DNA sequence evolution through Integral Value Transformations

Abstract

In deciphering the DNA structures, evolutions and functions, Cellular Automata (CA) plays a significant role. DNA can be thought as a one-dimensional multi-state CA, more precisely four states of CA namely A, T, C, and G which can be taken as numerals 0, 1, 2 and 3. Earlier, Sirakoulis et al. (2003) reported the DNA structure, evolution and function through quaternary logic one dimensional CA and the authors have found the simulation results of the DNA evolutions with the help of only four linear CA rules. The DNA sequences which are produced through the CA evolutions, however, are seen by us not to exist in the established databases of various genomes although the initial seed (initial global state of CA) was taken from the database. This problem motivated us to study the DNA evolutions from more fundamental point of view. Parallel to CA paradigm we have devised an enriched set of discrete transformations which have been named as Integral Value Transformations (IVT). Interestingly, on applying the IVT systematically, we have been able to show that each of the DNA sequence at various discrete time instances in IVT evolutions can be directly mapped to a specific DNA sequence existing in the database. This has been possible through our efforts of getting quantitative mathematical parameters of the DNA sequences involving fractals. Thus we have at our disposal some transformational mechanism between one DNA to another.