GetBonNie for building, analyzing and sharing rule-based models

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.

Using RuleBuilder to Graphically Define and Visualize BioNetGen-Language Patterns and Reaction Rules

RuleBuilder is a tool for drawing graphs that can be represented by the BioNetGen language (BNGL), which is used to formulate mathematical, rule-based models of biochemical systems. BNGL provides an intuitive plain text, or string, representation of such systems, which is based on a graphical formalism. Reactions are defined in terms of graph-rewriting rules that specify the necessary intrinsic properties of the reactants, a transformation, and a rate law. Rules also contain contextual constraints that restrict application of the rule. In some cases, the specification of contextual constraints can be verbose, making a rule difficult to read. RuleBuilder is designed to ease the task of reading and writing individual reaction rules or other BNGL patterns required for model formulation. The software assists in the reading of existing models by converting BNGL strings of interest into a graph-based representation composed of nodes and edges. RuleBuilder also enables the user to construct de novo a visual representation of BNGL strings using drawing tools available in its interface. As objects are added to the drawing canvas, the corresponding BNGL string is generated on the fly, and objects are similarly drawn on the fly as BNGL strings are entered into the application. RuleBuilder thus facilitates construction and interpretation of rule-based models.

MAMMOTh: A new database for curated mathematical models of biomolecular systems

MOTIVATION

Living systems have a complex hierarchical organization that can be viewed as a set of dynamically interacting subsystems. Thus, to simulate the internal nature and dynamics of the entire biological system, we should use the iterative way for a model reconstruction, which is a consistent composition and combination of its elementary subsystems. In accordance with this bottom-up approach, we have developed the MAthematical Models of bioMOlecular sysTems (MAMMOTh) tool that consists of the database containing manually curated MAMMOTh fitted to the experimental data and a software tool that provides their further integration.

RESULTS

The MAMMOTh database entries are organized as building blocks in a way that the model parts can be used in different combinations to describe systems with higher organizational level (metabolic pathways and/or transcription regulatory networks). The tool supports export of a single model or their combinations in SBML or Mathematica standards. The database currently contains 110 mathematical sub-models for Escherichia coli elementary subsystems (enzymatic reactions and gene expression regulatory processes) that can be combined in at least 5100 complex/sophisticated models concerning more complex biological processes as de novo nucleotide biosynthesis, aerobic/anaerobic respiration and nitrate/nitrite utilization in E. coli. All models are functionally interconnected and sufficiently complement public model resources.

AVAILABILITY

http://mammoth.biomodelsgroup.ru.

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.

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.

Mathematical modeling and validation of the ergosterol pathway in Saccharomyces cerevisiae

The de novo biosynthetic machinery for both sphingolipid and ergosterol production in yeast is localized in the endoplasmic reticulum (ER) and Golgi. The interconnections between the two pathways are still poorly understood, but they may be connected in specialized membrane domains, and specific knockouts strongly suggest that both routes have different layers of mutual control and are co-affected by drugs. With the goal of shedding light on the functional integration of the yeast sphingolipid-ergosterol (SL-E) pathway, we constructed a dynamic model of the ergosterol pathway using the guidelines of Biochemical Systems Theory (BST) (Savageau., J. theor. Biol., 25, 365–9, 1969). The resulting model was merged with a previous mathematical model of sphingolipid metabolism in yeast (Alvarez-Vasquez et al., J. theor. Biol., 226, 265–91, 2004; Alvarez-Vasquez et al., Nature433, 425–30, 2005). The S-system format within BST was used for analyses of consistency, stability, and sensitivity of the SL-E model, while the GMA format was used for dynamic simulations and predictions. Model validation was accomplished by comparing predictions from the model with published results on sterol and sterol-ester dynamics in yeast. The validated model was used to predict the metabolomic dynamics of the SL-E pathway after drug treatment. Specifically, we simulated the action of drugs affecting sphingolipids in the endoplasmic reticulum and studied changes in ergosterol associated with microdomains of the plasma membrane (PM).

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.

Systems biology in immunology: a computational modeling perspective

Systems biology is an emerging discipline that combines high-content, multiplexed measurements with informatic and computational modeling methods to better understand biological function at various scales. Here we present a detailed review of the methods used to create computational models and to conduct simulations of immune function. We provide descriptions of the key data-gathering techniques employed to generate the quantitative and qualitative data required for such modeling and simulation and summarize the progress to date in applying these tools and techniques to questions of immunological interest, including infectious disease. We include comments on what insights modeling can provide that complement information obtained from the more familiar experimental discovery methods used by most investigators and the reasons why quantitative methods are needed to eventually produce a better understanding of immune system operation in health and disease.

Hierarchical graphs for rule-based modeling of biochemical systems

Background

In rule-based modeling, graphs are used to represent molecules: a colored vertex represents a component of a molecule, a vertex attribute represents the internal state of a component, and an edge represents a bond between components. Components of a molecule share the same color. Furthermore, graph-rewriting rules are used to represent molecular interactions. A rule that specifies addition (removal) of an edge represents a class of association (dissociation) reactions, and a rule that specifies a change of a vertex attribute represents a class of reactions that affect the internal state of a molecular component. A set of rules comprises an executable model that can be used to determine, through various means, the system-level dynamics of molecular interactions in a biochemical system.

Results

For purposes of model annotation, we propose the use of hierarchical graphs to represent structural relationships among components and subcomponents of molecules. We illustrate how hierarchical graphs can be used to naturally document the structural organization of the functional components and subcomponents of two proteins: the protein tyrosine kinase Lck and the T cell receptor (TCR) complex. We also show that computational methods developed for regular graphs can be applied to hierarchical graphs. In particular, we describe a generalization of Nauty, a graph isomorphism and canonical labeling algorithm. The generalized version of the Nauty procedure, which we call HNauty, can be used to assign canonical labels to hierarchical graphs or more generally to graphs with multiple edge types. The difference between the Nauty and HNauty procedures is minor, but for completeness, we provide an explanation of the entire HNauty algorithm.

Conclusions

Hierarchical graphs provide more intuitive formal representations of proteins and other structured molecules with multiple functional components than do the regular graphs of current languages for specifying rule-based models, such as the BioNetGen language (BNGL). Thus, the proposed use of hierarchical graphs should promote clarity and better understanding of rule-based models.

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.

Results

Here, we present a software tool called RuleMonkey, which implements a network-free method for simulation of rule-based models that is similar to Gillespie's method. The method is suitable for rule-based models that can be encoded in BNGL, including models with rules that have global application conditions, such as rules for intramolecular association reactions. In addition, the method is rejection free, unlike other network-free methods that introduce null events, i.e., steps in the simulation procedure that do not change the state of the reaction system being simulated. We verify that RuleMonkey produces correct simulation results, and we compare its performance against DYNSTOC, another BNGL-compliant tool for network-free simulation of rule-based models. We also compare RuleMonkey against problem-specific codes implementing network-free simulation methods.

Conclusions

RuleMonkey enables the simulation of rule-based models for which the underlying reaction networks are large. It is typically faster than DYNSTOC for benchmark problems that we have examined. RuleMonkey is freely available as a stand-alone application http://public.tgen.org/rulemonkey. It is also available as a simulation engine within GetBonNie, a web-based environment for building, analyzing and sharing rule-based models.