Segmenting Low-resolutional Deforming Protein Structures
Yusu Wang
08/22/2005
Joint work with Leo Guibas
ITR 08/22/05
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
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Motivation
Snapshots : Several conformations
of one protein
Goal: No atomic structure
(low resolution) Study deformation,
pathways .. etc
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Problem
Input: Two surfaces Roughly rigid sub-
components
Output: Segmentation Correspondence
identification
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Where is the Difficulty
Coarse (rigid) alignments Not too hard
Nearest neighbors Based on Euclidean /
normals not good
Inherent coordinates invariant to such motion
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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
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Approach Overview
Identify a few landmarks from each surface
Induce segmentation / correspondences
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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
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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)
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Idea 2: Majority Wins
Given an alignment: Coord.: (x, y, z, d1, d2) NN(p) : nearest neighbor of p P in 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
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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
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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
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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
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Approach Overview
Identify a few landmarks
Induce segmentation / correspondences
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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
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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
i1 1
1 2
1 2
2 2
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Another Example
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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
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