Structure Alignment
Michael Schroeder
BioTechnological Center
TU Dresden
ms@biotec.tu-dresden.de
www.biotec.tu-dresden.de
Biotec
Structure Alignment
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By Michael Schroeder, Biotec
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Content
 Motivation
 Some basics
 Double Dynamic Programming
By Michael Schroeder, Biotec
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PART I: Motivation
By Michael Schroeder, Biotec
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Motivation: Conformational changes
 Upon ligand binding structures may change
 Structural alignment can highlight the changes
By Michael Schroeder, Biotec
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Conformational changes:
Small GTPases
 Small GTPases act as molecular
switches to control and regulate
important functions and pathways
within in cell
 Activated by
guanine nucleotide
exchange factors
(GEF)
 Inactivated by
GTPase activating
proteins (GAP)
GEFs
GAPs
By Michael Schroeder, Biotec
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G proteins: Conformational change in
GTP and GDP bound state
By Michael Schroeder, Biotec
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Open and closed conformation of
cytrate synthase (1cts,5cts)
 Open: oxalacetate, Closed: oxalacetate and co-enzyme A
 Loop between two helices moves by 6A and rotates by 28º, some atoms
move by 10A
By Michael Schroeder, Biotec
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By Michael Schroeder, Biotec
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Hinge motion in Lactoferrin (1lfh, 1lfg)
 Lactoferrin is an iron-binding protein found in
secretions such as milk or tears
 Rotation of 54º upon iron-binding
By Michael Schroeder, Biotec
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Hinge motion in Lactoferrin (1lfh, 1lfg)
 Lactoferrin is an iron-binding protein found in
secretions such as milk or tears
 Rotation of 54º upon iron-binding
By Michael Schroeder, Biotec
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By Michael Schroeder, Biotec
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Motivation: (Distant) Relatives
 Sequence similarity may be low, but structural
similarity can still be high
By Michael Schroeder, Biotec
Picture from www.jenner.ac.uk/YBF/DanielleTalbot.ppt
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Distant relatives
 Globins occur widely
 Primary function: binding oxygen
 Assembly of helices surrounding haem group
By Michael Schroeder, Biotec
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Relatives
SpermBywhale
myoglobin (2lh7) and Lupin leghaemoglobin (1mbd)
Michael Schroeder, Biotec
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Distant Relatives
By Michael Schroeder, Biotec
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Relatives
 Actinidin (2act) and Papain (9pap)
 Sequence identity 49%, rmsd 0.77A
 Same family: Papain-like
By Michael Schroeder, Biotec
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Relatives
 Plastocyanin (5pcy) and azurin (2aza)
 Core of structure is conserved
By Michael Schroeder, Biotec
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Relatives
 Structure classifications like CATH and FSSP use
structural alignments to identify superfamilies.
