Structural Bioinformatics

1
Structural Bioinformatics Structure Comparison

• Motivation
• Concepts
• Structure Comparison

2
Motivation

• Given structures A and B, are they similar?
• Implications
• A and B might share the same set of functions
• Given structure A, is a similar structure already
  known?
• Implications
• Each new experimentally solved structure can be
  placed in context of existing body of structural
  knowledge

3
Concepts

• For n sequences and s corresponding structural
  equivalence classes, n gtgt s. Possible reasons
• Structural divergence is slower than sequence
  divergence in evolution (à la RNA sequence
  alignment)
• Convergent evolution Some structures are
  preferred for a functional reason
• Coincidence Only so many structures are
  possible, for a given threshold of similarity
• Terms used to describe structure
• Architecture, Class, Fold, Super-family, Family

4
Superposition versus Alignment

• Structural superposition versus structural
  alignment
• Superposition
• Residue correspondence already known, based on a
  statistically significant sequence alignment
• Problem is that of finding optimal correspondence
  between two sets of points, given subset of
  equivalent points between the two sets
• Optimality measured by lowest value of Root Mean
  Square Deviation (RMSD)
• Alignment
• Residue correspondence unknown
• Need structure-based scoring function and
  evaluate this for all possible superposition of
  structures
• Optimal solution frequently impractical because
  of high complexity (NP-hard, Why?)

5
Heuristic Structure Alignment

• General strategy
• Summarized/reduced representation of each
  structure
• Consider only subsets of atoms (Just C? or C?)
• Use summarized vectors to represent organized
  sub-structures
• Approaches
• Dynamic programming with empirical scoring
  functions
• Distance-matrix correspondence in internal
  co-ordinate space

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Heuristic Structure Alignment

• Vector based strategies
• VAST (Vector Alignment Search Tool) Compare
  summarized vector representations
• SSAP (Secondary Structure Alignment Program)
  Compare nearest-neighbor vectors by double
  dynamic programming
• Distance matrix comparisons (à la Dot-matrix)
• DALI (Distance Alignment Tool) Subset of
  internal coordinate space

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VAST alignment (Fig. 10.13)

• Use only subset of atom coordinates
• Replace atom coordinates with vector coordinates
  corresponding to secondary structural elements
  (structural words)
• Compare sets of vectors to assess similarity

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Double dynamic programming (SSAP/CATH Fig. 10.14)

• First level
• Represent each residue by neighborhood vector for
  C?
• Compare n versus m neighborhood vectors
• Generate optimal alignment based on vector
  differences and dynamic programming
• Second Level
• Add matrix scores if paths cross in a cumulative
  matrix
• Generate optimal alignment based on the
  cumulative matrix

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Distance matrix based alignment (DALI Fig. 10.15)

• Generate dot-matrix of inter- C? distances, using
  threshold
• Pick out secondary structure elements based on
  matrix patterns
• Compare two matrices to generate structural
  alignment

10
Structure Comparison Databases

• Several databases (CATH, MMDB, FSSP) maintain a
  hierarchical classification of known structures,
  based on pair-wise structural alignment scores
• High complexity of the algorithms requires
  incremental additions
• Actual classification is algorithm-dependent,
  with some consensus, but significant differences
  exist

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Summary

• Sequence similarity (gt 50 identity) implies
  structural similarity. Converse not necessarily
  true (evolutionary convergence/information
  convergence)
• Structural similarity algorithms are heuristic
  ways to assess structural similarity
  independent of sequence similarity
• Structural variation is smaller than that
  suggested by the number of possible sequences