Learning Node Replacement Graph Grammars in Metabolic Pathways

Bioinformatics, 2010

Motivation: Subgraph extraction is a powerful technique to predict pathways from biological networks and a set of query items (e.g. genes, proteins, compounds, etc.). It can be applied to a variety of different data types, such as gene expression, protein levels, operons or phylogenetic profiles. In this article, we investigate different approaches to extract relevant pathways from metabolic networks. Although these approaches have been adapted to metabolic networks, they are generic enough to be adjusted to other biological networks as well. Results: We comparatively evaluated seven sub-network extraction approaches on 71 known metabolic pathways from Saccharomyces cerevisiae and a metabolic network obtained from MetaCyc. The best performing approach is a novel hybrid strategy, which combines a random walk-based reduction of the graph with a shortest pathsbased algorithm, and which recovers the reference pathways with an accuracy of ∼ 77%. Availability: Most of the presented algorithms are available as part of the network analysis tool set (NeAT). The kWalks method is released under the GPL3 license.

Methods in molecular biology (Clifton, NJ), 2012

Various methods result in groups of functionally related genes obtained from genomes (operons, regulons, syntheny groups, and phylogenetic profiles), transcriptomes (co-expression groups) and proteomes (modules of interacting proteins). When such groups contain two or more enzyme-coding genes, graph analysis methods can be applied to extract a metabolic pathway that interconnects them.

2013

Modeling molecules as undirected graphs and chemical reactions as graph rewriting operations is a natural and convenient approach to modeling chemistry. Graph grammar rules are most naturally employed to model elementary reactions like merging, splitting, and isomerisation of molecules. It is often convenient, in particular in the analysis of larger systems, to summarize several subsequent reactions into a single composite chemical reaction. We use a generic approach for composing graph grammar rules to define a chemically useful rule compositions. We iteratively apply these rule compositions to elementary transformations in order to automatically infer complex transformation patterns. This is useful for instance to understand the net effect of complex catalytic cycles such as the Formose reaction. The automatically inferred graph grammar rule is a generic representative that also covers the overall reaction pattern of the Formose cycle, namely two carbonyl groups that can react with a bound glycolaldehyde to a second glycolaldehyde. Rule composition also can be used to study polymerization reactions as well as more complicated iterative reaction schemes. Terpenes and the polyketides, for instance, form two naturally occurring classes of compounds of utmost pharmaceutical interest that can be understood as "generalized polymers" consisting of five-carbon (isoprene) and two-carbon units, respectively.

International Journal on Artificial Intelligence Tools, 2008

We describe an algorithm and experiments for inference of edge replacement graph grammars. This method generates candidate recursive graph grammar productions based on isomorphic subgraphs which overlap by two nodes. If there is no edge between the two overlapping nodes, the method generates a recursive graph grammar production with a virtual edge. We guide the search for the graph grammar based on the size of the grammar and the portion of the graph described by the grammar. We show experiments where we generate graphs from known graph grammars, use our method to infer the grammar from the generated graphs, and then measure the error between the original and inferred grammars. Experiments show that the method performs well on several types of grammars, and specifically that error decreases with increased numbers of unique labels in the graph.

The reconstruction of the metabolic network of an organism based on its genome sequence is a key challenge in systems biology. The aim of the work described here is to develop a new algorithm to predict pathway classes and individual pathways for a previously unknown query molecule. The main idea is to use a dense graph, where the compounds are represented as vertices and the enzymes are represented as edges, the weights are assigned to the edges according to the previous known pathways. The shortest path algorithm is applied for each missing enzyme in a pathway. A pathway is considered belong to an organism if the total cost between the initial and final compound is higher than a threshold. Validation experiments show that the suggested algorithm is capable to classify more than 90% of pathways correctly.

Formal Methods in Software and Systems …, 2005

In the beginning, one of the main fields of application of graph transformation was biology, and more specifically morphology. Later, however, it was like if the biological applications had been left aside by the graph transformation community, just to be moved back into the mainstream these very last years with a new interest in molecular biology. In this paper, we review several fields of application of graph grammars in molecular biology, including: the modeling higherdimensional structures of biomolecules, the description of biochemical reactions, the analysis of metabolic pathways, and their potential use in computational systems biology.

2006

Applications of Graph Transformations with Industrial Relevance, 2012

A graph grammar is a generative description of a graph language (a possibly infinite set of graphs). In this paper, we present a novel algorithm for inducing a graph grammar from a given set of 'positive' and 'negative' graphs. The algorithm is guaranteed to produce a grammar that can generate all of the positive and none of the negative input graphs. Driven by a heuristic specific-to-general search process, the algorithm tries to find a small grammar that generalizes beyond the positive input set. During the search, the algorithm employs a graph grammar parser to eliminate the candidate grammars that can generate at least one negative input graph. We validate our method by inducing grammars for chemical structural formulas and flowcharts and thereby show its potential applicability to chemical engineering and visual programming.

2011

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.

Background Metabolism is generally modeled by directed networks where nodes represent reactions and/or metabolites. In order to explore metabolic pathway conservation and divergence among organisms, previous studies were based on graph alignment to find similar pathways. Few years ago, the concept of chemical transformation modules, also called reaction modules, was introduced and correspond to sequences of chemical transformations which are conserved in metabolism. We propose here a novel graph representation of the metabolic network where reactions sharing a same chemical transformation type are grouped in Reaction Molecular Signatures (RMS). Results RMS were automatically computed for all reactions and encode changes in atoms and bonds. A reaction network containing all available metabolic knowledge was then reduced by an aggregation of reaction nodes and edges to obtain a RMS network. Paths in this network were explored and a substantial number of conserved chemical transformation modules was detected. Furthermore, this graph-based formalism allows us to define several path scores reflecting different biological conservation meanings. These scores are significantly higher for paths corresponding to known metabolic pathways and were used conjointly to build association rules that should predict metabolic pathway types like biosynthesis or degradation. Conclusions This representation of metabolism in a RMS network offers new insights to capture relevant metabolic contexts. Furthermore, along with genomic context methods, it should improve the detection of gene clusters corresponding to new metabolic pathways.