Hierarchical graphs for rule-based modeling of biochemical systems

Discovery of Functional Motifs from the Interface Region of Oligomeric Proteins Using Frequent Subgraph Mining

Modeling the interface region of a protein complex paves the way for understanding its dynamics and functionalities. Existing works model the interface region of a complex by using different approaches, such as, the residue composition at the interface region, the geometry of the interface residues, or the structural alignment of interface regions. These approaches are useful for ranking a set of docked conformation or for building scoring function for protein-protein docking, but they do not provide a generic and scalable technique for the extraction of interface patterns leading to functional motif discovery. In this work, we model the interface region of a protein complex by graphs and extract interface patterns of the given complex in the form of frequent subgraphs. To achieve this, we develop a scalable algorithm for frequent subgraph mining. We show that a systematic review of the mined subgraphs provides an effective method for the discovery of functional motifs that exist along the interface region of a given protein complex. In our experiments, we use three PDB protein structure datasets. The first two datasets are composed of PDB structures from different conformations of two dimeric protein complexes: HIV-1 protease (329 structures), and triosephosphate isomerase (TIM) (86 structures). The third dataset is a collection of different enzyme structures protein structures from the six top-level enzyme classes, namely: Oxydoreductase, Transferase, Hydrolase, Lyase, Isomerase, and Ligase. We show that for the first two datasets, our method captures the locking mechanism at the dimeric interface by taking into account the spatial positioning of the interfacial residues through graphs. Indeed, our frequent subgraph mining based approach discovers the patterns representing the dimerization lock which is formed at the base of the structure in 323 of the 329 HIV-1 protease structures. Similarly, for 86 TIM structures, our approach discovers the dimerization lock formation in 50 structures. For the enzyme structures, we show that we are able to capture the functional motifs (active sites) that are specific to each of the six top-level classes of enzymes through frequent subgraphs.

Fast Subgraph Matching Strategies Based on Pattern-Only Heuristics

Many scientific applications entail solving the subgraph isomorphism problem, i.e., given an input pattern graph, find all the subgraphs of a (usually much larger) target graph that are structurally equivalent to that input. Because subgraph isomorphism is NP-complete, methods to solve it have to use heuristics. This work evaluates subgraph isomorphism methods to assess their computational behavior on a wide range of synthetic and real graphs. Surprisingly, our experiments show that, among the leading algorithms, certain heuristics based only on pattern graphs are the most efficient.

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.

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.

Towards structural systems pharmacology to study complex diseases and personalized medicine

Genome-Wide Association Studies (GWAS), whole genome sequencing, and high-throughput omics techniques have generated vast amounts of genotypic and molecular phenotypic data. However, these data have not yet been fully explored to improve the effectiveness and efficiency of drug discovery, which continues along a one-drug-one-target-one-disease paradigm. As a partial consequence, both the cost to launch a new drug and the attrition rate are increasing. Systems pharmacology and pharmacogenomics are emerging to exploit the available data and potentially reverse this trend, but, as we argue here, more is needed. To understand the impact of genetic, epigenetic, and environmental factors on drug action, we must study the structural energetics and dynamics of molecular interactions in the context of the whole human genome and interactome. Such an approach requires an integrative modeling framework for drug action that leverages advances in data-driven statistical modeling and mechanism-based multiscale modeling and transforms heterogeneous data from GWAS, high-throughput sequencing, structural genomics, functional genomics, and chemical genomics into unified knowledge. This is not a small task, but, as reviewed here, progress is being made towards the final goal of personalized medicines for the treatment of complex diseases.

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).

Spatial rule-based modeling: a method and its application to the human mitotic kinetochore

A common problem in the analysis of biological systems is the combinatorial explosion that emerges from the complexity of multi-protein assemblies. Conventional formalisms, like differential equations, Boolean networks and Bayesian networks, are unsuitable for dealing with the combinatorial explosion, because they are designed for a restricted state space with fixed dimensionality. To overcome this problem, the rule-based modeling language, BioNetGen, and the spatial extension, SRSim, have been developed. Here, we describe how to apply rule-based modeling to integrate experimental data from different sources into a single spatial simulation model and how to analyze the output of that model. The starting point for this approach can be a combination of molecular interaction data, reaction network data, proximities, binding and diffusion kinetics and molecular geometries at different levels of detail. We describe the technique and then use it to construct a model of the human mitotic inner and outer kinetochore, including the spindle assembly checkpoint signaling pathway. This allows us to demonstrate the utility of the procedure, show how a novel perspective for understanding such complex systems becomes accessible and elaborate on challenges that arise in the formulation, simulation and analysis of spatial rule-based models.

A subgraph isomorphism algorithm and its application to biochemical data

Background

Graphs can represent biological networks at the molecular, protein, or species level. An important query is to find all matches of a pattern graph to a target graph. Accomplishing this is inherently difficult (NP-complete) and the efficiency of heuristic algorithms for the problem may depend upon the input graphs. The common aim of existing algorithms is to eliminate unsuccessful mappings as early as and as inexpensively as possible.

Results

We propose a new subgraph isomorphism algorithm which applies a search strategy to significantly reduce the search space without using any complex pruning rules or domain reduction procedures. We compare our method with the most recent and efficient subgraph isomorphism algorithms (VFlib, LAD, and our C++ implementation of FocusSearch which was originally distributed in Modula2) on synthetic, molecules, and interaction networks data. We show a significant reduction in the running time of our approach compared with these other excellent methods and show that our algorithm scales well as memory demands increase.

Conclusions

Subgraph isomorphism algorithms are intensively used by biochemical tools. Our analysis gives a comprehensive comparison of different software approaches to subgraph isomorphism highlighting their weaknesses and strengths. This will help researchers make a rational choice among methods depending on their application. We also distribute an open-source package including our system and our own C++ implementation of FocusSearch together with all the used datasets (http://ferrolab.dmi.unict.it/ri.html). In future work, our findings may be extended to approximate subgraph isomorphism algorithms.

Rule-based multi-level modeling of cell biological systems

BACKGROUND

Proteins, individual cells, and cell populations denote different levels of an organizational hierarchy, each of which with its own dynamics. Multi-level modeling is concerned with describing a system at these different levels and relating their dynamics. Rule-based modeling has increasingly attracted attention due to enabling a concise and compact description of biochemical systems. In addition, it allows different methods for model analysis, since more than one semantics can be defined for the same syntax.

RESULTS

Multi-level modeling implies the hierarchical nesting of model entities and explicit support for downward and upward causation between different levels. Concepts to support multi-level modeling in a rule-based language are identified. To those belong rule schemata, hierarchical nesting of species, assigning attributes and solutions to species at each level and preserving content of nested species while applying rules. Further necessities are the ability to apply rules and flexibly define reaction rate kinetics and constraints on nested species as well as species that are nested within others. An example model is presented that analyses the interplay of an intracellular control circuit with states at cell level, its relation to cell division, and connections to intercellular communication within a population of cells. The example is described in ML-Rules - a rule-based multi-level approach that has been realized within the plug-in-based modeling and simulation framework JAMES II.

CONCLUSIONS

Rule-based languages are a suitable starting point for developing a concise and compact language for multi-level modeling of cell biological systems. The combination of nesting species, assigning attributes, and constraining reactions according to these attributes is crucial in achieving the desired expressiveness. Rule schemata allow a concise and compact description of complex models. As a result, the presented approach facilitates developing and maintaining multi-level models that, for instance, interrelate intracellular and intercellular dynamics.

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.