RuleBender: integrated modeling, simulation and visualization for rule-based intracellular biochemistry

Reusable rule-based cell cycle model explains compartment-resolved dynamics of 16 observables in RPE-1 cells

The mammalian cell cycle is regulated by a well-studied but complex biochemical reaction system. Computational models provide a particularly systematic and systemic description of the mechanisms governing mammalian cell cycle control. By combining both state-of-the-art multiplexed experimental methods and powerful computational tools, this work aims at improving on these models along four dimensions: model structure, validation data, validation methodology and model reusability. We developed a comprehensive model structure of the full cell cycle that qualitatively explains the behaviour of human retinal pigment epithelial-1 cells. To estimate the model parameters, time courses of eight cell cycle regulators in two compartments were reconstructed from single cell snapshot measurements. After optimisation with a parallel global optimisation metaheuristic we obtained excellent agreements between simulations and measurements. The PEtab specification of the optimisation problem facilitates reuse of model, data and/or optimisation results. Future perturbation experiments will improve parameter identifiability and allow for testing model predictive power. Such a predictive model may aid in drug discovery for cell cycle-related disorders.

Nonself RNA rewires IFN-β signaling: A mathematical model of the innate immune response

Type I interferons (IFNs) are key coordinators of the innate immune response to viral infection, which, through activation of the transcriptional regulators STAT1 and STAT2 (STAT1/2) in bystander cells, induce the expression of IFN-stimulated genes (ISGs). Here, we showed that in cells transfected with poly(I:C), an analog of viral RNA, the transcriptional activity of STAT1/2 was terminated because of depletion of the interferon-β (IFN-β) receptor, IFNAR. Activation of RNase L and PKR, products of two ISGs, not only hindered the replenishment of IFNAR but also suppressed negative regulators of IRF3 and NF-κB, consequently promoting IFNB transcription. We incorporated these findings into a mathematical model of innate immunity. By coupling signaling through the IRF3-NF-κB and STAT1/2 pathways with the activities of RNase L and PKR, the model explains how poly(I:C) switches the transcriptional program from being STAT1/2 induced to being IRF3 and NF-κB induced, which converts IFN-β-responding cells to IFN-β-secreting cells.

RNA binding induces an allosteric switch in Cyp33 to repress MLL1-mediated transcription

Mixed-lineage leukemia 1 (MLL1) is a transcription activator of the HOX family, which binds to specific epigenetic marks on histone H3 through its third plant homeodomain (PHD3) domain. Through an unknown mechanism, MLL1 activity is repressed by cyclophilin 33 (Cyp33), which binds to MLL1 PHD3. We determined solution structures of Cyp33 RNA recognition motif (RRM) free, bound to RNA, to MLL1 PHD3, and to both MLL1 and the histone H3 lysine N6-trimethylated. We found that a conserved α helix, amino-terminal to the RRM domain, adopts three different positions facilitating a cascade of binding events. These conformational changes are triggered by Cyp33 RNA binding and ultimately lead to MLL1 release from the histone mark. Together, our mechanistic findings rationalize how Cyp33 binding to MLL1 can switch chromatin to a transcriptional repressive state triggered by RNA binding as a negative feedback loop.

THALIS: Human-Machine Analysis of Longitudinal Symptoms in Cancer Therapy

Although cancer patients survive years after oncologic therapy, they are plagued with long-lasting or permanent residual symptoms, whose severity, rate of development, and resolution after treatment vary largely between survivors. The analysis and interpretation of symptoms is complicated by their partial co-occurrence, variability across populations and across time, and, in the case of cancers that use radiotherapy, by further symptom dependency on the tumor location and prescribed treatment. We describe THALIS, an environment for visual analysis and knowledge discovery from cancer therapy symptom data, developed in close collaboration with oncology experts. Our approach leverages unsupervised machine learning methodology over cohorts of patients, and, in conjunction with custom visual encodings and interactions, provides context for new patients based on patients with similar diagnostic features and symptom evolution. We evaluate this approach on data collected from a cohort of head and neck cancer patients. Feedback from our clinician collaborators indicates that THALIS supports knowledge discovery beyond the limits of machines or humans alone, and that it serves as a valuable tool in both the clinic and symptom research.

A systems-biology model of the tumor necrosis factor (TNF) interactions with TNF receptor 1 and 2

MOTIVATION

Clustering enables TNF receptors to stimulate intracellular signaling. The differential soluble ligand-induced clustering behavior of TNF receptor 1 (TNFR1) and TNFR2 was modeled. A structured, rule-based model implemented ligand-independent pre-ligand binding assembly domain (PLAD)-mediated homotypic low affinity interactions of unliganded and liganded TNF receptors.

RESULTS

Soluble TNF initiates TNFR1 signaling but not TNFR2 signaling despite receptor binding unless it is secondarily oligomerized. We consider high affinity binding of TNF to signaling-incompetent pre-assembled dimeric TNFR1 and TNFR2 molecules and secondary clustering of liganded dimers to signaling competent ligand-receptor clusters. Published receptor numbers, affinities and measured different activities of clustered receptors validated model simulations for a large range of receptor and ligand concentrations. Different PLAD-PLAD affinities and different activities of receptor clusters explain the observed differences in the TNF receptor stimulating activities of soluble TNF.

