Groups of Symmetries of the Two Classes of Synthetases in the Four-Dimensional Hypercubes of the Extended Code Type II.

Aminoacyl-tRNA synthetases (aaRSs) originated from an ancestral bidirectional gene (mirror symmetry), and through the evolution of the genetic code, the twenty aaRSs exhibit a symmetrical distribution in a 6-dimensional hypercube of the Standard Genetic Code. In this work, we assume a primeval RNY code and the Extended Genetic RNA code type II, which includes codons of the types YNY, YNR, and RNR. Each of the four subsets of codons can be represented in a 4-dimensional hypercube. Altogether, these 4 subcodes constitute the 6-dimensional representation of the SGC. We identify the aaRSs symmetry groups in each of these hypercubes. We show that each of the four hypercubes contains the following sets of symmetries for the two known Classes of synthetases: RNY: dihedral group of order 4; YNY: binary group; YNR: amplified octahedral group; and RNR: binary group. We demonstrate that for each hypercube, the group of symmetries in Class 1 is the same as the group of symmetries in Class 2. The biological implications of these findings are discussed.

Symmetrical distributions of aminoacyl-tRNA synthetases during the evolution of the genetic code.

In this work, we formulate the following question: How the distribution of aminoacyl-tRNA synthetases (aaRSs) went from an ancestral bidirectional gene (mirror symmetry) to the symmetrical distribution of aaRSs in a six-dimensional hypercube of the Standard Genetic Code (SGC)? We assume a primeval RNY code, two Extended Genetic RNA codes type 1 and 2, and the SGC. We outline the types of symmetries of the distribution of aaRSs in each code. The symmetry groups of aaRSs in each code are described, until the symmetries of the SGC display a mirror symmetry. Considering both Extended RNA codes the 20 aaRSs were already present before the Last Universal Ancestor. These findings reveal intricacies in the diversification of aaRSs accompanied by the evolution of the genetic code.

How to eliminate taeniasis/cysticercosis: porcine vaccination and human chemotherapy (Part 2).

BACKGROUND: The application of effective vaccines against pig cysticercosis and mass chemotherapy against pig cysticercosis and human taeniasis have shown the feasibility of interrupting the parasite's life cycle in endemic areas. METHODS: A mathematical model that divides the population into susceptible, infected, and vaccinated individuals is formulated. The model is based upon the life cycle of the parasite. Computer numerical simulation experiments to evaluate the impact of pig vaccination under different vaccination schedules, and combined intervention strategies including pig vaccination and anthelmintic treatment against human taeniasis are carried out. RESULTS: Vaccination against either pig cysticercosis or against human taeniasis will influence the transmission dynamics not only among vaccinees but also the dynamics of the other hosts as well. When the protective efficacy and/or the coverage rate is less than 100%, different mass interventions like vaccinating the pig population twice in combination with chemotherapeutic treatment against human taeniasis, the elimination of the infection in both pigs and humans can also be achieved. CONCLUSIONS: Our mathematical model has the potential for planning, and designing effective intervention strategies including both mass vaccination and/or chemotherapeutic treatment to eliminate pig cysticercosis, human taeniasis and human neurocysticercosis. The model can be adapted to any given community with mild, moderate endemicity, or even in hyperendemic regions.

Mathematical model of the life cycle of taenia-cysticercosis: transmission dynamics and chemotherapy (Part 1).

BACKGROUND: Taenia solium is the aetiological agent of human taeniasis, pig cysticercosis and human neurocysticercosis, which are serious public health problems, especially in developing countries. METHODS: A mathematical model of the transmission dynamics of taeniasis-cysticercosis is formulated. The model consists of a coupled system of differential equations, which are density-dependent equations for describing the flow of the parasite through the life cycle. The model is hybrid since it comprises deterministic equations with stochastic elements which describe changes in the mean parasite burden and incorporates the overall pattern of the parasites' distribution. RESULTS: Sensitivity and bifurcation analyses were carried out to determine the range of values of the model. The model can reproduce the observed epidemiological patterns of human taeniasis, pig and human cysticercosis. For example, for a wide range of parameter values, the mean intensity of adult worms tends to rapidly stabilize in one parasite per individual host. From this model, we also derived a Susceptible-Infected model to describe the prevalence of infection in humans and pigs. Chemotherapeutic interventions against pig cysticercosis or human taeniasis may reduce rapidly and effectively the mean intensity of human taeniasis, pig cysticercosis and human cysticercosis. This effect can be achieved even if the protective efficacy of the drug is of the order of 90% and the coverage rate is 90%. This means that health in humans infected either with adult worms or cysticerci may be achieved by the application of anthelmintic drugs against pig cysticercosis. However, treatment against human cysticercosis alone, does not influence neither human teniasis nor pig cysticercosis. This is because human cysticercosis infection does not influence the value of the basic reproductive number (Ro). CONCLUSIONS: Even coverage of 100% in the administration of anthelmintics did not eliminate the infection. Then elimination of the infection in all hosts does not seem a feasible goal to achieve by administering only chemotherapeutic interventions. Throughout the manuscript a discussion of our model in the context of other models of taeniasis-cysticercosis is presented.

Symmetrical and Thermodynamic Properties of Phenotypic Graphs of Amino Acids Encoded by the Primeval RNY Code.

