Reductionism and Classification Require Detailed Comparison Consider 3D Comparison

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Reductionism and Classification Require Detailed
ComparisonConsider 3D Comparison

• Pharm 201/Bioinformatics I
• Philip E. Bourne
• Department of Pharmacology, UCSD
• Reading Chapter 16, Structural Bioinformatics

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Consider this Course a Workflow
Understand the experiment to understand
the errors
Data In
Understand the scope and complexity of the data
Understand how to best represent (model) the data
Understand the methods to physically
instantiate the model
From initial analysis understand how to
control data in
Recognize redundancy In the data
Classify the data
Visualize the data
Analyze the data
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From Last Time

• We established the complex relationship between
• Sequence and Structure
• Structure and Structure
• Structure and Function
• Today we analyze how the relationships between
  structure and structure are established

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Agenda

• Understand why structure comparison is important
• Understand why it is not a solved problem
• Understand the basics of the methods used to
  address the problem
• Understand one method (CE) in more detail
• Review an example where structure comparison has
  revealed new biological insights

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Why Structure Comparison is Important

• Reductionism needed to classify protein
  structures
• Functional assignment and hopefully new biology
• Alignment of predicted structure against
  structural templates
• Establish improved sequence relationships not
  possible from sequence alone
• Protein engineering

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Distinctions - Structure Superposition and
Structure Comparison and Alignment are Different

• Structure superposition assumes you already know
  which atoms to superimpose it merely optimizes
  for the atoms chosen (relatively simple)
• Structure alignment must first determine what
  atoms to align (difficult). We are concerned with
  alignment

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Distinctions Pair-wise Alignments are Different
from Multiple Structure Alignments

• Multiple structure alignment algorithms are rare
  and of questionable quality (see for example
  Nucleic Acids Research (2004), 32 W100-W103
• Multiple structure alignments should not be
  confused with multiple pair-wise alignments
• Here we focus on single pair-wise comparison and
  alignment

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Why is it Not a Solved Problem?
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Current State of the Art

• There are many papers published on this, but
  relatively few have code to download or Web sites
  from which to perform comparisons
• All methods can identify obvious similarities
  between two structures
• Remote similarities are detected by a subset of
  methods different remote similarities are
  recognized by different methods
• Good alignments are much harder to come by
• Speed is a serious issue with some algorithms

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Desirables

• Biologically meaningful alignments not just
  geometrically meaningful
• Complete database of all alignments
• Ability to apply to structures not in the PDB

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Biological vs Geometric Alignments Plastocyanin
versus Azurin (from Godzik 1996)
Maintain 9 of 10 interactions RMSD 1.5 Å
Maintain 5 of 10 interactions RMSD 0.5 Å
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Literature Alignments - Flavodoxin vs Che Y
Protein From Godzik (1996) Protein Science, 5,
1325-1338.
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Understand the basics of the methods used to
address the problem
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See also http//en.wikipedia.org/wiki/Structural_a
lignment_software
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How to Compare Structures?
Structure 1
Structure 2
Feature extraction
1.
Structure description 1
Structure description 2
Comparison algorithm
2.
3.
Scores
Statistical significance
Similarity, classification
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Components of Structure Alignment

• Structure Description

• Local geometry
• Side chain contacts
• Geometric hashing
• Distance matrix (Dali, 1993)
• Properties (secondary structure, hydrophobic
  clusters (Comparer, 1990)
• Secondary structure elements (VAST, 1996)
• Distances of inter intra aligned fragment
  pairs (CE, 1998)
• Contact map (Celera, 2004)
• Geometry invariants (Jia et al, 2004)

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Components of Structure Alignment

• 2. Alignment algorithms
• Monte Carlo (Dali, VAST)
• Heuristics (CE)
• Dynamic Programming (CE)
• Probabilistic
• Statistical significance

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Components of Structure Alignment
2. Alignment algorithms

• Input output of alignment algorithm
• Input two proteins and
• Output An alignment
• and scores
• Constraints
• min rmsd
• max L
• min Gaps

• Dynamic programming, Integer programming, Monte
  Carlo

3. Statistical significance

• Levitt and Gerstein, PNAS, 1998
• Random Model and CE scoring function (Jia et al,
  2004)

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Understand one method (CE) in more detail

• I.N. Shindyalov and P.E. Bourne Protein
  Engineering 1998, 11(9) 739-747. Protein
  Structure Alignment by Incremental Combinatorial
  Extension of the Optimum Path. PDF File 793
  citations!