AVAILABILITY AND IMPLEMENTATION

All scripts and data are in manuscript and supplement at Bioinformatics online.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Atlas: automatic modeling of regulation of bacterial gene expression and metabolism using rule-based languages

MOTIVATION

Cells are complex systems composed of hundreds of genes whose products interact to produce elaborated behaviors. To control such behaviors, cells rely on transcription factors to regulate gene expression, and gene regulatory networks (GRNs) are employed to describe and understand such behavior. However, GRNs are static models, and dynamic models are difficult to obtain due to their size, complexity, stochastic dynamics and interactions with other cell processes.

RESULTS

We developed Atlas, a Python software that converts genome graphs and gene regulatory, interaction and metabolic networks into dynamic models. The software employs these biological networks to write rule-based models for the PySB framework. The underlying method is a divide-and-conquer strategy to obtain sub-models and combine them later into an ensemble model. To exemplify the utility of Atlas, we used networks of varying size and complexity of Escherichia coli and evaluated in silico modifications, such as gene knockouts and the insertion of promoters and terminators. Moreover, the methodology could be applied to the dynamic modeling of natural and synthetic networks of any bacteria.

AVAILABILITY AND IMPLEMENTATION

Code, models and tutorials are available online (https://github.com/networkbiolab/atlas).

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Quantifying the roles of space and stochasticity in computer simulations for cell biology and cellular biochemistry

Most of the fascinating phenomena studied in cell biology emerge from interactions among highly organized multimolecular structures embedded into complex and frequently dynamic cellular morphologies. For the exploration of such systems, computer simulation has proved to be an invaluable tool, and many researchers in this field have developed sophisticated computational models for application to specific cell biological questions. However, it is often difficult to reconcile conflicting computational results that use different approaches to describe the same phenomenon. To address this issue systematically, we have defined a series of computational test cases ranging from very simple to moderately complex, varying key features of dimensionality, reaction type, reaction speed, crowding, and cell size. We then quantified how explicit spatial and/or stochastic implementations alter outcomes, even when all methods use the same reaction network, rates, and concentrations. For simple cases, we generally find minor differences in solutions of the same problem. However, we observe increasing discordance as the effects of localization, dimensionality reduction, and irreversible enzymatic reactions are combined. We discuss the strengths and limitations of commonly used computational approaches for exploring cell biological questions and provide a framework for decision making by researchers developing new models. As computational power and speed continue to increase at a remarkable rate, the dream of a fully comprehensive computational model of a living cell may be drawing closer to reality, but our analysis demonstrates that it will be crucial to evaluate the accuracy of such models critically and systematically.

Artificial intelligence for modeling uveal melanoma

Understanding of the cellular signaling pathways involved in cancer disease is of great importance. These complex biological mechanisms can be thoroughly revealed by their structure, dynamics, and control methods. Artificial intelligence offers rule-based models that favor the research of human signaling processes. In this paper, we give an overview of the advantages of the formalism of symbolic models in medical biology and cell biology of the uveal melanoma. A language is described that allows us: (1) To define the system states and elements with their alterations; (2) To model the dynamics of the cellular system; and (3) To perform inference-based analysis with the logical tools of the language.

A compiler for biological networks on silicon chips

The explosive growth in semiconductor integrated circuits was made possible in large part by design automation software. The design and/or analysis of synthetic and natural circuits in living cells could be made more scalable using the same approach. We present a compiler which converts standard representations of chemical reaction networks and circuits into hardware configurations that can be used to simulate the network on specialized cytomorphic hardware. The compiler also creates circuit–level models of the target configuration, which enhances the versatility of the compiler and enables the validation of its functionality without physical experimentation with the hardware. We show that this compiler can translate networks comprised of mass–action kinetics, classic enzyme kinetics (Michaelis–Menten, Briggs–Haldane, and Botts–Morales formalisms), and genetic repressor kinetics, thereby allowing a large class of models to be transformed into a hardware representation. Rule–based models are particularly well–suited to this approach, as we demonstrate by compiling a MAP kinase model. Development of specialized hardware and software for simulating biological networks has the potential to enable the simulation of larger kinetic models than are currently feasible or allow the parallel simulation of many smaller networks with better performance than current simulation software.

We present a “silicon compiler” that is capable of translating biochemical models encoded in the SBML standard into specialized analog cytomorphic hardware and transfer function–level simulations of such hardware. We show how the compiler and hardware address challenges in analog computing: 1) We ensure that the integration of errors due to the mismatch between analog circuit parameters does not become infinite over time but always remains finite via the use of total variables (the solution of the “divergence problem”); 2) We describe the compilation process through a series of examples using building blocks of biological networks, and show the results of compiling two SBML models from the literature: the Elowitz repressilator model and a rule–based model of a MAP kinase cascade. Source code for the compiler is available at https://doi.org/10.5281/zenodo.3948393.

Deterministic modeling of single-channel and whole-cell currents

As a complement to the experimental work, mathematical models are extensively used to study the functional properties of ionic channels. Even though it is generally assumed that the gating of ionic channels is a Markovian phenomenon, reports based on non-traditional analyses of experimental recordings suggest that non-Markovian processes might be also present. While the stochastic Markov models are by far the most adopted approach for the modeling of ionic channels, a model based on the idea of a deterministic process underlying the gating of ionic channels was proposed by Liebovitch and Toth (Liebovitch, L.S. and Toth, T.I., 1991. Journal of Theoretical Biology, 148(2), pp.243-267.) Here, by using a voltage-dependent K⁺ channel as a first approximation, we propose a modified version of the deterministic model of Liebovitch and Toth that, in addition to reproducing the single-channel currents simulated by a two-states Markov model, it is capable of reproducing the whole-cell currents produced by a population of K⁺ channels.

