Geometric continuity and compatibility conditions for 4-patch surfaces

When considering regularity of surfaces, it is its geometry that is of interest. Thus, the concept of geometric regularity or geometric continuity of a specific order is a relevant concept. In this paper we discuss necessary and sufficient conditions for a 4-patch surface to be geometrically continuous of order one and two or, in other words, being tangent plane continuous and curvature continuous respectively. The focus is on the regularity at the point where the four patches meet and the compatibility conditions that must appear in this case. In this article the compatibility conditions are proved to be independent of the patch parametrization, i.e., the compatibility conditions are universal. In the end of the paper these results are applied to a specific parametrization such as Bezier representation in order to generalize a 4-patch surface result by Sarraga.Comment: 25 pages, 6 figure

Interaction of the Xanthine Nucleotide Binding Goα Mutant with G Protein-coupled Receptors

We constructed a double mutant version of the α subunit of Go that was regulated by xanthine nucleotides instead of guanine nucleotides (GoαX). We investigated the interaction between GoαX and G protein-coupled receptors in vitro. First, we found that the activated m2 muscarinic cholinergic receptor (MAChR) could facilitate the exchange of XTPγS for XDP in the GoαXβγ heterotrimer. Second, the GoαXβγ complex was able to induce the high affinity ligand-binding state in the N-formyl peptide receptor (NFPR). These experiments demonstrated that GoαX was able to interact effectively with G protein-coupled receptors. Third, we found that the empty form of GoαX, lacking a bound nucleotide and βγ, formed a stable complex with the m2 muscarinic cholingeric receptor associated with the plasma membrane. Finally, we investigated the interaction of GoαX with receptor in COS-7 cells. The empty form of GoαX bound tightly to the receptor and was not activated because XTP was not available intracellularly. We tested the ability of GoαX to inhibit the activities of several different G protein-coupled receptors in transfected COS-7 cells and found that Goα X specifically inhibited Go-coupled receptors. Thus the modified G proteins may act as dominant-negative mutants to trap and inactivate specific subsets of receptors

Casimir experiments showing saturation effects

We address several different Casimir experiments where theory and experiment disagree. First out is the classical Casimir force measurement between two metal half spaces; here both in the form of the torsion pendulum experiment by Lamoreaux and in the form of the Casimir pressure measurement between a gold sphere and a gold plate as performed by Decca et al.; theory predicts a large negative thermal correction, absent in the high precision experiments. The third experiment is the measurement of the Casimir force between a metal plate and a laser irradiated semiconductor membrane as performed by Chen et al.; the change in force with laser intensity is larger than predicted by theory. The fourth experiment is the measurement of the Casimir force between an atom and a wall in the form of the measurement by Obrecht et al. of the change in oscillation frequency of a 87 Rb Bose-Einstein condensate trapped to a fused silica wall; the change is smaller than predicted by theory. We show that saturation effects can explain the discrepancies between theory and experiment observed in all these cases.Comment: 10 pages, 11 figure

Inhibition of Subsets of G Protein-coupled Receptors by Empty Mutants of G Protein α Subunits in Go, G11, and G16

We previously reported that the xanthine nucleotide binding Goα mutant, GoαX, inhibited the activation of Gi-coupled receptors. We constructed similar mutations in G11α and G16α and characterized their nucleotide binding and receptor interaction. First, we found that G11αX and G16αX expressed in COS-7 cells bound xanthine 5'-O-(thiotriphosphate) instead of guanosine 5'-O-(thiotriphosphate). Second, we found that G11αX and G16αX interacted with βγ subunits in the presence of xanthine diphosphate. These experiments demonstrated that G11aαX and G16αX were xanthine nucleotide-binding proteins, similar to GoαX. Third, in COS-7 cells, both G11αX and G16αX inhibited the activation of Gq-coupled receptors, whereas only G16αX inhibited the activation of Gi-coupled receptors. Therefore, when in the nucleotide-free state, empty G11αX and G16αX appeared to retain the same receptor binding specificity as their wild-type counterparts. Finally, we found that GoαX, G11αX, and G16αX all inhibited the endogenous thrombin receptors and lysophosphatidic acid receptors in NIH3T3 cells, whereas G11αX and G16αX, but not GoαX, inhibited the activation of transfected m1 muscarinic receptor in these cells. We conclude that these empty G protein mutants of Goα, G11α, and G16α can act as dominant negative inhibitors against specific subsets of G protein-coupled receptors

On the validity of the method of reduction of dimensionality: area of contact, average interfacial separation and contact stiffness

It has recently been suggested that many contact mechanics problems between solids can be accurately studied by mapping the problem on an effective one dimensional (1D) elastic foundation model. Using this 1D mapping we calculate the contact area and the average interfacial separation between elastic solids with nominally flat but randomly rough surfaces. We show, by comparison to exact numerical results, that the 1D mapping method fails even qualitatively. We also calculate the normal interfacial stiffness $K$ and compare it with the result of an analytical study. We attribute the failure of the elastic foundation model to the neglect of the long-range elastic coupling between the asperity contact regions.Comment: 5 pages, 4 figures, 29 reference

Did Earth-approaching asteroids 3551, 3908, or 4055 produce meteorites?

Orbital integrations show that Amor asteroid 3908 could have ejected one out of four plausible groups of meteorite producing fireballs during a collision in the asteroid belt. It was suggested by others that such a collision may also have split asteroids 3551 and 3908. A member of this group of fireballs is listed as one of the better possibilities for recovery