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Mining Patterns from Protein Structures

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Mining Patterns from Protein Structures

Wei Wang

University of North Carolina at Chapel Hill

- Introduction
- Motivation
- Challenges

- Graph-based Pattern Discovery in Protein Structures
- Applications
- Conclusions
- Future Directions

Lys

Lys

Gly

Gly

Leu

Val

Ala

His

Oxygen

Nitrogen

Carbon

Sulfur

Ribbon

- Protein
- A sequence from 20 amino acids
- Adopts a stable 3D structure that can be measured experimentally

Serine protease active center

1HJ9

1R64

1SSX

- Structure patterns are geometric arrangements of amino acids that are common to a group of different proteins.

Three proteins with the same function

- Structure patterns are useful in:
- Protein structure alignment
- Protein design
- Prediction of protein-protein interactions
- Understanding protein folding
- Drug design

- Develop techniques to discover structure patterns that are
- Efficient
- Effective

Growth of Known Structures in Protein Data Bank

35,000

The total number of known

protein structures

Newly characterized proteins

in that year

# of structures

1988

2005

Year

- Define mathematical models to represent protein structures
- Point set
- Labeled graph

- Define computational components
- Define structure pattern
- Specify a matching condition
- Design a search procedure

- Evaluate the results
- computational efficiency and effectiveness

….

- The ball-stick model is an element-based structure representation
- A structure is decomposed into a set of amino acids
- Proteingeometry,topology,andattributesare defined with respect to the amino acid set

- The definition of patterns
- Geometry vs. topology

- The matching condition
- Measures the fitness of a pattern to a set of protein structures

- The search procedure

Protein Local Structure Comparison Problem

Pattern Discovery

Pattern Matching

- ASSAM, Artymiuk et al., JMB’94
- TESS, Wallace et al., Prot. Sci. ‘97

Sequence-dependent

Sequence-independent

- TRILOGY, Bradley et al., RECOMB’01

Multi-way comparison

Pair-wise comparison

- PINTS, Russell, JMB’98
- Geometric Hashing, Fischer et al., Prot. Sci.’94
- Graph Matching, Schmitt et al., JMB’02
- Evolutionary Trace, Lichtarge et al., JMB’96

- FFSM & its variants, Huan et al., ICDM’03, RECOMB’04, CSB’06

Huan et al. Advances in Computers

A group of protein structures

Represent each structure as a labeled graph

Discover frequent occurring subgraphs

Map subgraphs to protein structures and obtain structure patterns

Predict protein function

Identify functional sites in proteins

Discover patterns in structure evolution

- Introduction
- Graph-based Pattern Discovery in Protein Structures
- Labeled graphs and representing structures as labeled graphs
- Frequent subgraph mining

- Applications
- Conclusions
- Future Directions

p5

p2

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y

p1

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p4

p3

G1

q1

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s2

q2

a

a

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y

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b

s3

q3

G3

G2

- A labeled graph is a graph where each node and each edge has a label.

- Use a labeled graph to represent a protein structure
- Nodesrepresent amino acids,labeled by theidentityof the amino acids
- Edgesconnect two amino acids if their Euclidian distance is less than a certain threshold

Contact

A protein

p5

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g3

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G2

G

- A graph G is subgraph isomorphic to a graph G’, denoted by G G’, if
- there exists a 1-1 mapping from nodes in G to G’ such that node labels, edges, and edge labels are preserved with the mapping.

- A pattern is a graph. Pattern Gmatches G’ if G G’
- Goccurs in G’ if G G’.
- With a label set, a graph space is a collection of graphs whose labels are from the set.

- The support value of a pattern P in a collection of graphs G is the fraction of graphs in G where Poccurs.
- Given a collection of graphs G and a threshold 0 < 1, the frequent subgraph mining problem is the identification of all patterns that have support at least .

p5

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+

P6

P5

s3

q3

+

P4

G3

G2

The induced subgraph isomorphism penalizes any unmatched edges

= 2/3

b

y

f=2/3

f=0/3

f=2/3

f = 1/3

f = 3/3

a

y

b

P1

+: induced frequent subgraphs

p5

p2

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f=3/3

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f=2/3

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f=2/3

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P6

P5

s3

q3

P4

G3

G2

Maximal frequent subgraph are ones that none of their supergraphs are frequent

Other criteria for selecting subgraphs may be incorporated

= 2/3

f=2/3

!

