Cell shape and negative links in regulatory motifs together control spatial information flow in signaling networks.

The role of cell size and shape in controlling local intracellular signaling reactions, and how this spatial information originates and is propagated, is not well understood. We have used partial differential equations to model the flow of spatial information from the beta-adrenergic receptor to MAPK1,2 through the cAMP/PKA/B-Raf/MAPK1,2 network in neurons using real geometries. The numerical simulations indicated that cell shape controls the dynamics of local biochemical activity of signal-modulated negative regulators, such as phosphodiesterases and protein phosphatases within regulatory loops to determine the size of microdomains of activated signaling components. The model prediction that negative regulators control the flow of spatial information to downstream components was verified experimentally in rat hippocampal slices. These results suggest a mechanism by which cellular geometry, the presence of regulatory loops with negative regulators, and key reaction rates all together control spatial information transfer and microdomain characteristics within cells.

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.

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.

NMRbox: A Resource for Biomolecular NMR Computation.

Advances in computation have been enabling many recent advances in biomolecular applications of NMR. Due to the wide diversity of applications of NMR, the number and variety of software packages for processing and analyzing NMR data is quite large, with labs relying on dozens, if not hundreds of software packages. Discovery, acquisition, installation, and maintenance of all these packages is a burdensome task. Because the majority of software packages originate in academic labs, persistence of the software is compromised when developers graduate, funding ceases, or investigators turn to other projects. To simplify access to and use of biomolecular NMR software, foster persistence, and enhance reproducibility of computational workflows, we have developed NMRbox, a shared resource for NMR software and computation. NMRbox employs virtualization to provide a comprehensive software environment preconfigured with hundreds of software packages, available as a downloadable virtual machine or as a Platform-as-a-Service supported by a dedicated compute cloud. Ongoing development includes a metadata harvester to regularize, annotate, and preserve workflows and facilitate and enhance data depositions to BioMagResBank, and tools for Bayesian inference to enhance the robustness and extensibility of computational analyses. In addition to facilitating use and preservation of the rich and dynamic software environment for biomolecular NMR, NMRbox fosters the development and deployment of a new class of metasoftware packages. NMRbox is freely available to not-for-profit users.

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.

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.

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.

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.

Virtual NEURON: a strategy for merged biochemical and electrophysiological modeling.

Because of its highly branched dendrite, the Purkinje neuron requires significant computational resources if coupled electrical and biochemical activity are to be simulated. To address this challenge, we developed a scheme for reducing the geometric complexity; while preserving the essential features of activity in both the soma and a remote dendritic spine. We merged our previously published biochemical model of calcium dynamics and lipid signaling in the Purkinje neuron, developed in the Virtual Cell modeling and simulation environment, with an electrophysiological model based on a Purkinje neuron model available in NEURON. A novel reduction method was applied to the Purkinje neuron geometry to obtain a model with fewer compartments that is tractable in Virtual Cell. Most of the dendritic tree was subject to reduction, but we retained the neuron's explicit electrical and geometric features along a specified path from spine to soma. Further, unlike previous simplification methods, the dendrites that branch off along the preserved explicit path are retained as reduced branches. We conserved axial resistivity and adjusted passive properties and active channel conductances for the reduction in surface area, and cytosolic calcium for the reduction in volume. Rallpacks are used to validate the reduction algorithm and show that it can be generalized to other complex neuronal geometries. For the Purkinje cell, we found that current injections at the soma were able to produce similar trains of action potentials and membrane potential propagation in the full and reduced models in NEURON; the reduced model produces identical spiking patterns in NEURON and Virtual Cell. Importantly, our reduced model can simulate communication between the soma and a distal spine; an alpha function applied at the spine to represent synaptic stimulation gave similar results in the full and reduced models for potential changes associated with both the spine and the soma. Finally, we combined phosphoinositol signaling and electrophysiology in the reduced model in Virtual Cell. Thus, a strategy has been developed to combine electrophysiology and biochemistry as a step toward merging neuronal and systems biology modeling.

Correction to: Meeting report from the fourth meeting of the Computational Modeling in Biology Network (COMBINE).

[This corrects the article DOI: 10.4056/sigs.5279417.].

Phosphorylation state-dependent interaction between AKAP7δ/γ and phospholamban increases phospholamban phosphorylation.