NERDSS: A Nonequilibrium Simulator for Multibody Self-Assembly at the Cellular Scale

Currently, a significant barrier to building predictive models of cellular self-assembly processes is that molecular models cannot capture minutes-long dynamics that couple distinct components with active processes, whereas reaction-diffusion models cannot capture structures of molecular assembly. Here, we introduce the nonequilibrium reaction-diffusion self-assembly simulator (NERDSS), which addresses this spatiotemporal resolution gap. NERDSS integrates efficient reaction-diffusion algorithms into generalized software that operates on user-defined molecules through diffusion, binding and orientation, unbinding, chemical transformations, and spatial localization. By connecting the fast processes of binding with the slow timescales of large-scale assembly, NERDSS integrates molecular resolution with reversible formation of ordered, multisubunit complexes. NERDSS encodes models using rule-based formatting languages to facilitate model portability, usability, and reproducibility. Applying NERDSS to steps in clathrin-mediated endocytosis, we design multicomponent systems that can form lattices in solution or on the membrane, and we predict how stochastic but localized dephosphorylation of membrane lipids can drive lattice disassembly. The NERDSS simulations reveal the spatial constraints on lattice growth and the role of membrane localization and cooperativity in nucleating assembly. By modeling viral lattice assembly and recapitulating oscillations in protein expression levels for a circadian clock model, we illustrate the adaptability of NERDSS. NERDSS simulates user-defined assembly models that were previously inaccessible to existing software tools, with broad applications to predicting self-assembly in vivo and designing high-yield assemblies in vitro.

Applications of personalised signalling network models in precision oncology

As our ability to provide in-depth, patient-specific characterisation of the molecular alterations within tumours rapidly improves, it is becoming apparent that new approaches will be required to leverage the power of this data and derive the full benefit for each individual patient. Systems biology approaches are beginning to emerge within this field as a potential method of incorporating large volumes of network level data and distilling a coherent, clinically-relevant prediction of drug response. However, the initial promise of this developing field is yet to be realised. Here we argue that in order to develop these precise models of individual drug response and tailor treatment accordingly, we will need to develop mathematical models capable of capturing both the dynamic nature of drug-response signalling networks and key patient-specific information such as mutation status or expression profiles. We also review the modelling approaches commonly utilised within this field, and outline recent examples of their use in furthering the application of systems biology for a precision medicine approach to cancer treatment.

Cohort-based T-SSIM Visual Computing for Radiation Therapy Prediction and Exploration

We describe a visual computing approach to radiation therapy (RT) planning, based on spatial similarity within a patient cohort. In radiotherapy for head and neck cancer treatment, dosage to organs at risk surrounding a tumor is a large cause of treatment toxicity. Along with the availability of patient repositories, this situation has lead to clinician interest in understanding and predicting RT outcomes based on previously treated similar patients. To enable this type of analysis, we introduce a novel topology-based spatial similarity measure, T-SSIM, and a predictive algorithm based on this similarity measure. We couple the algorithm with a visual steering interface that intertwines visual encodings for the spatial data and statistical results, including a novel parallel-marker encoding that is spatially aware. We report quantitative results on a cohort of 165 patients, as well as a qualitative evaluation with domain experts in radiation oncology, data management, biostatistics, and medical imaging, who are collaborating remotely.

Interactive Multiresolution Visualization of Cellular Network Processes

Visualization plays a central role in the analysis of biochemical network models to identify patterns that arise from reaction dynamics and perform model exploratory analysis. To facilitate these analyses, we developed PyViPR, a visualization tool that generates static and dynamic representations of biochemical network processes within a Python-based environment. PyViPR embeds network visualizations within Jupyter notebooks, thus enabling integration with modeling, simulation, and analysis workflows. To present the capabilities of PyViPR, we explore execution mechanisms of extrinsic apoptosis in HeLa cells. We show that community-detection algorithms identify groups of molecular species that capture key biological functions and ease exploration of the apoptosis network. We then show how different kinetic parameter sets that fit the experimental data equally well exhibit significantly different signal-execution dynamics as the system progresses toward mitochondrial outer-membrane permeabilization. Therefore, PyViPR aids the conceptual understanding of dynamic network processes and accelerates hypothesis generation for further testing and validation.

A Step-by-Step Guide to Using BioNetFit

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.

MCell-R: A Particle-Resolution Network-Free Spatial Modeling Framework

Spatial heterogeneity can have dramatic effects on the biochemical networks that drive cell regulation and decision-making. For this reason, a number of methods have been developed to model spatial heterogeneity and incorporated into widely used modeling platforms. Unfortunately, the standard approaches for specifying and simulating chemical reaction networks become untenable when dealing with multistate, multicomponent systems that are characterized by combinatorial complexity. To address this issue, we developed MCell-R, a framework that extends the particle-based spatial Monte Carlo simulator, MCell, with the rule-based model specification and simulation capabilities provided by BioNetGen and NFsim. The BioNetGen syntax enables the specification of biomolecules as structured objects whose components can have different internal states that represent such features as covalent modification and conformation and which can bind components of other molecules to form molecular complexes. The network-free simulation algorithm used by NFsim enables efficient simulation of rule-based models even when the size of the network implied by the biochemical rules is too large to enumerate explicitly, which frequently occurs in detailed models of biochemical signaling. The result is a framework that can efficiently simulate systems characterized by combinatorial complexity at the level of spatially resolved individual molecules over biologically relevant time and length scales.

