Guidelines for visualizing and annotating rule-based models

Rule-based modeling provides a means to represent cell signaling systems in a way that captures site-specific details of molecular interactions. For rule-based models to be more widely understood and (re)used, conventions for model visualization and annotation are needed. We have developed the concepts of an extended contact map and a model guide for illustrating and annotating rule-based models. An extended contact map represents the scope of a model by providing an illustration of each molecule, molecular component, direct physical interaction, post-translational modification, and enzyme-substrate relationship considered in a model. A map can also illustrate allosteric effects, structural relationships among molecular components, and compartmental locations of molecules. A model guide associates elements of a contact map with annotation and elements of an underlying model, which may be fully or partially specified. A guide can also serve to document the biological knowledge upon which a model is based. We provide examples of a map and guide for a published rule-based model that characterizes early events in IgE receptor (FcεRI) signaling. We also provide examples of how to visualize a variety of processes that are common in cell signaling systems but not considered in the example model, such as ubiquitination. An extended contact map and an associated guide can document knowledge of a cell signaling system in a form that is visual as well as executable. As a tool for model annotation, a map and guide can communicate the content of a model clearly and with precision, even for large models.     

Exact Hybrid Particle/Population Simulation of Rule-Based Models of Biochemical Systems

Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational modifications. Rule-based modeling overcomes this problem by representing molecules as structured objects and encoding their interactions as pattern-based rules. This greatly simplifies the process of model specification, avoiding the tedious and error prone task of manually enumerating all species and reactions that can potentially exist in a system. From a simulation perspective, rule-based models can be expanded algorithmically into fully-enumerated reaction networks and simulated using a variety of network-based simulation methods, such as ordinary differential equations or Gillespie''s algorithm, provided that the network is not exceedingly large. Alternatively, rule-based models can be simulated directly using particle-based kinetic Monte Carlo methods. This “network-free” approach produces exact stochastic trajectories with a computational cost that is independent of network size. However, memory and run time costs increase with the number of particles, limiting the size of system that can be feasibly simulated. Here, we present a hybrid particle/population simulation method that combines the best attributes of both the network-based and network-free approaches. The method takes as input a rule-based model and a user-specified subset of species to treat as population variables rather than as particles. The model is then transformed by a process of “partial network expansion” into a dynamically equivalent form that can be simulated using a population-adapted network-free simulator. The transformation method has been implemented within the open-source rule-based modeling platform BioNetGen, and resulting hybrid models can be simulated using the particle-based simulator NFsim. Performance tests show that significant memory savings can be achieved using the new approach and a monetary cost analysis provides a practical measure of its utility.     

Modeling Regulatory Networks to Understand Plant Development: Small Is Beautiful

We now have unprecedented capability to generate large data sets on the myriad genes and molecular players that regulate plant development. Networks of interactions between systems components can be derived from that data in various ways and can be used to develop mathematical models of various degrees of sophistication. Here, we discuss why, in many cases, it is productive to focus on small networks. We provide a brief and accessible introduction to relevant mathematical and computational approaches to model regulatory networks and discuss examples of small network models that have helped generate new insights into plant biology (where small is beautiful), such as in circadian rhythms, hormone signaling, and tissue patterning. We conclude by outlining some of the key technical and modeling challenges for the future.     

ECHO,the executable CHOndrocyte: A computational model to study articular chondrocytes in health and disease

