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A PolynomialTime Algorithm for De Novo Protein Backbone Structure Determination from Nuclear Magnetic Resonance Data
"... We describe an efficient algorithm for protein backbone structure determination from solution Nuclear Magnetic Resonance (NMR) data. A key feature of our algorithm is that it finds the conformation and orientation of secondary structure elements as well as the global fold in polynomial time. This is ..."
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We describe an efficient algorithm for protein backbone structure determination from solution Nuclear Magnetic Resonance (NMR) data. A key feature of our algorithm is that it finds the conformation and orientation of secondary structure elements as well as the global fold in polynomial time. This is the first polynomialtime algorithm for de novo highresolution biomacromolecular structure determination using experimentally recorded data from either NMR spectroscopy or Xray crystallography. Previous algorithmic formulations of this problem focused on using local distance restraints from NMR (e.g., nuclear Overhauser effect [NOE] restraints) to determine protein structure. This approach has been shown to be NPhard, essentially due to the local nature of the constraints. In practice, approaches such as molecular dynamics and simulated annealing, which lack both combinatorial precision and guarantees on running time and solution quality, are used routinely for structure determination. We show that residual dipolar coupling (RDC) data, which gives global restraints on the orientation of internuclear bond vectors, can be used in conjunction with very sparse NOE data to obtain a polynomialtime algorithm for structure determination. Furthermore, an implementation of our algorithm has been applied to six different real biological NMR data sets recorded for three proteins. Our algorithm is combinatorially precise, polynomialtime, and uses much less NMR data to produce results that are as good or better than previous approaches in terms of accuracy of the computed structure as well as running time.
Efficient Protein Tertiary Structure Retrievals and Classifications Using Content Based Comparison Algorithms
, 2007
"... that in their opinion it is worthy of acceptance. ..."
THE FUNDAMENTAL GROUP, COVERING SPACES AND TOPOLOGY IN BIOLOGY
"... Abstract. We give a short introduction to homotopy theory. We pass to the concepts of a pointed space (X, x0), the fundamental group of X, a simply connected space (with the example of the space contractible to a point), introduce basic concepts of covering spaces (e.g. covering map/space, fiber ove ..."
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Abstract. We give a short introduction to homotopy theory. We pass to the concepts of a pointed space (X, x0), the fundamental group of X, a simply connected space (with the example of the space contractible to a point), introduce basic concepts of covering spaces (e.g. covering map/space, fiber over x, Path lifting Theorem). With the use of the exponential map and the idea of the index of a loop, we show that the fundamental group of the circle S 1 is isomorphic to the integers Z with addition. We mention some other interesting fundamental groups (e.g. the fundamental group of a torus or of the figure eight). We also present some very interesting applications of topological concepts in Molecular Biology. Algebraic topology tries to connect topological spaces with algebraical objects in such a way that topological problems can be translated into algebraical problems which can possibly be easier to solve. This paper is an introduction into the theory of homotopy and the basic concepts that concern it. Apart from the homotopy theory we present at the end of the paper interesting applications of topology in Molecular Biology. In the paper I denotes the closed interval [0, 1]. 1. Homotopy Definition 1 (Homotopy). Let X and Y be topological spaces. Let X ′ ⊂ X and f0, f1: X → Y be continuous and agree on X ′. f0 is homotopic to f1 relative to X ′ if there exists a continuous map F: X×I → Y such that F (x, 0) = f0(x), F (x, 1) = f1(x) for x ∈ X and F (x, t) = f0(x) for x ∈ X ′ and t ∈ I. If f0 and f1 are homotopic relative to X ′ we write f0 � f1 rel X ′. If X ′ = ∅ we omit writing rel X ′.
A TOPOLOGICAL CHARACTERIZATION OF PROTEIN STRUCTURE
"... We develop an objective characterization of protein structure based entirely on the geometry of its parts. The threedimensional alpha complex filtration of the protein represented as a union of balls (one per residue) captures all the relevant information about the geometry and topology of the mole ..."