Strategy-Driven Exploration for Rule-Based Models of Biochemical Systems with PORGY

This chapter presents PORGY-an interactive visual environment for rule-based modelling of biochemical systems. We model molecules and molecule interactions as port graphs and port graph rewrite rules, respectively. We use rewriting strategies to control which rules to apply, and where and when to apply them. Our main contributions to rule-based modelling of biochemical systems lie in the strategy language and the associated visual and interactive features offered by PORGY. These features facilitate an exploratory approach to test different ways of applying the rules while recording the model evolution, and tracking and plotting parameters. We illustrate PORGY's features with a study of the role of a scaffold protein in RAF/MEK/ERK signalling.

Modeling the Self-Assembly of Protein Complexes through a Rigid-Body Rotational Reaction-Diffusion Algorithm

The reaction-diffusion equations provide a powerful framework for modeling nonequilibrium, cell-scale dynamics over the long time scales that are inaccessible by traditional molecular modeling approaches. Single-particle reaction-diffusion offers the highest resolution technique for tracking such dynamics, but it has not been applied to the study of protein self-assembly due to its treatment of reactive species as single-point particles. Here, we develop a relatively simple but accurate approach for building rigid structure and rotation into single-particle reaction-diffusion methods, providing a rate-based method for studying protein self-assembly. Our simplifying assumption is that reactive collisions can be evaluated purely on the basis of the separations between the sites, and not their orientations. The challenge of evaluating reaction probabilities can then be performed using well-known equations based on translational diffusion in both 3D and 2D, by employing an effective diffusion constant we derive here. We show how our approach reproduces both the kinetics of association, which is altered by rotational diffusion, and the equilibrium of reversible association, which is not. Importantly, the macroscopic kinetics of association can be predicted on the basis of the microscopic parameters of our structurally resolved model, allowing for critical comparisons with theory and other rate-based simulations. We demonstrate this method for efficient, rate-based simulations of self-assembly of clathrin trimers, highlighting how formation of regular lattices impacts the kinetics of association.

The Kappa platform for rule-based modeling

Motivation

We present an overview of the Kappa platform, an integrated suite of analysis and visualization techniques for building and interactively exploring rule-based models. The main components of the platform are the Kappa Simulator, the Kappa Static Analyzer and the Kappa Story Extractor. In addition to these components, we describe the Kappa User Interface, which includes a range of interactive visualization tools for rule-based models needed to make sense of the complexity of biological systems. We argue that, in this approach, modeling is akin to programming and can likewise benefit from an integrated development environment. Our platform is a step in this direction.

Results

We discuss details about the computation and rendering of static, dynamic, and causal views of a model, which include the contact map (CM), snaphots at different resolutions, the dynamic influence network (DIN) and causal compression. We provide use cases illustrating how these concepts generate insight. Specifically, we show how the CM and snapshots provide information about systems capable of polymerization, such as Wnt signaling. A well-understood model of the KaiABC oscillator, translated into Kappa from the literature, is deployed to demonstrate the DIN and its use in understanding systems dynamics. Finally, we discuss how pathways might be discovered or recovered from a rule-based model by means of causal compression, as exemplified for early events in EGF signaling.

Availability and implementation

The Kappa platform is available via the project website at kappalanguage.org. All components of the platform are open source and freely available through the authors' code repositories.

Stoichiometric balance of protein copy numbers is measurable and functionally significant in a protein-protein interaction network for yeast endocytosis

Stoichiometric balance, or dosage balance, implies that proteins that are subunits of obligate complexes (e.g. the ribosome) should have copy numbers expressed to match their stoichiometry in that complex. Establishing balance (or imbalance) is an important tool for inferring subunit function and assembly bottlenecks. We show here that these correlations in protein copy numbers can extend beyond complex subunits to larger protein-protein interactions networks (PPIN) involving a range of reversible binding interactions. We develop a simple method for quantifying balance in any interface-resolved PPINs based on network structure and experimentally observed protein copy numbers. By analyzing such a network for the clathrin-mediated endocytosis (CME) system in yeast, we found that the real protein copy numbers were significantly more balanced in relation to their binding partners compared to randomly sampled sets of yeast copy numbers. The observed balance is not perfect, highlighting both under and overexpressed proteins. We evaluate the potential cost and benefits of imbalance using two criteria. First, a potential cost to imbalance is that ‘leftover’ proteins without remaining functional partners are free to misinteract. We systematically quantify how this misinteraction cost is most dangerous for strong-binding protein interactions and for network topologies observed in biological PPINs. Second, a more direct consequence of imbalance is that the formation of specific functional complexes depends on relative copy numbers. We therefore construct simple kinetic models of two sub-networks in the CME network to assess multi-protein assembly of the ARP2/3 complex and a minimal, nine-protein clathrin-coated vesicle forming module. We find that the observed, imperfectly balanced copy numbers are less effective than balanced copy numbers in producing fast and complete multi-protein assemblies. However, we speculate that strategic imbalance in the vesicle forming module allows cells to tune where endocytosis occurs, providing sensitive control over cargo uptake via clathrin-coated vesicles.