P3

!: Maximal frequent subgraphs

- Task: identify all frequently occurring subgraphs from a group of graphs, or a graph database
- Support anti-monotonicity
- Any supergraph of an infrequent subgraph is infrequent
- Known as the Apriori property

- Level-wise search
- Keep all patterns with the same size in memory (poor memory utilization)

- Depth-firstsearch
- Better memory utilization
- May repeatedly search patterns in the DAG (redundant candidates)

- Level-wise search
- AGM: Inokuchi et al., PKDD’00
- FSG: Kuramochi & Karypis, ICDM’01

- Depth-first search
- gSpan, Yan & Han, ICDM’02, KDD’03
- FFSM, Huan et al., ICDM’03

- Path-based search
- Vanetik, et al., ICDM’02, ICDE’04
- GASTON: Nijssen & Kok, KDD’04

- Tree-based search
- SPIN, Huan et al., SIGKDD’04

- Mining with constraints
- CSM, Huan et al., CSB’06

- Graph normalization
- Graph Canonical Adjacency Matrix Tree (CAM Tree)
- Incremental subgraph isomorphism test

Huan et al. ICDM 2003

An arbitrary set

A Graph Space

A partial order defined on the graph space

A 1-1 mapping

A partial order defined on

- With a partially ordered set (, ),φ: G* → that maps a graph space G* to is a graph normalization function if φ is a 1-1 mapping.
- (mapping partial orderφ) Given a graph normalization φandits codomain(, ), we define a binary relation
φ G* G* such that P φQ if φ(P) φ(Q)

- Claim: φis a partial order

- Given a partially ordered codomain (, ),a normalization functionφ: G* → is an ideal normalization if
- φinduces a search tree (No redundant candidates)
- φ is a subset of the subgraph relation, i.e. for all graphs P and Q, P φQ implies PQ (anti-monotonicity of support )

p’2

P1 P2 P3 P4

P1 P2 P4 P3

P1 P4 P2 P3

b

x

p’1

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p’4

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M3

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(P’)

y

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(P)

- The Canonical Code (θ)maps a graph G to a string.
- Claim:θ: G* → (*, ) is a graph normalization
θ: G* → (*, ) is an ideal graph normalization

Code(M1): (1, 1, a)(2, 1, x) (2, 2, b) (3, 1, x) (3, 2, y) (3, 3, b) (4, 2, x) (4, 4, c)

Code(M1): (1, 1, a)(2, 1, x) (2, 2, b) (3, 1, x) (3, 2, y) (3, 3, b) (4, 2, x) (4, 4, c) <

Code(M2):(1, 1, a)(2, 1, x) (2, 2, b) (3, 2, x) (3, 3, c) (4, 1, x) (4, 2, y) (4, 4, b) <

Code(M3): (1, 1, a)(2, 2, c) (3, 1, x) (3, 2, x) (3, 3, b) (4, 1, x) (4, 3, y) (4, 4, b)

θ(P) = (1, 1, a)(2, 1, x) (2, 2, b) (3, 1, x) (3, 2, y) (3, 3, b) (4, 2, x) (4, 4, c)

- (i, j, Mi,j) (k, l, Mk,l) if
- i < k, or
- i = k, j < l, or
- i =k, j = l, Mi,j Mk,l

- Task: identify all frequently occurring subgraphs from a family of graphs
- Depth-firstsearch
- Better memory utilization

- Apriori property
- Eliminate unnecessary isomorphism checks

- Graph normalization
- Avoid redundant examination

- Subgraph isomorphism test is NP-complete
- Incremental isomorphism check

- Applies to frequent induced subgraph mining with minor modifications

+

O

=

_

_

C

C

C

Running time (s)

PTE (Predictive Toxicology Evaluation) data set

- Contains 340 chemicals
- Performances were collected from literatures where experiments were performed with different hardware configurations (400Mhz PIII to 2GHz PIV)
- Software downloadable from http://www.cs.unc.edu/~huan