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Basic Approach

• Compare octameric fragments an aligned fragment
  pair (AFP) (local alignments)
• Stitch together AFPs
• Find the optimal path through the AFPs
• Optimize the alignment through dynamic
  programming
• Measure the statistical significance of the
  alignment

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Why This Approach?Alignment Space is Very Large
and Must be Constrained Without Loosing
Meaningful Alignments

• Similarity Matrix S where
• S(nA-m).(nB-m)
• m Length of AFP
• nA Length of protein A
• This is very large to compute constraints are
  needed

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Definition of the Alignment Path

• pAi AFPs starting residue position in protein A
  at the ith position
• of the alignment path
• m longest continual path set as 8
• One of the conditions (1)-(3) should be satisfied
  for 2 consecutive AFPs i
• and i1 in the path
• 2 consecutive AFPs aligned without gaps
• Two consecutive AFPs with a gap in protein A
• Two consecutive AFPs with a gap in protein B

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Extension of the Alignment Path
Gap sizes are limited to G heuristically set as
30 residues
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Evaluation based upon the following three
distance similarity measures
1. Distance calculated from independent set of
inter-residue distances where each
distance is used only once - used for
combinations of 2 AFPs
2. Full set of inter-residue distances - used for
a single AFP
3. RMSD from least squares superposition - used
to select few best fragments
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Evaluation Based Upon the Following Three
Distance Similarity Measures
1. Distance calculated from independent set of
inter-residue distances where each
distance is used only once
2. Full set of inter-residue distances
3. RMSD from least squares superposition
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How to Extend the Path?
1. Consider all possible AFPs that extend the path
2. Consider only the best AFP
3. Use some intermediate strategy
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How to Extend the Path?
1. Consider all possible AFPs that extend the
path Computationally expensive
2. Consider only the best AFP Works well
with the right heuristics
3. Use some intermediate strategy
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What Heuristics?
Candidate AFPs are based upon (9) D0 3Å The
best AFP is based upon (10) D1 4Å The
decision to extend or terminate the path is based
upon (11)
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Z-Score

• Evaluate the probability of finding an alignment
  path of the same length or smaller gaps and
  distance from a random set of non-redundant
  structures

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Optimization of the Final Path
The 20 best alignments with a Z score above 3.5
are assessed based on RMSD and the best kept.
This produces approx. one error in 1000
structures
Each gap in this alignment is assessed for
relocation up to m/2
Iterative optimization using dynamic programming
is performed using residues for the superimposed
structures
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Test Case Phycocyanin versus Colicin A
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Cyclin-dependent kinases Open (purple) Closed
(blue) Pavelitch et al. (1997)
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Limitations

• Will not find non-topological alignments (outside
  the bounds of the dotted lines)
• What are the correct units to be comparing?
• CE works on chains as we shall see in future
  weeks domains are the correct units, but
  definition of the domains is not straightforward

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Computation of All x All

• Took 11,748 chain in the PDB (1/98)
• Computed for 1868 representatives
• 24,000 Cray T3E processor hours
• Loaded pairwise alignments into
• database

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1-2 Years Ago

• 40,000 proteins 70,000 chains
• 70,0002/2 30 seconds 2330 yrs
• Options
• Use a redundant set of chains
• Use parallel architectures
• D. Pekurovsky, I.N. Shindyalov, P.E. Bourne 2004
  High Throughput Biological Data Processing on
  Massively Parallel Computers. A Case Study of
  Pairwise Structure Comparison and Alignment Using
  the Combinatorial Extension (CE) Algorithm.
  Bioinformatics, 20(12) 1940-1947 PDF.

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Now

• Using egrid to compute all by all for CE and
  FatCat

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One Criteria for Redundancy

• Remove highly homologous chains
• The  RMSD between two chains is less than 2Å
• The length difference between two chains is less
  than 10
• The number of gap positions in alignment between
  two chains is less than 20 of aligned residue
  positions
• At least 2/3 of the residue positions in the
  represented chain are aligned with the
  representing chain.

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Review example where structure comparison has
revealed new biological insights
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Example

• CE revealed putative Ca binding domain in
  acetylcholinesterase
• Sequence similarity to neuroligins predicts Ca
  binding too confirmed experimentally
• Members of the a/b hydrolase family bind Ca
  which may be important for heterologous cell
  associations

Structural similarity between Acetylcholinesterase
and Calmodulin found using CE (Tsigelny et al,
Prot Sci, 2000, 9180)
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The Future(also a general rule)

• Gold standards are important
• For structure comparison a human generated
  alignment standard is important
• Algorithms are then challenged to meet the
  standard
• Eventually those algorithms highlight problems
  with the standard
• The cycle continues