Fractal and Mathematical Morphology in Intricate Comparison between Tertiary Protein Structures

TL;DR

This paper introduces a novel approach using fractal geometry and mathematical morphology to compare 3D protein structures at both global and atomic levels, aiming for more precise structural differences than traditional methods.

Contribution

It presents new techniques employing fractal and morphological operations for detailed protein structure comparison, surpassing existing backbone alignment methods.

Findings

Enhanced accuracy in detecting structural differences.

Ability to distinguish superficial and local similarities.

Provides deeper insights into protein functions.

Abstract

Intricate comparison between two given tertiary structures of proteins is as important as the comparison of their functions. Several algorithms have been devised to compute the similarity and dissimilarity among protein structures. But, these algorithms compare protein structures by structural alignment of the protein backbones which are usually unable to determine precise differences. In this paper, an attempt has been made to compute the similarities and dissimilarities among 3D protein structures using the fundamental mathematical morphology operations and fractal geometry which can resolve the problem of real differences. In doing so, two techniques are being used here in determining the superficial structural (global similarity) and local similarity in atomic level of the protein molecules. This intricate structural difference would provide insight to Biologists to understand the protein structures and their functions more precisely.