Fuzzy genomes
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].
Section snippets
DNA and RNA as ordered fuzzy sets
In this section, we will represent the nucleic acids DNA and RNA as ordered fuzzy sets to inquire into the ontology and geometry of genetic information in the next section. Since our presentation is intended to be self-contained, a few terminological arrangements on nucleic acids and fuzzy sets may be in order (see Appendix A).
The geometry of polynucleotides
Through its fuzzy code, a polynucleotide is representable as a point in a unit hypercube. This unit hypercube whose points are polynucleotides is dubbed a fuzzy polynucleotide space. It allows for a geometry of polynucleotides that appears a promising approach in genetic taxonomy and diagnosis. In this section we will introduce this geometry. To this end, some terminology on the unit hypercube representability of polynucleotides may be useful (for details, see [11], [13]). The geometry of the
Conclusion
We have transformed polynucleotide chains to ordered fuzzy sets. The ordered membership vector of such a fuzzy set, termed its fuzzy code, represents a point in an n-dimensional unit hypercube. A polynucleotide thus becomes a unique point in the hypercube. We have therefore dubbed this cube a fuzzy polynucleotide space. The geometry, topology and logic that can be done in this space render polynucleotides directly amenable to fuzzy theory. We have demonstrated this approach by difference,
Acknowledgements
I thank my son Manuel for drawing the figures for this paper.
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