We study the statistical topology of folding configurations of hand folded paper balls. Specifically, we are studying the distribution of two sides of the sheet along the ball surface and the distribution of sheet fragments when the ball is cut in half. We found that patterns obtained by mapping of ball surface into unfolded flat sheet exhibit the fractal properties characterized by two fractal dimensions which are independent on the sheet size and the ball diameter. The mosaic patterns obtained by sheet reconstruction from fragments of two parts (painted in two different colors) of the ball cut in half also possess a fractal scale invariance characterized by the box fractal dimension DBF=1.68 ± 0.04 , which is independent on the sheet size. Furthermore, we noted that DBF, at least numerically, coincide with the universal fractal dimension of the intersection of hand folded paper ball with a plane. Some other fractal properties of folding configurations are recognized.

No abstract

No abstract

We study the lateral deformations of randomly folded elasto-plastic and predominantly plastic thin sheets under the uniaxial and radial compressions. We found that the lateral deformations of cylinders folded from elasto-plastic sheets of paper obey a power law behavior with the universal Poisson's index 01 . 0 17 . 0 ± = ν , which does not depend neither the paper kind and sheet sizes (thickness, edge length), nor the folding confinement ratio. In contrast to this, the lateral deformations of randomly folded predominantly plastic aluminum foils display the linear dependence on the axial compression with the universal Poisson's ratio 01 . 0 33 . 0 ± = e ν. This difference is consistent with the difference in fractal topology of randomly folded elasto-plastic and predominantly plastic sheets, which is found to belong to different universality classes.The general form of constitutive stress-deformation relations for randomly folded elastoplastic sheets is suggested.

Vasoinhibins are a family of N-terminal prolactin (PRL) fragments that inhibit blood vessel growth, dilation, permeability, and survival. The aspartyl endoprotease cathepsin D is active at acidic pH and can cleave rat PRL to generate vasoinhibins. We investigated whether and where vasoinhibins could be generated by cathepsin D in the adenohypophysis of rats and mice and whether their production could be gender dependent. Vasoinhibins were detected in primary cultures of rat adenohypophyseal cells by Western blot with antibodies directed against the N terminus of PRL but not the C terminus. Ovariectomized, estrogen-treated females show greater levels of adenohypophyseal vasoinhibins than males. Peptide sequencing analysis revealed that the cleaved form of PRL in rat adenohypophyseal extracts contains the PRL N terminus and a second N terminus starting at Ser(149), the reported cleavage site of cathepsin D in rat PRL. In addition, cathepsin D inhibition by pepstatin A reduced vasoinhibin levels in rat adenohypophyseal cell cultures. Confocal and electron microscopy showed the colocalization of cathepsin D and PRL within rat adenohypophyseal cells and secretory granules, and a subcellular fraction of rat adenohypophysis enriched in secretory granules contained cathepsin D activity able to generate vasoinhibins from PRL. Of note, vasoinhibins were absent in the adenohypophysis of mice lacking the cathepsin D gene but not in wild-type mice. These findings show that cathepsin D is the main protease responsible for the generation of adenohypophyseal vasoinhibins and that its action can take place within the secretory granules of lactotrophs.