Chirality in a quaternionic representation of the genetic code

A quaternionic representation of the genetic code, previously reported by the authors, is updated in order to incorporate chirality of nucleotide bases and amino acids. The original representation assigns to each nucleotide base a prime integer quaternion of norm 7 and involves a function that associates with each codon, represented by three of these quaternions, another integer quaternion (amino acid type quaternion) in such a way that the essentials of the standard genetic code (particulaty its degeneration) are preserved. To show the advantages of such a quaternionic representation we have, in turn, associated with each amino acid of a given protein, besides of the type quaternion, another real one according to its order along the protein (order quaternion) and have designed an algorithm to go from the primary to the tertiary structure of the protein by using type and order quaternions. In this context, we incorporate chirality in our representation by observing that the set of eight integer quaternions of norm 7 can be partitioned into a pair of subsets of cardinality four each with their elements mutually conjugates and by putting they in correspondence one to one with the two sets of enantiomers (D and L) of the four nucleotide bases adenine, cytosine, guanine and uracil, respectively. Thus, guided by two diagrams proposed for the codes evolution, we define functions that in each case assign a L- (D-) amino acid type integer quaternion to the triplets of D- (L-) bases. The assignation is such that for a given D-amino acid, the associated integer quaternion is the conjugate of that one corresponding to the enantiomer L. The chiral type quaternions obtained for the amino acids are used, together with a common set of order quaternions, to describe the folding of the two classes, L and D, of homochiral proteins.Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1505.0465

Exact predictions from Edwards ensemble vs. realistic simulations of tapped narrow two-dimensional granular columns

We simulate via a Discrete Element Method the tapping of a narrow column of disk under gravity. For frictionless disks, this system has a simple analytic expression for the density of states in the Edwards volume ensemble. We compare the predictions of the ensemble at constant compactivity against the results for the steady states obtained in the simulations. We show that the steady states cannot be properly described since the microstates sampled are not in correspondence with the predicted distributions, suggesting that the postulates of flat measure and ergodicity are, either or both, invalid for this simple realization of a static granular system. However, we show that certain qualitative features of the volume fluctuations difficult to predict from simple arguments are captured by the theory.Comment: 11 pages, 6 figure

Quaternionic representation of the genetic code

A heuristic diagram of the evolution of the standard genetic code is presented. It incorporates, in a way that resembles the energy levels of an atom, the physical notion of broken symmetry and it is consistent with original ideas by Crick on the origin and evolution of the code as well as with the chronological order of appearence of the amino acids along the evolution as inferred from work that mixtures known experimental results with theoretical speculations. Suggested by the diagram we propose a Hamilton quaternions based mathematical representation of the code as it stands now-a-days. The central object in the description is a codon function that assigns to each amino acid an integer quaternion in such a way that the observed code degeneration is preserved. We emphasize the advantages of a quaternionic representation of amino acids taking as an example the folding of proteins. With this aim we propose an algorithm to go from the quaternions sequence to the protein three dimensional structure which can be compared with the corresponding experimental one stored at the Protein Data Bank. In our criterion the mathematical representation of the genetic code in terms of quaternions merits to be taken into account because it describes not only most of the known properties of the genetic code but also opens new perspectives that are mainly derived from the close relationship between quaternions and rotations.Comment: 19 pages, 11 figure