By Michael Schroeder, Biotec
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Motivation: Convergent Evolution
By Michael Schroeder, Biotec
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Sequence similarity: low
>1cse Subtilisin
AQTVPYGIPLIKADKVQAQGFKGANVKVAVLDTGIQA
SHPDLNVVGGASFVAGEAYNTDGNGHGTHVAGTVAAL
DNTTGVLGVAPSVSLYAVKVLNSSGSGSYSGIVSGIE
WATTNGMDVINMSLGGASGSTAMKQAVDNAYARGVVV
VAAAGNSGNSGSTNTIGYPAKYDSVIAVGAVDSNSNR
ASFSSVGAELEVMAPGAGVYSTYPTNTYATLNGTSMA
SPHVAGAAALILSKHPNLSASQVRNRLSSTATYLGSS
FYYGKGLINVEAAAQ
>1acb Chymotrypsin
CGVPAIQPVLSGLSRIVNGEEAVPGSWPWQVSLQDKT
GFHFCGGSLINENWVVTAAHCGVTTSDVVVAGEFDQG
SSSEKIQKLKIAKVFKNSKYNSLTINNDITLLKLSTA
ASFSQTVSAVCLPSASDDFAAGTTCVTTGWGLTRYTN
ANTPDRLQQASLPLLSNTNCKKYWGTKIKDAMICAGA
SGVSSCMGDSGGPLVCKKNGAWTLVGIVSWGSSTCST
STPGVYARVTALVNWVQQTLAAN
By Michael Schroeder, Biotec
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Structural similarity: low
By Michael Schroeder, Biotec
1CSE:E, 1ACB:E
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Convergent Evolution
 c.41.1 and b.47.1 share interaction partners
c.41.1
Subtilisin-like
d.40.1
CI-2 family of serine
protease inhibitors
d.58.3
Protease propeptides/
inhibitors
b.47.1
Trypsin-like
serine proteases
d.84.1
Subtilisin inhibitor
g.15.1
Ovomucoid/PCI-1
like inhibitor
By Michael Schroeder, Biotec
c.56.5
Zn-dependent
exopeptidase
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Convergent Evolution
1oyv
Ovomucoid/PCI-1 like inhibitor, g.15.1top
Subtilisin like c.41.1bottom
1OYV
By Michael Schroeder, Biotec
4sgb
Ovomucoid/PCI-1 like inhibitor, g.15.1, top
Trypsin-like serine proteases, b.47.1.2,
24 bottom
Convergent Evolution
 Aligned structures
1cse
CI-2 family of serine proteases inhitors, d.40.1 top
Subtilisin like c.41.1bottom
By Michael Schroeder, Biotec
1acb
CI-2 family of serine proteases inhitors, d.40.1 top
Trypsin-like serine proteases, b.47.1.2,25bottom
Catalytic Triad
>1cse Subtilisin
AQTVPYGIPLIKADKVQAQGFKGANVKVAVLDTGIQA
SHPDLNVVGGASFVAGEAYNTDGNGHGTHVAGTVAAL
DNTTGVLGVAPSVSLYAVKVLNSSGSGSYSGIVSGIE
WATTNGMDVINMSLGGASGSTAMKQAVDNAYARGVVV
VAAAGNSGNSGSTNTIGYPAKYDSVIAVGAVDSNSNR
ASFSSVGAELEVMAPGAGVYSTYPTNTYATLNGTSMA
SPHVAGAAALILSKHPNLSASQVRNRLSSTATYLGSS
FYYGKGLINVEAAAQ
>1acb Chymotrypsin
CGVPAIQPVLSGLSRIVNGEEAVPGSWPWQVSLQDKT
GFHFCGGSLINENWVVTAAHCGVTTSDVVVAGEFDQG
SSSEKIQKLKIAKVFKNSKYNSLTINNDITLLKLSTA
ASFSQTVSAVCLPSASDDFAAGTTCVTTGWGLTRYTN
ANTPDRLQQASLPLLSNTNCKKYWGTKIKDAMICAGA
SGVSSCMGDSGGPLVCKKNGAWTLVGIVSWGSSTCST
STPGVYARVTALVNWVQQTLAAN
By Michael Schroeder, Biotec
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Convergent evolution
A
B
C C
B
A
A’
C
A and B are native, C is viral
By Michael Schroeder, Biotec
Henschel et al., Bioinformatics
2006
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HIV Nef mimics kinase in binding SH3
Kinase (Src Haematopoeitic cell
kinase, Catalytic domain)
 Comparison of NefSH3 and intra-chain
interaction of
catalytic domain
and SH3 of Hck,
PDBs: 1efn and
2hck
 No evidence of
homology between
Nef and Kinase
HIV1-Nef
Fyn-SH3/Hck-SH3
By Michael Schroeder, Biotec
Henschel et al., Bioinformatics
2006
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Automatic calculation of equivalent residues
Nef Kinase
 Apart from PxxP motif
matches: Arg71/Lys249,
Phe90/His289
 Residues with equivalents
are strictly conserved in HIVNef
By Michael Schroeder, Biotec
Henschel et al., Bioinformatics
2006
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Mimickry of baculovirus p35 and
human inhibitor of apoptosis
 Caspase (red)
 P35 (yellow)
 IAP (green)
 Upon infection cell
starts apoptosis
programme, p35
tries to stop it
By Michael Schroeder, Biotec
Henschel et al., Bioinformatics
2006
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Mimickry of Capsids and Cyclophilin
 HIV capsid protein
(yellow)
 Cyclophilin (red, green)
 Cyclophilin A restricts
HIV infectivity
 Upon mutation of
cyclophilin or inhibition
with cyclophorin,
infectivity goes up >100
(Towers, Nature
Medicine, 2003)
By Michael Schroeder, Biotec
Henschel et al., Bioinformatics
2006
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PART II: Some basics
By Michael Schroeder, Biotec
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What do we need?