The 12 different types of graphs of the 8 amino acids encoded by the presumably primeval RNY code are derived. The symmetry groups of these graphs are analyzed and coincide with the corresponding values of polar requirement for each amino acid. The symmetry groups at the codon level are partially carried over as a group or subgroup at the amino acid level. Measures of centrality of the 12 graphs indicate that all amino acids were equally relevant irrespective of its chronological order of its appearance. The elimination of any amino acid would be strongly selected against and therefore the genetic code at this stage was already frozen.

Three-Dimensional Algebraic Models of the tRNA Code and 12 Graphs for Representing the Amino Acids.

Three-dimensional algebraic models, also called Genetic Hotels, are developed to represent the Standard Genetic Code, the Standard tRNA Code (S-tRNA-C), and the Human tRNA code (H-tRNA-C). New algebraic concepts are introduced to be able to describe these models, to wit, the generalization of the 2n-Klein Group and the concept of a subgroup coset with a tail. We found that the H-tRNA-C displayed broken symmetries in regard to the S-tRNA-C, which is highly symmetric. We also show that there are only 12 ways to represent each of the corresponding phenotypic graphs of amino acids. The averages of statistical centrality measures of the 12 graphs for each of the three codes are carried out and they are statistically compared. The phenotypic graphs of the S-tRNA-C display a common triangular prism of amino acids in 10 out of the 12 graphs, whilst the corresponding graphs for the H-tRNA-C display only two triangular prisms. The graphs exhibit disjoint clusters of amino acids when their polar requirement values are used. We contend that the S-tRNA-C is in a frozen-like state, whereas the H-tRNA-C may be in an evolving state.

Periodic distribution of a putative nucleosome positioning motif in human, nonhuman primates, and archaea: mutual information analysis.

Recently, Trifonov's group proposed a 10-mer DNA motif YYYYYRRRRR as a solution of the long-standing problem of sequence-based nucleosome positioning. To test whether this generic decamer represents a biological meaningful signal, we compare the distribution of this motif in primates and Archaea, which are known to contain nucleosomes, and in Eubacteria, which do not possess nucleosomes. The distribution of the motif is analyzed by the mutual information function (MIF) with a shifted version of itself (MIF profile). We found common features in the patterns of this generic decamer on MIF profiles among primate species, and interestingly we found conspicuous but dissimilar MIF profiles for each Archaea tested. The overall MIF profiles for each chromosome in each primate species also follow a similar pattern. Trifonov's generic decamer may be a highly conserved motif for the nucleosome positioning, but we argue that this is not the only motif. The distribution of this generic decamer exhibits previously unidentified periodicities, which are associated to highly repetitive sequences in the genome. Alu repetitive elements contribute to the most fundamental structure of nucleosome positioning in higher Eukaryotes. In some regions of primate chromosomes, the distribution of the decamer shows symmetrical patterns including inverted repeats.

On the evolution of the standard genetic code: vestiges of critical scale invariance from the RNA world in current prokaryote genomes.

Herein two genetic codes from which the primeval RNA code could have originated the standard genetic code (SGC) are derived. One of them, called extended RNA code type I, consists of all codons of the type RNY (purine-any base-pyrimidine) plus codons obtained by considering the RNA code but in the second (NYR type) and third (YRN type) reading frames. The extended RNA code type II, comprises all codons of the type RNY plus codons that arise from transversions of the RNA code in the first (YNY type) and third (RNR) nucleotide bases. In order to test if putative nucleotide sequences in the RNA World and in both extended RNA codes, share the same scaling and statistical properties to those encountered in current prokaryotes, we used the genomes of four Eubacteria and three Archaeas. For each prokaryote, we obtained their respective genomes obeying the RNA code or the extended RNA codes types I and II. In each case, we estimated the scaling properties of triplet sequences via a renormalization group approach, and we calculated the frequency distributions of distances for each codon. Remarkably, the scaling properties of the distance series of some codons from the RNA code and most codons from both extended RNA codes turned out to be identical or very close to the scaling properties of codons of the SGC. To test for the robustness of these results, we show, via computer simulation experiments, that random mutations of current genomes, at the rates of 10(-10) per site per year during three billions of years, were not enough for destroying the observed patterns. Therefore, we conclude that most current prokaryotes may still contain relics of the primeval RNA World and that both extended RNA codes may well represent two plausible evolutionary paths between the RNA code and the current SGC.

Prevalence of infection, mean worm burden and degree of worn aggregation as determinants of prevalence of disease due to intestinal helminths

Theoretical predictions of disease prevalence due to helminth infections based upon a simple probabilistica model which considers the infection prevalence, the mean worm urden and the degree of worm aggregation are presented. A numerical reappraisal of the likely estimates of the degree of aggregation based upon maximun likelihood estimates of the negative binomial distribution is presented. The prevalence of disease shows a positive relationship with the mean worm burden. This association is hyperbolic when helminth parasites are severely aggregated but is s-shaped when helminth parasites tend to be oversidpersed. The prevalence of disease decreases with the degree of worm aggregation whem the values of the mean intensity are low; as the mean intensity increases this association becomes positive. The relationship between prevalence of disease and prevalence of infection is hyperbolic for severe degrees of parasite aggregation and is s-shaped for intermediate degrees of aggregation. However, if the mean intesnsity is low and the degree of aggreation is high there could be a negative raltionship between the prevalence of disease due to helminth parasites is feasible for determined ranges of values of the infection prevalence, mena intensity and the degree of worm clumping