1 (c) Mark Gerstein, 1999, Yale, bioinfo.mbb.yale.edu Several motifs ( -sheet, beta-alpha-beta, helix-loop-helix) combine to form a compact globular

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•Several motifs (-sheet, beta-alpha-beta, helix-loop-helix) combine to form a compact globular structure termed a domain or tertiary structure

•A domain is defined as a polypeptide chain or part of a chain that can independently fold into a stable tertiary structure

•Domains are also units of function (DNA binding domain, antigen binding domain, ATPase domain, etc.)

•Another example of the helix-loop-helix motif is seen within several DNA binding domains including the homeobox proteins which are the master regulators of development

Modules

(Figures from Branden & Tooze)

HMMs, Profiles, Motifs, and Multiple Alignments used to define modules

COG 272, BRCT family

P. Bork et al

Five Principal Fold Classes

All folds

All folds

+ folds

/ folds

small irregular folds

SCOP - Protein Fold Hierarchy

Class - 5Fold - ~500

Superfamily - ~ 700Family ~ 1000

Family - domains with common evolutionary origin

Sequence Similarity May Miss Functional Homologies Which Can Be Detected by

3D Structural Analysis

Residues Aligned

% S

equ

ence

Id

enti

ty

Homologous 3D Structure

Non-homologous3D Structure

Adapted from Chris Sander

} “Twilight zone”

Structural Validation Structural Validation of Homologyof Homology

Adenylate Kinase Guanylate Kinase

19% Seq ID

Z = 12.2

CspA

CspB Topoisomerase I

Asp tRNA Synthetase

Staphylococcal Nuclease

Gene 5 ssDNA Binding Protein

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What is Protein Geometry?

• Coordinates (X, Y, Z’s)

• Dihedral Angles Assumes standard bond

lengths and bond angles

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Other Aspects of Structure, Besides just Comparing Atom Positions

Atom Position, XYZ triplets Lines, Axes,

AnglesSurfaces, Volumes

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Depicting Protein

Structure:Sperm Whale

Myoglobin

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Sperm Whale Myoglobin

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Structural Alignment of Two Globins

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Automatic Alignment to Build Fold LibraryHb

Mb

Alignment of Individual Structures

Fusing into a Single Fold “Template”

Hb VLSPADKTNVKAAWGKVGAHAGEYGAEALERMFLSFPTTKTYFPHF-DLS-----HGSAQVKGHGKKVADALTNAV ||| .. | |.|| | . | . | | | | | | | .| .| || | || . Mb VLSEGEWQLVLHVWAKVEADVAGHGQDILIRLFKSHPETLEKFDRFKHLKTEAEMKASEDLKKHGVTVLTALGAIL

Hb AHVD-DMPNALSALSDLHAHKLRVDPVNFKLLSHCLLVTLAAHLPAEFTPAVHASLDKFLASVSTVLTSKYR------ | | . || | .. . .| .. | |..| . . | | . ||.Mb KK-KGHHEAELKPLAQSHATKHKIPIKYLEFISEAIIHVLHSRHPGDFGADAQGAMNKALELFRKDIAAKYKELGYQG