- AGM: Inokuchi et al. PKDD’00
- FSG: Kuramochi & Karypis, ICDM’01
- gSpan: Yan & Han, ICDM’02

- FFSM: Huan et al. ICDM’03
- Gaston: Nijssen & Kok, KDD’04

Running time (s)

Serine protease:

- Contains 40 proteins
- Contact is defined between every pair of distinct residues if the distance between their C atoms is less than a certain upper-bound (e.g. 6.5 angstrom)
- Performances were measured in a single 2GHz PIV CPU with 2GB main memory
- gSpanhandles graphs with no more than 254 edges
- Gaston runs out of memory

- Introduction
- Graph-based Pattern Discovery in Protein Structures
- Applications
- MotifSpace Architecture
- Identify functional sites in proteins
- Predict protein function

- Conclusions
- Future Directions

- Serine proteases have three subclasses
- Subtilisins
- Eukaryotic serine proteases
- Prokaryotic serine proteases

1HJ9

1R64

1SSX

- 20 highly specific patterns mined from serine proteases

# of patterns is the total number of fingerprints a protein has. The coverage of a protein is the fraction of residues which are covered by at least one fingerprint (%), Length (of the protein) is displayed in unit of 200 residues

1HJ9

1MD8

1OP0

1OS8

1PQ7

1P57

1SSX

1S83

- Papain-like cysteine proteases
- Nuclear receptor ligand binding domains
- NADP/FAD binding proteins

Papain-like cysteine protease Nuclear Binding domains NADP binding proteins

How does a protein function in a biological system?

Function

Functional motifs carry out protein function

3D structure of a protein

Abr. Name #M #P

#M: number of members in a family

#P: number of patterns obtained from the family

- TIM barrel Fold contains many proteins with similar structures but different functions

Bandyopadhyay, Huan et al. Prot. Sci. ‘06

1ecs

1twu

Yyce

SCOP 54598

Antibiotic resistance protein

Glyoxalase / bleomycin resistance / dioxygenase superfamily

4 members (SCOP 1.65), 62 family specific spatial motifs

unknown function, not in SCOP 1.67, DALI z < 10 in Nov 2004

46 motifs found, structurally similar to the three new non-redundant AR proteins added in SCOP 1.67

G

O

C

A

T

H

S

C

O

P

Biological

Experiments

Protein

Data Bank

testable hypotheses

Experimental validation

protein

structures

protein family

Pattern

Filter

Pattern

Miner

Protein

Classifier

Pattern

Validation

Subgraph

mining

Visualization

Classification

Feature

selection

structure

patterns

family-specific

patterns

Structure Pattern

Database

Functional Motifs

Knowledgebase

Indexing &

Search

Knowledge

management

Huan et al. ISMB’05 demo, http://escience2-cs.cs.unc.edu/Default.aspx

Goal: pattern discovery in protein structures

- Develop labeled graph representations for protein structures
- Design algorithms to identify recurring subgraphs in a collection of graphs
- Frequent, constrained, maximal, or coherent subgraph mining
- Performance evaluation on various data sets

- Collaborate with domain experts to evaluate the utility of the algorithms
- Predict function for protein structures
- Identify structure patterns in protein fold families

- Pattern discovery in protein structures
- Approximate pattern discovery
- More applications:
- Protein-protein interaction
- Protein subcellular localization

Data Models Biological Data Volume

Biological systems at the molecular level

- Challenges:
- What are the nature of the data from biological systems?
- What are the computational tasks?
- How to divide the tasks into a group of computational components?
- How to evaluate the results?

Source: http://bioinformatics.ca/workshop_pages/bioinformatics/

- Collaborators: Charlie Carter (UNC School of Medicine), Nikolay Dokholyan (UNC School of Medicine),Leonard McMillan, Jan Prins, Jack Snoeyink,Alexander Tropsha (UNC School of Pharmacy)
- Students: Deepak Bandyopadhyay, Yetian Chen (UNC School of Pharmacy), Jun Huan, Jinze Liu, Ruchir Shah (UNC School of Pharmacy), Kiran Sidhu, Xueyi Wang, David Williams, Tao Xie, Jingdan Zhang