Cyclic Concatenated Genetic Encoder: A mathematical proposal for biological inferences

The organization of the genetic information and its ability to be conserved and translated to proteins with low error rates have been the subject of study by scientists from different disciplines. Recently, it has been proposed that living organisms display an intra-cellular transmission system of genetic information, similar to a model of digital communication system, in which there is the ability to detect and correct errors. In this work, the concept of Concatenated Genetic Encoder is introduced and applied to the analysis of protein sequences as a tool for exploring evolutionary relationships. For such purposes Error Correcting Codes (ECCs) are used to represent proteins. A methodology for representing or identifying proteins by use of BCH codes over ℤ20 and F4×ℤ5 is proposed and cytochrome b6-f complex subunit 6-OS sequences, corresponding to different plants species, are analyzed according to the proposed methodology and results are contrasted to phylogenetic and taxonomic analyses. Through the analyses, it was observed that using BCH codes only some sequences are identified, all of which differ in one amino acid from the original sequence. In addition, mathematical relationships among identified sequences are established by considering minimal polynomials, where such sequences showed a close relationship as revealed in the phylogenetic reconstruction. Results, here shown, point out that communication theory may provide biology of interesting and useful tools to identify biological relationships among proteins, however the proposed methodology needs to be improved and rigorously tested in order to become into an applicable tool for biological analysis.