Ovidioren "Heroides. Libri VII-XII" testuaren euskarazko itzulpena eta oharrak

info:eu-repo/semantics/openAccessGradu Amaierako Lan honen helburua Ovidio autorearen Heroides obraren zati bat euskaratzea da. Heroides fikziozko eskutitz bilduma bat da; hain zuzen ere, mitologia eta literatura klasikoko pertsonaiek haien maiteei idatzitako eskutitzen bilduma. Honako lan honek, zehazki, VII-XII eskutitzak landuko ditu. Itzulpena egitean buruan izan dudan hartzailearen profila literaturazale kultuarena da, latinik ez dakiena; betiere jatorrizko testua ahalik eta gehien errespetatuz, itzulpena hizkuntza ulergarria erabiliz egiten saiatu naiz. Aipatutako irakurle potentzial horrek ez du zertan mitologia klasikoari buruzko jakintza handirik izan behar; hori ikusita, eta testua ahalik eta hoberen ulertzeko, oin-oharrak gehitu ditut hainbat zatitan, erromatar kultura eta mitologiari buruzko nozio minimo batzuk emanez. Oin ohar horiek txertatzeko erabili dudan irizpidea ondorengoa izan da: ni ere mitologian eta literatura klasikoan aditua ez naizenez gero, kontsultatu behar izan dudan kontzeptu ororen azalpen txikia egin dut. Ovidioren testua, noski, latinez idatzita dago. Nik ez dakit latinik, eskolan urte bakarra eman bainuen; horregatik, ezinezkoa izango zen niretzat itzulpena jatorrizko testutik egitea. Zubi-hizkuntzak erabili behar izan ditut; hain zuzen ere, gaztelaniazko bat eta ingelesezko bat. Batez ere gaztelaniazkoa izan dut oinarri, latinezkotik oso gertu baitzegoen. Bertsio horretan, edukia latinetik gertu mantentzeari eman diote lehentasuna, formaren edertasunaren gainetik. Ingelesezkoan, berriz, itzultzaileak era libreagoan itzuli du. Gainera, itzulpena 1914. urtekoa da; beraz, nahiko librea izateaz gain, ez zen ulertzeko bereziki erraza. Hala ere, beti izan dut aurrean latinezko bertsioa, eta zalantzaren bat sortu zaidanean, saiatu naiz, hiztegia baliatuz, esaldien esanahia latinezko bertsiotik ateratzen. Heroides testu poetiko bat da, eta neurtitzetan dago idatzita. Lana hasterakoan hartu behar izan nuen erabakia neurtitz horiek mantendu edo ez mantentzearena izan zen. Tutorearen gomendioak jarraituz, nik prosaz itzultzea erabaki nuen, aurrerago azalduko ditudan arrazoien ondorioz. Paragrafoak zatitzeko, gaztelaniazko prosazko bertsioak zekarren egitura berbera mantendu dut. Lanaren egiturari dagokionez, hainbat zatitan banatu daiteke. Hasteko, Ovidiori buruzko oinarrizko informazioa txertatu dut. Bere bizitzari buruz aurki daitekeen informazioaren laburpena, batetik; bere obrari buruzko oinarrizko datuak, bestetik; 2 itzulpena hobeto ulertzeko, ezinbestekoa baita autorea eta bere obra ezagutzea, gainetik bada ere. Ondoren, itzulpen prozesuari buruzko iruzkina egin dut; bertan, itzultzen hasi aurretik egindako testuaren azterketari buruz aritzen naiz; itzulpen prozesuan zehar sortutako arazoak eta horiei emandako konponbideak azaltzen dira. Hurrengo zatia itzulpena bera da, lanaren zati luze eta garrantzitsuena. Bukatzeko, erabilitako iturrien bibliografia txertatu dut

Triazole-Directed Pd-Catalyzed C(sp2)–H Oxygenation of Arenes and Alkenes

Selective Pd-catalyzed C(sp2)–H oxygenation of 4-substituted 1,2,3-triazoles is described. Unlike previous metal-catalyzed C–H functionalization events, which preferentially occur at the activated heterocyclic C–H bond, the regioselective oxygenation of the arene/alkene moiety is now achieved featuring the unconventional role of a simple triazole scaffold as a modular and selective directing group.MINECO for a Ramon y Cajal research contract (RYC-2012-09873)

Modelling of the dielectric properties of trabecular bone samples at microwave frequency

In this paper the dielectric properties of human trabecular bone are evaluated under physiological condition in the microwave range. Assuming a two components medium, simulation and experimental data are presented and discussed. A special experimental setup is developed in order to deal with inhomogeneous samples. Simulation data are obtained using finite difference time domain from a realistic sample. The bone mineral density of the samples are also measured. The simulation and experimental results of the present study suggest that there is a negative relation between bone volume fraction (BV/TV) and permittivity (conductivity): the higher the BV/TV the lower the permittivity (conductivity). This is in agreement with the recently published in vivo data. Keywords: Bone dielectric properties, Microwave tomography, Finite difference time domain.Comment: 10 pages, 5 figures, 4 table