 To main operations to align structures:
 Translation
 Rotation
 How to evaluate a structural alignment?
 Root mean square deviation, rmsd
By Michael Schroeder, Biotec
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Basic Operations: Translation
By Michael Schroeder, Biotec
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Basic Operations: Translation
By Michael Schroeder, Biotec
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Basic Operations: Translation
By Michael Schroeder, Biotec
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Basic Operations: Rotation
By Michael Schroeder, Biotec
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Root Mean Square Deviation
 What is the distance between two points a with
coordinates xa and ya and b with coordinates xb and
yb?
 Euclidean distance:
d(a,b) = √ (xa--xb )2 + (ya -yb )2
a
b
 And in 3D?
By Michael Schroeder, Biotec
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Root Mean Square Deviation
 In a structure alignment the score measures how far
the aligned atoms are from each other on average
 Given the distances di between n aligned atoms, the
root mean square deviation is defined as
rmsd = √ 1/n ∑ di2
By Michael Schroeder, Biotec
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Quality of Alignment and Example
 Unit of RMSD => e.g. Ångstroms
 Identical structures => RMSD = “0”
 Similar structures => RMSD is small (1 – 3 Å)
 Distant structures => RMSD > 3 Å
By Michael Schroeder, Biotec
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PART III:
Dynamic Programming
By Michael Schroeder, Biotec
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A very simple algorithm…
 …to align identical structures with conformational
changes
 Generate a sequence alignment (not necessary if both
sequences are really 100% identical)
 Compute center of mass for both structures
 Move both structures so that the centers of mass are
the origin
 Compute the angle between all aligned residues
 Rotate structure by median of all angles
By Michael Schroeder, Biotec
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A very simple algorithm…
 …to align identical structures with conformational
changes
 Generate a sequence alignment (not necessary if both
sequences are really 100% identical)
 Compute center of mass for both structures
 Move both structures so that the centers of mass are
the origin
Question: How?
 Compute the angle between all aligned residues
Assume n atoms
 Rotate structure by median of (x
all ,y
angles
1 1,z1) to (xn,yn,zn)
(for one structure)
By Michael Schroeder, Biotec
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A very simple algorithm…
n atoms(x
Question:
…to alignHow?Assume
identical structures
with
1,yconformational
1,z1) to (xn,yn,zn:)
changesCenter of mass (xCoM,yCoM,zCoM) =
(1/n ni=1 xi , 1/n ni=1 yi 1/n ni=1 zi )
 Generate a sequence alignment (not necessary if both
sequences are really 100% identical)
 Compute center of mass for both structures
 Move both structures so that the centers of mass are
the origin
How?