Changes in heart rate and contractility in response to sympathetic stimulation occur via activation of cAMP dependent protein kinase A (PKA), leading to phosphorylation of numerous substrates that alter Ca(2+) cycling. Phosphorylation of these substrates is coordinated by A-kinase anchoring proteins (AKAPs), which recruit PKA to specific substrates [1]. Phosphorylation of the PKA substrate phospholamban (PLB) is a critical determinant of Ca(2+) re-entry into the sarcoplasmic reticulum and is coordinated by AKAP7δ/γ [2,3]. Here, we further these findings by showing that phosphorylation of PLB requires interaction with AKAP7δ/γ and that this interaction occurs only when PLB is unphosphorylated. Additionally, we find that two mutants of PLB (R9C and Δ14), which are associated with dilated cardiomyopathy in humans, prevent association with AKAP7δ/γ and display reduced phosphorylation in vitro. This finding implicates the AKAP7δ/γ-PLB interaction in the pathology of the disease phenotype. Further exploration of the AKAP7δ/γ-PLB association demonstrated a phosphorylation state-dependence of the interaction. Computational modeling revealed that this mode of interaction allows for small amounts of AKAP and PKA (100-200nM) to regulate the phosphorylation of large quantities of PLB (50µM). Our results confirm that AKAP7γ/δ binding to PLB is important for phosphorylation of PLB, and describe a novel phosphorylation state-dependent binding mechanism that explains how phosphorylation of highly abundant PKA substrates can be regulated by AKAPs present at ~100-200 fold lower concentrations.

Analysis of AKAP7γ Dimerization.

A-kinase anchoring proteins (AKAPs) constitute a family of scaffolding proteins that contribute to spatiotemporal regulation of PKA-mediated phosphorylation events. In particular, AKAP7 is a family of alternatively spliced proteins that participates in cardiac calcium dynamics. Here, we demonstrate via pull-down from transfected cells and by direct protein-protein association that AKAP7γ self-associates. Self-association appears to be an isoform specific phenomenon, as AKAP7α did not associate with itself or with AKAP7γ. However, AKAP7γ did associate with AKAP7δ, suggesting the long isoforms of the AKAP can form heterodimers. Surface plasmon resonance found that the AKAP7γ self-association occurs via two high affinity binding sites with K D values in the low nanomolar range. Mapping of the binding sites by peptide array reveals that AKAP7γ interacts with itself through multiple regions. Photon counting histogram analysis (PCH) of AKAP7γ-EGFP expressed in HEK-293 cells confirmed that AKAP7γ-EGFP self-associates in a cellular context. Lastly, computational modeling of PKA dynamics within AKAP7γ complexes suggests that oligomerization may augment phosphorylation of scaffolded PKA substrates. In conclusion, our study reveals that AKAP7γ forms both homo- and heterodimers with the long isoforms of the AKAP and that this phenomenon could be an important step in mediating effective substrate phosphorylation in cellular microdomains.

A wave of IP3 production accompanies the fertilization Ca2+ wave in the egg of the frog, Xenopus laevis: theoretical and experimental support.

The fertilization Ca2+ wave in Xenopus laevis is a single, large wave of elevated free Ca2+ that is initiated at the point of sperm-egg fusion and traverses the entire width of the egg. This Ca2+ wave involves an increase in inositol-1,4,5-trisphosphate (IP3) resulting from the interaction of the sperm and egg, which then results in the activation of the endoplasmic reticulum Ca2+ release machinery. The extraordinarily large size of this cell (1.2 mm diameter) together with the small surface region of sperm-receptor activation makes special demands on the IP3-dependent Ca2+ mobilizing machinery. We propose a detailed model of the fertilization Ca2+ wave in Xenopus eggs that requires an accompanying wave of IP3 production. While the Ca2+ wave is initiated by a localized increase of IP3 near the site of sperm-egg fusion, the Ca2+ wave propagates via IP3 production correlated with the Ca2+ wave-possibly via Ca(2+)-mediated PLC activation. Such a Ca(2+)-mediated IP(3) production wave has not been required previously to explain the fertilization Ca2+ wave in eggs; we argue this is necessary to explain the observed IP3 dynamics in Xenopus eggs. To test our hypothesis, we have measured the IP3 levels from 20 nl "sips" of the egg cortex during wave propagation. We were unable to detect the low IP3 levels in unfertilized eggs, but after fertilization, [IP3] ranged from 175 to 430 nM at the sperm entry point and from 120 to 700 nM 90 degrees away once the Ca2+ wave passed that region about 2 min after fertilization. Prior to the Ca2+ wave reaching that region the IP3 levels were undetectable. Since significant IP3 could not diffuse to this region from the sperm entry point within 2 min, this observation is consistent with a regenerative wave of IP3 production.

