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/.

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.

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.

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/.

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.

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.

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.

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.

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

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

The first 10 years of the international coordination network for standards in systems and synthetic biology (COMBINE).

This paper presents a report on outcomes of the 10th Computational Modeling in Biology Network (COMBINE) meeting that was held in Heidelberg, Germany, in July of 2019. The annual event brings together researchers, biocurators and software engineers to present recent results and discuss future work in the area of standards for systems and synthetic biology. The COMBINE initiative coordinates the development of various community standards and formats for computational models in the life sciences. Over the past 10 years, COMBINE has brought together standard communities that have further developed and harmonized their standards for better interoperability of models and data. COMBINE 2019 was co-located with a stakeholder workshop of the European EU-STANDS4PM initiative that aims at harmonized data and model standardization for in silico models in the field of personalized medicine, as well as with the FAIRDOM PALs meeting to discuss findable, accessible, interoperable and reusable (FAIR) data sharing. This report briefly describes the work discussed in invited and contributed talks as well as during breakout sessions. It also highlights recent advancements in data, model, and annotation standardization efforts. Finally, this report concludes with some challenges and opportunities that this community will face during the next 10 years.

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.

ModelBricks-modules for reproducible modeling improving model annotation and provenance.

Most computational models in biology are built and intended for "single-use"; the lack of appropriate annotation creates models where the assumptions are unknown, and model elements are not uniquely identified. Simply recreating a simulation result from a publication can be daunting; expanding models to new and more complex situations is a herculean task. As a result, new models are almost always created anew, repeating literature searches for kinetic parameters, initial conditions and modeling specifics. It is akin to building a brick house starting with a pile of clay. Here we discuss a concept for building annotated, reusable models, by starting with small well-annotated modules we call ModelBricks. Curated ModelBricks, accessible through an open database, could be used to construct new models that will inherit ModelBricks annotations and thus be easier to understand and reuse. Key features of ModelBricks include reliance on a commonly used standard language (SBML), rule-based specification describing species as a collection of uniquely identifiable molecules, association with model specific numerical parameters, and more common annotations. Physical bricks can vary substantively; likewise, to be useful the structure of ModelBricks must be highly flexible-it should encapsulate mechanisms from single reactions to multiple reactions in a complex process. Ultimately, a modeler would be able to construct large models by using multiple ModelBricks, preserving annotations and provenance of model elements, resulting in a highly annotated model. We envision the library of ModelBricks to rapidly grow from community contributions. Persistent citable references will incentivize model creators to contribute new ModelBricks.

Systems Biology Graphical Notation: Process Description language Level 1 Version 2.0.

The Systems Biology Graphical Notation (SBGN) is an international community effort that aims to standardise the visualisation of pathways and networks for readers with diverse scientific backgrounds as well as to support an efficient and accurate exchange of biological knowledge between disparate research communities, industry, and other players in systems biology. SBGN comprises the three languages Entity Relationship, Activity Flow, and Process Description (PD) to cover biological and biochemical systems at distinct levels of detail. PD is closest to metabolic and regulatory pathways found in biological literature and textbooks. Its well-defined semantics offer a superior precision in expressing biological knowledge. PD represents mechanistic and temporal dependencies of biological interactions and transformations as a graph. Its different types of nodes include entity pools (e.g. metabolites, proteins, genes and complexes) and processes (e.g. reactions, associations and influences). The edges describe relationships between the nodes (e.g. consumption, production, stimulation and inhibition). This document details Level 1 Version 2.0 of the PD specification, including several improvements, in particular: 1) the addition of the equivalence operator, subunit, and annotation glyphs, 2) modification to the usage of submaps, and 3) updates to clarify the use of various glyphs (i.e. multimer, empty set, and state variable).

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.

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.

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.