Biomedical subjects
Publications and source records attributed to A A Tsonis.
DNA sequences usually involve local construction rules that affect different scales. As such their "dictionary" may not follow Zipf's law (a power law) which is followed in every natural language. Indeed, analysis of many DNA sequences suggests that no linguistics connections to DNA exist and that even though it has structure DNA is not a language. Computer simulations and a biological approach to this problem further support these results.
A re-evaluation of the properties of the random walks generated from DNA sequences reveals that previously reported scaling (appropriate to either pure random walks or long-range correlations) cannot be justified. Thus our analysis cannot support the claim that different evolutionary categories exhibit different scaling.
In this paper we have employed Fourier analysis of DNA coding and non-coding sequences in an attempt to identify possible patterns in gene sequences. It was found that while intronic sequences show a rather random pattern, coding sequences show periodicities and in particular a periodicity of 3. We were able to reconstruct such patterns by assuming a gene having one codon occurring in about 40% of the sequence. This could indicate that the predominant presence of codons all starting from the same base could confer the observed periodicities. Indeed, it was found that proteins do obey this rule. Implications of this finding in gene evolution are discussed.
Ideas from the theory of dynamical systems are applied in biological pattern formation. By considering a simple reaction-diffusion model subjected to an external excitation, we find that the system can give rise to a great variety of periodic, quasiperiodic, and chaotic evolutions.
In this paper we review some of the basic principles of the theory of dynamical systems. We introduce the reader to the definition of chaos and strange attractors and we discuss their implications in biology.
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