{'fraction_non_alphanumeric': 0.01872871736662883, 'fraction_numerical': 0.0011350737797956867, 'mean_word_length': 5.8599221789883265, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Numerical Characterization of DNA Sequences for Alignment-free Sequence Comparison - A Review.

BACKGROUND
Biological macromolecules namely, DNA, RNA, and protein have their building blocks organized in a particular sequence and the sequential arrangement encodes evolutionary history of the organism (species). Hence, biological sequences have been used for studying evolutionary relationships among the species. This is usually carried out by multiple sequence algorithms (MSA). Due to certain limitations of MSA, alignment-free sequence comparison methods were developed. The present review is on alignment-free sequence comparison methods carried out using numerical characterization of DNA sequences. Discussion: The graphical representation of DNA sequences by chaos game representation and other 2-dimesnional and 3-dimensional methods are discussed. The evolution of numerical characterization from the various graphical representations and the application of the DNA invariants thus computed in phylogenetic analysis is presented. The extension of computing molecular descriptors in chemometrics to the calculation of new set of DNA invariants and their use in alignment-free sequence comparison in a N-dimensional space and construction of phylogenetic tress is also reviewed. Conclusion: The phylogenetic tress constructed by the alignment-free sequence comparison methods using DNA invariants were found to be better than those constructed using alignment-based tools such as PHLYIP and ClustalW. One of the graphical representation methods is now extended to study viral sequences of infectious diseases for the identification of conserved regions to design peptide-based vaccine by combining numerical characterization and graphical representation.