Protein copy numbers are often found to be stoichiometrically balanced for subunits of multi-protein complexes. Imbalance is believed to be deleterious because it lowers complex yield (the dosage balance hypothesis) and increases the risk of misinteractions, but imbalance may also provide unexplored functional benefits. We show here that the benefits of stoichiometric balance can extend to larger networks of interacting proteins. We develop a method to quantify to what degree protein networks are balanced, and apply it to two networks. We find that the clathrin-mediated endocytosis system in yeast is statistically balanced, but not perfectly so, and explore the consequences of imbalance in the form of misinteractions and endocytic function. We also show that biological networks are more robust to misinteractions than random networks when balanced, but are more sensitive to misinteractions under imbalance. This suggests evolutionary pressure for proteins to be balanced and that any conserved imbalance should occur for functional reasons. We explore one such reason in the form of bottlenecking the endocytosis process. Our method can be generalized to other networks and used to identify out-of-balance proteins. Our results provide insight into how network design, expression level regulation, and cell fitness are intertwined.

Dynamic Influence Networks for Rule-Based Models

We introduce the Dynamic Influence Network (DIN), a novel visual analytics technique for representing and analyzing rule-based models of protein-protein interaction networks. Rule-based modeling has proved instrumental in developing biological models that are concise, comprehensible, easily extensible, and that mitigate the combinatorial complexity of multi-state and multi-component biological molecules. Our technique visualizes the dynamics of these rules as they evolve over time. Using the data produced by KaSim, an open source stochastic simulator of rule-based models written in the Kappa language, DINs provide a node-link diagram that represents the influence that each rule has on the other rules. That is, rather than representing individual biological components or types, we instead represent the rules about them (as nodes) and the current influence of these rules (as links). Using our interactive DIN-Viz software tool, researchers are able to query this dynamic network to find meaningful patterns about biological processes, and to identify salient aspects of complex rule-based models. To evaluate the effectiveness of our approach, we investigate a simulation of a circadian clock model that illustrates the oscillatory behavior of the KaiC protein phosphorylation cycle.

Activity-Centered Domain Characterization for Problem-Driven Scientific Visualization

Although visualization design models exist in the literature in the form of higher-level methodological frameworks, these models do not present a clear methodological prescription for the domain characterization step. This work presents a framework and end-to-end model for requirements engineering in problem-driven visualization application design. The framework and model are based on the activity-centered design paradigm, which is an enhancement of human-centered design. The proposed activity-centered approach focuses on user tasks and activities, and allows an explicit link between the requirements engineering process with the abstraction stage-and its evaluation-of existing, higher-level visualization design models. In a departure from existing visualization design models, the resulting model: assigns value to a visualization based on user activities; ranks user tasks before the user data; partitions requirements in activity-related capabilities and nonfunctional characteristics and constraints; and explicitly incorporates the user workflows into the requirements process. A further merit of this model is its explicit integration of functional specifications, a concept this work adapts from the software engineering literature, into the visualization design nested model. A quantitative evaluation using two sets of interdisciplinary projects supports the merits of the activity-centered model. The result is a practical roadmap to the domain characterization step of visualization design for problem-driven data visualization. Following this domain characterization model can help remove a number of pitfalls that have been identified multiple times in the visualization design literature.

Automated visualization of rule-based models

Frameworks such as BioNetGen, Kappa and Simmune use "reaction rules" to specify biochemical interactions compactly, where each rule specifies a mechanism such as binding or phosphorylation and its structural requirements. Current rule-based models of signaling pathways have tens to hundreds of rules, and these numbers are expected to increase as more molecule types and pathways are added. Visual representations are critical for conveying rule-based models, but current approaches to show rules and interactions between rules scale poorly with model size. Also, inferring design motifs that emerge from biochemical interactions is an open problem, so current approaches to visualize model architecture rely on manual interpretation of the model. Here, we present three new visualization tools that constitute an automated visualization framework for rule-based models: (i) a compact rule visualization that efficiently displays each rule, (ii) the atom-rule graph that conveys regulatory interactions in the model as a bipartite network, and (iii) a tunable compression pipeline that incorporates expert knowledge and produces compact diagrams of model architecture when applied to the atom-rule graph. The compressed graphs convey network motifs and architectural features useful for understanding both small and large rule-based models, as we show by application to specific examples. Our tools also produce more readable diagrams than current approaches, as we show by comparing visualizations of 27 published models using standard graph metrics. We provide an implementation in the open source and freely available BioNetGen framework, but the underlying methods are general and can be applied to rule-based models from the Kappa and Simmune frameworks also. We expect that these tools will promote communication and analysis of rule-based models and their eventual integration into comprehensive whole-cell models.

Modeling of Receptor Tyrosine Kinase Signaling: Computational and Experimental Protocols

The advent of systems biology has convincingly demonstrated that the integration of experiments and dynamic modelling is a powerful approach to understand the cellular network biology. Here we present experimental and computational protocols that are necessary for applying this integrative approach to the quantitative studies of receptor tyrosine kinase (RTK) signaling networks. Signaling by RTKs controls multiple cellular processes, including the regulation of cell survival, motility, proliferation, differentiation, glucose metabolism, and apoptosis. We describe methods of model building and training on experimentally obtained quantitative datasets, as well as experimental methods of obtaining quantitative dose-response and temporal dependencies of protein phosphorylation and activities. The presented methods make possible (1) both the fine-grained modeling of complex signaling dynamics and identification of salient, course-grained network structures (such as feedback loops) that bring about intricate dynamics, and (2) experimental validation of dynamic models.

