Protein Structural Prediction

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Protein Structural Prediction
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Performance of Structure Prediction Methods
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TRILOGY SequenceStructure Patterns

• Identify short sequencestructure patterns 3
  amino acids
• Find statistically significant ones
  (hypergeometric distribution)
• Correct for multiple trials
• These patterns may have structural or functional
  importance
• Pseq R1xa-bR2xc-dR3
• Pstr 3 C? C? distances, 3 C? C? vectors
• Start with short patterns of 3 amino acids
• V, I, L, M, F, Y, W, D, E, K, R, H, N,
  Q, S, T, A, G, S
• Extend to longer patterns
• Bradley et al. PNAS 998500-8505, 2002

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TRILOGY
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TRILOGY Extension
Glue together two 3-aa patterns that overlap in 2
amino acids
P-score ?iMpat,,min(Mseq, Mstr) C(Mseq, i)
C(T Mseq, Mstr i) C(T, Mstr)-1
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TRILOGY Longer Patterns
?-?-? unit found in three proteins with the
TIM-barrel fold
NAD/RAD binding motif found in several folds
Type-II ? turn between unpaired ? strands
Helix-hairpin-helix DNA-binding motif
A ?-hairpin connected with a crossover to a third
?-strand
Three strands of an anti-parallel ?-sheet
A fold with repeated aligned ?-sheets
Four Cysteines forming 4 S-S disulfide bonds
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Small Libraries of Structural Fragments for
Representing Protein Structures
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Fragment Libraries For Structure Modeling
predicted structure
known structures
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Small Libraries of Protein Fragments

• Kolodny, Koehl, Guibas, Levitt, JMB 2002
• Goal
• Small alphabet of protein structural fragments
  that can be used to represent any structure
• Generate fragments from known proteins
• Cluster fragments to identify common structural
  motifs
• Test library accuracy on proteins not in the
  initial set

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Small Libraries of Protein Fragments

• Dataset 200 unique protein domains with most
  reliable distinct structures from SCOP
• 36,397 residues
• Divide each protein domain into consecutive
  fragments beginning at random initial position
• Library Four sets of backbone fragments
• 4, 5, 6, and 7-residue long fragments
• Cluster the resulting small structures into k
  clusters using cRMS, and applying k-means
  clustering with simulated annealing
• Cluster with k-means
• Iteratively break join clusters with simulated
  annealing to optimize total variance S(x µ)2

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Evaluating the Quality of a Library

• Test set of 145 highly reliable protein
  structures (Park Levitt)
• Protein structures broken into set of overlapping
  fragments of length f
• Find for each protein fragment the most similar
  fragment in the library (cRMS)
• Local Fit Average cRMS value over all fragments
  in all proteins in the test set
• Global Fit Find best composition of structure
  out of overlapping fragments
• Complexity is O(LibraryN)
• Greedy approach extends the C best structures so
  far from posn 1 to N

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Results
C
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Protein Side-Chain Packing

• Problem given the backbone coordinates of a
  protein, predict the coordinates of the
  side-chain atoms
• Method decompose a protein structure into very
  small blocks

Slide credits Jimbo Xu
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Protein Structure Prediction

• Stage 1 Backbone Prediction
• Ab initio folding
• Homology modeling
• Protein threading
• Stage 2 Loop Modeling
• Stage 3 Side-Chain Packing
• Stage 4 Structure Refinement

The picture is adapted from http//www.cs.ucdavis.
edu/koehl/ProModel/fillgap.html
Slide credits Jimbo Xu
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Side-Chain Packing
0.3
0.2
0.3
0.7
0.1
0.4
0.1
0.1
0.6
clash
Each residue has many possible side-chain
positions Each possible position is called a
rotamer Need to avoid atomic clashes
Slide credits Jimbo Xu
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Energy Function
Assume rotamer A(i) is assigned to residue i. The
side-chain packing quality is measured by
clash penalty
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clash penalty
0.82
1
occurring preference The higher the occurring
probability, the smaller the value
distance between two atoms atom radii
Minimize the energy function to obtain the best
side-chain packing.
Slide credits Jimbo Xu
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Related Work

• NP-hard Akutsu, 1997 Pierce et al., 2002 and
  NP-complete to achieve an approximation ratio
  O(N) Chazelle et al, 2004
• Dead-End Elimination eliminate rotamers
  one-by-one
• SCWRL biconnected decomposition of a protein
  structure Dunbrack et al., 2003
• One of the most popular side-chain packing
  programs
• Linear integer programming Althaus et al, 2000
  Eriksson et al, 2001 Kingsford et al, 2004
• Semidefinite programming Chazelle et al, 2004

Slide credits Jimbo Xu
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Algorithm Overview

• Model the potential atomic clash relationship
  using a residue interaction graph
• Decompose a residue interaction graph into many
  small subgraphs
• Do side-chain packing to each subgraph almost
  independently

Slide credits Jimbo Xu
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Residue Interaction Graph

• Vertices
• Each residue is a vertex
• Edges
• Two residues interact if there is a potential
  clash between their rotamer atoms

h
f
b
d
s
m
c
a
e
i
j
k
l
Residue Interaction Graph
Slide credits Jimbo Xu
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Key Observations

• A residue interaction graph is a geometric
  neighborhood graph
• Each rotamer is bound to its backbone position by
  a constant distance
• No interaction edge between two residues if
  distance gt D
• D constant depending on rotamer diameter
• A residue interaction graph is sparse!

Slide credits Jimbo Xu
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Tree DecompositionRobertson Seymour, 1986

• Definition. A tree decomposition (T, X) of a
  graph G (V, E)
• T(I, F) is a tree with node set I and edge set F
• X is a set of subsets of V, the components
  Union of elts. in X V
• 1-to-1 mapping between I and X
• For any edge (v,w) in E, there is at least one
  X(i) in X s.t. v, w are in X(i)
• In tree T, if node j is on the path from i to k,
  then X(i) n X(k) ? X(j)
• Tree width is defined to be the maximal component
  size minus 1

Slide credits Jimbo Xu
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Tree DecompositionRobertson Seymour, 1986
Greedy minimum degree heuristic
h

• Choose the vertex with minimal degree
• The chosen vertex and its neighbors form a
  component
• Add one edge to any two neighbors of the chosen
  vertex
• Remove the chosen vertex
• Repeat the above steps until the graph is empty

Slide credits Jimbo Xu
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Tree Decomposition (Contd)
Tree Decomposition
Tree width size of maximal component 1
Slide credits Jimbo Xu
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Side-Chain Packing Algorithm
Xr
Xir
Bottom-to-Top Calculate the minimal energy
function Top-to-Bottom Extract the optimal
assignment Time complexity Exponential in tree
width, linear in graph size
Xi
Xp
Xj
Xl
Xq
Xli
Xji
A tree decomposition rooted at Xr
Score of component Xi
Score of subtree rooted at Xl
Score of subtree rooted at Xi
Score of subtree rooted at Xj
Slide credits Jimbo Xu
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Empirical Component Size Distribution
Tested on the 180 proteins used by SCWRL
3.0. Components with size 2 ignored.
Slide credits Jimbo Xu
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Result
Theoretical time complexity ltlt is
the average number rotamers for each residue.
CPU time (seconds)

• Five times faster on average, tested on 180
  proteins used by SCWRL
• Same prediction accuracy as SCWRL 3.0

Slide credits Jimbo Xu
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Accuracy
A prediction is judged correct if its deviation
from the experimental value is within 40 degree.
Slide credits Jimbo Xu