protein strucure comparison chapter 6,7 orengo. helices α-helix4-turn helix, min. 4 residues 3 10...
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Protein Strucure Comparison
Chapter 6,7 Orengo
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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
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Strands and Sheets
• Formed by successive H-Bonds between residues can be far apart in sequence.
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Cartoons for Secondary Structure Elements (SSE)
• Topology of Protein Structure (TOPS)– Triangular symbols represent beta strands– Circular symbols represent helices (alpha and 310)
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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
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Strategy
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Two Approaches
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Example
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Intra
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RMSD
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Example
• Alignment– ACSL-DRTS-IRV– A-TLREKSSLIR-
• Know first 5 residues– ACSL-D– A-TLRE
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But not so with structures
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highest score alignment of entire structures
highest score alignment of first five residues
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Finding optimal Root mean square deviation
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Process
€
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)
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Example
• In two dimensions
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Translation
• In two dimensions
Shift Centroids to the origin
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Example HW 9.2
• In two dimensions• Rotation Matrix
-0.70721358 0.707213580.70721358 0.70721358
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The matrix in the book is just an angular rotation
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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
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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
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Alternating Superposition and Alignment
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Example
The best rotation and translation is then found and a newalignment is generated
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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/
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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
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