An Entropy-Based Alignment-Free Mathematical Framework for Protein Sequence Similarity Analysis

¹ Department of Mathematics, Sri Chandrasekharendra Saraswathi Viswa Mahavidyalaya Kanchipuram, Tamil Nadu, India This email address is being protected from spambots. You need JavaScript enabled to view it.
² Department of Mathematics, Kings Engineering college, Irungattukottai, Chennai, Tamil Nadu, India This email address is being protected from spambots. You need JavaScript enabled to view it.
³ Department of Mathematics, Bharath Instutue of Higher Education and Research, Chennai, Tamil Nadu, India This email address is being protected from spambots. You need JavaScript enabled to view it.

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 16 April 2026

Abstract

In this paper, a mathematical, alignment-free framework is proposed for quantifying similarity and dissimilarity among protein sequences using their physicochemical characteristics. The primary structure - the sequences of amino acids is modelled numerically by mapping each amino acid to a vector in a real-valued feature space determined by physicochemical properties, namely the hydropathy index (hI), first dissociation constant (pka1), and second dissociation constant (pka2). The considered properties play a key part in protein folding, stability, and function, and hence forms a meaningful basis for comparative analysis. The protein sequences are represented as discrete distributions using this numerical representation in a multidimensional parameter space. A Relative Distance Entropy measure is employed to compare the proteins independent of sequence alignment and length, thereby overcoming the limitations inherited in conventional homology-based methods. This enablessimilarity-measurement even in cases of low sequence identity while preserving functional characteristics. The proposed approach provides a computationally efficient and mathematically sound alternative for large-scale protein similarity analysis and functional classification. This method produces similarity values from 47%-100% providing a comparable trend with BLAST sequence identity percentage values for tested protein pairs. The proposed method emphasizes mathematical modelling and computational efficiency, making it suitable for large scale data.