Circular clustering of protein dihedral angles by Minimum Message Length

Area of Science:

• Structural Biology
• Computational Biology
• Bioinformatics

Background:

• Protein secondary structures, like helices and sheets, are traditionally classified at a high level.
• Previous computational methods used extensive Cartesian coordinates, which are highly correlated.
• A more compact and informative representation of protein structural data is needed.

Purpose of the Study:

• To apply information-theoretic Minimum Message Length (MML) classification to protein dihedral angles (phi and psi).
• To develop a more concise and orientation-invariant representation of local protein site properties.
• To identify and characterize novel structural groupings within proteins.

Main Methods:

• Utilized the Snob program with von Mises circular distribution for clustering dihedral angles.
• Represented protein local site properties using two dihedral angles (phi and psi), offering 2 degrees of freedom.
• Employed information-theoretic concepts and a symmetric distance measure to build a minimum spanning tree.

Main Results:

• Successfully clustered protein dihedral angles into distinct groups.
• Visualized these classes in (phi, psi) space, revealing specific structural regions.
• Identified a tight, abundant, and self-perpetuating structure formed by three classes in a specific dihedral angle region.

Conclusions:

• The dihedral angle representation is more compact and informative than Cartesian coordinates for protein structure analysis.
• Information-theoretic MML classification effectively identifies underlying patterns in protein secondary structures.
• The discovered self-perpetuating structure offers new insights into protein folding and stability.