Lie Superalgebras and the Multiplet Structure of the Genetic Code II: Branching Schemes

Continuing our attempt to explain the degeneracy of the genetic code using basic classical Lie superalgebras, we present the branching schemes for the typical codon representations (typical 64-dimensional irreducible representations) of basic classical Lie superalgebras and find three schemes that do reproduce the degeneracies of the standard code, based on the orthosymplectic algebra osp(5|2) and differing only in details of the symmetry breaking pattern during the last step.Comment: 34 pages, 9 tables, LaTe

The Poisson Bracket for Poisson Forms in Multisymplectic Field Theory

We present a general definition of the Poisson bracket between differential forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories and, more generally, on exact multisymplectic manifolds. It is well defined for a certain class of differential forms that we propose to call Poisson forms and turns the space of Poisson forms into a Lie superalgebra.Comment: 40 pages LaTe

Effects of blocking developmental cell death on sexually dimorphic calbindin cell groups in the preoptic area and bed nucleus of the stria terminalis

Background: Calbindin-D28 has been used as a marker for the sexually dimorphic nucleus of the preoptic area (SDN-POA). Males have a distinct cluster of calbindin-immunoreactive (ir) cells in the medial preoptic area (CALB-SDN) that is reduced or absent in females. However, it is not clear whether the sex difference is due to the absolute number of calbindin-ir cells or to cell position (that is, spread), and the cellular mechanisms underlying the sex difference are not known. We examined the number of cells in the CALB-SDN and surrounding regions of C57Bl/6 mice and used mice lacking the pro-death gene, Bax, to test the hypothesis that observed sex differences are due to cell death. Methods: Experiment 1 compared the number of cells in the CALB-SDN and surrounding regions in adult males, females, and females injected with estradiol benzoate on the day of birth. In experiment 2, cell number in the CALB-SDN and adjacent regions were compared in wild-type and Bax knockout mice of both sexes. In addition, calbindin-ir cells were quantified within the principal nucleus of the bed nucleus of the stria terminalis (BNSTp), a nearby region that is larger in males due to Bax-dependent cell death. Results: Males had more cells in the CALB-SDN as well as in surrounding regions than did females, and estradiol treatment of females at birth masculinized both measures. Bax deletion had no effect on cell number in the CALB-SDN or surrounding regions but increased calbindin-ir cell number in the BNSTp. Conclusions: The sex difference in the CALB-SDN of mice results from an estrogen-dependent difference in cell number with no evidence found for greater spread of cells in females. Blocking Bax-dependent cell death does not prevent sex differences in calbindin-ir cell number in the BNST or CALB-SDN but increases calbindin-ir cell number in the BNSTp of both sexes

Neonatal inhibition of DNA methylation disrupts testosterone-dependent masculinization of neurochemical phenotype

Many neural sex differences are differences in the number of neurons of a particular phenotype. For example, male rodents have more calbindin-expressing neurons in the medial preoptic area (mPOA) and bed nucleus of the stria terminalis (BNST), and females have more neurons expressing estrogen receptor alpha (ERα) and kisspeptin in the ventromedial nucleus of the hypothalamus (VMH) and the anteroventral periventricular nucleus (AVPV), respectively. These sex differences depend on neonatal exposure to testosterone, but the underlying molecular mechanisms are unknown. DNA methylation is important for cell phenotype differentiation throughout the developing organism. We hypothesized that testosterone causes sex differences in neurochemical phenotype via changes in DNA methylation, and tested this by inhibiting DNA methylation neonatally in male and female mice, and in females given a masculinizing dose of testosterone. Neonatal testosterone treatment masculinized calbindin, ERα and kisspeptin cell number of females at weaning. Inhibiting DNA methylation with zebularine increased calbindin cell number only in control females, thus eliminating sex differences in calbindin in the mPOA and BNST. Zebularine also reduced the sex difference in ERα cell number in the VMH, in this case by increasing ERα neuron number in males and testosterone-treated females. In contrast, the neonatal inhibition of DNA methylation had no effect on kisspeptin cell number. We conclude that testosterone normally increases the number of calbindin cells and reduces ERα cells in males through orchestrated changes in DNA methylation, contributing to, or causing, the sex differences in both cell types.Fil: Cisternas, Carla Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigación Médica Mercedes y Martín Ferreyra. Universidad Nacional de Córdoba. Instituto de Investigación Médica Mercedes y Martín Ferreyra; ArgentinaFil: Cortese, Maria Laura. Georgia State University; Estados UnidosFil: Golynker, Ilona. Georgia State University; Estados UnidosFil: Castillo-Ruiz, Alexandra. Georgia State University; Estados UnidosFil: Forger, Nancy G.. Georgia State University; Estados Unido

Symmetry Scheme for Amino Acid Codons

Group theoretical concepts are invoked in a specific model to explain how only twenty amino acids occur in nature out of a possible sixty four. The methods we use enable us to justify the occurrence of the recently discovered twenty first amino acid selenocysteine, and also enables us to predict the possible existence of two more, as yet undiscovered amino acids.Comment: 18 pages which include 4 figures & 3 table

Does Gender Leave an Epigenetic Imprint on the Brain?

