pharm 201 lecture 10, 20091 reductionism and classification require detailed comparison consider 3d...

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


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


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


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


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


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


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


Why is it Not a Solved Problem?


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


Desirables

• Biologically meaningful alignments not just geometrically meaningful

• Complete database of all alignments

• Ability to apply to structures not in the PDB


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)


Literature Alignments - Flavodoxin vs Che Y ProteinFrom Godzik (1996) Protein Science, 5, 1325-1338.


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


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.


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)


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


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!

http://www.sdsc.edu/pb/papers/ce98.pdf


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


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


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.


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


Extension of the Alignment Path

Gap sizes are limited to G – heuristically set as 30 residues


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


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


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


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


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)


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


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


Test Case: Phycocyanin versus Colicin A


Cyclin-dependent kinasesOpen (purple) Closed (blue)Pavelitch et al. (1997)


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


• 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


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].

http://www.sdsc.edu/pb/papers/cepar.pdf

http://www.sdsc.edu/pb/papers/cepar.pdf

Now

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



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.


Review example where structure comparison has revealed new

biological insights


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)


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

pharm 201 lecture 10, 20091 reductionism and classification require detailed comparison consider 3d...

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