Sequence order independent structural alignment

1
Sequence order independent structural alignment

• Joe Dundas, Andrew Binkowski, Bhaskar DasGupta,
  Jie Liang
• Department of Bioengineering/Bioinformatics,
  University of Illinois at Chicago

2
Background

• Extended Central Dogma of molecular biology
• DNA ? RNA ? primary structure ? 3D structure ?
  function
• Evolution conserves the 3D structure more than
  amino acid sequence.
• Structural similarity often reflects a common
  function or origin of proteins.1
• It is useful to classify proteins based on their
  structures. (SCOP, CATH, FSSP).
• Many methods for structure alignment have been
  reported. (CE, DALI, FAST, Matchprot)

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Circular Permutation

• Ligation of the N and C termini, and subsequent
  cleavage elsewhere.
• In 1979, first natural circular permutation was
  observed in favin vs. concanavalin A.2
• In 1983, the first engineered circular
  permutation was performed on bovine pancreatic
  trypsin inhibitor.3
• Since, studies have shown that artificially
  permuted proteins are able to fold into a stable
  structures that are similar to the native
  protein.4
• Circular permutations have been discovered in
  lectins, ß-glucanases, swaposin5

4
Alignment Problem

• Most structural alignment methods rely on the
  structural units of each protein to align
  sequentially i.e. CE, FAST.
• Some newer methods will perform non-sequential
  alignments i.e. Dali, Matchprot.
• After explaining our method, will we compare
  the results against Dali and Matchprot.

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Our Method

• We exhaustively fragment protein A and protein B
• into lengths ranging from 4 to 7 residues.
• Notation fragment ?a (a1, a2), where a1
  and a2 are the beginning and ending positions
  relative to the N termini of protein A.
• ?a ?a,1, ?a,2, ?a,n is the set of all
  fragments from protein A.
• La,i is the length of fragment ?a,I
• Each fragment from protein A is aligned to all
  fragments of protein B if La,I Lb,j, forming a
  set of Aligned Fragment Pairs ( ? ?a x ?b
  ).
• A similarity function s maps ? ?

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Similarity Function
All ?i with s(?i) gt Threshold are used to
create a conflict graph.
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Conflict Graph

• Two fragment pairs ?i and ?j are in conflict if
  any residue in ?i,A is also in ?j,A or any
  residue in ?i,B is also in ?j,B.

Simplified Example
Conflicts can be found by a vertex sweep.
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LP Formulation
x is a relaxed integer between 0 and 1 0 dont
use fragment 1 use fragment
Subject to
No conflicting residues in query or reference
protein.
Consistency between variables
All variables are between 0 and 1
Solve using linear programming package
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Local Conflict Number
s(?4) 15 x ?4 0.01 T?4 0.26

• LP will assign a number between 0 and 1 for each
  xd.
• For each ? compute a local conflict number T
• Define dmin as the vertex with the smallest
  local conflict number.
• Assign a new s
• Remove all vertices with s 0 from ? and push
  them onto a stack O in descending order of s

s(?1) 50 x ?1 .85 T?1 1.10
dmin
s(?3) 20 x ?3 0.6 T?3 0.85
s(?2) 20 x ?2 .25 T?2 1.46
s(?4) 0
s(?1) 50
s(?2) 15
s(?3) 20
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Repeat

• Repeat LP formulation until all vertices have
  been pushed onto the stack O.
• Begin with 5 empty alignments.
• While the stack is not empty, retrieve a aligned
  pair by popping the stack.
• Insert it into each non-empty alignment if and
  only if
• No residue conflicts occur.
• The global RMSD does not change by some
  threshold.
• If it can not be inserted into any alignment,
  insert it into an available empty alignment.
• Determine which alignment with highest similarity
  score.

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Results Circular Permutation?
1jqsC 70s ribosome functional complex Fold
Ribosome Ribosomal fragments
2pii PII (Product of glnB) Fold Ferredoxin-like
RMSD 2.3194
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Results Circular Permutation
1iudA Aspartate Racemase Fold ATC-like
1h0rA Type II 3-dehydrogenate dehydralase Fold
Flavodoxin
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Results
1vet Mitogen activated protein kinase
1fe0 ATX1 Metallochaperone Fold ferredoxin-like
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Results
1e50 Core binding factor Fold Core binding
factor beta
1pkv Riboflavin Synthase