 Compute the angle between allQuestion:
aligned residues
 Rotate structure by median of all angles
By Michael Schroeder, Biotec
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A very simple algorithm…
n atomswith
(x1,yconformational
Question:
…to alignHow?Assume
identical structures
1,z1) to (xn,yn,zn:)
changesCenter of mass (xCoM,yCoM,zCoM) =
(1/n ni=1 xi , 1/n ni=1 yi 1/n ni=1 zi
 Generate a sequence alignment (not necessary if both
sequences are really 100% identical)
 Compute center of mass for both structures
 Move both structures so that the centers of mass are
the origin
 Compute the angle between all aligned residues
 Rotate structure by median of all angles
For all i: do xi:= xi-xCoM, yi:= yi-yCoM, yi:= yi-yCoM,
By Michael Schroeder, Biotec
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A very simple algorithm…
 …to align identical structures with conformational
changes
 Generate a sequence alignment (not necessary if both
sequences are really 100% identical)
 Compute center of mass for both structures
 Move both structures so that the centers of mass are
the origin
 Compute the angle between all aligned residues
 Rotate structure by median of all angles
Why median and
not mean?
By Michael Schroeder, Biotec
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A refinement: Alternating
alignment and superposition
 1. P = initial alignment
(e.g. based on sequence alignment)
 2. Superpose structures A and B based on P
 3. Generate distance-based scoring matrix R from
superposition
 4. Use dynamic programming to align A and B using
scoring matrix R
 5. P‘ = new alignment derived from dynamic
programming step
 6. If P‘ is different from P then go to step 2 again
By Michael Schroeder, Biotec
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Distance-based scoring matrix
 Let d(Ai, Bj) be the Euclidean distance between Ai and Bj
 Let t be the upper distance limit for residues to be
rewarded
 The scoring matrix R is defined as follows:
R(Ai, Bj) = 1 / d(Ai, Bj) - 1 / t
if R(Ai, Bj) > max. score then R(Ai, Bj) = max. score
 The gap/mismatch penalty is set to 0
By Michael Schroeder, Biotec
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Distance-based scoring matrix
 Let d(Ai, Bj) be the Euclidean distance between Ai and Bj
 Let t be the upper distance limit for residues to be
rewarded
 The scoring matrix R is defined as follows:
R(Ai, Bj) = 1 / d(Ai, Bj) - 1 / t
if R(Ai, Bj) > max. scoreWhat
thensize
R(Adoes
i, Bj) = max. score
PAM have?
What size does
 The gap/mismatch penalty is set
to 0
R have?
By Michael Schroeder, Biotec
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Example
 R(Ai, Bj) = 1/d(Ai, Bj) - 1/t for t=1/10 and max. score =2
By Michael Schroeder, Biotec
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Part IV: Double dynamic
programming (chapter 9)
By Michael Schroeder, Biotec
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Doube dynamic programming
 Goal: Simultaniously align and superpose structures
 Double dynamic programming is a heuristic which
tries to achieve goal
 Implemented as part of SSAP (used e.g. by CATH)
By Michael Schroeder, Biotec
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Idea of double dynamic
programming
 Use two levels of dynamic programming:
 High level, which
summarises low
level DP
 Low level, which
generates alignment
based on assumption
that ai and bj are part
of an optimal alignment
By Michael Schroeder, Biotec
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Low level matrix
 ijR is the low level scoring matrix assuming the pair ai
and bj are aligned
 ijRkl is the score showing how well ak fits onto bl under
the constraint that ai and bj are aligned
 Perform dynamic programming for all pairs i,j using
ijR with constraint that optimal alignment includes (i,j)
By Michael Schroeder, Biotec
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By Michael Schroeder, Biotec
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Questions: How was max. score
set in this example?
By Michael Schroeder, Biotec
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By Michael Schroeder, Biotec
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Summary
 Structural alignments are useful to study
conformational changes, to classify domains into
families (DDP is used in CATH), to study proteins
with distant relationships and hence low sequence
similarity
 Algorithms
 Basic operations: translate and rotate
 Simple algorithm based on dynamic programming
 Double dynamic programming:
low-level programming using substitution matrix based
residue distance
Aggregation of best paths for high-level programming
By Michael Schroeder, Biotec
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