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We develop an objective characterization of protein structure based entirely on the geometry of its parts. The threedimensional alpha complex filtration of the protein represented as a union of balls (one per residue) captures all the relevant information about the geometry and topology of the molecule. The neighborhood of a strand of contiguous alpha carbon atoms along the backbone chain is defined as a “tube ” which is a subcomplex of the original complex that has been subdivided. We then define a retraction for the tube to another complex that is guaranteed to be a 2manifold with boundary. We capture the topology of the retracted tube by computing the most persistent connected components and holes in the entire filtration. A “motif ” for 3D structure is characterized by the number of persistent 0 and 1cycles, and the relative persistences of these cycles in the filtration of the “tube ” complex. These motifs represent nonrandom, recurrent, tertiary interactions between parts of the protein backbone chain that characterize the overall structure of the protein. A basis set of 1300 motifs are identified by analyzing the alpha complex filtrations of several proteins. Any test protein is represented by the number of times each motif from the basis set occurs in it. Preliminary results from the discrimination of protein families using this representation are provided.
BMC Bioinformatics BioMed Central Methodology article
, 2008
"... Using the longest significance run to estimate regionspecific pvalues in genetic association mapping studies ..."
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Using the longest significance run to estimate regionspecific pvalues in genetic association mapping studies
A MultiAdvisor Evaluation Module for the Accurate Prediction of Alpha Helix Pairs
, 2007
"... Accurate 3D protein structure prediction is one of the most challenging problems facing bioinformaticians today. This thesis develops and examines an evaluation module for ranking predicted supersecondary structures – specifically αhelix pairs – as part of a casebased reasoning system. The propos ..."
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Accurate 3D protein structure prediction is one of the most challenging problems facing bioinformaticians today. This thesis develops and examines an evaluation module for ranking predicted supersecondary structures – specifically αhelix pairs – as part of a casebased reasoning system. The proposed module is part of the Triptych project, which aims at the accurate prediction of the threedimensional structure of proteins from contact maps. Triptych is an advanced casebased reasoning system that utilizes a library of existing protein structures and motifs to help predict the structure of a known polypeptide chain of amino acids that represents a target αhelix pair. The proposed module evaluates possible solutions by integrating multiple strategies, learning methods and sources of knowledge in the form of expert advisors. It uses advisors which integrate knowledge from the fields of biology, biochemistry, classical physics, and statistical data analysis obtained from predetermined structures. Lastly, the proposed evaluation module would allow for the integration of more sources of knowledge, in the form of expert advisors, as well as serve as a framework for evaluating other structural motifs in future. i Acknowledgements I would like to thank Dr. Glasgow, and the entire Triptych team in the Molecular Scene Analysis lab at Queen’s University. This work would not be possible without their continued feedback and support. In particular, I would like to thank Tony Kuo, Jim Davies, and Robert Fraser, whom have all contributed a large amount of their time and research towards this project. I would also like to thank Mireille Gomes, Anjli Patel,
A Hierarchical Neighbor Finding Strategy for SamplingBased Motion Planning
"... Abstract — SamplingBased Motion Planning (SBMP) has been successful in planning the motion for a wide variety of robot types. An important primitive of these methods is selecting candidate neighbors and validating/invalidating the pathways between nodes of the map. These neighbors are commonly sele ..."
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Abstract — SamplingBased Motion Planning (SBMP) has been successful in planning the motion for a wide variety of robot types. An important primitive of these methods is selecting candidate neighbors and validating/invalidating the pathways between nodes of the map. These neighbors are commonly selected based on some distance metric (DM). An ideal distance metric for SBMP should identify configurations visible to each other, i.e., connectible by some local planner, such as straightline interpolations. However, no perfect DM exists as different DMs capture different aspects of configurations. In this work, we introduce a Hierarchical Neighbor Finding Strategy that applies multiple DMs in series. There are two main benefits of this strategy. First, this strategy applies cheaper and less accurate DMs to be used; then in succession, more expensive and accurate DMs can be applied on iteratively reduced sets of configurations, yielding high quality neighbor selection with reduced computation time. Additionally, this strategy enables the ability to use complementary DMs that handle different aspects of the geometry at once, which we show through the combination of a Knot Theory distance and a Scaled Euclidean disctance for highly articulated linkages. Our results show that this Hierarchical Neighbor Finding Strategy provides improved performance in terms of connectivity and efficiency for Probabilistic Roadmap Methods for DOF up to 1024. We also demonstrate how our method can provide improvements for roadmapbased protein folding applications. I.