Abstract
AbstractIn deciphering the DNA structures, evolutions and functions, Cellular Automata (CA) do have a significant role. DNA can be thought of 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, G.Ch. Sirakoulis et al reported the DNA structure, evolution and function through quaternary logic one dimensional CA and the authors have found the simulation results of 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 our research team 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 a more fundamental point of view. Parallel to the 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 sequences 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.
Highlights
We consider a DNA sequence as a one dimensional, one neighborhood, four states Cellular Automata (CA) where each nucleotide A, T, C and G is replaced by 0, 1, 2 and 3 respectively
The DNA sequences which are produced through the CA evolutions, are seen by our research team not to exist in the established databases of various genomes the initial seed was taken from the database
Parallel to CA paradigm we have devised an enriched set of discrete transformations which have been named as Integral Value Transformations (IVT)
Summary
We consider a DNA sequence as a one dimensional, one neighborhood, four states CA where each nucleotide A, T, C and G is replaced by 0, 1, 2 and 3 respectively. It is worth noting that there are only four linear CA rules namely f0, f27, f34 and f57 which were applied for generating sequences over the time state evolutions. Out of them only f27 and f57 are bijective They used uniform CA rules over the entire DNA sequence for CA evolutions. They did not find any significant results in existing gene database. It is worth noting that most of the rules applied in obtaining the sequences are non-linear as well as bijective. Thereby, the authors are confirmed that by systematic application of IVT as proposed, DNA sequences that exist in the database can be generated unlike the one proposed in [1]
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