Download Directions in Protein Contact Map Mining

Directions in Protein Contact
Map Mining
Mohammed J. Zaki
Computer Science Dept.
joint work with
Jingjing Hu & Xiaolan Shen, CS Dept.
Yu Shao & Prof. Chris Bystroff, Biology Dept.
Rensselaer Polytechnic Institute, Troy NY
Protein Structures

Primary structure
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Un-branched polymer
20 side chains (residues or amino acids)
PDB file 2IGD: MTPAVTTYSLVINGLTLSGU…..
Higher order structures
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Secondary: local (consecutive) in sequence
Tertiary: 3D fold of one polypeptide chain
Quaternary: Chains packing together
PDB protein 2IGD
Anti-parallel Beta Sheets
Alpha Helix
Parallel Beta Sheets
The Protein Folding Problem
Contact Map
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Amino acids Ai and Aj are in contact if
their 3D distance is less than contact
threshold (e.g., 7 Angstroms)
Sequence separation is given as |i-j|
Contact map C is a symmetric N x N
matrix with
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C(i,j) = 1 if Ai and Aj are in contact
C(i,j) = 0 otherwise
Consider all pairs with |i-j| >= 4
Amino Acid Aj
Parallel Beta Sheets
Anti-parallel Beta Sheets
Contact Map (2IGD)
Alpha Helix
Amino Acid Ai
Characterizing Physical, Proteinlike Contact Maps
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A very small subset of all contact maps
code for physically possible proteins
(self-avoiding, globular chains)
A contact map must:
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Satisfy geometric constraints
Represent low-energy structure
Characterizing Physical Contact
Maps in Proteins
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What are the typical non-local
interactions?
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Frequent dense 0/1 sub-matrices in contact
maps
3-step approach
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Dense pattern mining
Pruning mined patterns
Clustering dense patterns (non-local pattern
signatures)
Dense Pattern Mining
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Frequent 2D Pattern Mining
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Use WxW sliding window; W window size
Measure density under each window
(N-W)2 / 2 possible windows for N length
protein
Look for “minimum density” (number of 1’s)