Extending rule-based methods to model molecular geometry and 3D model resolution

BACKGROUND

Computational modeling is an important tool for the study of complex biochemical processes associated with cell signaling networks. However, it is challenging to simulate processes that involve hundreds of large molecules due to the high computational cost of such simulations. Rule-based modeling is a method that can be used to simulate these processes with reasonably low computational cost, but traditional rule-based modeling approaches do not include details of molecular geometry. The incorporation of geometry into biochemical models can more accurately capture details of these processes, and may lead to insights into how geometry affects the products that form. Furthermore, geometric rule-based modeling can be used to complement other computational methods that explicitly represent molecular geometry in order to quantify binding site accessibility and steric effects.

RESULTS

We propose a novel implementation of rule-based modeling that encodes details of molecular geometry into the rules and binding rates. We demonstrate how rules are constructed according to the molecular curvature. We then perform a study of antigen-antibody aggregation using our proposed method. We simulate the binding of antibody complexes to binding regions of the shrimp allergen Pen a 1 using a previously developed 3D rigid-body Monte Carlo simulation, and we analyze the aggregate sizes. Then, using our novel approach, we optimize a rule-based model according to the geometry of the Pen a 1 molecule and the data from the Monte Carlo simulation. We use the distances between the binding regions of Pen a 1 to optimize the rules and binding rates. We perform this procedure for multiple conformations of Pen a 1 and analyze the impact of conformation and resolution on the optimal rule-based model.

CONCLUSIONS

We find that the optimized rule-based models provide information about the average steric hindrance between binding regions and the probability that antibodies will bind to these regions. These optimized models quantify the variation in aggregate size that results from differences in molecular geometry and from model resolution.

A rule-based model of insulin signalling pathway

BACKGROUND

The insulin signalling pathway (ISP) is an important biochemical pathway, which regulates some fundamental biological functions such as glucose and lipid metabolism, protein synthesis, cell proliferation, cell differentiation and apoptosis. In the last years, different mathematical models based on ordinary differential equations have been proposed in the literature to describe specific features of the ISP, thus providing a description of the behaviour of the system and its emerging properties. However, protein-protein interactions potentially generate a multiplicity of distinct chemical species, an issue referred to as "combinatorial complexity", which results in defining a high number of state variables equal to the number of possible protein modifications. This often leads to complex, error prone and difficult to handle model definitions.

RESULTS

In this work, we present a comprehensive model of the ISP, which integrates three models previously available in the literature by using the rule-based modelling (RBM) approach. RBM allows for a simple description of a number of signalling pathway characteristics, such as the phosphorylation of signalling proteins at multiple sites with different effects, the simultaneous interaction of many molecules of the signalling pathways with several binding partners, and the information about subcellular localization where reactions take place. Thanks to its modularity, it also allows an easy integration of different pathways. After RBM specification, we simulated the dynamic behaviour of the ISP model and validated it using experimental data. We the examined the predicted profiles of all the active species and clustered them in four clusters according to their dynamic behaviour. Finally, we used parametric sensitivity analysis to show the role of negative feedback loops in controlling the robustness of the system.

CONCLUSIONS

The presented ISP model is a powerful tool for data simulation and can be used in combination with experimental approaches to guide the experimental design. The model is available at http://sysbiobig.dei.unipd.it/ was submitted to Biomodels Database ( https://www.ebi.ac.uk/biomodels-main/ # MODEL 1604100005).

Influence of model resolution on geometric simulations of antibody aggregation

It is estimated that allergies afflict up to 40% of the world's population. A primary mediator for allergies is the aggregation of antigens and IgE antibodies bound to cell-surface receptors, FcεRI. Antibody/antigen aggregate formation causes stimulation of mast cells and basophils, initiating cellular degranulation and releasing immune mediators which produce an allergic or anaphylactic response. Understanding the shape and structure of these aggregates can provide critical insights into the allergic response. We have previously developed methods to geometrically model, simulate and analyze antibody aggregation inspired by rigid body robotic motion simulations. Our technique handles the large size and number of molecules involved in aggregation, providing an advantage over traditional simulations such as molecular dynamics (MD) and coarse-grained energetic models. In this paper, we study the impact of model resolution on simulations of geometric structures using both our previously developed Monte Carlo simulation and a novel application of rule-based modeling. These methods complement each other, the former providing explicit geometric detail and the latter providing a generic representation where multiple resolutions can be captured. Our exploration is focused on two antigens, a man-made antigen with three binding sites, DF3, and a common shrimp allergen (antigen), Pen a 1. We find that impact of resolution is minimal for DF3, a small globular antigen, but has a larger impact on Pen a 1, a rod-shaped molecule. The volume reduction caused by the loss in resolution allows more binding site accessibility, which can be quantified using a rule-based model with implicit geometric input. Clustering analysis of our simulation shows good correlation when compared with available experimental results. Moreover, collisions in all-atom reconstructions are negligible, at around 0.2% at 90% reduction.

Modeling for (physical) biologists: an introduction to the rule-based approach

Models that capture the chemical kinetics of cellular regulatory networks can be specified in terms of rules for biomolecular interactions. A rule defines a generalized reaction, meaning a reaction that permits multiple reactants, each capable of participating in a characteristic transformation and each possessing certain, specified properties, which may be local, such as the state of a particular site or domain of a protein. In other words, a rule defines a transformation and the properties that reactants must possess to participate in the transformation. A rule also provides a rate law. A rule-based approach to modeling enables consideration of mechanistic details at the level of functional sites of biomolecules and provides a facile and visual means for constructing computational models, which can be analyzed to study how system-level behaviors emerge from component interactions.

