Robersy Sanchez

Gene algebra from a genetic code algebraic structure

By considering two important factors involved in the codon-anticodon interactions, the hydrogen bond number and the chemical type of bases, a codon array of the genetic code table as an increasing code scale of interaction energies of amino acids in proteins was obtained. Next, in order to consecutively obtain all codons from the codon AAC, a sum operation has been introduced in the set of codons. The group obtained over the set of codons is isomorphic to the group (Z64, +) of the integer module 64. On the Z64-algebra of the set of 64N codon sequences of length N, gene mutations are described by means of endomorphisms f:(Z64)N→(Z64)N. Endomorphisms and automorphisms helped us describe the gene mutation pathways. For instance, 77.7% mutations in 749 HIV protease gene sequences correspond to unique diagonal endomorphisms of the wild type strain HXB2. In particular, most of the reported mutations that confer drug resistance to the HIV protease gene correspond to diagonal automorphisms of the wild type. What is more, in the human beta-globin gene a similar situation appears where most of the single codon mutations correspond to automorphisms. Hence, in the analyses of molecular evolution process on the DNA sequence set of length N, the Z64-algebra will help us explain the quantitative relationships between genes.

An algebraic hypothesis about the primeval genetic code architecture

A plausible architecture of an ancient genetic code is derived from an extended base triplet vector space over the Galois field of the extended base alphabet {D,A,C,G,U}, where symbol D represents one or more hypothetical bases with unspecific pairings. We hypothesized that the high degeneration of a primeval genetic code with five bases and the gradual origin and improvement of a primeval DNA repair system could make possible the transition from ancient to modern genetic codes. Our results suggest that the Watson-Crick base pairing G identical with C and A=U and the non-specific base pairing of the hypothetical ancestral base D used to define the sum and product operations are enough features to determine the coding constraints of the primeval and the modern genetic code, as well as, the transition from the former to the latter. Geometrical and algebraic properties of this vector space reveal that the present codon assignment of the standard genetic code could be induced from a primeval codon assignment. Besides, the Fourier spectrum of the extended DNA genome sequences derived from the multiple sequence alignment suggests that the called period-3 property of the present coding DNA sequences could also exist in the ancient coding DNA sequences. The phylogenetic analyses achieved with metrics defined in the N-dimensional vector space (B(3))(N) of DNA sequences and with the new evolutionary model presented here also suggest that an ancient DNA coding sequence with five or more bases does not contradict the expected evolutionary history.

Feature extraction using clustering of protein

In this paper we investigate the usage of a clustering algorithm as a feature extraction technique to find new features to represent the protein sequence. In particular, our work focuses on the prediction of HIV protease resistance to drugs. We use a biologically motivated similarity function based on the contact energy of the amino acid and the position in the sequence. The performance measure was computed taking into account the clustering reliability and the classification validity. An SVM using 10-fold crossvalidation and the k-means algorithm were used for classification and clustering respectively. The best results were obtained by reducing an initial set of 99 features to a lower dimensional feature set of 36-66 features.

Boolean algebraic structures of the genetic code: possibilities of applications

Authors had reported before two dual Boolean algebras to understand the underlying logic of the genetic code structure. In such Boolean structures, deductions have physico-chemical meaning. We summarize here that these algebraic structures can help us to describe the gene evolution process. Particularly in the experimental confrontation, it was found that most of the mutations of several proteins correspond to deductions in these algebras and they have a small Hamming distance related to their respective wild type. Two applications of the corresponding codification system in bioinformatics problems are also shown. The first one is the classification of mutations in a protein. The other one is related with the problem of detecting donors and acceptors in DNA sequences. Besides, pure mathematical models, Statistical techniques (Decision Trees) and Artificial Intelligence techniques (Bayesian Networks) were used in order to show how to accomplish them to solve these knowledge-discovery practical problems.

Evolutionary analysis of DNA-protein-coding regions based on a genetic code cube metric.

The right estimation of the evolutionary distance between DNA or protein sequences is the cornerstone of the current phylogenetic analysis based on distance methods. Herein, it is demonstrated that the Manhattan distance (dw), weighted by the evolutionary importance of the nucleotide bases in the codon, is a naturally derived metric in the standard genetic code cube inserted into the three-dimensional Euclidean space. Based on the application of distance dw, a novel evolutionary model is proposed. This model includes insertion/deletion mutations that are very important for cancer studies, but usually discarded in classical evolutionary models. In this study, the new evolutionary model was applied to the phylogenetic analysis of the DNA protein-coding regions of 13 mammal mitochondrial genomes and of four cancer genetic- susceptibility genes (ATM, BRCA1, BRCA2 and p53) from nine mammals. The opossum (a marsupial) was used as an out-group species for both sets of sequences. The new evolutionary model yielded the correct topology, while the current models failed to separate the evolutionarily distant species of mouse and opossum.