Exploring the nonlinear geometry of protein homology

Stochastic proximity embedding on graphics processing units: taking multidimensional scaling to a new scale

Stochastic proximity embedding (SPE) was developed as a method for efficiently calculating lower dimensional embeddings of high-dimensional data sets. Rather than using a global minimization scheme, SPE relies upon updating the distances of randomly selected points in an iterative fashion. This was found to generate embeddings of comparable quality to those obtained using classical multidimensional scaling algorithms. However, SPE is able to obtain these results in O(n) rather than O(n²) time and thus is much better suited to large data sets. In an effort both to speed up SPE and utilize it for even larger problems, we have created a multithreaded implementation which takes advantage of the growing general computing power of graphics processing units (GPUs). The use of GPUs allows the embedding of data sets containing millions of data points in interactive time scales.

Molecular evolution of phosphoprotein phosphatases in Drosophila

Phosphoprotein phosphatases (PPP), these ancient and important regulatory enzymes are present in all eukaryotic organisms. Based on the genome sequences of 12 Drosophila species we traced the evolution of the PPP catalytic subunits and noted a substantial expansion of the gene family. We concluded that the 18–22 PPP genes of Drosophilidae were generated from a core set of 8 indispensable phosphatases that are present in most of the insects. Retropositons followed by tandem gene duplications extended the phosphatase repertoire, and sporadic gene losses contributed to the species specific variations in the PPP complement. During the course of these studies we identified 5, up till now uncharacterized phosphatase retrogenes: PpY+, PpD5+, PpD6+, Pp4+, and Pp6+ which are found only in some ancient Drosophila. We demonstrated that all of these new PPP genes exhibit a distinct male specific expression. In addition to the changes in gene numbers, the intron-exon structure and the chromosomal localization of several PPP genes was also altered during evolution. The G−C content of the coding regions decreased when a gene moved into the heterochromatic region of chromosome Y. Thus the PPP enzymes exemplify the various types of dynamic rearrangements that accompany the molecular evolution of a gene family in Drosophilidae.

LGL: creating a map of protein function with an algorithm for visualizing very large biological networks

Networks are proving to be central to the study of gene function, protein-protein interaction, and biochemical pathway data. Visualization of networks is important for their study, but visualization tools are often inadequate for working with very large biological networks. Here, we present an algorithm, called large graph layout (LGL), which can be used to dynamically visualize large networks on the order of hundreds of thousands of vertices and millions of edges. LGL applies a force-directed iterative layout guided by a minimal spanning tree of the network in order to generate coordinates for the vertices in two or three dimensions, which are subsequently visualized and interactively navigated with companion programs. We demonstrate the use of LGL in visualizing an extensive protein map summarizing the results of approximately 21 billion sequence comparisons between 145579 proteins from 50 genomes. Proteins are positioned in the map according to sequence homology and gene fusions, with the map ultimately serving as a theoretical framework that integrates inferences about gene function derived from sequence homology, remote homology, gene fusions, and higher-order fusions. We confirm that protein neighbors in the resulting map are functionally related, and that distinct map regions correspond to distinct cellular systems, enabling a computational strategy for discovering proteins' functions on the basis of the proteins' map positions. Using the map produced by LGL, we infer general functions for 23 uncharacterized protein families.

A method for quantifying and visualizing the diversity of QSAR models

Feature selection is one of the most commonly used and reliable methods for deriving predictive quantitative structure-activity relationships (QSAR). Many feature selection algorithms are stochastic in nature and often produce different solutions depending on the initialization conditions. Because some features may be highly correlated, models that are based on different sets of descriptors may capture essentially the same information, however, such models are difficult to recognize. Here, we introduce a measure of similarity between QSAR models that captures the correlation between the underlying features. This measure can be used in conjunction with stochastic proximity embedding (SPE) or multi-dimensional scaling (MDS) to create a meaningful visual representation of structure-activity model space and aid in the post-processing and analysis of results of feature selection calculations.