Structure Sequence Core Core

2hhb HAHU - D - - - M P N A L S A L S D L H A H K L - F - - R V D P V N K L L S H C L L V T L A A H <

HADG - D - - - L P G A L S A L S D L H A Y K L - F - - R V D P V N K L L S H C L L V T L A C H

HATS - D - - - L P T A L S A L S D L H A H K L - F - - R V D P A N K L L S H C I L V T L A C H

HABOKA - D - - - L P G A L S D L S D L H A H K L - F - - R V D P V N K L L S H S L L V T L A S H

HTOR - D - - - L P H A L S A L S H L H A C Q L - F - - R V D P A S Q L L G H C L L V T L A R H

HBA_CAIMO - D - - - I A G A L S K L S D L H A Q K L - F - - R V D P V N K F L G H C F L V V V A I H

HBAT_HO - E - - - L P R A L S A L R H R H V R E L - L - - R V D P A S Q L L G H C L L V T P A R H

1ecd GGICE3 P - - - N I E A D V N T F V A S H K P R G - L - N - - T H D Q N N F R A G F V S Y M K A H <

CTTEE P - - - N I G K H V D A L V A T H K P R G - F - N - - T H A Q N N F R A A F I A Y L K G H

GGICE1 P - - - T I L A K A K D F G K S H K S R A - L - T - - S P A Q D N F R K S L V V Y L K G A

1mbd MYWHP - K - G H H E A E L K P L A Q S H A T K H - L - H K I P I K Y E F I S E A I I H V L H S R <

MYG_CASFI - K - G H H E A E I K P L A Q S H A T K H - L - H K I P I K Y E F I S E A I I H V L Q S K

MYHU - K - G H H E A E I K P L A Q S H A T K H - L - H K I P V K Y E F I S E C I I Q V L Q S K

MYBAO - K - G H H E A E I K P L A Q S H A T K H - L - H K I P V K Y E L I S E S I I Q V L Q S K

Consensus Profile- c - - d L P A E h p A h p h ? H A ? K h - h - d c h p h c Y p h h S ? C h L V v L h p p <

Elements: Domain definitions; Aligned structures, collecting together Non-homologous Sequences; Core annotation

Previous work: Remington, Matthews ‘80; Taylor, Orengo ‘89, ‘94; Artymiuk, Rice, Willett ‘89; Sali, Blundell, ‘90; Vriend, Sander ‘91; Russell, Barton ‘92; Holm, Sander ‘93; Godzik, Skolnick ‘94; Gibrat, Madej, Bryant ‘96; Falicov, F Cohen, ‘96; Feng, Sippl ‘96; G Cohen ‘97; Singh & Brutlag, ‘98

Explain Concept of Distance Matrix on Blackboard

N x N distance matrix

N dimensional space

Metric matrixMij = Dij

2 - Dio2 - Djo

2

Eigenvectors of metric matrix

Principal component analysis

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Automatically Comparing Protein Structures

Given 2 Structures (A & B),

2 Basic Comparison Operations1 Given an alignment optimally

SUPERIMPOSE A onto BFind Best R & T to move A onto B

2 Find an Alignment between A and B based on their 3D coordinates

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RMS Superposition (1)

A

B

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RMS Superposition (2):Distance Between

an Atom in 2 Structures

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RMS Superposition (3):RMS Distance Between

Aligned Atoms in 2 Structures

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RMS Superposition (4):Rigid-Body Rotation and Translation

of One Structure (B)

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RMS Superposition (5):Optimal Movement of One Structure

to Minimize the RMS

Methods of Solution:

springs(F ~ kx)

SVD

Kabsch

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Alignment (1) Make a Similarity Matrix

(Like Dot Plot)

A B C N Y R Q C L C R P M

A 1

Y 1

C 1 1 1

Y 1

N 1

R 1 1

C 1 1 1

K

C 1 1 1

R 1 1

B 1

P 1

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Structural Alignment (1b) Make a Similarity Matrix

(Generalized Similarity Matrix)• PAM(A,V) = 0.5

Applies at every position

• S(aa @ i, aa @ J) Specific Matrix for each pair of

residues i in protein 1 and J in protein 2

Example is Y near N-term. matches any C-term. residue (Y at J=2)

• S(i,J) Doesn’t need to depend on a.a.

identities at all! Just need to make up a score

for matching residue i in protein 1 with residue J in protein 2

1 2 3 4 5 6 7 8 9 10 11 12 13

A B C N Y R Q C L C R P M1 A 12 Y 1 5 5 5 5 5 53 C 1 1 14 Y 15 N 16 R 1 17 C 1 1 18 K9 C 1 1 110 R 1 111 B 112 P 1

J

i

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Seq. Alignment, Struc. Alignment, Threading

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Structural Alignment (1c*)Similarity Matrix

for Structural Alignment• Structural Alignment

Similarity Matrix S(i,J) depends on the 3D coordinates of residues i and J

Distance between CA of i and J

M(i,j) = 100 / (5 + d2)

• Threading S(i,J) depends on the how well

the amino acid at position i in protein 1 fits into the 3D structural environment at position J of protein 2

222 )()()( JiJiJi zzyyxxd −+−+−=

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Alignment (2): Dynamic Programming,Start Computing the Sum Matrixnew_value_cell(R,C) <= cell(R,C) { Old value, either 1 or 0 } + Max[ cell (R+1, C+1), { Diagonally Down, no gaps } cells(R+1, C+2 to C_max),{ Down a row, making col. gap } cells(R+2 to R_max, C+2) { Down a col., making row gap } ]


