docking iii: matching via critical points yusu wang joint work with p. k. agarwal, h. edelsbrunner,...
TRANSCRIPT
Docking III:Matching via Critical Points
Yusu Wang
Joint Work with P. K. Agarwal, H. Edelsbrunner, J. Harer
Duke University
Motivation
Docking problem Partial matching Two steps
Find coarse matching Local improvement
Input: protein A and B Output: a set of coarse alignments
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
Our Approach
Overview:
Step 1. Extract critical points Design Morse function
Step 2. Align critical points Use both topological and geometric info.
Critical Points
: manifold (closed curves/surfaces) : Morse function Critical points: min, max, saddles for
RMF :
M
F
max saddle min
Pairing
Critical points capture topological information Critical pairs, persistence of critical pairs
Some Morse Functions
Curvature Too local
Connolly function Ratio of inside/outside perimeters
Atomic Density Function
Proposed by Kuhn et al.
Best fit
cy cp )(
c
416 100
in 3D
Height Function
Atomic density function: Critical points nice Critical pairs good for removing noise But …
Height function Captures good features in vertical direction
Elevation Function
Each point critical in normal direction
Define )()()( qpkp n
Surgery
However: not continuous
MM̂
RM ˆ:
Blame the manifold! : apply surgery on Elevation function:
in 2D
~12~30
Surgery in 2D
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))
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
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
Illustration
2D Results
NaiveMatch
PairMatch
2D Results – Cont’
: top r ranked transformations of : top s ranked transformations of How well does covers ?
sTnaiveT
rTpairT
sT rT
Future Work
Implement Elevation function in 3D Better matching algorithm in 3D?
Local improvement starting from a position with collision