A three-dimensional representation for base composition of protein-coding DNA sequences

Statistics of trinucleotides in coding sequences and evolution

The aim of this paper is to give measurements indicative of evolutional stages of the species. Two types of statistics of trinucleotides in coding regions are analysed for 27 species. The first one is the codon space, the nucleotide ratio for each of the three codon positions. We apply principal component analysis on this space and extract two principal components faithfully describing the original distribution of the codon space. The first principal component corresponds to the GC content. The second principal component classifies the species into three evolutional groups, Archaea, Bacteria and Eukaryota. The second statistics is the real and theoretical frequency of amino acids. The real frequency of an amino acid in a coding sequence is its frequency in the translated protein. The theoretical frequency is the expected frequency calculated from the ratio of nucleotides. We introduce the discrepancy between these two frequencies as an index of non-randomness of nucleotides in the sequence. This index of non-randomness divides the species into two groups: eukaryotes having smaller non-randomness (i.e. being more random) and prokaryotes having higher non-randomness.

On the validity of Shannon-information calculations for molecular biological sequences

The usefulness of information-theoretic measures of the Shannon-Weaver type, when applied to molecular biological systems such as DNA or protein sequences, has been critically evaluated. It is shown that entropy can be re-expressed in dimensionless terms, thereby making it commensurate with information. Further, we have identified processes in which entropy S and information H change in opposite directions. These processes of opposing signs for delta S and delta H demonstrate that while the Second Law of Thermodynamics mandates that entropy always increases, it places no such restrictions on changes in information. Additionally, we have developed equations permitting information calculations, incorporating conditional occurrence probabilities, on DNA and protein sequences. When the results of such calculations are compared for sequences of various general types, there are no informational content patterns. We conclude that information-theoretic calculations of the present level of sophistication do not provide any useful insights into molecular biological sequences.