Session Introduction: Graph Representations and Algorithms in Biomedicine.

The following sections are included: Introduction, Understanding and Predicting Molecular Networks, Understanding and Predicting Molecular Networks, Making Use of Family Structure, Applying Traditional Graph Algorithms to Novel Tasks, Representing Uncertainty in Networks, Conclusion, References.

Hypergraph models of biological networks to identify genes critical to pathogenic viral response.

BACKGROUND: Representing biological networks as graphs is a powerful approach to reveal underlying patterns, signatures, and critical components from high-throughput biomolecular data. However, graphs do not natively capture the multi-way relationships present among genes and proteins in biological systems. Hypergraphs are generalizations of graphs that naturally model multi-way relationships and have shown promise in modeling systems such as protein complexes and metabolic reactions. In this paper we seek to understand how hypergraphs can more faithfully identify, and potentially predict, important genes based on complex relationships inferred from genomic expression data sets. RESULTS: We compiled a novel data set of transcriptional host response to pathogenic viral infections and formulated relationships between genes as a hypergraph where hyperedges represent significantly perturbed genes, and vertices represent individual biological samples with specific experimental conditions. We find that hypergraph betweenness centrality is a superior method for identification of genes important to viral response when compared with graph centrality. CONCLUSIONS: Our results demonstrate the utility of using hypergraphs to represent complex biological systems and highlight central important responses in common to a variety of highly pathogenic viruses.

A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information.

Integration of multiple, heterogeneous sensors is a challenging problem across a range of applications. Prominent among these are multi-target tracking, where one must combine observations from different sensor types in a meaningful and efficient way to track multiple targets. Because different sensors have differing error models, we seek a theoretically justified quantification of the agreement among ensembles of sensors, both overall for a sensor collection, and also at a fine-grained level specifying pairwise and multi-way interactions among sensors. We demonstrate that the theory of mathematical sheaves provides a unified answer to this need, supporting both quantitative and qualitative data. Furthermore, the theory provides algorithms to globalize data across the network of deployed sensors, and to diagnose issues when the data do not globalize cleanly. We demonstrate and illustrate the utility of sheaf-based tracking models based on experimental data of a wild population of black bears in Asheville, North Carolina. A measurement model involving four sensors deployed among the bears and the team of scientists charged with tracking their location is deployed. This provides a sheaf-based integration model which is small enough to fully interpret, but of sufficient complexity to demonstrate the sheaf's ability to recover a holistic picture of the locations and behaviors of both individual bears and the bear-human tracking system. A statistical approach was developed in parallel for comparison, a dynamic linear model which was estimated using a Kalman filter. This approach also recovered bear and human locations and sensor accuracies. When the observations are normalized into a common coordinate system, the structure of the dynamic linear observation model recapitulates the structure of the sheaf model, demonstrating the canonicity of the sheaf-based approach. However, when the observations are not so normalized, the sheaf model still remains valid.

An analysis of multi-type relational interactions in FMA using graph motifs with disjointness constraints.

The interaction of multiple types of relationships among anatomical classes in the Foundational Model of Anatomy (FMA) can provide inferred information valuable for quality assurance. This paper introduces a method called Motif Checking (MOCH) to study the effects of such multi-relation type interactions for detecting logical inconsistencies as well as other anomalies represented by the motifs. MOCH represents patterns of multi-type interaction as small labeled (with multiple types of edges) sub-graph motifs, whose nodes represent class variables, and labeled edges represent relational types. By representing FMA as an RDF graph and motifs as SPARQL queries, fragments of FMA are automatically obtained as auditing candidates. Leveraging the scalability and reconfigurability of Semantic Web Technology, we performed exhaustive analyses of a variety of labeled sub-graph motifs. The quality assurance feature of MOCH comes from the distinct use of a subset of the edges of the graph motifs as constraints for disjointness, whereby bringing in rule-based flavor to the approach as well. With possible disjointness implied by antonyms, we performed manual inspection of the resulting FMA fragments and tracked down sources of abnormal inferred conclusions (logical inconsistencies), which are amendable for programmatic revision of the FMA. Our results demonstrate that MOCH provides a unique source of valuable information for quality assurance. Since our approach is general, it is applicable to any ontological system with an OWL representation.

A categorization approach to automated ontological function annotation.

Automated function prediction (AFP) methods increasingly use knowledge discovery algorithms to map sequence, structure, literature, and/or pathway information about proteins whose functions are unknown into functional ontologies, typically (a portion of) the Gene Ontology (GO). While there are a growing number of methods within this paradigm, the general problem of assessing the accuracy of such prediction algorithms has not been seriously addressed. We present first an application for function prediction from protein sequences using the POSet Ontology Categorizer (POSOC) to produce new annotations by analyzing collections of GO nodes derived from annotations of protein BLAST neighborhoods. We then also present hierarchical precision and hierarchical recall as new evaluation metrics for assessing the accuracy of any predictions in hierarchical ontologies, and discuss results on a test set of protein sequences. We show that our method provides substantially improved hierarchical precision (measure of predictions made that are correct) when applied to the nearest BLAST neighbors of target proteins, as compared with simply imputing that neighborhood's annotations to the target. Moreover, when our method is applied to a broader BLAST neighborhood, hierarchical precision is enhanced even further. In all cases, such increased hierarchical precision performance is purchased at a modest expense of hierarchical recall (measure of all annotations that get predicted at all).

Protein annotation as term categorization in the gene ontology using word proximity networks.

BACKGROUND: We participated in the BioCreAtIvE Task 2, which addressed the annotation of proteins into the Gene Ontology (GO) based on the text of a given document and the selection of evidence text from the document justifying that annotation. We approached the task utilizing several combinations of two distinct methods: an unsupervised algorithm for expanding words associated with GO nodes, and an annotation methodology which treats annotation as categorization of terms from a protein's document neighborhood into the GO. RESULTS: The evaluation results indicate that the method for expanding words associated with GO nodes is quite powerful; we were able to successfully select appropriate evidence text for a given annotation in 38% of Task 2.1 queries by building on this method. The term categorization methodology achieved a precision of 16% for annotation within the correct extended family in Task 2.2, though we show through subsequent analysis that this can be improved with a different parameter setting. Our architecture proved not to be very successful on the evidence text component of the task, in the configuration used to generate the submitted results. CONCLUSION: The initial results show promise for both of the methods we explored, and we are planning to integrate the methods more closely to achieve better results overall.

The gene ontology categorizer.

The Gene Ontology Categorizer, developed jointly by the Los Alamos National Laboratory and Procter & Gamble Corp., provides a capability for the categorization task in the Gene Ontology (GO): given a list of genes of interest, what are the best nodes of the GO to summarize or categorize that list? The motivating question is from a drug discovery process, where after some gene expression analysis experiment, we wish to understand the overall effect of some cell treatment or condition by identifying 'where' in the GO the differentially expressed genes fall: 'clustered' together in one place? in two places? uniformly spread throughout the GO? 'high', or 'low'? In order to address this need, we view bio-ontologies more as combinatorially structured databases than facilities for logical inference, and draw on the discrete mathematics of finite partially ordered sets (posets) to develop data representation and algorithms appropriate for the GO. In doing so, we have laid the foundations for a general set of methods to address not just the categorization task, but also other tasks (e.g. distances in ontologies and ontology merger and exchange) in both the GO and other bio-ontologies (such as the Enzyme Commission database or the MEdical Subject Headings) cast as hierarchically structured taxonomic knowledge systems.