bnglViz: online visualization of rule-based models.

MOTIVATION: Rule-based modeling is a powerful method to describe and simulate interactions among multi-site molecules and multi-molecular species, accounting for the internal connectivity of molecules in chemical species. This modeling technique is implemented in BioNetGen software that is used by various tools and software frameworks, such as BioNetGen stand-alone software, NFSim simulation engine, Virtual Cell simulation and modeling framework, SmolDyn and PySB software tools. These tools exchange models using BioNetGen scripting language (BNGL). Until now, there was no online visualization of such rule-based models. Modelers and researchers reading the manuscripts describing rule-based models had to learn BNGL scripting or master one of these tools to understand the models. RESULTS: Here, we introduce bnglViz, an online platform for visualizing BNGL files as graphical cartoons, empowering researchers to grasp the nuances of rule-based models swiftly and efficiently, and making the exploration of complex biological systems more accessible than ever before. The produced visualizations can be used as supplemental figures in publications or as a way to annotate BNGL models on web repositories. AVAILABILITY AND IMPLEMENTATION: Available at https://bnglviz.github.io/.

MolClustPy: a Python package to characterize multivalent biomolecular clusters.

SUMMARY: Low-affinity interactions among multivalent biomolecules may lead to the formation of molecular complexes that undergo phase transitions to become supply-limited large clusters. In stochastic simulations, such clusters display a wide range of sizes and compositions. We have developed a Python package, MolClustPy, which performs multiple stochastic simulation runs using NFsim (Network-Free stochastic simulator); MolClustPy characterizes and visualizes the distribution of cluster sizes, molecular composition, and bonds across molecular clusters. The statistical analysis offered by MolClustPy is readily applicable to other stochastic simulation software, such as SpringSaLaD and ReaDDy. AVAILABILITY AND IMPLEMENTATION: The software is implemented in Python. A detailed Jupyter notebook is provided to enable convenient running. Code, user guide, and examples are freely available at https://molclustpy.github.io/.

SBGN Bricks Ontology as a tool to describe recurring concepts in molecular networks.

A comprehensible representation of a molecular network is key to communicating and understanding scientific results in systems biology. The Systems Biology Graphical Notation (SBGN) has emerged as the main standard to represent such networks graphically. It has been implemented by different software tools, and is now largely used to communicate maps in scientific publications. However, learning the standard, and using it to build large maps, can be tedious. Moreover, SBGN maps are not grounded on a formal semantic layer and therefore do not enable formal analysis. Here, we introduce a new set of patterns representing recurring concepts encountered in molecular networks, called SBGN bricks. The bricks are structured in a new ontology, the Bricks Ontology (BKO), to define clear semantics for each of the biological concepts they represent. We show the usefulness of the bricks and BKO for both the template-based construction and the semantic annotation of molecular networks. The SBGN bricks and BKO can be freely explored and downloaded at sbgnbricks.org.

RunBioSimulations: an extensible web application that simulates a wide range of computational modeling frameworks, algorithms, and formats.

Comprehensive, predictive computational models have significant potential for science, bioengineering, and medicine. One promising way to achieve more predictive models is to combine submodels of multiple subsystems. To capture the multiple scales of biology, these submodels will likely require multiple modeling frameworks and simulation algorithms. Several community resources are already available for working with many of these frameworks and algorithms. However, the variety and sheer number of these resources make it challenging to find and use appropriate tools for each model, especially for novice modelers and experimentalists. To make these resources easier to use, we developed RunBioSimulations (https://run.biosimulations.org), a single web application for executing a broad range of models. RunBioSimulations leverages community resources, including BioSimulators, a new open registry of simulation tools. These resources currently enable RunBioSimulations to execute nine frameworks and 44 algorithms, and they make RunBioSimulations extensible to additional frameworks and algorithms. RunBioSimulations also provides features for sharing simulations and interactively visualizing their results. We anticipate that RunBioSimulations will foster reproducibility, stimulate collaboration, and ultimately facilitate the creation of more predictive models.

SBML Level 3: an extensible format for the exchange and reuse of biological models.

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.

Multivalent Molecules as Modulators of RNA Granule Size and Composition.