Spatial modeling of cell signaling networks.

The shape of a cell, the sizes of subcellular compartments, and the spatial distribution of molecules within the cytoplasm can all control how molecules interact to produce a cellular behavior. This chapter describes how these spatial features can be included in mechanistic mathematical models of cell signaling. The Virtual Cell computational modeling and simulation software is used to illustrate the considerations required to build a spatial model. An explanation of how to appropriately choose between physical formulations that implicitly or explicitly account for cell geometry and between deterministic versus stochastic formulations for molecular dynamics is provided, along with a discussion of their respective strengths and weaknesses. As a first step toward constructing a spatial model, the geometry needs to be specified and associated with the molecules, reactions, and membrane flux processes of the network. Initial conditions, diffusion coefficients, velocities, and boundary conditions complete the specifications required to define the mathematics of the model. The numerical methods used to solve reaction-diffusion problems both deterministically and stochastically are then described and some guidance is provided in how to set up and run simulations. A study of cAMP signaling in neurons ends the chapter, providing an example of the insights that can be gained in interpreting experimental results through the application of spatial modeling.

Reproducible computational biology experiments with SED-ML--the Simulation Experiment Description Markup Language.

BACKGROUND: The increasing use of computational simulation experiments to inform modern biological research creates new challenges to annotate, archive, share and reproduce such experiments. The recently published Minimum Information About a Simulation Experiment (MIASE) proposes a minimal set of information that should be provided to allow the reproduction of simulation experiments among users and software tools. RESULTS: In this article, we present the Simulation Experiment Description Markup Language (SED-ML). SED-ML encodes in a computer-readable exchange format the information required by MIASE to enable reproduction of simulation experiments. It has been developed as a community project and it is defined in a detailed technical specification and additionally provides an XML schema. The version of SED-ML described in this publication is Level 1 Version 1. It covers the description of the most frequent type of simulation experiments in the area, namely time course simulations. SED-ML documents specify which models to use in an experiment, modifications to apply on the models before using them, which simulation procedures to run on each model, what analysis results to output, and how the results should be presented. These descriptions are independent of the underlying model implementation. SED-ML is a software-independent format for encoding the description of simulation experiments; it is not specific to particular simulation tools. Here, we demonstrate that with the growing software support for SED-ML we can effectively exchange executable simulation descriptions. CONCLUSIONS: With SED-ML, software can exchange simulation experiment descriptions, enabling the validation and reuse of simulation experiments in different tools. Authors of papers reporting simulation experiments can make their simulation protocols available for other scientists to reproduce the results. Because SED-ML is agnostic about exact modeling language(s) used, experiments covering models from different fields of research can be accurately described and combined.

XML Encoding of Features Describing Rule-Based Modeling of Reaction Networks with Multi-Component Molecular Complexes.

Multi-state molecules and multi-component complexes are commonly involved in cellular signaling. Accounting for molecules that have multiple potential states, such as a protein that may be phosphorylated on multiple residues, and molecules that combine to form heterogeneous complexes located among multiple compartments, generates an effect of combinatorial complexity. Models involving relatively few signaling molecules can include thousands of distinct chemical species. Several software tools (StochSim, BioNetGen) are already available to deal with combinatorial complexity. Such tools need information standards if models are to be shared, jointly evaluated and developed. Here we discuss XML conventions that can be adopted for modeling biochemical reaction networks described by user-specified reaction rules. These could form a basis for possible future extensions of the Systems Biology Markup Language (SBML).

Kinetic Modeling using BioPAX ontology.

Thousands of biochemical interactions are available for download from curated databases such as Reactome, Pathway Interaction Database and other sources in the Biological Pathways Exchange (BioPAX) format. However, the BioPAX ontology does not encode the necessary information for kinetic modeling and simulation. The current standard for kinetic modeling is the System Biology Markup Language (SBML), but only a small number of models are available in SBML format in public repositories. Additionally, reusing and merging SBML models presents a significant challenge, because often each element has a value only in the context of the given model, and information encoding biological meaning is absent. We describe a software system that enables a variety of operations facilitating the use of BioPAX data to create kinetic models that can be visualized, edited, and simulated using the Virtual Cell (VCell), including improved conversion to SBML (for use with other simulation tools that support this format).