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Pharm 201 Lecture 10, 2009 1
Reductionism and Classification Require Detailed Comparison
Consider 3D Comparison
Pharm 201/Bioinformatics I
Philip E. BourneDepartment of Pharmacology, UCSD
Reading Chapter 16, Structural Bioinformatics
Pharm 201 Lecture 10, 2009 2
Consider this Course a Workflow
Data In Understand the scopeand complexity of the
data
Understand theexperiment to understand the
errors
Understand howto best represent(model) the data
Understand the methods to
physically instantiatethe model
From initialanalysis understand
how to controldata in
Recognize redundancyIn the data
Classify the data Visualize the data
Analyze the data
Pharm 201 Lecture 10, 2009 3
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
Pharm 201 Lecture 10, 2009 4
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
Pharm 201 Lecture 10, 2009 5
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
Pharm 201 Lecture 10, 2009 6
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
Pharm 201 Lecture 10, 2009 7
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
Pharm 201 Lecture 10, 2009 8
Why is it Not a Solved Problem?
Pharm 201 Lecture 10, 2009 9
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
Pharm 201 Lecture 10, 2009 10
Desirables
• Biologically meaningful alignments not just geometrically meaningful
• Complete database of all alignments
• Ability to apply to structures not in the PDB
Pharm 201 Lecture 10, 2009 11
Maintain 9 of 10 interactionsRMSD 1.5 Å
Maintain 5 of 10 interactionsRMSD 0.5 Å
Biological vs Geometric Alignments Plastocyanin versus Azurin (from Godzik 1996)
Pharm 201 Lecture 10, 2009 12
Literature Alignments - Flavodoxin vs Che Y ProteinFrom Godzik (1996) Protein Science, 5, 1325-1338.
Pharm 201 Lecture 10, 2009 13
Understand the basics of the methods used to address the
problem
Pharm 201 Lecture 10, 200914
See also http://en.wikipedia.org/wiki/Structural_alignment_software
Pharm 201 Lecture 10, 2009 15
How to Compare Structures?
Structure 1 Structure 2
Feature extraction
Structure description 1 Structure description 2
Comparison algorithm
Scores
Statistical significance
Similarity, classification
1.
2.
3.
Pharm 201 Lecture 10, 2009 16
Components of Structure Alignment1. 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)
Pharm 201 Lecture 10, 2009 17
Components of Structure Alignment
2. Alignment algorithms– Monte Carlo (Dali, VAST)– Heuristics (CE)– Dynamic Programming (CE)– Probabilistic
3. Statistical significance
Components of Structure Alignment2. Alignment algorithms
Dynamic programming, Integer programming, Monte Carlo…
3. Statistical significanceLevitt and Gerstein, PNAS, 1998
Random Model and CE scoring function (Jia et al, 2004)
Input & output of alignment algorithm
Input: two proteins: and
Output: An alignment
and scores
Constraints:
min rmsd:
max L
min Gaps:
},,{ 1 maaA },,{ 1 nbbB
LL
jiji
jjjiii
babaBALLL
2121 ,
)},,(,),,{(),(11
L
Tbarmsd
L
kji
T
kk
1
2)(min
1
111 11
L
ttttt jjiiGaps
18
Pharm 201 Lecture 10, 2009 19
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!
Pharm 201 Lecture 10, 2009 20
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
Pharm 201 Lecture 10, 2009 21
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
Pharm 201 Lecture 10, 2009 22
Calculation of distance: (a) Dij for alignment represented by two AFPs i and j from the
path; (b) Dii for single AFP i from the path.
Pharm 201 Lecture 10, 2009 23
Definition of the Alignment Path
pAi = AFPs starting residue position in protein A at the ith position
of the alignment pathm = longest continual path – set as 8One of the conditions (1)-(3) should be satisfied for 2 consecutive AFPs i and i+1 in the path (1) = 2 consecutive AFPs aligned without gaps(2) = Two consecutive AFPs with a gap in protein A(3) = Two consecutive AFPs with a gap in protein B
Pharm 201 Lecture 10, 2009 24
Extension of the Alignment Path
Gap sizes are limited to G – heuristically set as 30 residues
Pharm 201 Lecture 10, 2009 25
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
Evaluation based upon the following three distance similarity measures
Pharm 201 Lecture 10, 2009 26
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
Evaluation Based Upon the Following Three Distance Similarity Measures
Pharm 201 Lecture 10, 2009 27
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
Pharm 201 Lecture 10, 2009 28
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
Pharm 201 Lecture 10, 2009 29
What Heuristics?
Candidate AFPs are based upon (9) D0 = 3ÅThe best AFP is based upon (10) D1 = 4ÅThe decision to extend or terminate the path is based upon (11)
Pharm 201 Lecture 10, 2009 30
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
Pharm 201 Lecture 10, 2009 31
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 performedusing residues for the superimposed structures
Optimization of the Final Path
Pharm 201 Lecture 10, 2009 32
Test Case: Phycocyanin versus Colicin A
Pharm 201 Lecture 10, 2009 33
Cyclin-dependent kinasesOpen (purple) Closed (blue)Pavelitch et al. (1997)
Pharm 201 Lecture 10, 2009 34
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
Pharm 201 Lecture 10, 2009 35
• Took 11,748 chain in the PDB (1/98)
• Computed for 1868 representatives
• 24,000 Cray T3E processor hours
• Loaded pairwise alignments into database
Computation of All x All
Pharm 201 Lecture 10, 2009 36
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].
Now
• Using egrid to compute all by all for CE and FatCat
Pharm 201 Lecture 10, 2009 37
Pharm 201 Lecture 10, 2009 38
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.
Pharm 201 Lecture 10, 2009 39
Review example where structure comparison has revealed new
biological insights
Pharm 201 Lecture 10, 2009 40
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, 9:180)
Pharm 201 Lecture 10, 2009 41
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