Data Mining for Protein Structure Prediction

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Data Mining for Protein Structure Prediction

• Mohammed J. Zaki
• SPIDER Data Mining Project Scalable, Parallel
  and Interactive Data Mining and Exploration at
  RPI
• http//www.cs.rpi.edu/zaki

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Outline of the Talk

• How do proteins form?
• Protein folding problem
• Contact map mining
• Using HMMs based on local motifs
• Mining physical dense frequent patterns
  (non-local motifs)
• Future directions
• Heuristic rules
• Folding pathways

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How do Proteins Form?
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How do Proteins Form?

• Building Blocks of Biological Systems
• DNA (nucleotides, 4 types) information
  carrier/encoder
• RNA bridge from DNA to protein
• Protein (amino acids, 20 types) action
  molecules.
• Processes
• Replication of DNA
• Transcription of gene (DNA) to messenger RNA
  (mRNA)
• Splicing of non-coding regions of the genes
  (introns)
• Translation of mRNA into proteins
• Folding of proteins into 3D structure
• Biochemical or structural functions of proteins

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Protein Folding Problem
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Protein Structures

• Primary structure
• Un-branched polymer
• 20 side chains (residues or amino acids)
• Higher order structures
• Secondary local (consecutive) in sequence
• Tertiary 3D fold of one polypeptide chain
• Quaternary Chains packing together

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Amino Acid
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Polypeptide Chain
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Torsion Angles
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The Protein Folding Problem
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Contact Map Mining
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Contact Map

• Amino acids Ai and Aj are in contact if their 3D
  distance is less than threshold (7å)
• Sequence separation is given as i-j
• Contact map C is an N x N matrix, where
• C(i,j) 1 if Ai and Aj are in contact
• C(i,j) 0 otherwise
• Consider all pairs with i-j gt 4

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Protein 2igd 3D Structure
Anti-parallel Beta Sheets
Alpha Helix
Parallel Beta Sheets
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Contact Map (2igd PDB)
Anti-parallel Beta Sheets
Parallel Beta Sheets
Alpha Helix
Amino Acid Aj
Amino Acid Ai
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How much information in Amino Acids Alone
Classification Problem

• A pair of amino acids (Ai,Aj) is an instance
• The class C (1) or NC (0), i.e., contact or
  non-contact
• Highly skewed class distribution
• 1.7 C and 98.3 NC 300K C vs 17,3M NC
• Features for each instance
• Ai and Aj
• Class C or NC

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Predicting Protein Contacts

• Predict contacts for new sequence

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Classification via Association Mining

• Association mining good for skewed data
• Mining Mine frequent itemsets in C data (Dc)
• P(X Dc) Frequency(X Dc) / Dc
• Counting find P(X Dnc)
• Pruning
• Likelihood of a contact r P(XDc) / P(XDnc)
• Prune pattern X if ratio r of contact to
  non-contact probability is less then some
  threshold
• i.e., keep only the patterns highly predictive of
  contacts

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Testing Phase

• 90-10 split into training and testing
• 2.4 million pairs, with 36K contacts (1.5)
• Evidence calculation
• Find matching patterns P for each instance
• Compute cumulative frequency in C and NC
• Sc Sum of frequency (X Dc) where X in P
• Snc Sum of frequency (X Dnc) where X in P
• Compute evidence ratio of Sc / Snc
• Prediction Sort instances on evidence
• Predict top PR fraction as contacts

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Experiments

• 794 Proteins from Protein Data Bank
• Distinct structures (lt 25 similarity)
• Longest 907, Smallest 35 amino acids
• 90-10 split for training-testing
• Total pairs 20 million (gt 2.5 GB)
• Contacts 330 thousand (1.6)
• Highly uneven class distribution

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Evaluation Metrics

• Na set of all pairs
• Na all pairs with positive evidence
• Ntc true contacts in test data
• Ntc true contacts with positive evidence
• Npc predicted contacts
• Ntpc correctly predicted contacts
• Accuracy Ntpc / Npc
• Coverage Ntpc / Ntc
• Prediction Ratio (PR) Ntc/Na
• Random Predictor Accuracy Ntc/Na

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Results (Amino Acids All Lengths)
Crossover 7 accuracy and 7 coverage 2 times
over Random
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Results (Amino Acids by length)
1-100 12 accuracy(A) and coverage (C) 100-170
6 A and C
170-300 4.5 A and C 300 2 A and C
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Using HMMs based on Local Motifs to Improve
Classification
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An HMM for Local Predictions

• HMMSTR (Chris Bystroff, Biology, RPI)
• Build a library of short sequences that tend to
  fold uniquely across protein families the
  I-Sites Library
• Treat each motif as a Markov chain
• Merge the motifs into a global HMM for local
  structure prediction

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Training the HMM

• Build I-sites Library
• Short sequence motifs (3 to 19)
• Exhaustive clustering of sequences
• Non-redundant PDB dataset (lt 25 similarity)
• Build an HMM
• Each of 262 motifs is a chain of Markov states
• Each state has sequence and structure for one
  position
• Merge I-sites motifs hierarchically to get one
  global HMM for all the motifs

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HMM Output

• Total of 282 States in the HMM
• Each state produces or emits
• Amino acid profile (20 probability values)
• Secondary structure (D) (helix, strand or loop)
• Backbone angles (R) (11 dihedral angle symbols)
• Finer structural context (C) (10 context symbols)

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I-Sites Motifs (Initiation Sites)
Beta Hairpin
Beta to Alpha
Helix C-Cap
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Data Format and Preparation

