Extending the Belavin-Knizhnik "wonderful formula" by the characterization of the Jacobian

A long-standing question in string theory is to find the explicit expression of the bosonic measure, a crucial issue also in determining the superstring measure. Such a measure was known up to genus three. Belavin and Knizhnik conjectured an expression for genus four which has been proved in the framework of the recently introduced vector-valued Teichmueller modular forms. It turns out that for g>3 the bosonic measure is expressed in terms of such forms. In particular, the genus four Belavin-Knizhnik "wonderful formula" has a remarkable extension to arbitrary genus whose structure is deeply related to the characterization of the Jacobian locus. Furthermore, it turns out that the bosonic string measure has an elegant geometrical interpretation as generating the quadrics in P^{g-1} characterizing the Riemann surface. All this leads to identify forms on the Siegel upper half-space that, if certain conditions related to the characterization of the Jacobian are satisfied, express the bosonic measure as a multiresidue in the Siegel upper half-space. We also suggest that it may exist a super analog on the super Siegel half-space.Comment: 15 pages. Typos corrected, refs. and comments adde

Iron-Responsive Olfactory Uptake of Manganese Improves Motor Function Deficits Associated with Iron Deficiency

Iron-responsive manganese uptake is increased in iron-deficient rats, suggesting that toxicity related to manganese exposure could be modified by iron status. To explore possible interactions, the distribution of intranasally-instilled manganese in control and iron-deficient rat brain was characterized by quantitative image analysis using T1-weighted magnetic resonance imaging (MRI). Manganese accumulation in the brain of iron-deficient rats was doubled after intranasal administration of MnCl2 for 1- or 3-week. Enhanced manganese level was observed in specific brain regions of iron-deficient rats, including the striatum, hippocampus, and prefrontal cortex. Iron-deficient rats spent reduced time on a standard accelerating rotarod bar before falling and with lower peak speed compared to controls; unexpectedly, these measures of motor function significantly improved in iron-deficient rats intranasally-instilled with MnCl2. Although tissue dopamine concentrations were similar in the striatum, dopamine transporter (DAT) and dopamine receptor D1 (D1R) levels were reduced and dopamine receptor D2 (D2R) levels were increased in manganese-instilled rats, suggesting that manganese-induced changes in post-synaptic dopaminergic signaling contribute to the compensatory effect. Enhanced olfactory manganese uptake during iron deficiency appears to be a programmed “rescue response” with beneficial influence on motor impairment due to low iron status

Disease-Toxicant Interactions in Manganese Exposed Huntington Disease Mice: Early Changes in Striatal Neuron Morphology and Dopamine Metabolism

YAC128 Huntington's disease (HD) transgenic mice accumulate less manganese (Mn) in the striatum relative to wild-type (WT) littermates. We hypothesized that Mn and mutant Huntingtin (HTT) would exhibit gene-environment interactions at the level of neurochemistry and neuronal morphology. Twelve-week-old WT and YAC128 mice were exposed to MnCl2-4H2O (50 mg/kg) on days 0, 3 and 6. Striatal medium spiny neuron (MSN) morphology, as well as levels of dopamine (DA) and its metabolites (which are known to be sensitive to Mn-exposure), were analyzed at 13 weeks (7 days from initial exposure) and 16 weeks (28 days from initial exposure). No genotype-dependent differences in MSN morphology were apparent at 13 weeks. But at 16 weeks, a genotype effect was observed in YAC128 mice, manifested by an absence of the wild-type age-dependent increase in dendritic length and branching complexity. In addition, genotype-exposure interaction effects were observed for dendritic complexity measures as a function of distance from the soma, where only YAC128 mice were sensitive to Mn exposure. Furthermore, striatal DA levels were unaltered at 13 weeks by genotype or Mn exposure, but at 16 weeks, both Mn exposure and the HD genotype were associated with quantitatively similar reductions in DA and its metabolites. Interestingly, Mn exposure of YAC128 mice did not further decrease DA or its metabolites versus YAC128 vehicle exposed or Mn exposed WT mice. Taken together, these results demonstrate Mn-HD disease-toxicant interactions at the onset of striatal dendritic neuropathology in YAC128 mice. Our results identify the earliest pathological change in striatum of YAC128 mice as being between 13 to 16 weeks. Finally, we show that mutant HTT suppresses some Mn-dependent changes, such as decreased DA levels, while it exacerbates others, such as dendritic pathology

Bioavailable Trace Metals in Neurological Diseases

Medical treatment in Wilson’s disease includes chelators (d-penicillamine and trientine) or zinc salts that have to be maintain all the lifelong. This pharmacological treatment is categorised into two phases; the first being a de-coppering phase and the second a maintenance one. The best therapeutic approach remains controversial, as only a few non-controlled trials have compared these treatments. During the initial phase, progressive increase of chelators’ doses adjusted to exchangeable copper and urinary copper might help to avoid neurological deterioration. Liver transplantation is indicated in acute fulminant liver failure and decompensated cirrhosis; in cases of neurologic deterioration, it must be individually discussed. During the maintenance phase, the most important challenge is to obtain a good adherence to lifelong medical therapy. Neurodegenerative diseases that lead to a mislocalisation of iron can be caused by a culmination of localised overload (pro-oxidant siderosis) and localised deficiency (metabolic distress). A new therapeutic concept with conservative iron chelation rescues iron-overloaded neurons by scavenging labile iron and, by delivering this chelated metal to endogenous apo-transferrin, allows iron redistribution to avoid systemic loss of iron

Low Concentrations of Methamphetamine Can Protect Dopaminergic Cells against a Larger Oxidative Stress Injury: Mechanistic Study

Mild stress can protect against a larger insult, a phenomenon termed preconditioning or tolerance. To determine if a low intensity stressor could also protect cells against intense oxidative stress in a model of dopamine deficiency associated with Parkinson disease, we used methamphetamine to provide a mild, preconditioning stress, 6-hydroxydopamine (6-OHDA) as a source of potentially toxic oxidative stress, and MN9D cells as a model of dopamine neurons. We observed that prior exposure to subtoxic concentrations of methamphetamine protected these cells against 6-OHDA toxicity, whereas higher concentrations of methamphetamine exacerbated it. The protection by methamphetamine was accompanied by decreased uptake of both [3H] dopamine and 6-OHDA into the cells, which may have accounted for some of the apparent protection. However, a number of other effects of methamphetamine exposure suggest that the drug also affected basic cellular survival mechanisms. First, although methamphetamine preconditioning decreased basal pERK1/2 and pAkt levels, it enhanced the 6-OHDA-induced increase in these phosphokinases. Second, the apparent increase in pERK1/2 activity was accompanied by increased pMEK1/2 levels and decreased activity of protein phosphatase 2. Third, methamphetamine upregulated the pro-survival protein Bcl-2. Our results suggest that exposure to low concentrations of methamphetamine cause a number of changes in dopamine cells, some of which result in a decrease in their vulnerability to subsequent oxidative stress. These observations may provide insights into the development of new therapies for prevention or treatment of PD