Structure Alignment

1
Structure Alignment
2
Structure Alignment

3
Content

• Motivation
• Some basics
• Double Dynamic Programming

4
PART I Motivation
5
Motivation Conformational changes

• Upon ligand binding structures may change
• Structural alignment can highlight the changes

6
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)

7
G proteins Conformational change in GTP and GDP
bound state
8
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

9
(No Transcript)
10
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

11
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

12
(No Transcript)
13
Motivation (Distant) Relatives

• Sequence similarity may be low, but structural
  similarity can still be high

Picture from www.jenner.ac.uk/YBF/DanielleTalbot.p
pt
14
Distant relatives

• Globins occur widely
• Primary function binding oxygen
• Assembly of helices surrounding haem group

15
Relatives

• Sperm whale myoglobin (2lh7) and Lupin
  leghaemoglobin (1mbd)

16
Distant Relatives
17
Relatives

• Actinidin (2act) and Papain (9pap)
• Sequence identity 49, rmsd 0.77A
• Same family Papain-like

18
Relatives

• Plastocyanin (5pcy) and azurin (2aza)
• Core of structure is conserved

19
Relatives

• Structure classifications like CATH and FSSP use
  structural alignments to identify superfamilies.

20
Motivation Convergent Evolution
21
Sequence similarity low
gt1cse Subtilisin AQTVPYGIPLIKADKVQAQGFKGANVKVAVLD
TGIQA SHPDLNVVGGASFVAGEAYNTDGNGHGTHVAGTVAAL DNTTGV
LGVAPSVSLYAVKVLNSSGSGSYSGIVSGIE WATTNGMDVINMSLGGAS
GSTAMKQAVDNAYARGVVV VAAAGNSGNSGSTNTIGYPAKYDSVIAVGA
VDSNSNR ASFSSVGAELEVMAPGAGVYSTYPTNTYATLNGTSMA SPHV
AGAAALILSKHPNLSASQVRNRLSSTATYLGSS FYYGKGLINVEAAAQ
gt1acb Chymotrypsin CGVPAIQPVLSGLSRIVNGEEAVPGSWPWQV
SLQDKT GFHFCGGSLINENWVVTAAHCGVTTSDVVVAGEFDQG SSSEK
IQKLKIAKVFKNSKYNSLTINNDITLLKLSTA ASFSQTVSAVCLPSASD
DFAAGTTCVTTGWGLTRYTN ANTPDRLQQASLPLLSNTNCKKYWGTKIK
DAMICAGA SGVSSCMGDSGGPLVCKKNGAWTLVGIVSWGSSTCST STP
GVYARVTALVNWVQQTLAAN
22
Structural similarity low
1CSEE, 1ACBE
23
Convergent Evolution

• c.41.1 and b.47.1 share interaction partners

d.40.1 CI-2 family of serine protease inhibitors
d.58.3Protease propeptides/inhibitors
c.41.1 Subtilisin-like
b.47.1Trypsin-likeserine proteases
d.84.1Subtilisin inhibitor
c.56.5 Zn-dependentexopeptidase
g.15.1 Ovomucoid/PCI-1 like inhibitor
24
Convergent Evolution
1oyv Ovomucoid/PCI-1 like inhibitor,
g.15.1top Subtilisin like c.41.1bottom
1OYV
4sgb Ovomucoid/PCI-1 like inhibitor, g.15.1,
top Trypsin-like serine proteases, b.47.1.2,
bottom
25
Convergent Evolution

