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We give a simple and constructive extension of Rai\c{t}\u{a}'s result that every constant-rank operator possesses an exact potential and an exact annihilator. Our construction is completely self-contained and provides an improvement on the order of the operators constructed by Rai\c{t}\u{a}, as well as the order of the explicit annihilators for elliptic operators due to Van Schaftingen. We also give an abstract construction of an optimal annihilator for constant-rank operators, which extends the optimal construction of Van Schaftingen for elliptic operators. Lastly, we establish a generalized Poincar\'e lemma for constant-rank operators and homogeneous spaces on $\mathbb{R}^d$, and we prove that the existence of potentials on spaces of periodic maps requires a strictly weaker condition than the constant-rank property., Comment: v3 22 pages, we added an an observation about the homology associated with operators acting on periodic maps, comments still welcome!

International audience; An evaluation of the characteristics of the influent and effluent water of a semi-intensive shrimp farm of Sonora that operated with one cycle of six months, a mean water exchange of 12.7%·d-1 and had mean final yields of 2,000 ± 85 kg·ha-1 (FCR = 2.15 ± 0.21), showed that during that cycle the farm discharged 547 kg N·ha-1 and 73 kg P·ha-1. The respective net exports were 122 kg N·ha-1 and 14 kg P·ha-1. The total solids discharged were 20.8 tons·ha-1 (73.4% inorganic) and the net amounts exported were 7.52 tons·ha-1 of inorganic particulates and 0.92 tons ·ha-1 of organic suspended matter. The water body that receives these discharges is the Moroncarit lagoon, which has an estimated mean water residence time of 3 to 5 d and receives also agricultural drains and sediments of marine origin. For this reason, the nutrients and the sediments discharged by this farm could contribute significantly to the evolution of this lagoon, as well as to its trophic status.

The androgen receptor (AR) is a signal-transducing protein required for sexual differentiation, development, and expression of the male phenotype. A series of human AR deletion mutants were created either by site-directed mutagenesis using restriction enzyme digestion, the polymerase chain reaction, or, for a series of unidirectional NH2-terminal deletions, exonuclease III digestion. Receptor mutants were expressed in monkey kidney COS cells as truncated AR proteins between 20 and 107 kDa as revealed on immunoblots, where wild type AR was a doublet of 114 and 108 kDa. Subcellular localization by immunocytochemical staining demonstrated androgen-dependent nuclear uptake of AR from a perinuclear region of the cytoplasm. A nuclear targeting signal similar in sequence and position to the glucocorticoid receptor and homologous to the SV40 large T antigen was required for androgen-induced nuclear uptake of wild type AR. AR mutants lacking the NH2-terminal and/or steroid binding domains were constitutively nuclear with reduced transcriptional activity. Transcriptional activation by wild type AR was androgen-dependent in cotransfection studies of CV1 cells using the chloramphenicol acetyltransferase reporter gene linked to the mouse mammary tumor virus promoter. Deletion mutagenesis revealed within the NH2-terminal region a domain required for full transcriptional activity and within the steroid binding domain, an inhibitory function, deletion of which yielded a constitutively active receptor. Inhibition of wild type AR by coexpression with an inactive NH2-terminal fragment suggested competition for nuclear factors required for transcriptional regulation. These studies demonstrate a concerted interplay among the domains of the AR protein in regulating gene transcription.

The complete form of androgen insensitivity is an inherited X-linked syndrome in which genetic males fail to undergo masculinization in utero due to defective functioning of the androgen receptor (AR). The molecular basis of androgen insensitivity was investigated in the testicular feminized (Tfm) rat with this syndrome. AR mRNA size and amount, as well as nuclear AR protein revealed by immunocytochemistry, suggested normal expression of the AR gene in the Tfm rat. Sequence analysis of the AR coding region from Tfm and wild-type littermate male rats revealed a single transition mutation, guanine to adenine, within exon E, changing arginine 734 to glutamine within the steroid-binding domain of the AR. This arginine is highly conserved among the family of nuclear receptors and may be part of a phosphorylation recognition site. A recreated mutant AR (Arg734----Gln) expressed in COS cells had only 10-15% of the androgen-binding capacity of wild-type AR; the reduced androgen-binding capacity was similar to that of AR in tissue extracts of the Tfm rat. Stimulation of transcriptional activity by the recreated mutant AR was reduced relative to wild-type AR in cotransfection assays in CV1 cells using as reporter plasmid the mouse mammary tumor virus promoter linked to the chloramphenicol acetyltransferase gene. Thus, arginine 734 appears essential for normal AR function both in androgen binding and transcriptional activation. Absence of these functions results in androgen insensitivity and lack of male sexual development.

Androgens act through a receptor protein (AR) to mediate sex differentiation and development of the male phenotype. The authors have isolated the eight exons in the amino acid coding region of the AR gene from a human X chromosome library. Nucleotide sequences of the AR gene intron/exon boundaries were determined for use in designing synthetic oligonucleotide primers to bracket coding exons for amplification by the polymerase chain reaction. Genomic DNA was amplified from 46, XY phenotypic female siblings with complete androgen insensitivity syndrome. AR binding affinity for dihydrotestosterone in the affected siblings was lower than in normal males, but the binding capacity was normal. Sequence analysis of amplified exons demonstrated within the AR steroid-binding domain (exon G) a single guanine to adenine mutation, resulting in replacement of valine with methionine at amino acid residue 866. As expected, the carrier mother had both normal and mutant AR genes. Thus, a single point mutation in the steroid-binding domain of the AR gene correlated with the expression of an AR protein ineffective in stimulating male sexual development.