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Segmenting Low-resolutional Deforming Protein Structures

Segmenting Low-resolutional Deforming Protein Structures. Yusu Wang 08/22/2005 Joint work with Leo Guibas. Introduction. Molecular structure Crucial in understanding functionality Hard to obtain high-resolution struct. Snapshots Low-resolution structure Cryo-EM :

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Segmenting Low-resolutional Deforming Protein Structures

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  1. Segmenting Low-resolutional Deforming Protein Structures Yusu Wang 08/22/2005 Joint work with Leo Guibas

  2. Introduction • Molecular structure • Crucial in understanding functionality • Hard to obtain high-resolution struct. • Snapshots • Low-resolution structure • Cryo-EM : • Fitting detailed atomic structure • Direct manipulation ITR 08/22/05

  3. Motivation • Snapshots : • Several conformations of one protein • Goal: • No atomic structure (low resolution) • Study deformation, pathways .. etc ITR 08/22/05

  4. Problem • Input: • Two surfaces • Roughly rigid sub-components • Output: • Segmentation • Correspondence identification ITR 08/22/05

  5. Where is the Difficulty • Coarse (rigid) alignments • Not too hard • Nearest neighbors • Based on Euclidean / normals not good Inherent coordinates invariant to such motion ITR 08/22/05

  6. Geodesic Distances • To get a coord. sys: • Use landmarks: one set on each surface • A: (a1, a2, .., ak) • B: (b1, b2, .., bk) • Geodesic dist to landmarks • Landmarks: • A few reliable correspondences • At least one from each component ITR 08/22/05

  7. Approach Overview • Identify a few landmarks from each surface • Induce segmentation / correspondences ITR 08/22/05

  8. Preprocessing • Given surfaces A and B: • Compute elevation max for each surface • Each max: a point pair capturing a meaningful feature • P (Q): set of points from elevation max from A (B) • P’(Q’) : set of corresponding point-pairs ITR 08/22/05

  9. Idea 1 : Every good Alignment Counts • Align any two elevation pairs • p from P’ and q from Q’ • Score the resulting alignments • Collect S: • Set of good alignments (i.e., with high score) ITR 08/22/05

  10. Idea 2: Majority Wins • Given an alignment: • Coord.: (x, y, z, d1, d2) • NN(p) : nearest neighbor of p  Pin Q • Distance measure: • both geometric and geodesic • Given S : • Vote(p, q) : number of times q Q is NN(p) • High votes indicates reliable correspondences ITR 08/22/05

  11. Idea 3: Point is Not Enough • Molecular surfaces: • Homogeneous • Point is not discriminative enough • Larger features: • Segments, triangles, etc • Balance between complexity and quality Vote for point-pairs, instead of points ITR 08/22/05

  12. Putting Everything Together • Given A and B • Compute set of elevation max P, Q, (P’, Q’) • Compute S • By aligning point-pairs P’ and Q’ • For each point-pair from P’, vote for its NN in Q’ • Based on only good alignments S • Take top votes • C: a set of reliable correspondences between point-pairs ITR 08/22/05

  13. Select Landmarks • C : a set of good corresponding point-pairs • Choose top-ranked pair • Choose second pair • Output: • 2 pairs (4 points) on each surface ITR 08/22/05

  14. Approach Overview • Identify a few landmarks • Induce segmentation / correspondences ITR 08/22/05

  15. Segmentation • Given 4 landmarks on each surface • Coord.: • (x, y, z, d1, d2, d3, d4) • Point-pairs p1(q1) and p2(q2) • Align p1 with q1 => transformation T1 • Align p2 with q2 => transformation T2 align component 1 align component 2 ITR 08/22/05

  16. 2 1 Segmentation -- cont. • To segment component 1 and 2: • Define f : A -> R as • f (x) = Dist (x, NN(x, T (B) ) ) • f (x) = Dist (x, NN(x, T (B) ) ) • Classify x  A to be in component • 1 : if f (x) < f (x) • 2 : otherwise i 1 1 2 2 1 2 ITR 08/22/05

  17. Another Example ITR 08/22/05

  18. Next Step • Correspondence based on segmentation • More correspondences based on landmarks • As-rigid-as-possible deformation • Pseudo-atoms that respects the segmentation • Normal modes analysis • What if geodesics also fail ? • Voting + virtrual coordinates ITR 08/22/05

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