Protein Strucure Comparison

Chapter 6,7 Orengo

Helices

• α-helix 4-turn helix, min. 4 residues310-helix 3-turn helix, min. 3 residuesπ-helix 5-turn helix, min. 5 residues

• Formed by H-Bonds between residues in the same helix

Strands and Sheets

• Formed by successive H-Bonds between residues can be far apart in sequence.

Cartoons for Secondary Structure Elements (SSE)

• Topology of Protein Structure (TOPS)– Triangular symbols represent beta strands– Circular symbols represent helices (alpha and 310)

Multiple structural alignment by CORA allows identification of consensus secondary structure and embellishments

Some families show great structural diversitySome families show great structural diversity

In 117 superfamilies relatives expanded by >2 fold or more

2DSEC algorithm2DSEC algorithm

These families represent more than half the genome sequences of known These families represent more than half the genome sequences of known foldfold

Gabrielle Reeves

Strategy

Two Approaches

Example

Intra

RMSD

Example

• Alignment– ACSL-DRTS-IRV– A-TLREKSSLIR-

• Know first 5 residues– ACSL-D– A-TLRE

But not so with structures

Dyn

amic

Pro

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can

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dir

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highest score alignment of entire structures

highest score alignment of first five residues

Finding optimal Root mean square deviation

Process

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Let (α 1,β1),...,(α r,β r ) Be coordinate sets of equivalenced elements

minimize the expression (Rα i + t −β i)i=1

r

∑

where R is a rotation and t is a translation

Degrees of freedom include1) Equivalenced elements2) Rotation3) Translation (usually centroid)

Example

• In two dimensions

Translation

• In two dimensions

Shift Centroids to the origin

Example HW 9.2

• In two dimensions• Rotation Matrix

-0.70721358 0.707213580.70721358 0.70721358

The matrix in the book is just an angular rotation

The first step

• Transpose centroids to the origin

• Foreach angular displacement in x– Foreach angular displacement in y

• Foreach angular displacement in x– Calculate RMSD– If this RMSD is less than current minimum, save it

But, how did we get the equivalenced elements?

• First seed the problem with an initial equivalence E0

• Then find the Transformation that results in a minimum RMSD

• Use this Transformation to find a better equivalence

Alternating Superposition and Alignment

Example

The best rotation and translation is then found and a newalignment is generated

Structural Classification of Proteins (SCOP)

SCOP describes protein structures using a hierarchical classification scheme:

ClassesFoldsSuperfamilies (likely evolutionary relationship)FamiliesDomainsIndividual PDB entries

http://scop.mrc-lmb.cam.ac.uk/scop/

Class, Architecture, Topology, andHomologous Superfamily (CATH) database

Page 293

CATH clusters proteins at four levels:

C Class (, , & folds)A Architecture (shape of domain, e.g. jelly roll)T Topology (fold families; not necessarily homologous)H Homologous superfamily

http://www.biochem.ucl.ac.uk/basm/cath_new