A 1

Y 1

C 1 1 1

Y 1

N 1

R 1 1

C 1 1 1

K

C 1 1 1

R 1 2 0 0

B 1 2 1 1 1 1 1 1 1 1 1 0 0

P 0 0 0 0 0 0 0 0 0 0 0 1 0


A 1

Y 1

C 1 1 1

Y 1

N 1

R 1 1

C 1 1 1

K

C 1 1 1

R 1 1

B 1

P 1

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Alignment (3):Dynamic Programming, Keep Going


A 1

Y 1

C 1 1 1

Y 1

N 1

R 5 4 3 3 2 2 0 0

C 3 3 4 3 3 3 3 4 3 3 1 0 0

K 3 3 3 3 3 3 3 3 3 2 1 0 0

C 2 2 3 2 2 2 2 3 2 3 1 0 0

R 2 1 1 1 1 2 1 1 1 1 2 0 0

B 1 2 1 1 1 1 1 1 1 1 1 0 0

P 0 0 0 0 0 0 0 0 0 0 0 1 0


A 1

Y 1

C 1 1 1

Y 1

N 1

R 1 1

C 1 1 1

K

C 1 1 1

R 1 2 0 0

B 1 2 1 1 1 1 1 1 1 1 1 0 0

P 0 0 0 0 0 0 0 0 0 0 0 1 0

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Alignment (4): Dynamic Programming, Sum Matrix All Done

A B C N Y R Q C L C R P MA 8 7 6 6 5 4 4 3 3 2 1 0 0

Y 7 7 6 6 6 4 4 3 3 2 1 0 0C 6 6 7 6 5 4 4 4 3 3 1 0 0Y 6 6 6 5 6 4 4 3 3 2 1 0 0N 5 5 5 6 5 4 4 3 3 2 1 0 0R 4 4 4 4 4 5 4 3 3 2 2 0 0C 3 3 4 3 3 3 3 4 3 3 1 0 0K 3 3 3 3 3 3 3 3 3 2 1 0 0C 2 2 3 2 2 2 2 3 2 3 1 0 0R 2 1 1 1 1 2 1 1 1 1 2 0 0B 1 2 1 1 1 1 1 1 1 1 1 0 0P 0 0 0 0 0 0 0 0 0 0 0 1 0


A 1

Y 1

C 1 1 1

Y 1

N 1

R 5 4 3 3 2 2 0 0

C 3 3 4 3 3 3 3 4 3 3 1 0 0

K 3 3 3 3 3 3 3 3 3 2 1 0 0

C 2 2 3 2 2 2 2 3 2 3 1 0 0

R 2 1 1 1 1 2 1 1 1 1 2 0 0

B 1 2 1 1 1 1 1 1 1 1 1 0 0

P 0 0 0 0 0 0 0 0 0 0 0 1 0

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Alignment (5): TracebackFind Best Score (8) and Trace BackA B C N Y - R Q C L C R - P MA Y C - Y N R - C K C R B P


A 8 7 6 6 5 4 4 3 3 2 1 0 0

Y 7 7 6 6 6 4 4 3 3 2 1 0 0

C 6 6 7 6 5 4 4 4 3 3 1 0 0

Y 6 6 6 5 6 4 4 3 3 2 1 0 0

N 5 5 5 6 5 4 4 3 3 2 1 0 0

R 4 4 4 4 4 5 4 3 3 2 2 0 0

C 3 3 4 3 3 3 3 4 3 3 1 0 0

K 3 3 3 3 3 3 3 3 3 2 1 0 0

C 2 2 3 2 2 2 2 3 2 3 1 0 0

R 2 1 1 1 1 2 1 1 1 1 2 0 0

B 1 2 1 1 1 1 1 1 1 1 1 0 0

P 0 0 0 0 0 0 0 0 0 0 0 1 0

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In Structural Alignment, Not Yet Done (Step 6*)

• Use Alignment to LSQ Fit Structure B onto Structure A However, movement of B will now

change the Similarity Matrix

• This Violates Fundamental Premise of Dynamic Programming Way Residue at i is aligned can

now affect previously optimal alignment of residues(from 1 to i-1)

ACSQRP--LRV-SH -R SENCVA-SNKPQLVKLMTH VK DFCV-

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How central idea of dynamic programming is violated in structural

alignment

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Structural Alignment (7*), Iterate Until Convergence

1 Compute Sim. Matrix

2 Align via Dyn. Prog.

3 RMS Fit Based on Alignment

4 Move Structure B

5 Re-compute Sim. Matrix

6 If changed from #1, GOTO #2

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Some Similarities are Readily Apparent others are more Subtle

