Polynomials for crystal frameworks and the rigid unit mode spectrum.

To each discrete translationally periodic bar-joint framework C in Rd, we associate a matrix-valued function ΦC(Z) defined on the d-torus. The rigid unit mode (RUM) spectrum Ω(C) of C is defined in terms of the multi-phases of phase-periodic infinitesimal flexes and is shown to correspond to the singular points of the function Z → rankΦC(Z) and also to the set of wavevectors of harmonic excitations which have vanishing energy in the long wavelength limit. To a crystal framework in Maxwell counting equilibrium, which corresponds to ΦC(Z) being square, the determinant of ΦC(Z) gives rise to a unique multi-variable polynomial p(C)(Z1, . . . , Zd). For ideal zeolites, the algebraic variety of zeros of pC(Z) on the d-torus coincides with the RUM spectrum. The matrix function is related to other aspects of idealized framework rigidity and flexibility, and in particular leads to an explicit formula for the number of supercell-periodic floppy modes. In the case of certain zeolite frameworks in dimensions two and three, direct proofs are given to show the maximal floppy mode property (order N). In particular, this is the case for the cubic symmetry sodalite framework and some other idealized zeolites.

Retinoic acid is essential for Shh/Hoxd signaling during rat limb outgrowth but not for limb initiation.

Retinoids long have been implicated in limb development and their endogenous contributions to this process are finally being elucidated. Here we use an established model of retinoid depletion during specific gestational windows to investigate the role of endogenous retinoic acid (RA) in supporting limb outgrowth. Rat embryos were deprived of RA starting at days-postcoitum (dpc) 3.0, 5.5, or 7.0 and harvested at the 35-somite stage (dpc 12-12.5). Although embryos from all these windows possessed many characteristics of gestational retinoid deficiency (frontonasal hypoplasia, straight tail, reduced CRBPI and RAR beta), their limb buds emerged with only modest size reductions. Molecular analysis of RA-deficient limb buds revealed enhanced gli-3 and reduced hoxd-12, hoxd-13, shh, and fgf-4, while fgf-8, en-1, and wnt-7a expression remained unaltered. Occasional posterior truncations were observed at low incidence in the longest deficiency window; otherwise, the deficiency window length had no discernable impact on the severity of these changes. At the 45-somite stage, RA-deficient limbs had additional losses of hoxd-13 and fgf-8, accompanied by a flattened AER, suggestive of an ultimate failure in limb bud outgrowth. Results could not confirm a function for endogenous retinoids in limb initiation, but show they are required to maintain the signaling loops between the developing mesenchyme and AER that govern limb outgrowth after the initial emergence of limb bud.

Retinoids and their receptors in vertebrate embryogenesis.

Vitamin A and its derivatives, the retinoids, participate in formation of diverse embryonic structures, including face, heart, eye, limb and nervous system. Studies of retinoid-deficient and -treated embryos, and of receptor null mutants, provide evidence that this participation involves interactions between retinoids and their receptors. Targeted retinoid application and retinoid deficiency, using in ovo avian embryos, has identified early cardiogenic contributions, including cardiocyte gene expression and differentiation, heart tube fusion and laterality, and segmental identity. Also useful is a mammalian model, which targets retinoid deficiency to distinct gestational windows, circumventing limitations of traditional deficiency studies and current null mutant technologies. Rat embryos made deficient in retinoids during gestational d 11.5-13.5 exhibit specific cardiac, limb, ocular and nervous system deficits. That many of the anomalies previously reported in retinoid receptor null mutants are observed in deficiency confirms that ligand-receptor interactions are essential for embryonic development. Other defects are novel, reemphasizing the functional redundancy of retinoid receptors and that retinoid receptors have multiple and overlapping contributions to morphogenesis.

Urethral sphincter mechanism incompetence in the male dog: importance of bladder neck position, proximal urethral length and castration.

The radiographs of 37 incontinent adult male dogs with urethral sphincter mechanism incompetence were compared with those of 28 control dogs to determine if, as in the bitch, differences in bladder neck position and urethral length were implicated in the pathophysiology of urethral sphincter mechanism incompetence. Bladder neck position was significantly different; compared with continent dogs, incontinent animals were significantly more likely (P < 0.005) to have intrapelvic than intra-abdominal bladder necks. However, after allowing for the influence of body size, and unlike the situation in the bitch, there was no significant difference in proximal urethral length between the two groups. Bladder neck position was significantly related to prostate size (P < 0.001) and it is suggested that this is one reason why castrated male dogs are more prone to urethral sphincter mechanism incompetence than entire animals. A logistic regression analysis revealed that both bladder neck position and castration status were significant risk factors for incontinence and that they appeared to be acting independently of each other.

Positive regulation of the vHNF1 promoter by the orphan receptors COUP-TF1/Ear3 and COUP-TFII/Arp1.

vHNF1 (also termed HNF1 beta) is a member of the hepatocyte nuclear fa ctor 1 (HNF1; also termed HNF1 alpha) family of homeodomain-containing transcription factors that interact with a sequence motif found in the regulatory regions of a large number of genes expressed mainly in the liver. It has been suggested that vHNF1 plays a role in early differentiation of specialized epithelia of several endoderm- and mesoderm-derived organs, with HNF1 playing a role in later stages. In support of this idea, expression of vHNF1 but not HNF1 is induced upon treatment of the embryonal carcinoma cell line F9 with retinoic acid. We have cloned and analyzed the vHNF1 promoter to gain a better understanding of the regulation of vHNF1 expression and how it relates to the expression of HNF1. We have identified five sites of DNA-protein interaction within the first 260 bp upstream of the transcription start site, which involve at least three different families of transcription factors. Two sites, a distal DR-1 motif and a proximal octamer motif, are the most important for promoter activity. The DR-1 motif interacts with several members of the steroid hormone receptor superfamily including HNF4, COUP-TFI/Ear3, COUP-TFII/Arp1, and RAR alpha/RXR alpha heterodimers. The vHNF1 promoter is transactivated by COUP-TFI/Ear3 and COUP-TFII/Arp1 and, unlike the HNF1 promoter, is virtually unaffected by HNF4. Interestingly, the proximal octamer site and not the DR-1 site is required for COUP-TFI/Ear3 and COUP-TFII/Arp1 transactivation of the vHNF1 promoter. COUP-TFI/Ear3 does not bind directly to this proximal octamer site. We present evidence of an interaction between COUP-TFI/Ear3 and the octamer-binding proteins in vitro and in the cell, suggesting that COUP-TFI and COUP-TFII activate the vHNF1 promoter via an indirect mechanism.

Isolation and functional analysis of the promoter of the bovine serum albumin gene.

The bovine serum albumin (bSA) promoter has been cloned from bovine genomic DNA using the polymerase chain reaction. In common with other albumin promoters, this promoter functions efficiently in the differentiated rat hepatoma cell line H4II and not in the its dedifferentiated derivative, H5. Analysis of 5' deletions of the bSA promoter after transient transfection into H4II has revealed that a short construct containing the HNF1 binding site and TATA box functions efficiently but requires the presence of the more upstream sequences to achieve full activity Footprint analysis of the promoter reveals seven sites of DNA protein interaction extending from -31 to -213. One of these sites, extending from -170 to -236, whose deletion results in a four fold increase in promoter activity. This site has not previously been reported in other albumin promoters and is bound by the C/EBP-like family of proteins.