Appendix: Automated Methods for Structure Comparison

• Basic problem: how are any two given structures to be automatically compared in a meaningful way?

• How are distant relationships to be recognized?

program method

DALI distance matrix comparison (basis

for FSSP structural classification)

SSAP dynamic programming (used in CATH

to classify topologies)

VAST convert secondary structures to vectors

and align vectors

Structure comparison is pretty easy when two proteins are very similar

• when two proteins are so similar that the sequences can be reliably aligned, say >35% identical, structure comparison can proceed from the seq. alignment:

1. Align the sequences

sequence 1: YIREV-GKL

sequence 2: YITQVRNKA

2. Superpose the structures to minimize the RMSD for equivalent residue pairs in the alignment

note: thesestructures do notcorrespond to the sequences above

it is harder when the proteins are very

different... • if one cannot align the sequence reliably, how does one

establish which residues, if any, play equivalent structural roles in the two proteins?

• the answer is to attempt to align the structures directly in such a way that structural equivalencies in the two proteins are revealed

• we will discuss how the distance-matrix based algorithm of DALI solves this problem

Distance Matrices•2D representation of 3D structure•plot sequence against itself•identify pairs of residues which are close in space to each other•usually distance between C-alpha carbons is used•identify closeness between residues as dark parts of the matrix

Distance matrices

Different substructures, such as secondary or supersecondary structures, give rise to distinct patterns in the matrix

e.g. antiparallel vs.parallel beta-sheets

in principle, onecould recognizestructural similarityin two proteinsby comparing patternsin distance matrices,but it’s not that simple

Problem: two structures with the same topology may differin the precise location of secondary structure elements alongthe sequence, i.e. loop lengths may differ

samefold,differentmatrices

Or two common architectures may differ in connectivity (topology)...

boththree-strandedantiparallelbeta-sheets

how mightwe comparetheir distancematrices to reveal thissimilarity?

DALI algorithm

• not useful to compare entire matrices

• instead, chop distance matrices into all possible submatrices of 6x6 amino acids

• compare this set of submatrices for pattern similarities rather than comparing entire matrix

1. identify a pair of matching submatrices within the two matrices

make an initialsequence alignment from this match...

2. Identify a second pair which overlaps the first(contains one common structural element)

3. Combine overlapping pairs

overall alignmentof structurallyequivalent sequenceregions

4. Rearrange and “collapse” the matrixaccording to the aligned regions of the sequence

now the commonstructural elementsare aligned as arethe structurallyequivalent residuesin the sequence!

All together now...

The Power of DALI

• DALI is quite powerful because it can recognize architectural similarities even when topologies are different.

• It is also flexible because it can be made more topologically restrictive (i.e. no swapping of segments in chain allowed) to focus on closer relationships

FSSP uses DALI alignments to classify structures

all PDB entries

representative set of structures

representative set of domains

group domains into fold types

(clusters of similar structures)

and make set of representatives of each fold

eliminate similar sequences

divide into domains

align domains with DALI!

8320

947

1484

540

Judging DALI alignments• Z-score: how much better than average is the alignment,

i.e. how many standard deviations from the mean of a distribution of alignments of random pairs of proteins.

>16 very close, 8-16 pretty close, <8 not so close.

• RMSD: root mean square deviation of alpha carbons for the matching portion of the structures.

• LALI: length of alignment (recognizably matching portion of the structures)

• LSEQ2: total length of the sequence being matched.

• %IDE: % sequence identity between the two sequences

if you go into FSSP, and search for a particular structure, you’ll get an output of its best DALI alignments with other structures

STRID2 Z RMSD LALI LSEQ2 %IDE PROTEIN

1plc 24.4 0.0 99 99 100 Plastocyanin (cu2+, ph 6.0)

2pcy 23.4 0.2 99 99 100 Apo-plastocyanin (pH 6.0)

1bqk 12.1 2.0 89 124 29 pseudoazurin

1aac 11.0 1.9 84 104 24 amicyanin

1ibzA 9.1 2.5 83 111 19 nitrosocyanin

1qhqA 8.3 2.4 87 139 29 auracyanin

1rcy 8.2 2.5 90 151 17 rusticyanin biological_unit

1qniA 7.7 2.2 78 572 19 nitrous-oxide reductase

1kcw 7.1 2.4 81 1017 17 ceruloplasmin biological_unit

2cuaA 7.0 2.2 80 122 15 cua fragment

1nwpA 6.7 3.1 85 128 24 azurin