Exploring protein folding trajectories using geometric spanners

Computer Science Department, Stanford, CA 94305, USA.
Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing 02/2005; DOI: 10.1142/9789812702456_0005
Source: PubMed


We describe the 3-D structure of a protein using geometric spanners--geometric graphs with a sparse set of edges where paths approximate the n2 inter-atom distances. The edges in the spanner pick out important proximities in the structure, labeling a small number of atom pairs or backbone region pairs as being of primary interest. Such compact multiresolution views of proximities in the protein can be quite valuable, allowing, for example, easy visualization of the conformation over the entire folding trajectory of a protein and segmentation of the trajectory. These visualizations allow one to easily detect formation of secondary and tertiary structures as the protein folds.

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    • "In the light of abovementioned definition of SKDS, to our knowledge, deformable spanner (DS) (Gao et al., 2006) is the first SKDS that maintains its structure under formerly unknown motion models in 3D. DS supports all the criteria of uniformity, controllability, locality, being discrete and proximity based that a good KDS would provide (Alexandron et al., 2007; Russel and Guibas, 2005). These criteria facilitate spanner's usage in different application areas. "
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    ABSTRACT: Motivation: The medical imaging and image processing techniques, ranging from microscopic to macroscopic, has become one of the main components of diagnostic procedures to assist dermatologists in their medical decision-making processes. Computer-aided segmentation and border detection on dermoscopic images is one of the core components of diagnostic procedures and therapeutic interventions for skin cancer. Automated assessment tools for dermoscopic images have become an important research field mainly because of inter- and intra-observer variations in human interpretations. In this study, a novel approach—graph spanner—for automatic border detection in dermoscopic images is proposed. In this approach, a proximity graph representation of dermoscopic images in order to detect regions and borders in skin lesion is presented. Results: Graph spanner approach is examined on a set of 100 dermoscopic images whose manually drawn borders by a dermatologist are used as the ground truth. Error rates, false positives and false negatives along with true positives and true negatives are quantified by digitally comparing results with manually determined borders from a dermatologist. The results show that the highest precision and recall rates obtained to determine lesion boundaries are 100%. However, accuracy of assessment averages out at 97.72% and borders errors' mean is 2.28% for whole dataset. Contact:
    Full-text · Article · Jun 2010 · Bioinformatics
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    • "Since low size and low weight spanners are important, the greedy spanner is used in several applications, despite its high time complexity. For example, it has been used for protein visualization as a low-weight data structure, which is used as a contact map, that allows approximate reconstruction of the full distance matrix; see [21]. The authors needed a low weight spanner that consists of short edges because the interactions in a protein are local. "
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    ABSTRACT: The greedy algorithm produces high-quality spanners and, therefore, is used in several applications. However, even for points in d-dimensional Euclidean space, the greedy algorithm has near-cubic running time. In this paper, we present an algorithm that computes the greedy spanner for a set of n points in a metric space with bounded doubling dimension in O(n2logn)\ensuremath {\mathcal {O}}(n^{2}\log n) time. Since computing the greedy spanner has an Ω(n 2) lower bound, the time complexity of our algorithm is optimal within a logarithmic factor. KeywordsSpanner-Dilation-Stretch factor-Greedy algorithm-Doubling dimension
    Full-text · Article · Feb 2008 · Algorithmica
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    • "Although summary statistics are commonly used for comparison, they can only capture biased and limited global properties of the conformation. Recently, Russel et al. [3] suggested using geometric spanners for mapping a simulation to a more discrete combinatorial representation. They apply geometric spanners to discover the proximity between different segments of a protein across a range of scales, and track the changes of such proximity over time. "
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    ABSTRACT: Understanding the protein folding mechanism remains a grand challenge in structural biology. In the past several years, computational theories in molecular dynamics have been employed to shed light on the folding process. Coupled with high computing power and large scale storage, researchers now can computationally simulate the protein folding process in atomistic details at femtosecond temporal resolution. Such simulation often produces a large number of folding trajectories, each consisting of a series of 3D conformations of the protein under study. As a result, effectively managing and analyzing such trajectories is becoming increasingly important. In this article, we present a spatio-temporal mining approach to analyze protein folding trajectories. It exploits the simplicity of contact maps, while also integrating 3D structural information in the analysis. It characterizes the dynamic folding process by first identifying spatio-temporal association patterns in contact maps, then studying how such patterns evolve along a folding trajectory. We demonstrate that such patterns can be leveraged to summarize folding trajectories, and to facilitate the detection and ordering of important folding events along a folding path. We also show that such patterns can be used to identify a consensus partial folding pathway across multiple folding trajectories. Furthermore, we argue that such patterns can capture both local and global structural topology in a 3D protein conformation, thereby facilitating effective structural comparison amongst conformations. We apply this approach to analyze the folding trajectories of two small synthetic proteins-BBA5 and GSGS (or Beta3S). We show that this approach is promising towards addressing the above issues, namely, folding trajectory summarization, folding events detection and ordering, and consensus partial folding pathway identification across trajectories.
    Full-text · Article · Feb 2007 · Algorithms for Molecular Biology
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