Visinets: a web-based pathway modeling and dynamic visualization tool

In this report we describe a novel graphically oriented method for pathway modeling and a software package that allows for both modeling and visualization of biological networks in a user-friendly format. The Visinets mathematical approach is based on causal mapping (CMAP) that has been fully integrated with graphical interface. Such integration allows for fully graphical and interactive process of modeling, from building the network to simulation of the finished model. To test the performance of Visinets software we have applied it to: a) create executable EGFR-MAPK pathway model using an intuitive graphical way of modeling based on biological data, and b) translate existing ordinary differential equation (ODE) based insulin signaling model into CMAP formalism and compare the results. Our testing fully confirmed the potential of the CMAP method for broad application for pathway modeling and visualization and, additionally, showed significant advantage in computational efficiency. Furthermore, we showed that Visinets web-based graphical platform, along with standardized method of pathway analysis, may offer a novel and attractive alternative for dynamic simulation in real time for broader use in biomedical research. Since Visinets uses graphical elements with mathematical formulas hidden from the users, we believe that this tool may be particularly suited for those who are new to pathway modeling and without the in-depth modeling skills often required when using other software packages.

Modeling biomolecular site dynamics in immunoreceptor signaling systems

The immune system plays a central role in human health. The activities of immune cells, whether defending an organism from disease or triggering a pathological condition such as autoimmunity, are driven by the molecular machinery of cellular signaling systems. Decades of experimentation have elucidated many of the biomolecules and interactions involved in immune signaling and regulation, and recently developed technologies have led to new types of quantitative, systems-level data. To integrate such information and develop nontrivial insights into the immune system, computational modeling is needed, and it is essential for modeling methods to keep pace with experimental advances. In this chapter, we focus on the dynamic, site-specific, and context-dependent nature of interactions in immunoreceptor signaling (i.e., the biomolecular site dynamics of immunoreceptor signaling), the challenges associated with capturing these details in computational models, and how these challenges have been met through use of rule-based modeling approaches.

MOSBIE: a tool for comparison and analysis of rule-based biochemical models

Background

Mechanistic models that describe the dynamical behaviors of biochemical systems are common in computational systems biology, especially in the realm of cellular signaling. The development of families of such models, either by a single research group or by different groups working within the same area, presents significant challenges that range from identifying structural similarities and differences between models to understanding how these differences affect system dynamics.

Results

We present the development and features of an interactive model exploration system, MOSBIE, which provides utilities for identifying similarities and differences between models within a family. Models are clustered using a custom similarity metric, and a visual interface is provided that allows a researcher to interactively compare the structures of pairs of models as well as view simulation results.

Conclusions

We illustrate the usefulness of MOSBIE via two case studies in the cell signaling domain. We also present feedback provided by domain experts and discuss the benefits, as well as the limitations, of the approach.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-316) contains supplementary material, which is available to authorized users.

Systems biology of cancer: a challenging expedition for clinical and quantitative biologists

A systems-biology approach to complex disease (such as cancer) is now complementing traditional experience-based approaches, which have typically been invasive and expensive. The rapid progress in biomedical knowledge is enabling the targeting of disease with therapies that are precise, proactive, preventive, and personalized. In this paper, we summarize and classify models of systems biology and model checking tools, which have been used to great success in computational biology and related fields. We demonstrate how these models and tools have been used to study some of the twelve biochemical pathways implicated in but not unique to pancreatic cancer, and conclude that the resulting mechanistic models will need to be further enhanced by various abstraction techniques to interpret phenomenological models of cancer progression.

eXamine: exploring annotated modules in networks

Background

Biological networks have a growing importance for the interpretation of high-throughput “omics” data. Integrative network analysis makes use of statistical and combinatorial methods to extract smaller subnetwork modules, and performs enrichment analysis to annotate the modules with ontology terms or other available knowledge. This process results in an annotated module, which retains the original network structure and includes enrichment information as a set system. A major bottleneck is a lack of tools that allow exploring both network structure of extracted modules and its annotations.

Results

This paper presents a visual analysis approach that targets small modules with many set-based annotations, and which displays the annotations as contours on top of a node-link diagram. We introduce an extension of self-organizing maps to lay out nodes, links, and contours in a unified way. An implementation of this approach is freely available as the Cytoscape app eXamine

Conclusions

eXamine accurately conveys small and annotated modules consisting of several dozens of proteins and annotations. We demonstrate that eXamine facilitates the interpretation of integrative network analysis results in a guided case study. This study has resulted in a novel biological insight regarding the virally-encoded G-protein coupled receptor US28.

NetworkViewer: visualizing biochemical reaction networks with embedded rendering of molecular interaction rules

Background

Network representations of cell-biological signaling processes frequently contain large numbers of interacting molecular and multi-molecular components that can exist in, and switch between, multiple biochemical and/or structural states. In addition, the interaction categories (associations, dissociations and transformations) in such networks cannot satisfactorily be mapped onto simple arrows connecting pairs of components since their specifications involve information such as reaction rates and conditions with regard to the states of the interacting components. This leads to the challenge of having to reconcile competing objectives: providing a high-level overview without omitting relevant information, and showing interaction specifics while not overwhelming users with too much detail displayed simultaneously. This problem is typically addressed by splitting the information required to understand a reaction network model into several categories that are rendered separately through combinations of visualizations and/or textual and tabular elements, requiring modelers to consult several sources to obtain comprehensive insights into the underlying assumptions of the model.

