Protein Structure Prediction

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Protein Structure Prediction

• Samantha Chui
• Oct. 26, 2004

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Central Dogma of Biology

• Question Given a protein sequence, to what
  conformation will it fold?

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How does nature do it?

• Hydrophobicity vs. hydrophilicity
• Van der Waals interaction
• Electrostatic interaction
• Hydrogen bonds
• Disulfide bonds

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Current Approaches

• Experimental Methods
• X-ray crystallography
• NMR spectroscopy
• Computational Methods
• Homology modeling
• Similar sequences fold into similar structures
• Threading
• Dissimilar sequences may fold into similar
  structures
• Ab initio
• No similarity assumptions
• Conformational search

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Assembly of sub-structural units
predicted structure
known structures
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Small Libraries of Protein Fragments Model
Native Protein Structures AccuratelyRachel
Kolodny, Patrice Koehl, Leonidas Guibas, and
Michael Levitt, 2002

• Goal Find finite set of protein fragments that
  can be used to construct accurate discrete
  conformations for any protein
• 1. Generate fragments from known proteins
• 2. Cluster fragments to identify common
  structural motifs
• 3. Test library accuracy on proteins not in the
  initial set

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Datasets of protein fragments

• 200 unique protein domains from Protein Data Bank
  (PDB)
• 36,397 residues
• Four sets of backbone fragments
• 4, 5, 6, and 7-residue long fragments
• Divide each protein domain into consecutive
  fragments beginning at random initial position

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Fragment structural similarity

• Coordinate root-mean-square (cRMS) deviation of
  Ca atoms
• cRMS(A,B) sqrt(Sdi2/N)
• one to one mapping between atoms in structure A
  and structure B
• Translate and rotate to find best alignment
• 0 if superimpose perfectly

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Pruning and clustering

• Outliers have large cRMS deviation from all other
  fragments
• Discard according to some fragment-length
  specific threshold
• k-means simulated annealing clustering
• Repeatedly run k-means clustering, merge nearby
  clusters and split disperse clusters
• Scoring function total variance S (x µ)2
• Less sensitive to initial choice of cluster
  centers than k-means

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Compiling the libraries

• Select cluster centroids as library entries
• Minimum sum of cRMS deviations from all the other
  cluster fragments
• Form representative set of protein fragments
• Library contents highly dependent upon clustering
  procedure
• For each set of fragments, start with 50 random
  seeds and choose library with minimal total
  variance score

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Evaluating quality of a library

• Local-fit
• How well library fits local conformation of all
  proteins in test set.
• Global-fit
• How well library fits global three-dimensional
  conformation of all proteins in test set

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Local-fit method

• Protein structures broken into set of all
  overlapping fragments of length f
• Find for each protein fragment the most similar
  fragment in the library (cRMS)
• Score Average cRMS value over all fragments in
  all proteins in the test set

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Local-fit results
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Global-fit method

• Concatenate best local-fit library fragments just
  found
• Determine fragments orientation by superimposing
  its first three Ca atoms onto last three Ca atoms
  of preceding fragment

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Global-fit method

• Number of possible sequences of fragments
  exponential in proteins length
• Greedy algorithm finds good rather than best
  global-fit approximation
• Start at N terminus, approximate increasingly
  larger segments of the protein
• Concatenate library fragment which will yield
  structure of minimal cRMS deviation from
  corresponding segment
• Deterministic, linear time

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Global-fit results
0.91 Å
1.85 Å
2.78 Å
50 fragments 7 residues 2.66 states/residue
100 fragments 5 residues 10 states/residue
20 fragments 5 residues 4.47 states/residue
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Assembly of sub-structural units
predicted structure
known structures
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Protein structure prediction via combinatorial
assembly of sub-structural unitsYuval Inbar,
Hadar Benyamini, Ruth Nussinov, and Haim J.
Wolfson, 2003
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CombDock

• Input structural units (SUs) with known 3D
  conformations
• SUs considered rigid bodies
• rotated and translated with respect to each other
• Goal predict overall structure
• Constraints
• Penetration avoid steric clashes
• Backbone restriction on maximum distance between
  consecutive SUs

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All pairs docking

• N(N-1)/2 pairs of SUs
• Calculate candidate transformations according to
  matching complementary local features on surface
  of SUs
• Apply transformation on 2nd SU of pair
• Keep K best for each
• Clustering to ensure all K transformations yield
  significantly different complexes

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Combinatorial assembly

• Multigraph representation
• Vertices SUs
• Edges transformations between two SUs
• K parallel edges between any two vertices
• Final protein conformation spanning tree
• N SUs, one connectivity component, no cycles

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Combinatorial Assembly

• NN-2KN-1 different spanning trees
• Not all spanning trees are valid complexes
• Use heuristical algorithm
• Two subtrees adjacent iff there exists an index i
  so that vertex i is in one subtree and i1 is in
  the other
• Sequential tree recursive definition
• One vertex
• Tree with edge that connects two adjacent
  sequential trees

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Combinatorial Assembly

• Hierarchical algorithm of N stages
• ith stage generate sequential trees with i
  vertices
• Construct trees by connecting adjacent sequential
  trees of smaller sizes generated earlier
• Keep D best sequential trees at each step
• Discard trees which do not meet backbone and
  penetration constraints
• Score sum of scores of transformations

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Combinatorial Assembly
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CombDock Results
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Conclusion
protein sequence
predicted structure
known structures
fragment library

• Experimental Methods
• X-ray crystallography
• NMR spectroscopy
• Computational Methods
• Homology modeling
• Similar sequences fold into similar structures
• Threading
• Dissimilar sequences may fold into similar
  structures
• Ab initio
• No similarity assumptions
• Conformational search

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References

• Kolodny et al., Small libraries of protein
  fragments model protein structures accurately
• Inbar et al., Protein structure prediction via
  combinatorial assembly of sub-structural units