Computational modeling can be used to investigate complex signaling networks in biology. However, most modeling tools are not suitable for molecular cell biologists with little background in mathematics. We have built a visual-based modeling tool for the investigation of dynamic networks. Here, we describe the development of computational models of cartilage development and osteoarthritis, in which a panel of relevant signaling pathways are integrated. In silico experiments give insight in the role of each of the pathway components and reveal which perturbations may deregulate the basal healthy state of cells and tissues.We used a previously developed computational modeling tool Analysis of Networks with Interactive Modeling (ANIMO) to generate an activity network integrating 7 signal transduction pathways resulting in a network containing over 50 nodes and 200 interactions. We performed in silico experiments to characterize molecular mechanisms of cell fate decisions. The model was used to mimic biological scenarios during cell differentiation using RNA-sequencing data of a variety of stem cell sources as input. In a case-study, we wet-lab-tested the model-derived hypothesis that expression of DKK1 (Dickkopf-1) and FRZB (Frizzled related protein, WNT antagonists) and GREM1 (gremlin 1, BMP antagonist) prevents IL1β (Interleukin 1 beta)-induced MMP (matrix metalloproteinase) expression, thereby preventing cartilage degeneration, at least in the short term. We found that a combination of DKK1, FRZB and GREM1 may play a role in modulating the effects of IL1β induced inflammation in human primary chondrocytes.     

BioNetGen: software for rule-based modeling of signal transduction based on the interactions of molecular domains

BioNetGen allows a user to create a computational model that characterizes the dynamics of a signal transduction system, and that accounts comprehensively and precisely for specified enzymatic activities, potential post-translational modifications and interactions of the domains of signaling molecules. The output defines and parameterizes the network of molecular species that can arise during signaling and provides functions that relate model variables to experimental readouts of interest. Models that can be generated are relevant for rational drug discovery, analysis of proteomic data and mechanistic studies of signal transduction.     

Non-linear dimensionality reduction of signaling networks

Background  

Systems wide modeling and analysis of signaling networks is essential for understanding complex cellular behaviors, such as the biphasic responses to different combinations of cytokines and growth factors. For example, tumor necrosis factor (TNF) can act as a proapoptotic or prosurvival factor depending on its concentration, the current state of signaling network and the presence of other cytokines. To understand combinatorial regulation in such systems, new computational approaches are required that can take into account non-linear interactions in signaling networks and provide tools for clustering, visualization and predictive modeling.     

Rule-based modeling and simulations of the inner kinetochore structure

Background

Combinatorial complexity is a central problem when modeling biochemical reaction networks, since the association of a few components can give rise to a large variation of protein complexes. Available classical modeling approaches are often insufficient for the analysis of very large and complex networks in detail. Recently, we developed a new rule-based modeling approach that facilitates the analysis of spatial and combinatorially complex problems. Here, we explore for the first time how this approach can be applied to a specific biological system, the human kinetochore, which is a multi-protein complex involving over 100 proteins.

Results

Applying our freely available SRSim software to a large data set on kinetochore proteins in human cells, we construct a spatial rule-based simulation model of the human inner kinetochore. The model generates an estimation of the probability distribution of the inner kinetochore 3D architecture and we show how to analyze this distribution using information theory. In our model, the formation of a bridge between CenpA and an H3 containing nucleosome only occurs efficiently for higher protein concentration realized during S-phase but may be not in G1. Above a certain nucleosome distance the protein bridge barely formed pointing towards the importance of chromatin structure for kinetochore complex formation. We define a metric for the distance between structures that allow us to identify structural clusters. Using this modeling technique, we explore different hypothetical chromatin layouts.

Conclusions

Applying a rule-based network analysis to the spatial kinetochore complex geometry allowed us to integrate experimental data on kinetochore proteins, suggesting a 3D model of the human inner kinetochore architecture that is governed by a combinatorial algebraic reaction network. This reaction network can serve as bridge between multiple scales of modeling. Our approach can be applied to other systems beyond kinetochores.     

