structure alignment

Michael Schroeder BioTechnological CenterTU [email protected] Biotec

Structure Alignment

By Michael Schroeder, Biotec 2

Structure Alignment

+


Content

Motivation Some basics Double Dynamic Programming


PART I: Motivation


Motivation: Conformational changes

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


GEFs

GAPs

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)


G proteins: Conformational change in GTP and GDP bound state


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


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


Motivation: (Distant) Relatives Sequence similarity may be low, but structural

similarity can still be high

Picture from www.jenner.ac.uk/YBF/DanielleTalbot.ppt


Distant relatives

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


Relatives

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


Distant Relatives


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


Relatives

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


Relatives

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


Motivation: Convergent Evolution


Sequence similarity: low

>1cse SubtilisinAQTVPYGIPLIKADKVQAQGFKGANVKVAVLDTGIQASHPDLNVVGGASFVAGEAYNTDGNGHGTHVAGTVAALDNTTGVLGVAPSVSLYAVKVLNSSGSGSYSGIVSGIEWATTNGMDVINMSLGGASGSTAMKQAVDNAYARGVVVVAAAGNSGNSGSTNTIGYPAKYDSVIAVGAVDSNSNRASFSSVGAELEVMAPGAGVYSTYPTNTYATLNGTSMASPHVAGAAALILSKHPNLSASQVRNRLSSTATYLGSSFYYGKGLINVEAAAQ>1acb ChymotrypsinCGVPAIQPVLSGLSRIVNGEEAVPGSWPWQVSLQDKTGFHFCGGSLINENWVVTAAHCGVTTSDVVVAGEFDQGSSSEKIQKLKIAKVFKNSKYNSLTINNDITLLKLSTAASFSQTVSAVCLPSASDDFAAGTTCVTTGWGLTRYTNANTPDRLQQASLPLLSNTNCKKYWGTKIKDAMICAGASGVSSCMGDSGGPLVCKKNGAWTLVGIVSWGSSTCSTSTPGVYARVTALVNWVQQTLAAN


Structural similarity: low

1CSE:E, 1ACB:E


Convergent Evolution

c.41.1 and b.47.1 share interaction partners

c.41.1Subtilisin-like

d.58.3Protease propeptides/

inhibitors

d.84.1Subtilisin inhibitor

d.40.1

CI-2 family of serine protease inhibitors

b.47.1Trypsin-like

serine proteases

c.56.5

Zn-dependentexopeptidase

g.15.1Ovomucoid/PCI-1

like inhibitor



1OYV

4sgbOvomucoid/PCI-1 like inhibitor, g.15.1, topTrypsin-like serine proteases, b.47.1.2, bottom

1oyvOvomucoid/PCI-1 like inhibitor, g.15.1topSubtilisin like c.41.1bottom


Aligned structures

1cseCI-2 family of serine proteases inhitors, d.40.1 topSubtilisin like c.41.1bottom

1acbCI-2 family of serine proteases inhitors, d.40.1 topTrypsin-like serine proteases, b.47.1.2, bottom



Catalytic Triad

>1cse SubtilisinAQTVPYGIPLIKADKVQAQGFKGANVKVAVLDTGIQASHPDLNVVGGASFVAGEAYNTDGNGHGTHVAGTVAALDNTTGVLGVAPSVSLYAVKVLNSSGSGSYSGIVSGIEWATTNGMDVINMSLGGASGSTAMKQAVDNAYARGVVVVAAAGNSGNSGSTNTIGYPAKYDSVIAVGAVDSNSNRASFSSVGAELEVMAPGAGVYSTYPTNTYATLNGTSMASPHVAGAAALILSKHPNLSASQVRNRLSSTATYLGSSFYYGKGLINVEAAAQ>1acb ChymotrypsinCGVPAIQPVLSGLSRIVNGEEAVPGSWPWQVSLQDKTGFHFCGGSLINENWVVTAAHCGVTTSDVVVAGEFDQGSSSEKIQKLKIAKVFKNSKYNSLTINNDITLLKLSTAASFSQTVSAVCLPSASDDFAAGTTCVTTGWGLTRYTNANTPDRLQQASLPLLSNTNCKKYWGTKIKDAMICAGASGVSSCMGDSGGPLVCKKNGAWTLVGIVSWGSSTCSTSTPGVYARVTALVNWVQQTLAAN


Convergent evolution

A and B are native, C is viral

C

BA

A’

A CB C

Henschel et al., Bioinformatics 2006


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

Kinase (Src Haematopoeitic cell kinase, Catalytic domain)

Fyn-SH3/Hck-SH3

HIV Nef mimics kinase in binding SH3



Automatic calculation of equivalent residues

Apart from PxxP motif matches: Arg71/Lys249, Phe90/His289

Residues with equivalents are strictly conserved in HIV-Nef

Nef Kinase



Caspase (red) P35 (yellow) IAP (green)

Upon infection cell starts apoptosis programme, p35 tries to stop it

Mimickry of baculovirus p35 and human inhibitor of apoptosis



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)

Mimickry of Capsids and Cyclophilin



PART II: Some basics


What do we need?

To main operations to align structures: Translation Rotation

How to evaluate a structural alignment? Root mean square deviation, rmsd


Basic Operations: Translation


Basic Operations: Rotation


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

And in 3D?

a

b


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


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


PART III: Dynamic Programming


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)







Question: How?

Question: How?Assume n atoms(x1,y1,z1) to (xn,yn,zn:)Center of mass (xCoM,yCoM,zCoM) = (1/n n

i=1 xi , 1/n ni=1 yi 1/n n

i=1 zi )







For all i: do xi:= xi-xCoM, yi:= yi-yCoM, yi:= yi-yCoM,

Question: How?Assume n atoms (x1,y1,z1) to (xn,yn,zn:)Center of mass (xCoM,yCoM,zCoM) = (1/n n

i=1 xi , 1/n ni=1 yi 1/n n

i=1 zi







Why median andnot mean?


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


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


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

Distance-based scoring matrix

What size doesPAM have?

What size doesR have?


Example

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


Part IV: Double dynamic programming (chapter 9)


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)


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


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)


Questions: How was max. score set in this example?


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

structure alignment

Documents

mbdcity university

conservedcity university

changescity university

inhibitorcity university

acity university

motivationcity university

ironbindingcity university

papainlikecity university