Fuzzy genomes

Abstract

A metric space — dubbed the fuzzy polynucleotide space — is presented for diagnostic purposes in the widest sense to measure the degree of difference and similarity between sequences of nucleic acids. To this end, these acids are transformed to ordered fuzzy sets. They thus become representable as points in n-dimensional unit hypercubes that may be endowed with various metrics. In this way, genetic information in particular and genetics in general become amenable to fuzzy theory, geometry, and topology.

Introduction

Medicine at the turn of the century is characterized by the deepest change it has ever been subject to in its history, i.e. its transformation from a healing profession to a branch of biotechnology. Viewed from an evolutionary perspective, this transformation appears as an aspect of a Darwin–Lamarckian autoevolution of life on earth [14]. The nucleic acids DNA and RNA as the genetic material of living things and viruses play the pivotal role in this arena. Necessary techniques in dealing with this material are sequence analysis and sequence comparison.

Sequence analysis or sequencing aims at determining the building blocks of a nucleic acid, i.e. its monomeric units — nucleotides — and their order in the molecular chain of the acid. It commenced in the early 1960s with the deciphering of the genetic code. Sequence comparison is, by contrast, a taxonomic and diagnostic task to determine the structural relationships such as identity, difference, and similarity between chains of nucleic acids whose sequences have already been analyzed and are known. It deals with questions such as, for example, ‘is this piece of RNA before my eyes an HIV or something else?’. To answer questions of this type requires reliable techniques of sequence comparison between the unknown and the known. We will in the following be concerned with this problem and will present a novel methodology based on fuzzy theory.

In Section 2, nucleic acids (DNA and RNA) are transformed to ordered fuzzy sets. In so doing our primary aim is to make genes, genomes, and genetics directly amenable to fuzzy theory. A first step in this direction is taken by investigating the unit hypercube geometry of nucleic acids in Section 3. Measures of identity, difference, and similarity for genetic material are provided that contribute to the enhancement of taxonomic and diagnostic accuracy and computation in genetics, microbiology, biochemistry, and biotechnology. Two interesting by-products of our analysis are the recognition that the genetic code is 12-dimensional, and the view that genes and genomes are fuzzy entities. Although our methodology in this paper is applied only to nucleic acids, it is general enough to cover all polymers [15].