Efficient modeling, simulation and coarse-graining of biological complexity with NFsim

Managing the overwhelming numbers of molecular states and interactions is a fundamental obstacle to building predictive models of biological systems. Here we introduce the Network-Free Stochastic Simulator (NFsim), a general-purpose modeling platform that overcomes the combinatorial nature of molecular interactions. Unlike standard simulators that represent molecular species as variables in equations, NFsim uses a biologically intuitive representation: objects with binding and modification sites acted on by reaction rules. During simulations, rules operate directly on molecular objects to produce exact stochastic results with performance that scales independently of the reaction network size. Reaction rates can be defined as arbitrary functions of molecular states to provide powerful coarse-graining capabilities, for example to merge Boolean and kinetic representations of biological networks. NFsim enables researchers to simulate many biological systems that were previously inaccessible to general-purpose software, as we illustrate with models of immune system signaling, microbial signaling, cytoskeletal assembly and oscillating gene expression.     

Machines vs. Ensembles: Effective MAPK Signaling through Heterogeneous Sets of Protein Complexes

Despite the importance of intracellular signaling networks, there is currently no consensus regarding the fundamental nature of the protein complexes such networks employ. One prominent view involves stable signaling machines with well-defined quaternary structures. The combinatorial complexity of signaling networks has led to an opposing perspective, namely that signaling proceeds via heterogeneous pleiomorphic ensembles of transient complexes. Since many hypotheses regarding network function rely on how we conceptualize signaling complexes, resolving this issue is a central problem in systems biology. Unfortunately, direct experimental characterization of these complexes has proven technologically difficult, while combinatorial complexity has prevented traditional modeling methods from approaching this question. Here we employ rule-based modeling, a technique that overcomes these limitations, to construct a model of the yeast pheromone signaling network. We found that this model exhibits significant ensemble character while generating reliable responses that match experimental observations. To contrast the ensemble behavior, we constructed a model that employs hierarchical assembly pathways to produce scaffold-based signaling machines. We found that this machine model could not replicate the experimentally observed combinatorial inhibition that arises when the scaffold is overexpressed. This finding provides evidence against the hierarchical assembly of machines in the pheromone signaling network and suggests that machines and ensembles may serve distinct purposes in vivo. In some cases, e.g. core enzymatic activities like protein synthesis and degradation, machines assembled via hierarchical energy landscapes may provide functional stability for the cell. In other cases, such as signaling, ensembles may represent a form of weak linkage, facilitating variation and plasticity in network evolution. The capacity of ensembles to signal effectively will ultimately shape how we conceptualize the function, evolution and engineering of signaling networks.     

Algebraic dependency models of protein signal transduction networks from time-series data

Signal transduction networks are crucial for inter- and intra-cellular signaling. Signals are often transmitted via covalent modification of protein structure, with phosphorylation/dephosphorylation as the primary example. In this paper, we apply a recently described method of computational algebra to the modeling of signaling networks, based on time-course protein modification data. Computational algebraic techniques are employed to construct next-state functions. A Monte Carlo method is used to approximate the Deegan-Packel Index of Power corresponding to the respective variables. The Deegan-Packel Index of Power is used to conjecture dependencies in the cellular signaling networks. We apply this method to two examples of protein modification time-course data available in the literature. These experiments identified protein carbonylation upon exposure of cells to sub-lethal concentrations of copper. We demonstrate that this method can identify protein dependencies that might correspond to regulatory mechanisms to shut down glycolysis in a reverse, step-wise fashion in response to copper-induced oxidative stress in yeast. These examples show that the computational algebra approach can identify dependencies that may outline signaling networks involved in the response of glycolytic enzymes to the oxidative stress caused by copper.     

Competing to coordinate cell fate decisions: the MST2-Raf-1 signaling device

How do biochemical signaling pathways generate biological specificity? This question is fundamental to modern biology, and its enigma has been accentuated by the discovery that most proteins in signaling networks serve multifunctional roles. An answer to this question may lie in analyzing network properties rather than individual traits of proteins in order to elucidate design principles of biochemical networks that enable biological decision-making. We discuss how this is achieved in the MST2/Hippo-Raf-1 signaling network with the help of mathematical modeling and model-based analysis, which showed that competing protein interactions with affinities controlled by dynamic protein modifications can function as Boolean computing devices that determine cell fate decisions. In addition, we discuss areas of interest for future research and highlight how systems approaches would be of benefit.     

