On the threshold-width of graphs

The GG-width of a class of graphs GG is defined as follows. A graph G has GG-width k if there are k independent sets N1,...,Nk in G such that G can be embedded into a graph H in GG such that for every edge e in H which is not an edge in G, there exists an i such that both endpoints of e are in Ni. For the class TH of threshold graphs we show that TH-width is NP-complete and we present fixed-parameter algorithms. We also show that for each k, graphs of TH-width at most k are characterized by a finite collection of forbidden induced subgraphs

Multipartite Graph Algorithms for the Analysis of Heterogeneous Data

The explosive growth in the rate of data generation in recent years threatens to outpace the growth in computer power, motivating the need for new, scalable algorithms and big data analytic techniques. No field may be more emblematic of this data deluge than the life sciences, where technologies such as high-throughput mRNA arrays and next generation genome sequencing are routinely used to generate datasets of extreme scale. Data from experiments in genomics, transcriptomics, metabolomics and proteomics are continuously being added to existing repositories. A goal of exploratory analysis of such omics data is to illuminate the functions and relationships of biomolecules within an organism. This dissertation describes the design, implementation and application of graph algorithms, with the goal of seeking dense structure in data derived from omics experiments in order to detect latent associations between often heterogeneous entities, such as genes, diseases and phenotypes. Exact combinatorial solutions are developed and implemented, rather than relying on approximations or heuristics, even when problems are exceedingly large and/or difficult. Datasets on which the algorithms are applied include time series transcriptomic data from an experiment on the developing mouse cerebellum, gene expression data measuring acute ethanol response in the prefrontal cortex, and the analysis of a predicted protein-protein interaction network. A bipartite graph model is used to integrate heterogeneous data types, such as genes with phenotypes and microbes with mouse strains. The techniques are then extended to a multipartite algorithm to enumerate dense substructure in multipartite graphs, constructed using data from three or more heterogeneous sources, with applications to functional genomics. Several new theoretical results are given regarding multipartite graphs and the multipartite enumeration algorithm. In all cases, practical implementations are demonstrated to expand the frontier of computational feasibility

Transcriptomic Data Analysis Using Graph-Based Out-of-Core Methods

Biological data derived from high-throughput microarrays can be transformed into finite, simple, undirected graphs and analyzed using tools first introduced by the Langston Lab at the University of Tennessee. Transforming raw data can be broken down into three main tasks: data normalization, generation of similarity metrics, and threshold selection. The choice of methods used in each of these steps effect the final outcome of the graph, with respect to size, density, and structure. A number of different algorithms are examined and analyzed to illustrate the magnitude of the effects. Graph-based tools are then used to extract putative gene networks. These tools are loosely based on the concept of clique, which generates clusters optimized for density. Innovative additions to the paraclique algorithm, developed at the Langston Lab, are introduced to generate results that have highest average correlation or highest density. A new suite of algorithms is then presented that exploits the use of a priori gene interactions. Aptly named the anchored analysis toolkit, these algorithms use known interactions as anchor points for generating subgraphs, which are then analyzed for their graph structure. This results in clusters that might have otherwise been lost in noise. A main product of this thesis is a novel collection of algorithms to generate exact solutions to the maximum clique problem for graphs that are too large to fit within core memory. No other algorithms are currently known that produce exact solutions to this problem for extremely large graphs. A combination of in-core and out-of-core techniques is used in conjunction with a distributed-memory programming model. These algorithms take into consideration such pitfalls as external disk I/O and hardware failure and recovery. Finally, a web-based tool is described that provides researchers access the aforementioned algorithms. The Graph Algorithms Pipeline for Pathway Analysis tool, GrAPPA, was previously developed by the Langston Lab and provides the software needed to take raw microarray data as input and preprocess, analyze, and post-process it in a single package. GrAPPA also provides access to high-performance computing resources, via the TeraGrid

Quantitative surface field analysis: learning causal models to predict ligand binding affinity and pose.

We introduce the QuanSA method for inducing physically meaningful field-based models of ligand binding pockets based on structure-activity data alone. The method is closely related to the QMOD approach, substituting a learned scoring field for a pocket constructed of molecular fragments. The problem of mutual ligand alignment is addressed in a general way, and optimal model parameters and ligand poses are identified through multiple-instance machine learning. We provide algorithmic details along with performance results on sixteen structure-activity data sets covering many pharmaceutically relevant targets. In particular, we show how models initially induced from small data sets can extrapolatively identify potent new ligands with novel underlying scaffolds with very high specificity. Further, we show that combining predictions from QuanSA models with those from physics-based simulation approaches is synergistic. QuanSA predictions yield binding affinities, explicit estimates of ligand strain, associated ligand pose families, and estimates of structural novelty and confidence. The method is applicable for fine-grained lead optimization as well as potent new lead identification