RNA granules are ensembles of specific RNA and protein molecules that mediate localized translation in eukaryotic cells. The mechanisms for formation and selectivity of RNA granules are unknown. Here we present a model for assembly of one type of RNA granule based on experimentally measured binding interactions among three core multivalent molecular components necessary for such assembly: specific RNA molecules that contain a cis-acting sequence called the A2 response element (A2RE), hnRNP A2 proteins that bind specifically (with high affinity) to A2RE sequences or nonspecifically (with lower affinity) to other RNA sequences, and heptavalent protein cytoskeleton-associated protein 5 (CKAP5, an alternative name for TOG protein) that binds both hnRNP A2 molecules and RNA. Non-A2RE RNA molecules (RNA without the A2RE sequence) that may be recruited to the granules through nonspecific interactions are also considered in the model. Modeling multivalent molecular interactions in granules is challenging because of combinatorial complexity in the number of potential molecular complexes among these core components and dynamic changes in granule composition and structure in response to changes in local intracellular environment. We use a hybrid modeling approach (deterministic-stochastic-statistical) that is appropriate when the overall compositions of multimolecular ensembles are of greater importance than the specific interactions among individual molecular components. Modeling studies titrating the concentrations of various granule components and varying effective site pair affinities and RNA valency demonstrate that interactions between multivalent components (TOG and RNA) are modulated by a bivalent adaptor molecule (hnRNP A2). Formation and disruption of granules, as well as RNA selectivity in granule composition are regulated by distinct concentration regimes of A2. Our results suggest that granule assembly is tightly controlled by multivalent molecular interactions among RNA molecules, adaptor proteins, and scaffold proteins.

Compartmental and Spatial Rule-Based Modeling with Virtual Cell.

In rule-based modeling, molecular interactions are systematically specified in the form of reaction rules that serve as generators of reactions. This provides a way to account for all the potential molecular complexes and interactions among multivalent or multistate molecules. Recently, we introduced rule-based modeling into the Virtual Cell (VCell) modeling framework, permitting graphical specification of rules and merger of networks generated automatically (using the BioNetGen modeling engine) with hand-specified reaction networks. VCell provides a number of ordinary differential equation and stochastic numerical solvers for single-compartment simulations of the kinetic systems derived from these networks, and agent-based network-free simulation of the rules. In this work, compartmental and spatial modeling of rule-based models has been implemented within VCell. To enable rule-based deterministic and stochastic spatial simulations and network-free agent-based compartmental simulations, the BioNetGen and NFSim engines were each modified to support compartments. In the new rule-based formalism, every reactant and product pattern and every reaction rule are assigned locations. We also introduce the rule-based concept of molecular anchors. This assures that any species that has a molecule anchored to a predefined compartment will remain in this compartment. Importantly, in addition to formulation of compartmental models, this now permits VCell users to seamlessly connect reaction networks derived from rules to explicit geometries to automatically generate a system of reaction-diffusion equations. These may then be simulated using either the VCell partial differential equations deterministic solvers or the Smoldyn stochastic simulator.

Rule-based modeling with Virtual Cell.

UNLABELLED: Rule-based modeling is invaluable when the number of possible species and reactions in a model become too large to allow convenient manual specification. The popular rule-based software tools BioNetGen and NFSim provide powerful modeling and simulation capabilities at the cost of learning a complex scripting language which is used to specify these models. Here, we introduce a modeling tool that combines new graphical rule-based model specification with existing simulation engines in a seamless way within the familiar Virtual Cell (VCell) modeling environment. A mathematical model can be built integrating explicit reaction networks with reaction rules. In addition to offering a large choice of ODE and stochastic solvers, a model can be simulated using a network free approach through the NFSim simulation engine. AVAILABILITY AND IMPLEMENTATION: Available as VCell (versions 6.0 and later) at the Virtual Cell web site (http://vcell.org/). The application installs and runs on all major platforms and does not require registration for use on the user's computer. Tutorials are available at the Virtual Cell website and Help is provided within the software. Source code is available at Sourceforge. CONTACT: vcell_support@uchc.edu SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Pathway Commons at virtual cell: use of pathway data for mathematical modeling.

UNLABELLED: Pathway Commons is a resource permitting simultaneous queries of multiple pathway databases. However, there is no standard mechanism for using these data (stored in BioPAX format) to annotate and build quantitative mathematical models. Therefore, we developed a new module within the virtual cell modeling and simulation software. It provides pathway data retrieval and visualization and enables automatic creation of executable network models directly from qualitative connections between pathway nodes. AVAILABILITY AND IMPLEMENTATION: Available at Virtual Cell (http://vcell.org/). Application runs on all major platforms and does not require registration for use on the user's computer. Tutorials and video are available at user guide page.