The words “sex” and “gender” are often used interchangeably in common usage. In fact, the Merriam-Webster dictionary offers “sex” as the definition of gender. The authors of this review are neuroscientists, and the words “sex” and “gender” mean very different things to us: sex is based on biological factors such as sex chromosomes and gonads, whereas gender has a social component and involves differential expectations or treatment by conspecifics, based on an individual’s perceived sex. While we are accustomed to thinking about “sex” and differences between males and females in epigenetic marks in the brain, we are much less used to thinking about the biological implications of gender. Nonetheless, careful consideration of the field of epigenetics leads us to conclude that gender must also leave an epigenetic imprint on the brain. Indeed, it would be strange if this were not the case, because all environmental influences of any import can epigenetically change the brain. In the following pages, we explain why there is now sufficient evidence to suggest that an epigenetic imprint for gender is a logical conclusion. We define our terms for sex, gender, and epigenetics, and describe research demonstrating sex differences in epigenetic mechanisms in the brain which, to date, is mainly based on work in non-human animals. We then give several examples of how gender, rather than sex, may cause the brain epigenome to differ in males and females, and finally consider the myriad of ways that sex and gender interact to shape gene expression in the brain

Plasma 25-hydroxyvitamin D and risk of premenstrual syndrome in a prospective cohort study

Background: Moderate to severe premenstrual syndrome (PMS) affects 8–20 percent of premenopausal women. Previous studies suggest that high dietary vitamin D intake may reduce risk. However, vitamin D status is influenced by both dietary vitamin D intake and sunlight exposure and the association of vitamin D status with PMS remains unclear. Methods: We assessed the relation of plasma 25-hydroxyvitamin D (25OHD), total calcium and parathyroid hormone levels with risk of PMS and specific menstrual symptoms in a case–control study nested within the prospective Nurses’ Health Study II. Cases were 401 women free from PMS at baseline who developed PMS during follow-up (1991–2005). Controls were women not experiencing PMS (1991–2005), matched 1:1 with cases on age and other factors. Timed luteal phase blood samples were collected between 1996 and 1999 from cases and controls. We used conditional logistic regression to model the relation of 25OHD levels with risk of PMS and individual menstrual symptoms. Results: In analyses of all cases and controls, 25OHD levels were not associated with risk of PMS. However, results differed when the timing of blood collection vs. PMS diagnosis was considered. Among cases who had already been diagnosed with PMS at the time of blood collection (n = 279), 25OHD levels were positively associated with PMS, with each 10 nmol/L change in 25OHD associated with a 13% higher risk. Among cases who developed PMS after blood collection (n = 123), 25OHD levels were unrelated to risk of PMS overall, but inversely related to risk of specific menstrual symptoms. For example, each 10 nmol/L increase was associated with a significant 21% lower risk of breast tenderness (P = 0.02). Total calcium or parathyroid hormone levels were unrelated to PMS. Conclusions: 25OHD levels were not associated with overall risk of PMS. The positive association observed among women already experiencing PMS at the time of 25OHD measurement is likely due to confounding by indication related to use of dietary supplements to treat menstrual symptoms. Results from prospective analyses, which were less likely influenced by this bias, suggest that higher 25OHD levels may be inversely related to the development of specific menstrual symptoms

On algebraic structures in supersymmetric principal chiral model

Using the Poisson current algebra of the supersymmetric principal chiral model, we develop the algebraic canonical structure of the model by evaluating the fundamental Poisson bracket of the Lax matrices that fits into the rs matrix formalism of non-ultralocal integrable models. The fundamental Poisson bracket has been used to compute the Poisson bracket algebra of the monodromy matrix that gives the conserved quantities in involution

The non-dynamical r-matrices of the degenerate Calogero-Moser models

A complete description of the non-dynamical r-matrices of the degenerate Calogero-Moser models based on $gl_n$ is presented. First the most general momentum independent r-matrices are given for the standard Lax representation of these systems and those r-matrices whose coordinate dependence can be gauged away are selected. Then the constant r-matrices resulting from gauge transformation are determined and are related to well-known r-matrices. In the hyperbolic/trigonometric case a non-dynamical r-matrix equivalent to a real/imaginary multiple of the Cremmer-Gervais classical r-matrix is found. In the rational case the constant r-matrix corresponds to the antisymmetric solution of the classical Yang-Baxter equation associated with the Frobenius subalgebra of $gl_n$ consisting of the matrices with vanishing last row. These claims are consistent with previous results of Hasegawa and others, which imply that Belavin's elliptic r-matrix and its degenerations appear in the Calogero-Moser models. The advantages of our analysis are that it is elementary and also clarifies the extent to which the constant r-matrix is unique in the degenerate cases.Comment: 25 pages, LaTeX; expanded by an appendix detailing the proof of Theorem 1 and a concluding section in version