Results

We report the development of an application, the Simmune NetworkViewer, that visualizes biochemical reaction networks using iconographic representations of protein interactions and the conditions under which the interactions take place using the same symbols that were used to specify the underlying model with the Simmune Modeler. This approach not only provides a coherent model representation but, moreover, following the principle of “overview first, zoom and filter, then details-on-demand,” can generate an overview visualization of the global network and, upon user request, presents more detailed views of local sub-networks and the underlying reaction rules for selected interactions. This visual integration of information would be difficult to achieve with static network representations or approaches that use scripted model specifications without offering simple but detailed symbolic representations of molecular interactions, their conditions and consequences in terms of biochemical modifications.

Conclusions

The Simmune NetworkViewer provides concise, yet comprehensive visualizations of reaction networks created in the Simmune framework. In the near future, by adopting the upcoming SBML standard for encoding multi-component, multi-state molecular complexes and their interactions as input, the NetworkViewer will, moreover, be able to offer such visualization for any rule-based model that can be exported to that standard.

Multistate Model Builder (MSMB): a flexible editor for compact biochemical models

Background

Building models of molecular regulatory networks is challenging not just because of the intrinsic difficulty of describing complex biological processes. Writing a model is a creative effort that calls for more flexibility and interactive support than offered by many of today’s biochemical model editors. Our model editor MSMB — Multistate Model Builder — supports multistate models created using different modeling styles.

Results

MSMB provides two separate advances on existing network model editors. (1) A simple but powerful syntax is used to describe multistate species. This reduces the number of reactions needed to represent certain molecular systems, thereby reducing the complexity of model creation. (2) Extensive feedback is given during all stages of the model creation process on the existing state of the model. Users may activate error notifications of varying stringency on the fly, and use these messages as a guide toward a consistent, syntactically correct model. MSMB default values and behavior during model manipulation (e.g., when renaming or deleting an element) can be adapted to suit the modeler, thus supporting creativity rather than interfering with it. MSMB’s internal model representation allows saving a model with errors and inconsistencies (e.g., an undefined function argument; a syntactically malformed reaction). A consistent model can be exported to SBML or COPASI formats. We show the effectiveness of MSMB’s multistate syntax through models of the cell cycle and mRNA transcription.

Conclusions

Using multistate reactions reduces the number of reactions need to encode many biochemical network models. This reduces the cognitive load for a given model, thereby making it easier for modelers to build more complex models. The many interactive editing support features provided by MSMB make it easier for modelers to create syntactically valid models, thus speeding model creation. Complete information and the installation package can be found at http://www.copasi.org/SoftwareProjects. MSMB is based on Java and the COPASI API.

Rule-based modeling: a computational approach for studying biomolecular site dynamics in cell signaling systems

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 posttranslational 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).

Programming biological models in Python using PySB

PySB is a framework for creating biological models as Python programs using a high-level, action-oriented vocabulary that promotes transparency, extensibility and reusability. PySB interoperates with many existing modeling tools and supports distributed model development.

PySB models are programs and leverage existing programming tools for documentation, testing, and collaborative development.

Reusable functions can encode common low-level biochemical processes as well as high-level modules, making models transparent and concise.

Modeling workflow is accelerated through close integration with Python numerical tools and interoperability with existing modeling software.

We demonstrate the use of PySB to encode 15 alternative hypotheses for the mitochondrial regulation of apoptosis, including a new ‘Embedded Together' model based on recent biochemical findings.

Mathematical equations are fundamental to modeling biological networks, but as networks get large and revisions frequent, it becomes difficult to manage equations directly or to combine previously developed models. Multiple simultaneous efforts to create graphical standards, rule-based languages, and integrated software workbenches aim to simplify biological modeling but none fully meets the need for transparent, extensible, and reusable models. In this paper we describe PySB, an approach in which models are not only created using programs, they are programs. PySB draws on programmatic modeling concepts from little b and ProMot, the rule-based languages BioNetGen and Kappa and the growing library of Python numerical tools. Central to PySB is a library of macros encoding familiar biochemical actions such as binding, catalysis, and polymerization, making it possible to use a high-level, action-oriented vocabulary to construct detailed models. As Python programs, PySB models leverage tools and practices from the open-source software community, substantially advancing our ability to distribute and manage the work of testing biochemical hypotheses. We illustrate these ideas using new and previously published models of apoptosis.

Recent progress using systems biology approaches to better understand molecular mechanisms of immunity

The immune system is composed of multiple dynamic molecular and cellular networks, the complexity of which has been revealed by decades of exacting reductionist research. However, understanding of the immune system sufficient to anticipate its response to novel perturbations requires a more integrative or systems approach to immunology. While methods for unbiased high-throughput data acquisition and computational integration of the resulting datasets are still relatively new, they have begun to substantially enhance our understanding of immunological phenomena. Such approaches have expanded our view of interconnected signaling and transcriptional networks and have highlighted the function of non-linear processes such as spatial regulation and feedback loops. In addition, advances in single cell measurement technology have demonstrated potential sources and functions of response heterogeneity in system behavior. The success of the studies reviewed here often depended upon integration of one or more systems biology approaches with more traditional methods. We hope these examples will inspire a broader range of immunologists to probe questions in a quantitative and integrated manner, advancing collective efforts to understand the immune "system".