Published Paper


Mass - Radius Fractal Analysis of Protein Structures from PDB Coordinates

1 S. Pavithra
1 Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Thandalam, Chennai, 602105, Tamil Nadu, India
Page: 1503-1512
Published on: 2025 December

Abstract

Proteins exhibit highly complex three-dimensional structures characterized by irregular geometry, hierarchical organization, and multiscale heterogeneity that are not adequately described by classical Euclidean models. Fractal modeling provides a powerful mathematical framework to capture these intrinsic structural features by exploiting self-similarity and scale invariance inherent in protein folding. In this approach, protein backbones, residue packing, and molecular surfaces are analyzed using fractal descriptors such as fractal dimension, mass–radius relationships, and box-counting methods. These measures quantitatively characterize protein compactness, backbone complexity, and surface roughness across different spatial scales. Fractal analysis has proven effective in distinguishing between ordered and intrinsically disordered regions, comparing native and misfolded conformations, and elucidating structure–function relationships, particularly at active and binding sites. By integrating concepts from polymer physics, statistical mechanics, and nonlinear geometry, fractal modeling enhances our understanding of protein organization beyond conventional structural parameters. This framework offers valuable insights into protein stability, folding dynamics, and biological functionality, and serves as a complementary tool in structural biology, computational biophysics, and bioinformatics.

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