Nonparametric simulation of signal transduction networks with semi-synchronized update

Simulating signal transduction in cellular signaling networks provides predictions of network dynamics by quantifying the changes in concentration and activity-level of the individual proteins. Since numerical values of kinetic parameters might be difficult to obtain, it is imperative to develop non-parametric approaches that combine the connectivity of a network with the response of individual proteins to signals which travel through the network. The activity levels of signaling proteins computed through existing non-parametric modeling tools do not show significant correlations with the observed values in experimental results. In this work we developed a non-parametric computational framework to describe the profile of the evolving process and the time course of the proportion of active form of molecules in the signal transduction networks. The model is also capable of incorporating perturbations. The model was validated on four signaling networks showing that it can effectively uncover the activity levels and trends of response during signal transduction process.     

Structure-based kinetic models of modular signaling protein function: focus on Shp2

We present here a computational, rule-based model to study the function of the SH2 domain-containing protein tyrosine phosphatase, Shp2, in intracellular signal transduction. The two SH2 domains of Shp2 differentially regulate the enzymatic activity by a well-characterized mechanism, but they also affect the targeting of Shp2 to signaling receptors in cells. Our kinetic model integrates these potentially competing effects by considering the intra- and intermolecular interactions of the Shp2 SH2 domains and catalytic site as well as the effect of Shp2 phosphorylation. Even for the isolated Shp2/receptor system, which may seem simple by certain standards, we find that the network of possible binding and phosphorylation states is composed of over 1000 members. To our knowledge, this is the first kinetic model to fully consider the modular, multifunctional structure of a signaling protein, and the computational approach should be generally applicable to other complex intermolecular interactions.     

RuleMonkey: software for stochastic simulation of rule-based models

Background  

The system-level dynamics of many molecular interactions, particularly protein-protein interactions, can be conveniently represented using reaction rules, which can be specified using model-specification languages, such as the BioNetGen language (BNGL). A set of rules implicitly defines a (bio)chemical reaction network. The reaction network implied by a set of rules is often very large, and as a result, generation of the network implied by rules tends to be computationally expensive. Moreover, the cost of many commonly used methods for simulating network dynamics is a function of network size. Together these factors have limited application of the rule-based modeling approach. Recently, several methods for simulating rule-based models have been developed that avoid the expensive step of network generation. The cost of these "network-free" simulation methods is independent of the number of reactions implied by rules. Software implementing such methods is now needed for the simulation and analysis of rule-based models of biochemical systems.     

A biological approach to computational models of proteomic networks

Computational modeling is useful as a means to assemble and test what we know about proteins and networks. Models can help address key questions about the measurement, definition and function of proteomic networks. Here, we place these biological questions at the forefront in reviewing the computational strategies that are available to analyze proteomic networks. Recent examples illustrate how models can extract more information from proteomic data, test possible interactions between network proteins and link networks to cellular behavior. No single model can achieve all these goals, however, which is why it is critical to prioritize biological questions before specifying a particular modeling approach.     

Prediction of protein-protein interactions: unifying evolution and structure at protein interfaces

The vast majority of the chores in the living cell involve protein-protein interactions. Providing details of protein interactions at the residue level and incorporating them into protein interaction networks are crucial toward the elucidation of a dynamic picture of cells. Despite the rapid increase in the number of structurally known protein complexes, we are still far away from a complete network. Given experimental limitations, computational modeling of protein interactions is a prerequisite to proceed on the way to complete structural networks. In this work, we focus on the question 'how do proteins interact?' rather than 'which proteins interact?' and we review structure-based protein-protein interaction prediction approaches. As a sample approach for modeling protein interactions, PRISM is detailed which combines structural similarity and evolutionary conservation in protein interfaces to infer structures of complexes in the protein interaction network. This will ultimately help us to understand the role of protein interfaces in predicting bound conformations.