• Aligned structures

1cse CI-2 family of serine proteases inhitors,
d.40.1 top Subtilisin like c.41.1bottom
1acb CI-2 family of serine proteases inhitors,
d.40.1 top Trypsin-like serine proteases,
b.47.1.2, bottom
26
Catalytic Triad
gt1cse Subtilisin AQTVPYGIPLIKADKVQAQGFKGANVKVAVLD
TGIQA SHPDLNVVGGASFVAGEAYNTDGNGHGTHVAGTVAAL DNTTGV
LGVAPSVSLYAVKVLNSSGSGSYSGIVSGIE WATTNGMDVINMSLGGAS
GSTAMKQAVDNAYARGVVV VAAAGNSGNSGSTNTIGYPAKYDSVIAVGA
VDSNSNR ASFSSVGAELEVMAPGAGVYSTYPTNTYATLNGTSMA SPHV
AGAAALILSKHPNLSASQVRNRLSSTATYLGSS FYYGKGLINVEAAAQ
gt1acb Chymotrypsin CGVPAIQPVLSGLSRIVNGEEAVPGSWPWQV
SLQDKT GFHFCGGSLINENWVVTAAHCGVTTSDVVVAGEFDQG SSSEK
IQKLKIAKVFKNSKYNSLTINNDITLLKLSTA ASFSQTVSAVCLPSASD
DFAAGTTCVTTGWGLTRYTN ANTPDRLQQASLPLLSNTNCKKYWGTKIK
DAMICAGA SGVSSCMGDSGGPLVCKKNGAWTLVGIVSWGSSTCST STP
GVYARVTALVNWVQQTLAAN
27
Convergent evolution
A
B
C
A
A

• A and B are native, C is viral

Henschel et al., Bioinformatics 2006
28
HIV Nef mimics kinase in binding SH3
Kinase (Src Haematopoeitic cell kinase,
Catalytic domain)

• Comparison of Nef-SH3 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
Henschel et al., Bioinformatics 2006
29
Automatic calculation of equivalent residues
Nef
Kinase

• Apart from PxxP motif matches Arg71/Lys249,
  Phe90/His289
• Residues with equivalents are strictly conserved
  in HIV-Nef

Henschel et al., Bioinformatics 2006
30
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

Henschel et al., Bioinformatics 2006
31
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 gt100 (Towers,
  Nature Medicine, 2003)

Henschel et al., Bioinformatics 2006
32
PART II Some basics
33
What do we need?

• To main operations to align structures
• Translation
• Rotation
• How to evaluate a structural alignment?
• Root mean square deviation, rmsd

34
Basic Operations Translation
35
Basic Operations Translation
36
Basic Operations Translation
37
Basic Operations Rotation
38
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 distanced(a,b) v (xa--xb )2 (ya
  -yb )2
• And in 3D?

39
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 v 1/n ? di2

40
Quality of Alignment and Example

• Unit of RMSD gt e.g. Ångstroms
• Identical structures gt RMSD 0
• Similar structures gt RMSD is small (1 3 Å)
• Distant structures gt RMSD gt 3 Å

41
PART III Dynamic Programming
42
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

43
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

Question How? Assume n atoms (x1,y1,z1) to
(xn,yn,zn) (for one structure)
44
A very simple algorithm
Question How?Assume n atoms(x1,y1,z1) to
(xn,yn,zn) Center of mass (xCoM,yCoM,zCoM)
(1/n ?ni1 xi , 1/n ?ni1 yi 1/n ?ni1 zi )

• 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

Question How?
45
A very simple algorithm
Question How?Assume n atoms (x1,y1,z1) to
(xn,yn,zn) Center of mass (xCoM,yCoM,zCoM)
(1/n ?ni1 xi , 1/n ?ni1 yi 1/n ?ni1 zi

• 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

For all i do xi xi-xCoM, yi yi-yCoM, yi
yi-yCoM,
46
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?
47
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

48
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) gt max. score then R(Ai, Bj)
  max. score
• The gap/mismatch penalty is set to 0

49
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) gt max. score then R(Ai, Bj)
  max. score
• The gap/mismatch penalty is set to 0

What size doesPAM have? What size doesR have?
50
Example

• R(Ai, Bj) 1/d(Ai, Bj) - 1/t for t1/10 and max.
  score 2

51
Part IV Double dynamic programming (chapter 9)
52
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)

53
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

54
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)

55
(No Transcript)
56
(No Transcript)
57
Questions How was max. score set in this
example?
58
(No Transcript)
59
(No Transcript)
60
(No Transcript)
61
(No Transcript)
62
(No Transcript)
63
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