scale away from diagonal
Try different window sizes
Counting Dense Patterns
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Naïve Approach: for W=5, N=60 there
are 1485 windows per protein.
28 million possible windows for 18,544
proteins (in PDB)
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Test if two sub-matrices are equal
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Linear search: O(P x W2) with P current dense
patterns
Hash based: O(W2)
Our Approach: 2-level Hashing
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O(W) time
Pattern (WxW Sub-matrix)
Encoding
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Encode sub-matrix as string (W ints)
Sub-matrix Integer Value
00000
0
01100
12
01000
8
01000
8
00000
0
Concatenated String: 0.12.8.8.0
Two-level Hashing
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String-ID(M) =
v1.v2 .....vW
W
h1( M )   v
i
i 1
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Level1 (approximate):
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Level2 (exact): h2(M) = String-ID(M)
Binding Patterns to Protein
Sequence and Structure
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StringID:0.12.8.8.0, Support = 170 (window size W=5)
00000
01100
01000
01000
00000
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Occurrences:
pdb-name (X,Y) X_sequence Y_sequence
1070.0
52,30
ILLKN TFVRI
1145.0
51,13
VFALH GFHIA
1251.2
42,6
EVCLR GSKFG
1312.0
54,11
HGYDE ATFAK
1732.0
49,6
HRFAK KELAG
2895.0
49,7
SRCLD DTIYY
...
Interaction
alpha::beta
alpha::strand
alpha::strand
alpha::beta
alpha::beta
alpha::beta
Frequent Dense Local Patterns
Submatrix
0 0
0
0 0
1
0 0
0
0 0
0
0 0
0
0 0
0
0 1
0
1 0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0 0 0
0 0 0
0 0 1
0 1 0
1 0 0
0 0 0
0 0 0
0 0 0
0 0
0
0 0
0
0 0
0
0 0
0
1 0
0
1 1
0
1 1
0
0 1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 0 0
1 0
0
1 1
0
1 1
0
0 1
0
0 0
0
0 0
0
0 0
1
0 0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0 0 0
0 0 0
0 0 0
1 0 0
1 1 0
1 1 1
0 1 1
0 0 1
Pruning Patterns
Same pattern (shifted to right) but different String-IDs
00000
01000
01000
01000
00000
00000
00100
00100
00100
00000
00000
00010
00010
00010
00000
Merge horizontally or vertically shifted patterns
Prune away the local patterns (alpha/beta)
Dense Pattern Mining Results
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2702 non-redundant proteins from PDB
Min-Support = 1 (exhaustive patterns)
Window size = 5, Min-Density = 5
Contact Threshold
5 Angstroms
Number of Patterns
2508
6 Angstroms
9929
7 Angstroms
21231
Frequent Dense Non-Local
Patterns
Alpha – Alpha
Alpha – Beta Sheet
Frequent Dense Non-Local
Patterns
Alpha – Beta Turn
Beta Sheet – Beta Turn
Clustering Dense Patterns
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Distance: Mi, Mj are dense sub-matrices
W2
d ( M i , M j )   | M i [k ]  M j [k ] |
k 1
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Use agglomerative hierarchical clustering
Find each cluster’s (c) representative (n patterns)
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Conceptually the super-imposition of n sub-matrices
Compute contact probability at each position
n
pc [k ] 
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 M [k ]
i
i 1
n
Note a 1 whenever contact probability is more than a probability
threshold
Cluster Representative
Contact Probabilities:
0: 0.05
1: 0.05
2: 0.68
5: 0.03
6: 0.02
7: 0.14
10: 0.05 11: 0.05 12: 0.12
15: 0.03 16: 0.05 17: 0.15
20: 0.25 21: 0.10 22: 0.59
3: 0.85
8: 0.07
13: 0.09
18: 0.27
23: 0.92
Representative contact pattern:
00111
00000
00000
00001
00011
4: 0.71
9: 0.09
14: 0.03
19: 0.85
24: 0.83
Clustering Quality
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High and low value of pc[k] are good (most
cluster members agree on k)
For a cluster c, define quality Qc:
W2
Sc1   pc [k ], ( pc [k ]  0.5)
k 1
W2
Sc0  1  pc [k ], ( pc [k ]  0.5)
Qc  S  S
1
c
k 1
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Overall clustering quality (0.5 <= Q <= 1)
NC
Q
| c | Q
i 1
i
NP
ci
NC = Number of Clusters
NP = Number of Patterns
0
c
Example 1: Mined Cluster
#1355 #3496 #6282 #7980 representative
00011
00011
01111
11000
10000
00001
00101
11111
11000
10000
00010
00000
11000
10000
10000
00011
00101
11100
10000
00000
00011
00001
11100
10000
10000
Cluster patterns (beta-beta strand)
Example 2: Mined Cluster
#196
#503
#2834
#8697
representative
11010
01111
01000
01000
11000
01000
01110
01000
01000
11000
11000
01100
01110
01000
01000
11010
01110
01100
01100
01000
11000
01110
01000
01000
01000
Cluster Patterns (beta-beta turn)
Clustering Results
Contact
Threshold
5A
Number of Number of Cluster
Patterns
Clusters
Quality
2508
83
0.89
6A
9929
99
0.86
7A
21231
367
0.84
Future Work
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Comprehensive list of non-local motifs
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I-sites library (by Prof. Bystroff) catalogs
local motifs
Future Directions
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Improving prediction of contact maps
Mining heuristic rules for “physicality”
Protein folding pathways
Improving Contact Map
Prediction
Physically Impossible
Physically Impossible
Mining Physicality Rules
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Mining heuristic rules for “physicality”
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Based on simple geometric constraints
Rules governing contacts and non-contacts
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Parallel Beta Sheets:
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Anti-parallel Beta Sheets:
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If C(i,j) = 1 and C(i+2,j+2) = 1,
then C(i,j+2) = 0 and C(i+2,j) = 0
If C(i,j+2) = 1 and C(i+2,j) = 1,
then C(i,j) = 0 and C(i+2,j+2) = 0
Alpha Helices:
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If C(i,i+4) = 1, C(i,j) = 1, and C(i+4,j) = 1,
then C(i+2,j) = 0
Heuristic Rules of Physicality
Anti-parallel Beta Sheets
i+2
j
i
j+2
If C(i,j+2) = 1 and C(i+2,j) = 1,
then C(i,j) = 0 and C(i+2,j+2) = 0
Heuristic Rules of Physicality
Parallel Beta Sheets
i+2
j+2
i
j
If C(i,j) = 1 and C(i+2,j+2) = 1,
then C(i,j+2) = 0 and C(i+2,j) = 0
Heuristic Rules of Physicality
Alpha Helix
i+4
j
i+2
i
If C(i,j) = 1 and C(i+4,j) = 1 and C(I,i+4) = 1,
then C(i+2,j) = 0
Protein Folding Pathways
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Rules for Pathways in Contact Map Space
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Pathway is time-ordered sequence of contacts
Consider only native contacts (those that are
present in the true map)
Condensation rule: New contacts within Smax
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U(i,j) <= Smax; U(i,j) unfolded residues from i to j
Pathway prediction is complementary to
structure prediction
Contact Map Folding Pathways