Network scaling invariants help to elucidate basic topological principles of proteins

Area of Science:

• Structural biology
• Computational biology
• Network science

Background:

• Protein folding into tertiary structures involves independent subunit stabilization.
• Defining these independent subunits (domains) lacks a universally accepted method.
• Existing definitions do not fully leverage fundamental properties of protein 3D structure.

Purpose of the Study:

• To establish an unequivocal definition of protein domains based on inter-residue contact networks.
• To represent protein residues using network invariants (intramodule degree z and participation coefficient P).
• To explore the link between protein sequence, structure, and dynamics using this network approach.

Main Methods:

• Representing proteins as networks based on inter-residue contact adjacency matrices.
• Applying a global network module identification algorithm to maximize modularity.
• Analyzing residues based on their intramodule degree (z) and participation coefficient (P).

Main Results:

• Protein structures share a common topological design characterized by the P/z ratio.
• High P/z residues play a role in the protein folding process.
• Protein architecture displays hierarchical organization, linking sequence, secondary, and tertiary structures.
• Identified repeatable scaling laws across different organizational levels, from sequence to folding units.

Conclusions:

• The network-based P/z characterization provides an invariant representation of protein structures.
• This approach reveals a universal hierarchical organization in protein architecture.
• The findings suggest a unified framework for understanding protein sequence-structure-dynamics relationships.