Easy:Globins

125 res., ~1.5 Å

Tricky:Ig C & V

85 res., ~3 Å

Very Subtle: G3P-dehydro-genase, C-term. Domain >5 Å

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Some Similarities are Readily Apparent others are more Subtle

Easy:Globins

125 res.,

~1.5 Å

Tricky:Ig C & V

85 res., ~3 Å

Very Subtle: G3P-dehydro-genase, C-term. Domain >5 Å

DALI: Protein Structure Comparison by Alignment of Distance Matrices

L. Holm and C. Sander J. Mol. Biol. 233: 123 (1993)

• Generate C-C distance matrix for each protein A and B• Decompose into elementary contact patterns; e.g. hexapeptide-

hexapeptide submatrices• Systematic comparisons of all elementary contact patterns in the

2 distance matrices; similar contact patterns are stored in a “pair list”

• Assemble pairs of contact patterns into larger consistent sets of pairs (alignments), maximizing the similarity score between these local structures

• A Monte-Carlo algorithm is used to deal with the combinatorial complexity of building up alignments from contact patterns

• Dali Z score - number of standard deviations away from mean pairwise similarity value

Structural Validation Structural Validation of Homologyof Homology

Adenylate Kinase Guanylate Kinase

19% Seq ID

Z = 12.2

Dali Domain DictionaryDeitman, Park, Notredame, Heger, Lappe, and Holm

Nucleic Acids Res. 29: 5557 (2001)

• Dali Domain Dictionary is a numerical taxonomy of all known domain structures in the PDB

• Evolves from Dali / FSSP Database Holm & Sander, Nucl. Acid Res. 25: 231-234 (1997)

• Dali Domain Dictionary Sept 2000 10,532 PDB enteries 17,101 protein chains 5 supersecondary structure motifs (attractors) 1375 fold types 2582 functional families 3724 domain sequence families

SCOP the Structural Classification Of Proteins database

This contains all proteins, and protein domains,

of known structure classified in terms of

their structure and evolutionary relationships.

SUPERFAMILY This database contains:

(a) hidden Markov models (HMMs) of all the

proteins and protein domains in SCOP

(b) a list of the matches made by these HMMs to

the sequences of 56 genomes classsified by family.

http://stash.mrc-lmb.cam.ac.uk/SUPERFAMILY/

courtesy of C. Chothia

Most proteins in biology have been

produced by the duplication,

divergence and recombination of

the members of a small number of

protein families.


SUPERFAMILY matches to genome sequences

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

hs at ce dm mk sc pa eo ec mu bs bh mb vc cc cs dr ss xf sa af ll nn ph hb nm pm mt tm pb mj hi sq cj ml hp aa tv hq ta cq cp cr tp cm ct bb rp mq mp uu bn mg

Genomes

% Coverage

GenesGenome


SUPERFAMILY Results forBuchnera and Human Genome Sequences

Buchnera HumansNumber of sequences 564 23867Sequences matched by SUPERFAMILY 410 12616Coverage of genome 61% 41%Number of matched domains 609 22548Number of families 277 648Mean family size 2.2 35Number of large families that form

half the matched domains 37 17


SUPERFAMILY Results forBuchnera and Human Genome Sequences:

Top Five Domain Families

BuchneraP-loop containing nucleotide triphosphate hydrolasesNucleic acid binding proteinsNAD-binding Rossman domainsNucleotidylyl transferasesClass II aaRS synthetases

HumansClassic zinc fingersImmunoglobulin superfamilyP-loop containing nucleotide triphosphate hydrolasesEGF/LamininCadherin


