable predictions. 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., 23 pages, 1 figure, 1 table

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

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.

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.

Gillespie's direct method for stochastic simulation of chemical kinetics is a staple of computational systems biology research. However, the algorithm requires explicit enumeration of all reactions and all chemical species that may arise in the system. In many cases, this is not feasible due to the combinatorial explosion of reactions and species in biological networks. Rule-based modeling frameworks provide a way to exactly represent networks containing such combinatorial complexity, and generalizations of Gillespie's direct method have been developed as simulation engines for rule-based modeling languages. Here, we provide both a high-level description of the algorithms underlying the simulation engines, termed network-free simulation algorithms, and how they have been applied in systems biology research. We also define a generic rule-based modeling framework and describe a number of technical details required for adapting Gillespie's direct method for network-free simulation. Finally, we briefly discuss potential avenues for advancing network-free simulation and the role they continue to play in modeling dynamical systems in biology.

Single-molecule imaging was used to quantify the transient nature of FcεRI-Syk interactions in a rodent mast cell line. A functional mutation that increases Syk off-rate leads to altered Syk phosphorylation patterns and impaired signaling, highlighting the importance of finely tuned protein interactions in directing cellular outcomes., 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.

Systems biology has experienced dramatic growth in the number, size, and complexity of computational models. To reproduce simulation results and reuse models, researchers must exchange unambiguous model descriptions. We review the latest edition of the Systems Biology Markup Language (SBML), a format designed for this purpose. A community of modelers and software authors developed SBML Level 3 over the past decade. Its modular form consists of a core suited to representing reaction‐based models and packages that extend the core with features suited to other model types including constraint‐based models, reaction‐diffusion models, logical network models, and rule‐based models. The format leverages two decades of SBML and a rich software ecosystem that transformed how systems biologists build and interact with models. More recently, the rise of multiscale models of whole cells and organs, and new data sources such as single‐cell measurements and live imaging, has precipitated new ways of integrating data with models. We provide our perspectives on the challenges presented by these developments and how SBML Level 3 provides the foundation needed to support this evolution., Over the past two decades, scientists from different fields have been developing SBML, a standard format for encoding computational models in biology and medicine. This article summarizes recent progress and gives perspectives on emerging challenges.

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 sub-volume $\lambda \Omega$ ($0, Comment: 18 pages, 7 figures, 1 table

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.