Possible links between BL Lacertae objects and quasars from very long baseline interferometry radio data.

Systematic differences in the very long baseline interferometry (VLBI) radio polarization structure and average VLBI component speeds of BL Lacertae objects and quasars support the view that the observational distinction between these classes, based in large part on the strength of their optical line emission, is meaningful; in other words, this distinction reflects significant differences in the physical conditions in these sources. Possible models providing a link between the optical and VLBI properties of BL Lacertae objects and quasars are discussed. Most VLBI polarization observations to date have been global observations made at 6 cm; recent results suggest that the VLBI polarization structure of some sources may change dramatically on scales smaller than those probed by these 6-cm observations.

Superluminal sources.

Predictions for the apparent velocity statistics under simple beaming models are presented and compared to the observations. The potential applications for tests of unification models and for cosmology (source counts, measurements of the Hubble constant H0 and the deceleration parameter q0) are discussed. First results from a large homogeneous survey are presented. The data do not show compelling evidence for the existence of intrinsically different populations of galaxies, BL Lacertae objects, or quasars. Apparent velocities betaapp in the range 1-5 h-1, where h = H0/100 km.s-1.Mpc-1 [1 megaparsec (Mpc) = 3.09 x 10(22) m], occur with roughly equal frequency; higher values, up to betaapp = 10 h-1, are rather more scarce than appeared to be the case from earlier work, which evidently concentrated on sources that are not representative of the general population. The betaapp distribution suggests that there might be a skewed distribution of Lorentz factors over the sample, with a peak at gammab approximately 2 h-1 and a tail up to at least gammab approximately 10 h-1. There appears to be a clearly rising upper envelope to the betaapp distribution when plotted as a function of observed 5-GHz luminosity; a combination of source counts and the apparent velocity statistics in a larger sample could provide much insight into the properties of radio jet sources.

PDZ Motifs in PTP-BL and RIL Bind to Internal Protein Segments in the LIM Domain Protein RIL

The specificity of protein–protein interactions in cellular signaling cascades is dependent on the sequence and intramolecular location of distinct amino acid motifs. We used the two-hybrid interaction trap to identify proteins that can associate with the PDZ motif-rich segment in the protein tyrosine phosphatase PTP-BL. A specific interaction was found with the Lin-11, Isl-1, Mec-3 (LIM) domain containing protein RIL. More detailed analysis demonstrated that the binding specificity resides in the second and fourth PDZ motif of PTP-BL and the LIM domain in RIL. Immunohistochemistry on various mouse tissues revealed a submembranous colocalization of PTP-BL and RIL in epithelial cells. Remarkably, there is also an N-terminal PDZ motif in RIL itself that can bind to the RIL-LIM domain. We demonstrate here that the RIL-LIM domain can be phosphorylated on tyrosine in vitro and in vivo and can be dephosphorylated in vitro by the PTPase domain of PTP-BL. Our data point to the presence of a double PDZ-binding interface on the RIL-LIM domain and suggest tyrosine phosphorylation as a regulatory mechanism for LIM-PDZ associations in the assembly of multiprotein complexes. These findings are in line with an important role of PDZ-mediated interactions in the shaping and organization of submembranous microenvironments of polarized cells.

Tight frames of k-plane ridgelets and the problem of representing objects that are smooth away from d-dimensional singularities in Rn

For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L2 (Rn), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions that are smooth away from singularities along k-planes in Rn. We also develop tools to help decide whether k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tight frame on the X-ray bundle χn,k—the fiber bundle having the Grassman manifold Gn,k of k-planes in Rn for base space, and for fibers the orthocomplements of those planes. This wavelet-like tight frame is the pushout to χn,k, via the smooth local coordinates of Gn,k, of an orthonormal basis of tensor Meyer wavelets on Euclidean space Rk(n−k) × Rn−k. We then use the X-ray isometry [Solmon, D. C. (1976) J. Math. Anal. Appl. 56, 61–83] to map this tight frame isometrically to a tight frame for L2(Rn)—the k-plane ridgelets. This construction makes analysis of a function f ∈ L2(Rn) by k-plane ridgelets identical to the analysis of the k-plane X-ray transform of f by an appropriate wavelet-like system for χn,k. As wavelets are typically effective at representing point singularities, it may be expected that these new systems will be effective at representing objects whose k-plane X-ray transform has a point singularity. Objects with discontinuities across hyperplanes are of this form, for k = n − 1.

TectoRNA: modular assembly units for the construction of RNA nano-objects

Structural information on complex biological RNA molecules can be exploited to design tectoRNAs or artificial modular RNA units that can self-assemble through tertiary interactions thereby forming nanoscale RNA objects. The selective interactions of hairpin tetraloops with their receptors can be used to mediate tectoRNA assembly. Here we report on the modulation of the specificity and the strength of tectoRNA assembly (in the nanomolar to micromolar range) by variation of the length of the RNA subunits, the nature of their interacting motifs and the degree of flexibility of linker regions incorporated into the molecules. The association is also dependent on the concentration of magnesium. Monitoring of tectoRNA assembly by lead(II) cleavage protection indicates that some degree of structural flexibility is required for optimal binding. With tectoRNAs one can compare the binding affinities of different tertiary motifs and quantify the strength of individual interactions. Furthermore, in analogy to the synthons used in organic chemistry to synthesize more complex organic compounds, tectoRNAs form the basic assembly units for constructing complex RNA structures on the nanometer scale. Thus, tectoRNA provides a means for constructing molecular scaffoldings that organize functional modules in three-dimensional space for a wide range of applications.

Statistical analysis of shape of objects based on landmark data.

Two objects with homologous landmarks are said to be of the same shape if the configurations of landmarks of one object can be exactly matched with that of the other by translation, rotation/reflection, and scaling. The observations on an object are coordinates of its landmarks with reference to a set of orthogonal coordinate axes in an appropriate dimensional space. The origin, choice of units, and orientation of the coordinate axes with respect to an object may be different from object to object. In such a case, how do we quantify the shape of an object, find the mean and variation of shape in a population of objects, compare the mean shapes in two or more different populations, and discriminate between objects belonging to two or more different shape distributions. We develop some methods that are invariant to translation, rotation, and scaling of the observations on each object and thereby provide generalizations of multivariate methods for shape analysis.

Optical evidence for the unification of active galactic nuclei and quasi-stellar objects.

There is a variety of optical evidence for some unification of different types of active galactic nuclei and quasi-stellar objects (QSOs). The case is very strong for the unification of at least some Seyfert galaxies, where polarization data show that the type assigned to the Seyfert galaxy must depend on viewing direction. It has been proposed that Fanaroff-Riley type 2 (FR2) radio galaxies are quasars seen in a direction from which the quasar is obscured, and there is some limited direct evidence for this picture. The broad absorption line QSOs may be normal QSOs seen from a special direction. Some of the sources observed to have high luminosities in the far infrared could be obscured QSOs and active nuclei. Mergers and interactions are likely to play an important role in nuclear activity, and active galaxies and QSOs could change their apparent types through these encounters followed by subsequent evolution.