Pleomorphic ensembles: formation of large clusters composed of weakly interacting multivalent molecules.

Molecular interactions of importance to cell biology are subject to sol-gel transitions: large clusters of weakly interacting multivalent molecules (gel phase) are produced at a critical concentration of monomers. Examples include cell-cell and cell-matrix adhesions, nucleoprotein bodies, and cell signaling platforms. We use the term pleomorphic ensembles (PEs) to describe these clusters, because they have dynamic compositions and sizes and have rapid turnover of their molecular constituents; this plasticity can be highly responsive to cellular signals. The classical polymer physical chemistry theory developed by Flory and Stockmayer provides a brilliant framework for treating multivalent interactions for simple idealized systems. But the complexity and variability of PEs challenges existing modeling approaches. Here we describe and validate a computational algorithm that extends the Flory-Stockmayer formalism to overcome the limitations of analytic theories. We divide the problem by deterministically calculating the fraction of bound sites for each type of binding site, followed by the stochastic assignment of the bonds to a finite number of molecules. The method allows for high valency within many different kinds of interacting molecules and site types, permits simulation of steady-state distributions, as well as assembly kinetics, and can treat cooperative binding within one of the interacting molecules. We then apply our method to the analysis of interactions in the nephrin-Nck-N-Wasp signaling system, demonstrating how multivalent layered scaffolds produce PEs at low monomer concentrations despite weak binding interactions. We show how the experimental data for this system are most consistent with synergistic cooperative interactions between Nck and N-Wasp.

A predictive mathematical model of the DNA damage G2 checkpoint.

A predictive mathematical model of the transition from the G2 phase in the cell cycle to mitosis (M) was constructed from the known interactions of the proteins that are thought to play significant roles in the G2 to M transition as well as the DNA damage- induced G2 checkpoint. The model simulates the accumulation of active cyclin B1/Cdk1 (MPF) complexes in the nucleus to activate mitosis, the inhibition of this process by DNA damage, and transport of component proteins between cytoplasm and nucleus. Interactions in the model are based on activities of individual phospho-epitopes and binding sites of proteins involved in G2/M. Because tracking phosphoforms leads to combinatorial explosion, we employ a rule-based approach using the BioNetGen software. The model was used to determine the effects of depletion or over-expression of selected proteins involved in the regulation of the G2 to M transition in the presence and absence of DNA damage. Depletion of Plk1 delayed mitotic entry and recovery from the DNA damage-induced G2 arrest and over-expression of MPF attenuated the DNA damage-induced G2 delay. The model recapitulates the G2 delay observed in the biological response to varying levels of a DNA damage signal. The model produced the novel prediction that depletion of pkMyt1 results in an abnormal biological state in which G2 cells with DNA damage accumulate inactive nuclear MPF. Such a detailed model may prove useful for predicting DNA damage G2 checkpoint function in cancer and, therefore, sensitivity to cancer therapy.

Logic modeling and the ridiculome under the rug.

Logic-derived modeling has been used to map biological networks and to study arbitrary functional interactions, and fine-grained kinetic modeling can accurately predict the detailed behavior of well-characterized molecular systems; at present, however, neither approach comes close to unraveling the full complexity of a cell. The current data revolution offers significant promises and challenges to both approaches - and could bring them together as it has spurred the development of new methods and tools that may help to bridge the many gaps between data, models, and mechanistic understanding.

MolClustPy: A Python Package to Characterize Multivalent Biomolecular Clusters.

S ummary: Low-affinity interactions among multivalent biomolecules may lead to the formation of molecular complexes that undergo phase transitions to become extra-large clusters. Characterizing the physical properties of these clusters is important in recent biophysical research. Due to weak interactions such clusters are highly stochastic, demonstrating a wide range of sizes and compositions. We have developed a Python package to perform multiple stochastic simulation runs using NFsim (Network-Free stochastic simulator), characterize and visualize the distribution of cluster sizes, molecular composition, and bonds across molecular clusters and individual molecules of different types. A vailability and implementation: The software is implemented in Python. A detailed Jupyter notebook is provided to enable convenient running. Code, user guide and examples are freely available at https://molclustpy.github.io/. C ontact: achattaraj007@gmail.com , blinov@uchc.edu. S upplementary information: Available at https://molclustpy.github.io/.

Dynamic model assuming mutually inhibitory biomarkers of frailty suggests bistability with contrasting mobility phenotypes.

