Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes

We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces

Embryonic Protein Undernutrition by Albumen Removal Programs the Hepatic Amino Acid and Glucose Metabolism during the Perinatal Period in an Avian Model.

Different animal models have been used to study the effects of prenatal protein undernutrition and the mechanisms by which these occur. In mammals, the maternal diet is manipulated, exerting both direct nutritional and indirect hormonal effects. Chicken embryos develop independent from the hen in the egg. Therefore, in the chicken, the direct effects of protein deficiency by albumen removal early during incubation can be examined. Prenatal protein undernutrition was established in layer-type eggs by the partial replacement of albumen by saline at embryonic day 1 (albumen-deprived group), compared to a mock-treated sham and a non-treated control group. At hatch, survival of the albumen-deprived group was lower compared to the control and sham group due to increased early mortality by the manipulation. No treatment differences in yolk-free body weight or yolk weight could be detected. The water content of the yolk was reduced, whereas the water content of the carcass was increased in the albumen-deprived group, compared to the control group, indicating less uptake of nutrients from the yolk. At embryonic day 16, 20 and at hatch, plasma triiodothyronine (T3), corticosterone, lactate or glucose concentrations and hepatic glycogen content were not affected by treatment. At embryonic day 20, the plasma thyroxine (T4) concentrations of the albumen-deprived embryos was reduced compared to the control group, indicating a decreased metabolic rate. Screening for differential protein expression in the liver at hatch using two-dimensional difference gel electrophoresis revealed not only changed abundance of proteins important for amino acid metabolism, but also of enzymes related to energy and glucose metabolism. Interestingly, GLUT1, a glucose transporter, and PCK2 and FBP1, two out of three regulatory enzymes of the gluconeogenesis were dysregulated. No parallel differences in gene expressions causing the differences in protein abundance could be detected pointing to post-transcriptional or post-translational regulation of the observed differences