Prof. Dr.-Ing. Werner Henkel
This research contains two separate parts. In the first part, we have used classical multidimensional scaling (CMD) technique to scale down a 64-dimensional empirical codon mutation (ECM) matrix and a 20-dimensional chemical distance matrix to two dimensions (2-D). The 2-D plots of ECM show that most mutations occur between codons that encode the same amino acid, i.e., the changes from one codon to another will not change the amino acid to be produced. Furthermore, most of the highly probable inter-amino acid mutations will not result in a dramatic change of chemical properties. However, we have seen some inconsistencies in comparing the 2-D plots of ECM and chemical distance matrices, in which codons near to each other in mutation distance have a significant difference in chemical properties. This may lead to a severe effect, and hence the results point out that some protection mechanism is needed to counteract. In addition, the arrangement of the amino acids is very much in line with the so-called Taylor classification. In the second part of the research, we have focused on investigating the relationship between Shannon and Boltzmann entropies using the complete genome sequence of the bacteria E. coli. There are positions in which parallel and anti parallel relationships exist. We have found that around the terminus, the two entropies seem to have an opposite trend with high Shannon and low Boltzmann entropies, meaning that the sequence is more random and at the same time less stable. In general, the Boltzmann entropy decreases as we move along the gene from the origin to the terminus. Furthermore, with the cooperation with a molecular biology colleague, we have compared the entropies with the number of different types of functional genes (anabolic, catabolic, aerobic, and anaerobic) located at the same positions. We have seen that there is a strong similarity between the distribution of anabolic genes and the two entropies.
[Report] Encoding of Amino Acids and Proteins from a Communications and Information Theoretic Perspective