Bistability is a fundamental biological phenomenon associated with "switch-like" behavior reflecting the capacity of a system to exist in either of two stable states. It plays a role in gene regulation, cell fate switch, signal transduction and cell oscillation, with relevance for cognition, hearing, vision, sleep, gait and voiding. Here we consider a potential role for bistability in the existence of specific frailty states or phenotypes as part of disablement pathways. We use mathematical modeling with two frailty biomarkers (insulin growth factor-1, IGF-1 and interleukin-6, IL-6), which mutually inhibit each other. In our model, we demonstrate that small variations around critical IGF-1 or IL-6 blood levels lead to strikingly different mobility outcomes. We employ deterministic modeling of mobility outcomes, calculating the average trends in population health. Our model predicts the bistability of clinical outcomes: the deterministically-computed likelihood of an individual remaining mobile, becoming less mobile, or dying over time either increases to almost 100% or decreases to almost zero. Contrary to statistical models that attempt to estimate the likelihood of final outcomes based on probabilities and correlations, our model predicts functional outcomes over time based on specific hypothesized molecular mechanisms. Instead of estimating probabilities based on stochastic distributions and arbitrary priors, we deterministically simulate model outcomes over a wide range of physiological parameter values within experimentally derived boundaries. Our study is "a proof of principle" as it is based on a major assumption about mutual inhibition of pathways that is oversimplified. However, by making such an assumption, interesting effects can be described qualitatively. As our understanding of molecular mechanisms involved in aging deepens, we believe that such modeling will not only lead to more accurate predictions, but also help move the field from using mostly studies of associations to mechanistically guided approaches.

Mixed selling of different poultry species facilitates emergence of public-health-threating avian influenza viruses.

ABSTRACTLive poultry markets (LPMs) are regarded as hubs for avian influenza virus (AIV) transmission in poultry and are a major risk factor in human AIV infections. We performed an AIV surveillance study at a wholesale LPM, where different poultry species were sold in separate stalls, and nine retail LPMs, which received poultry from the wholesale LPM but where different poultry species were sold in one stall, in Guangdong province from 2017 to 2019. A higher AIV isolation rate was observed at the retail LPMs than the wholesale LPM. H9N2 was the dominant AIV subtype and was mainly present in chickens and quails. The genetic diversity of H9N2 viruses was greater at the retail LPMs, where a complex system of two-way transmission between different poultry species had formed. The isolated H9N2 viruses could be classed into four genotypes: G57 and the three novel genotypes, NG164, NG165, and NG166. The H9N2 AIVs isolated from chickens and quails at the wholesale LPM only belonged to the G57 and NG164 genotypes, respectively. However, the G57, NG164, and NG165 genotypes were identified in both chickens and quails at the retail LPMs. We found that the replication and transmission of the NG165 genotype were more adaptive to both poultry and mammalian models than those of its precursor genotype, NG164. Our findings revealed that mixed poultry selling at retail LPMs has increased the genetic diversity of AIVs, which might facilitate the emergence of novel viruses that threaten public health.

A detailed mathematical model predicts that serial engagement of IgE-Fc epsilon RI complexes can enhance Syk activation in mast cells.

The term serial engagement was introduced to describe the ability of a single peptide, bound to a MHC molecule, to sequentially interact with TCRs within the contact region between a T cell and an APC. In addition to ligands on surfaces, soluble multivalent ligands can serially engage cell surface receptors with sites on the ligand, binding and dissociating from receptors many times before all ligand sites become free and the ligand leaves the surface. To evaluate the role of serial engagement in Syk activation, we use a detailed mathematical model of the initial signaling cascade that is triggered when FcepsilonRI is aggregated on mast cells by multivalent Ags. Although serial engagement is not required for mast cell signaling, it can influence the recruitment of Syk to the receptor and subsequent Syk phosphorylation. Simulating the response of mast cells to ligands that serially engage receptors at different rates shows that increasing the rate of serial engagement by increasing the rate of dissociation of the ligand-receptor bond decreases Syk phosphorylation. Increasing serial engagement by increasing the rate at which receptors are cross-linked (for example by increasing the forward rate constant for cross-linking or increasing the valence of the ligand) increases Syk phosphorylation. When serial engagement enhances Syk phosphorylation, it does so by partially reversing the effects of kinetic proofreading. Serial engagement rapidly returns receptors that have dissociated from aggregates to new aggregates before the receptors have fully returned to their basal state.

Leveraging modeling approaches: reaction networks and rules.

