Direct Sum Simplex Signal Space Codes for DNA Nucleotides and Amino Acid Codons

Abstract

A genomic symbol to signal conversion concept is introduced and demonstrated on nucleotide base pairs and amino acid codons. Binary encodings of the presence or absence of bioinformatic attributes (e.g., physical, chemical, functional, structural, etc.) onto Euclidean signal space points of $+1$ or $-1$ is performed for individual base pairs or blocks of DNA symbols such as amino acid codons. The symbol to Euclidean space mapping is further encoded into an expanded digital representation based on a direct sum $M$ -ary tree structure called a $\sigma$ -tree. For bioinformatic query sequences, the $\sigma$ -tree provides a rapid search mechanism to find near neighbor similarity sets within warehouses of heterogeneous bioinformatic data. Bioinformatic utility will be achieved in data mining systems based on the proposed symbol-to-signal mapping method through trend analysis of bioinformatic attribute data within similarity set aggregates. Query specific feature/attribute similarity sets are revealed by high dimensional Euclidean signal space clusters. The proposed binary encoded signal vectors provide an equal energy Euclidean space simplex code in the sense of channel coding signal constellation design. Use of an equal energy simplex code prevents biases from being introduced among different attributes during the symbol sequence to signal sequence mapping. The inappropriate use of a multienergy, low dimension, signal point mapping is replaced with a same-energy, high dimension, signal point mapping. The $M$ -ary digital encoding and associated near neighbor search method is extensible to nucleotide sequence blocks of any length, producing digitally expressed signal space simplex representations on a hypersphere of high dimension. Moreover, the direct sum structure empowers computation and memory efficiencies that grow only linearly with increasing sequence length and signal set dimensionality. The bioinformatic attribute encoding method and efficient $\sigma$ -tree expanded digital representation introduced here will provide a foundation for constructing novel genomic driven data mining systems.