• Take the 794 PDB proteins
• Compute optimal alignment to HMM
• Find best state sequence for the observed acids
• Output probability distribution of a residue over
  all the 282 HMM states
• Integrate the 3 datasets
• Alignment probability distribution (Nx282)
• Amino acid and context information (D, R, C)
• Contact map (NxN)

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HMMSTR Output (per Protein)
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Adding features from HMMSTR

• The class C (1) or NC (0)
• Highly skewed class distribution
• Approx 1.5 C and 98.5 NC
• Features for each instance
• Ai Aj Di Dj Ri Rj Ci Cj
• Profile pi1 pi2 pi20 pj1 pj2 pj20
• HMM States qi1 qi2 .. qi282 qj1 qj2 .. qj282
• Class C or NC

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HMM and AA (R,D,C) All Lengths
Left Crossover 19 accuracy and coverage 5.3
times over Random
Right Crossover (RDC) 17 accuracy and
coverage 5 times over Random
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HMM AA R,D,C (by length)
1-100 30 accuracy(A) and coverage (C) 100-170
17 A and C
170-300 10 A and C 300 6 A and C
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Predicted Contact Map (2igd)
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Summary of Classification Results

• Challenging prediction problem
• In essence, we have to predict a contact matrix
  for a new protein
• Hybrid HMM/Associations approach
• Best results to-date 19 overall
  accuracy/coverage, 30 for short proteins
• 14.4 Accuracy (Fariselli, Casadio 99 NN)
• 13 Accuracy (Thomas et al 96)
• Short proteins 26 (Olmea, Valencia, 97)

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Mining Physical Dense Frequent Patterns
(non-local motifs)
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Characterizing Physical, Protein-like Contact Maps

• A very small subset of all contact maps code for
  physically possible proteins (self-avoiding,
  globular chains)
• A contact map must
• Satisfy geometric constraints
• Represent low-energy structure
• What are the typical non-local interactions?
• Frequent dense 0/1 submatrices in contact maps
• 3-step approach 1) data generation, 2) dense
  pattern mining, and 3) mapping to structure space

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Dense Pattern Mining

• 12,524 protein-like 60 residue structures
• Use HMMSTR to generate protein-like sequences
• Use ROSETTA to generate their structures
• Monte Carlo fragment insertion (from I-sites
  library)
• Up to 5 possible low-energy structures retained
• Frequent 2D Pattern Mining
• Use WxW sliding window W window size
• Measure density under each window
• (N-W)2 / 2 possible windows per N length protein
• Look for minimum density scale away from diag
• Try different window sizes

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Counting Dense Patterns

• Naïve Approachfor W5, N60 there are 1485
  windows per protein. Total 15 Million possible
  windows for 12,524 proteins
• Test if two submatrices are equal
• Linear search O(P x W2) with P current dense
  patterns
• Hash based O(W2)
• Our Approach 2-level Hashing
• O(W) time

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Pattern (WxW Submatrix) Encoding

• Encode submatrix as string (W integers)
• Submatrix Integer Value
• 00000 0
• 01100 12
• 01000 8
• 01000 8
• 00000 0
• Concatenated String 0.12.8.8.0

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Two-level Hashing

• String ID (M)
• Level 1 (approximate)
• Level2 (exact) h2 (M) StringID (M)

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Binding Patterns to Proteins Sequence and
Structure

• Using window size, W5
• StringID0.12.8.8.0, Support 170
• 00000
• 01100
• 01000
• 01000
• 00000
• Occurrences
• pdb-name (X,Y) X_sequence Y_sequence Interaction
• 1070.0 52,30 ILLKN TFVRI
  alphabeta
• 1145.0 51,13 VFALH GFHIA
  alphastrand
• 1251.2 42,6 EVCLR GSKFG
  alphastrand
• 1312.0 54,11 HGYDE ATFAK
  alphabeta
• 1732.0 49,6 HRFAK KELAG
  alphabeta
• 2895.0 49,7 SRCLD DTIYY
  alphabeta
• ...

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Frequent Dense Local Patterns
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Frequent Dense Non-Local Patterns
Alpha Alpha
Alpha Beta Sheet
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Frequent Dense Non-Local Patterns
Alpha Beta Turn
Beta Sheet Beta Turn
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Future Directions
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Mining Physicality Rules

• Comprehensive list of non-local motifs
• I-sites library catalogs local motifs
• Mining heuristic rules for physicality
• Based on simple geometric constraints
• Rules governing contacts and non-contacts
• Parallel Beta Sheets If C(i,j) 1 and
  C(i2,j2) 1, then C(i,j2) 0 and C(i2,j)
  0
• Anti-parallel Beta Sheets If C(i,j2) 1 and
  C(i2,j) 1, then C(i,j) 0 and C(i2,j2) 0
• Alpha Helices If C(i,i4) 1, C(i,j) 1, and
  C(i4,j) 1, then C(i2,j) 0

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Heuristic Rules of Physicality
Parallel Beta Sheets
Anti-parallel Beta Sheets
i2
j2
i2
j
i
j
i
j2
If C(i,j2) 1 and C(i2,j) 1, then C(i,j) 0
and C(i2,j2) 0
If C(i,j) 1 and C(i2,j2) 1, then C(i,j2)
0 and C(i2,j) 0
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Protein Folding Pathways

• Rules for Pathways in Contact Map Space
• Pathway is time-ordered sequence of contacts
• Condensation rule New contact within Smax
• U(i,j) lt Smax U(i,j) is unfolded residues from
  i to j
• Pathway prediction is complementary to structure
  prediction

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Contact Map Folding Pathways