We have witnessed an explosive growth in research involving mathematical models and computer simulations of intracellular molecular interactions, ranging from metabolic pathways to signaling and gene regulatory networks. Many software tools have been developed to aid in the study of such biological systems, some of which have a wealth of features for model building and visualization, and powerful capabilities for simulation and data analysis. Novel high-resolution and/or high-throughput experimental techniques have led to an abundance of qualitative and quantitative data related to the spatiotemporal distribution of molecules and complexes, their interactions kinetics, and functional modifications. Based on this information, computational biology researchers are attempting to build larger and more detailed models. However, this has proved to be a major challenge. Traditionally, modeling tools require the explicit specification of all molecular species and interactions in a model, which can quickly become a major limitation in the case of complex networks - the number of ways biomolecules can combine to form multimolecular complexes can be combinatorially large. Recently, a new breed of software tools has been created to address the problems faced when building models marked by combinatorial complexity. These have a different approach for model specification, using reaction rules and species patterns. Here we compare the traditional modeling approach with the new rule-based methods. We make a case for combining the capabilities of conventional simulation software with the unique features and flexibility of a rule-based approach in a single software platform for building models of molecular interaction networks.

The solubility product extends the buffering concept to heterotypic biomolecular condensates.

Biomolecular condensates are formed by liquid-liquid phase separation (LLPS) of multivalent molecules. LLPS from a single ("homotypic") constituent is governed by buffering: above a threshold, free monomer concentration is clamped, with all added molecules entering the condensed phase. However, both experiment and theory demonstrate that buffering fails for the concentration dependence of multicomponent ("heterotypic") LLPS. Using network-free stochastic modeling, we demonstrate that LLPS can be described by the solubility product constant (Ksp): the product of free monomer concentrations, accounting for the ideal stoichiometries governed by the valencies, displays a threshold above which additional monomers are funneled into large clusters; this reduces to simple buffering for homotypic systems. The Ksp regulates the composition of the dilute phase for a wide range of valencies and stoichiometries. The role of Ksp is further supported by coarse-grained spatial particle simulations. Thus, the solubility product offers a general formulation for the concentration dependence of LLPS.

Systems biology graphical notation markup language (SBGNML) version 0.3.

This document defines Version 0.3 Markup Language (ML) support for the Systems Biology Graphical Notation (SBGN), a set of three complementary visual languages developed for biochemists, modelers, and computer scientists. SBGN aims at representing networks of biochemical interactions in a standard, unambiguous way to foster efficient and accurate representation, visualization, storage, exchange, and reuse of information on all kinds of biological knowledge, from gene regulation, to metabolism, to cellular signaling. SBGN is defined neutrally to programming languages and software encoding; however, it is oriented primarily towards allowing models to be encoded using XML, the eXtensible Markup Language. The notable changes from the previous version include the addition of attributes for better specify metadata about maps, as well as support for multiple maps, sub-maps, colors, and annotations. These changes enable a more efficient exchange of data to other commonly used systems biology formats (e. g., BioPAX and SBML) and between tools supporting SBGN (e. g., CellDesigner, Newt, Krayon, SBGN-ED, STON, cd2sbgnml, and MINERVA). More details on SBGN and related software are available at http://sbgn.org. With this effort, we hope to increase the adoption of SBGN in bioinformatics tools, ultimately enabling more researchers to visualize biological knowledge in a precise and unambiguous manner.

Two MYB Proteins in a Self-Organizing Activator-Inhibitor System Produce Spotted Pigmentation Patterns.

Many organisms exhibit visually striking spotted or striped pigmentation patterns. Developmental models predict that such spatial patterns can form when a local autocatalytic feedback loop and a long-range inhibitory feedback loop interact. At its simplest, this self-organizing network only requires one self-activating activator that also activates a repressor, which inhibits the activator and diffuses to neighboring cells. However, the molecular activators and inhibitors fully fitting this versatile model remain elusive in pigmentation systems. Here, we characterize an R2R3-MYB activator and an R3-MYB repressor in monkeyflowers (Mimulus). Through experimental perturbation and mathematical modeling, we demonstrate that the properties of these two proteins correspond to an activator-inhibitor pair in a two-component, reaction-diffusion system, explaining the formation of dispersed anthocyanin spots in monkeyflower petals. Notably, disrupting this pattern impacts pollinator visitation. Thus, subtle changes in simple activator-inhibitor systems are likely essential contributors to the evolution of the remarkable diversity of pigmentation patterns in flowers.