Accessory parameters for Liouville theory on the torus

We give an implicit equation for the accessory parameter on the torus which is the necessary and sufficient condition to obtain the monodromy of the conformal factor. It is shown that the perturbative series for the accessory parameter in the coupling constant converges in a finite disk and give a rigorous lower bound for the radius of convergence. We work out explicitly the perturbative result to second order in the coupling for the accessory parameter and to third order for the one-point function. Modular invariance is discussed and exploited. At the non perturbative level it is shown that the accessory parameter is a continuous function of the coupling in the whole physical region and that it is analytic except at most a finite number of points. We also prove that the accessory parameter as a function of the modulus of the torus is continuous and real-analytic except at most for a zero measure set. Three soluble cases in which the solution can be expressed in terms of hypergeometric functions are explicitly treated.Comment: 30 pages, LaTex; typos corrected, discussion of eq.(74) improve

The non-octarepeat copper binding site of the prion protein is a key regulator of prion conversion

The conversion of the prion protein (PrP(C)) into prions plays a key role in transmissible spongiform encephalopathies. Despite the importance for pathogenesis, the mechanism of prion formation has escaped detailed characterization due to the insoluble nature of prions. PrP(C) interacts with copper through octarepeat and non-octarepeat binding sites. Copper coordination to the non-octarepeat region has garnered interest due to the possibility that this interaction may impact prion conversion. We used X-ray absorption spectroscopy to study copper coordination at pH 5.5 and 7.0 in human PrP(C) constructs, either wild-type (WT) or carrying pathological mutations. We show that mutations and pH cause modifications of copper coordination in the non-octarepeat region. In the WT at pH 5.5, copper is anchored to His96 and His111, while at pH 7 it is coordinated by His111. Pathological point mutations alter the copper coordination at acidic conditions where the metal is anchored to His111. By using in vitro approaches, cell-based and computational techniques, we propose a model whereby PrP(C) coordinating copper with one His in the non-octarepeat region converts to prions at acidic condition. Thus, the non-octarepeat region may act as the long-sought-after prion switch, critical for disease onset and propagation

Different tool training induces specific effects on body metric representation

Morphology and functional aspects of the tool have been proposed to be critical factors modulating tool use-induced plasticity. However, how these aspects contribute to changing body representation has been underinvestigated. In the arm bisection task, participants have to estimate the length of their own arm by indicating its midpoint, a paradigm used to investigate the representation of the metric properties of the body. We employed this paradigm to investigate the impact of different actions onto tool embodiment. Our findings suggest that a training requiring actions mostly with proximal (shoulder) or distal (wrist) parts induces a different shift in the perceived arm midpoint. This effect is independent of, but enhanced by, the use of the tool during the training and in part influenced by specific demands of the task. These results suggest that specific motor patterns required by the training can induce different changes of body representation, calling for rethinking the concept of tool embodiment, which would be characterized not simply by the morphology of the tools, but also by the actions required for their specific use