Eukaryotes

0

5000

10000

15000

20000

25000

30000

sc at dm ce hs

Other families

dm+ce+hs: 45 families

at+dm+ce+hs: 56 families

All: 381 families


CDH-4

CDH-3

HMR-1b

CDH-6

CDH-10

CDH-8

CDH-5

CDH-11

CDH-9

T01D3.1

Y37E11A.94.a

Cadherin Proteins in Caenorhabditis elegans

233

95

120

143

56

64

156

113

82

4307

3343

2920

HMR-1a120

1223

2610

2302

1671

1507

984

1156

623

3191

411

S

S

S

S

S

S

S

S

S

S

S

S

3 2 2 3 1 2 3

3 3 3 3 2 3 3

3 3 2 1 2 1 3 1 3 3 3 3 0 3 3 3

0 3 3 21 1 0 3 3 0

0 3 3 3 3 3

3 0 1

3 3 0 0

33 1 1 3

3 2

2

33 3 3

22 2 1

3 3 3 3 3 3 3 2

3 2

1 3 2 0 0 3 1 2 3 0 3 1 2 3 3 1 3 3 1 3 3 3 3 2

CDH-7 76S

111 2 2 3 3

CDH-1 2072775S

3 3 0 3 0 3 0 3 3 3 0 1 0 2 0 1 3 0 3 3 1 3 0 2

CDH-12 1243017S

332 1 0 10 0 3 1 3 3 1 3 0 0 3

Fat

CG7749

Stan

Ds

CadN

CG14900

CG3389

CG15511/CG7805

CG6445

CG7527

Shg

CG4655/CG4509

CG6977

CG11059

CG10421

Cadherin Proteins in Drosophila melanogaster538

320

613

437

158

332

132

286

43

227

158

968

80

189

5147

4643

3666

3503

3097

2204

2005

1821

1820

1783

1507

1963

1346

978

678

S

S

S

S

S

S

S

S

S

S

3 3 3 3

2? 3 3 3

3 3 0 3 3 3 2 3 3 3 1 3 3 3 3 3 3 3 3 2 3 3 3 1 1 3 3 3 3

3 3 3 3 3 3 1 3 3 3 3 3 3 3 1 3 3 3 1

1 3 2 3 0 3 3 3 3 1 3 3 3 3 3 3 3

3 3 3 3

3

3 3 3 33 2

3 3 3 1 3 3 2

3 2 1 3 3 1 3 3 3 3 2 3 3 3 3 3 3 33 3 1 3 3 3 3 3 3 2 1 3 2 1 1

3 3 2 3 3 3 3 2 3 3 3

3 3 3 3 3 3 3 3 3 3 3 3 32

3 2 3 3 3 3 2 3 3

3

3 ?3

3 3 3 3 3 3 3

2? 3 3 3 3 3 3

1 3

3 0 3 3 3 3 3

3 3 3

33 3

2

3 3 1 3 2 3 3 1 33

CG10244/HD-14 503838S

Ret 5181120

S Signal peptide

Cadherin

EGF

EGF_CA

Laminin G

HormR

GPS

Transmembrane Helix

7 Pass Transmembrane Domain

Classic cytoplasmic domain

Tyrosine Kinase cytoplasmic domain

Type 1 Cytoplasmic domain

Type 2 Cytoplasmic domain

Other Cytoplasmic domainMerge Position

Cadherins


Domain Combinations in Genome Sequences

In bacteria close to1/3 of proteins consist of one domain and2/3 consist of two or more domains.

In eukaryotes close to1/4 of proteins consist of one domain and3/4 consist of two or more domains.


Bacteria

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

mk pa eo ec bs bh mb mu cc vc sm ca cs dr au ss sa af ll pm av xf st sr tm hb nn nm mt hi ml aa sq pb ph cj mj ap ta tv hq hp tp cp cr cq cm ct rp bb bn mq mp uu mg

Genome

TotalEC +BS


A Global Representation of Protein Fold Space Hou, Sims, Zhang, Kim, PNAS 100: 2386 - 2390 (2003)

Database of 498 SCOP “Folds” or “Superfamilies”

The overall pair-wise comparisons of 498 folds lead to a 498 x 498 matrix of similarity scores Sijs, where Sij is the alignment score between the ith and jth folds.

An appropriate method for handling such data matrices as a whole is metric matrix distance geometry . We first convert the similarity score matrix [S ij] to a distance matrix [Dij] by using Dij = Smax - Sij, where Smax is the maximum similarity score among all pairs of folds.

We then transform the distance matrix to a metric (or Gram) matrix [M ij] by using Mij = Dij

2 - Dio2 - Djo

2

where Di0, the distance between the ith fold and the geometric centroid of all N = 498 folds. The eigen values of the metric matrix define an orthogonal system of axes, called factors. These axes pass through the geometric centroid of the points representing all observed folds and correspond to a decreasing order of the amount of information each factor represents.

A Global Representation of Protein Fold Space Hou, Sims, Zhang, Kim, PNAS 100: 2386 - 2390 (2003)

Documents

1 (c) Mark Gerstein, 1999, Yale, bioinfo.mbb.yale.edu Several motifs ( -sheet, beta-alpha-beta, helix-loop-helix) combine to form a compact globular