Protein Structural Prediction
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Transcript of Protein Structural Prediction
Protein Structural Prediction
Performance of Structure Prediction Methods
TRILOGY: Sequence–Structure Patterns
• Identify short sequence–structure patterns 3 amino acids• Find statistically significant ones (hypergeometric distribution)
Correct for multiple trials• These patterns may have structural or functional importance
1. Pseq: R1xa-bR2xc-dR3
2. 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 99:8500-8505, 2002
TRILOGY
TRILOGY: Extension
Glue together two 3-aa patterns that overlap in 2 amino acids
P-score = i:Mpat,…,min(Mseq, Mstr) C(Mseq, i) C(T – Mseq, Mstr – i) C(T, Mstr)-1
TRILOGY: Longer PatternsType-II turn between unpaired strands
NAD/RAD binding motif found in several folds
-- unit found in three proteins with the TIM-barrel fold
Helix-hairpin-helix DNA-binding motif
Four Cysteines forming 4 S-S disulfide bonds
A fold with repeated aligned -sheets
Three strands of an anti-parallel -sheet
A -hairpin connected with a crossover to a third -strand
Small Libraries of Structural Fragments for Representing Protein
Structures
Fragment Libraries For Structure Modeling
knownstructures
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fragmentlibrary
proteinsequence
predictedstructure
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
1. Generate fragments from known proteins2. Cluster fragments to identify common structural motifs3. Test library accuracy on proteins not in the initial set
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Small Libraries of Protein FragmentsDataset: 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 Σ(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(|Library|N) Greedy approach extends the C best
structures so far from pos’n 1 to N
Results
C =
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
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.htmlSlide credits: Jimbo Xu
Side-Chain Packing
clash
Each residue has many possible side-chain positionsEach possible position is called a rotamerNeed to avoid atomic clashes
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Slide credits: Jimbo Xu
Energy Function
))(),(,,())(,( jAiAjiPiAiSi
Minimize the energy function to obtain the best side-chain packing.
Assume rotamer A(i) is assigned to residue i. The side-chain packing quality is measured by
clash penalty
occurring preferenceThe higher the occurring probability, the smaller the value
0.82
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1ba
ba
rrd
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clash penalty
: distance between two atoms :atom radiibad ,
ba rr ,
Slide credits: Jimbo Xu
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
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
Residue Interaction Graph
• Vertices:Each residue is a vertex
• Edges:Two residues interact if there is a potential clash between their rotamer atoms
Residue Interaction Graph
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Slide credits: Jimbo Xu
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 > D• D: constant depending on rotamer diameter
• A residue interaction graph is sparse!
Slide credits: Jimbo Xu
Tree Decomposition[Robertson & 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) ∩ X(k) X(j)
• Tree width is defined to be the maximal component size minus 1
Slide credits: Jimbo Xu
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Greedy: minimum degree heuristic
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1. Choose the vertex with minimal degree2. The chosen vertex and its neighbors form a
component3. Add one edge to any two neighbors of the chosen
vertex4. Remove the chosen vertex5. Repeat the above steps until the graph is empty
Slide credits: Jimbo Xu
Tree Decomposition[Robertson & Seymour, 1986]
Tree Decomposition (Cont’d)
Tree Decomposition
Tree width: size of maximal component – 1
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gabd acd
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cdem defm
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Slide credits: Jimbo Xu
Side-Chain Packing Algorithm
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
))(,())(,())(,())(,( min)A(
iililjijXX
iri XAXScoreXAXFXAXFXAXFri
Score of subtree rooted at Xi
Score of component Xi
Score of subtree rooted at Xj
Xr
Xp Xi
Xj XlXq
Xir
XjiXli
A tree decomposition rooted at Xr
Score of subtree rooted at Xl
Slide credits: Jimbo Xu
Empirical Component Size Distribution
Tested on the 180 proteins used by SCWRL 3.0.Components with size ≤ 2 ignored.
Slide credits: Jimbo Xu
Result
protein size SCWRL SCATD speedup
1gai 472 266 3 88
1a8i 812 184 9 20
1b0p 2462 300 21 14
1bu7 910 56 8 7
1xwl 580 27 5 5
Five times faster on average, tested on 180 proteins used by SCWRL
Same prediction accuracy as SCWRL 3.0
CPU time (seconds)
Theoretical time complexity: << is the average number rotamers for each residue.
)( log3/2 NNNO N
Slide credits: Jimbo Xu
Accuracy
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ASN ASP CYS HIS ILE SER TYR VAL
SCATDSCWRL
A prediction is judged correct if its deviation from the experimental value is within 40 degree.
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Slide credits: Jimbo Xu