Alpha Shapes Herbert Edelsbrunner Duke University, Computer Science (Raindrop) Geomagic LEIDEN 2006.
Docking III: Matching via Critical Points Yusu Wang Joint Work with P. K. Agarwal, H. Edelsbrunner,...
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Transcript of Docking III: Matching via Critical Points Yusu Wang Joint Work with P. K. Agarwal, H. Edelsbrunner,...
![Page 1: Docking III: Matching via Critical Points Yusu Wang Joint Work with P. K. Agarwal, H. Edelsbrunner, J. Harer Duke University.](https://reader034.fdocuments.in/reader034/viewer/2022051517/5697bfeb1a28abf838cb81dc/html5/thumbnails/1.jpg)
Docking III:Matching via Critical Points
Yusu Wang
Joint Work with P. K. Agarwal, H. Edelsbrunner, J. Harer
Duke University
![Page 2: Docking III: Matching via Critical Points Yusu Wang Joint Work with P. K. Agarwal, H. Edelsbrunner, J. Harer Duke University.](https://reader034.fdocuments.in/reader034/viewer/2022051517/5697bfeb1a28abf838cb81dc/html5/thumbnails/2.jpg)
Motivation
Docking problem Partial matching Two steps
Find coarse matching Local improvement
Input: protein A and B Output: a set of coarse alignments
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Matching Surfaces
Model protein As a surface instead of set of balls
Sample special points Knobs and caves
Align two sets of points Under collision-free constraint
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Our Approach
Overview:
Step 1. Extract critical points Design Morse function
Step 2. Align critical points Use both topological and geometric info.
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Critical Points
: manifold (closed curves/surfaces) : Morse function Critical points: min, max, saddles for
RMF :
M
F
max saddle min
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Pairing
Critical points capture topological information Critical pairs, persistence of critical pairs
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Some Morse Functions
Curvature Too local
Connolly function Ratio of inside/outside perimeters
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Atomic Density Function
Proposed by Kuhn et al.
Best fit
cy cp )(
c
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416 100
in 3D
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Height Function
Atomic density function: Critical points nice Critical pairs good for removing noise But …
Height function Captures good features in vertical direction
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Elevation Function
Each point critical in normal direction
Define )()()( qpkp n
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Surgery
However: not continuous
MM̂
RM ˆ:
Blame the manifold! : apply surgery on Elevation function:
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in 2D
~12~30
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Surgery in 2D
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Alignment
Input: Two proteins A and B (P and Q) Two sets of critical points/pairs
Output: Set of transformations for protein B
Sorted by score(A, T(B))
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NaïveMatch
NaiveMatch Alg:
Output:
Take a pair from P, a pair from Q Align two pairs, get transformation T Compute score between A and T(B) Rank transformations by score
naiveT
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PairMatch
PairMatch Alg: Take a critical pair from each set Align two critical pairs, get transformation T Rank T ’s by their scores
Output: pairT
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Illustration
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2D Results
NaiveMatch
PairMatch
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2D Results – Cont’
: top r ranked transformations of : top s ranked transformations of How well does covers ?
sTnaiveT
rTpairT
sT rT
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Future Work
Implement Elevation function in 3D Better matching algorithm in 3D?
Local improvement starting from a position with collision