Protein Structure Alignment

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Protein Structure Alignment
Human Hemoglobin alpha-chain pdb1jebA
Human Myoglobin pdb2mm1
Another example G-Proteins 1c1yA,
1kk1A6-200 Sequence id 18 Structural id 72
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Transformations

• Translation
• Translation and Rotation
• Rigid Motion (Euclidian Trans.)
• Translation, Rotation Scaling

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Inexact Alignment. Simple case two closely
related proteins with the same number of
amino acids.
Question how to measure an alignment error?
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Distance Functions

• Two point sets Aai i1n
• Bbj j1m
• Pairwise Correspondence
• (ak1,bt1) (ak2,bt2) (akN,btN)

(1) Exact Matching aki bti0
(2) Bottleneck max aki bti (3) RMSD
(Root Mean Square Distance) Sqrt(
Saki bti2/N)
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Superposition - best least squares(RMSD Root
Mean Square Deviation)
Given two sets of 3-D points Ppi, Qqi ,
i1,,n rmsd(P,Q) v S ipi - qi 2 /n Find a
3-D rigid transformation T such that rmsd(
T(P), Q ) minT v S iT(pi) - qi 2 /n
A closed form solution exists for this task. It
can be computed in O(n) time.
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Correspondence is Unknown
Given two configurations of points in the
three dimensional space,
find those rotations and translations of one
of the point sets which produce large
superimpositions of corresponding 3-D
points.
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A 3-D reference frame can be uniquely defined by
the ordered vertices of a non-degenerate triangle
p1
p2
p3
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Sequence Based Structure Alignment

• Run pairwise sequence alignment.
• Based on sequence correspondence compute 3D
  transformation (least square fit can be applied).
• Iteratively improve structural superposition.

Not a good approach sequence alignment can be
incorrect.
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Structure Alignment (Straightforward Algorithm)

• For each pair of triplets, one from each molecule
  which define almost congruent triangles compute
  the rigid transformation that superimposes them.
• Count the number of aligned point pairs and sort
  the hypotheses by this number.

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• For the highest ranking hypotheses improve the
  transformation by replacing it by the best RMSD
  transformation for all the matching pairs.
• Complexity O(n3m3 ) O(nm) .
• Applying 3D grid gives practically O(n3m3)
  O(n)
• If one exploits protein backbone geometry 3D
  grid
• O(nm) O(n)

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Structural Alignment Approaches
Two interrelated problems 3D transformation and
point correspondence (matching, alignment)
Some methods

1. Generate a set of 3D transformations.
2. Cluster similar transformations.
3. Compute 3D alignment for each cluster
   representative.

1. Generate a set of 3D transformations.
2. Compute 3D alignment for each transformation.

Geometric Hashing Combines transformation and
correspondence detection in one scheme.
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Accuracy improvement during detection of 3D
transformation.
Instead of 3 points use more. How many?
Align any possible pair of fragments - Fij(k)
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Accept Fij(k) if rmsd(Fij(k)) lte. Complexity
O(n3 n) O(n) (assume nm) (For each Fij(k)
we need compute its rmsd) can be reduced to
O(n3) O(n)
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Improvement BLAST idea - detect short similar
fragments, then extend as much as possible.
i1
i-1
i
j-1
j1
j
ai-1 ai ai1 bj-1 bj bj1
Extend while rmsd(Fij(k)) lte.
Complexity O(n2)O(n)
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• Sequence-order Independent Alignment

P
Q
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4-helix bundle
2cblA
1f4nA
1rhgA
1b3q
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Sequence Order Independent Alignment
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Sequence Order Independent Alignment
2cblA 1f4n 1rhgA 1b3q
51
103
113
169
chain A
chain B
3
58
54
7
73
126
34
12
171
147
chain A
chain B
306
355
354
305
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The C2 domain calcium-binding motif
E. A. NALEFSKI and J. J. FALKE The C2 domain
calcium-binding motif Structural and functional
diversity Protein Sci 1996 5 2375-2390
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TRAF-Immunoglobulin Ensemble
E- strand

• Ensemble 8 proteins from 2 folds.
• Core sandwich of 6 strands
• Runtime 21 seconds

- helices - strands
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Some Links

• Rasmol Molecular Visualization
• SCOP - Structural Classification of Proteins
• MultiProt - Protein Structural (pairwise/multiple)
  Alignment
• MASS Secondary Structure Based
  (pairwise/multiple) Alignment