Hyers–Ulam stability of functional equations with a square-symmetric operation

The stability of the functional equation f(x ○ y) = H(f(x), f(y)) (x, y ∈ S) is investigated, where H is a homogeneous function and ○ is a square-symmetric operation on the set S. The results presented include and generalize the classical theorem of Hyers obtained in 1941 on the stability of the Cauchy functional equation.

Ol-Prx 3, a member of an additional class of homeobox genes, is unimodally expressed in several domains of the developing and adult central nervous system of the medaka (Oryzias latipes)

Large-scale genetic screens for mutations affecting early neurogenesis of vertebrates have recently been performed with an aquarium fish, the zebrafish. Later stages of neural morphogenesis have attracted less attention in small fish species, partly because of the lack of molecular markers of developing structures that may facilitate the detection of discrete structural alterations. In this context, we report the characterization of Ol-Prx 3 (Oryzias latipes-Prx 3). This gene was isolated in the course of a large-scale screen for brain cDNAs containing a highly conserved DNA binding region, the homeobox helix-three. Sequence analysis revealed that this gene belongs to another class of homeobox genes, together with a previously isolated mouse ortholog, called OG-12 [Rovescalli, A. C., Asoh, S. & Nirenberg, M. (1996) Proc. Natl. Acad. Sci. USA 93, 10691–10696] and with the human SHOX gene [Rao, E., Weiss, B., Fukami, M., Rump, A., Niesler, B., et al. (1997) Nat. Genet. 16, 54–62], thought to be involved in the short-stature phenotype of Turner syndrome patients. These three genes exhibit a moderate level of identity in the homeobox with the other genes of the paired-related (PRX) gene family. Ol-Prx 3, as well as the PRX genes, are expressed in various cartilaginous structures of head and limbs. These genes might thus be involved in common regulatory pathways during the morphogenesis of these structures. Moreover, this paper reports a complex and monophasic pattern of Ol-Prx 3 expression in the central nervous system, which differs markedly from the patterns reported for the PRX genes, Prx 3 excluded: this gene begins to be expressed in a variety of central nervous system territories at late neurula stage. Strikingly, it remains turned on in some of the derivatives of each territory during the entire life of the fish. We hope this work will thus help identify common features for the PRX 3 family of homeobox genes.

Association of Rab25 and Rab11a with the Apical Recycling System of Polarized Madin–Darby Canine Kidney Cells

Recent evidence suggests that apical and basolateral endocytic pathways in epithelia converge in an apically located, pericentriolar endosomal compartment termed the apical recycling endosome. In this compartment, apically and basolaterally internalized membrane constituents are thought to be sorted for recycling back to their site of origin or for transcytosis to the opposite plasma membrane domain. We report here that in the epithelial cell line Madin–Darby Canine Kidney (MDCK), antibodies to Rab11a label an apical pericentriolar endosomal compartment that is dependent on intact microtubules for its integrity. Furthermore, this compartment is accessible to a membrane-bound marker (dimeric immunoglobulin A [IgA]) internalized from either the apical or basolateral pole, functionally defining it as the apical recycling endosome. We have also examined the role of a closely related epithelial-specific Rab, Rab25, in the regulation of membrane recycling and transcytosis in MDCK cells. When cDNA encoding Rab25 was transfected into MDCK cells, the protein colocalized with Rab11a in subapical vesicles. Rab25 transfection also altered the distribution of Rab11a, causing the coalescence of immunoreactivity into multiple denser vesicular structures not associated with the centrosome. Nevertheless, nocodazole still dispersed these vesicles, and dimeric IgA internalized from either the apical or basolateral membrane was detected in endosomes labeled with antibodies to both Rab11a and Rab25. Overexpression of Rab25 decreased the rate of IgA transcytosis and of apical, but not basolateral, recycling of internalized ligand. Conversely, expression of the dominant-negative Rab25T26N did not alter either apical recycling or transcytosis. These results indicate that both Rab11a and Rab25 associate with the apical recycling system of epithelial cells and suggest that Rab25 may selectively regulate the apical recycling and/or transcytotic pathways.

Facilitated diffusion of fructose via the phosphoenolpyruvate/glucose phosphotransferase system of Escherichia coli

From mutants of Escherichia coli unable to utilize fructose via the phosphoenolpyruvate/glycose phosphotransferase system (PTS), further mutants were selected that grow on fructose as the sole carbon source, albeit with relatively low affinity for that hexose (Km for growth ≈8 mM but with Vmax for generation time ≈1 h 10 min); the fructose thus taken into the cells is phosphorylated to fructose 6-phosphate by ATP and a cytosolic fructo(manno)kinase (Mak). The gene effecting the translocation of fructose was identified by Hfr-mediated conjugations and by phage-mediated transduction as specifying an isoform of the membrane-spanning enzyme IIGlc of the PTS, which we designate ptsG-F. Exconjugants that had acquired ptsG+ from Hfr strains used for mapping (designated ptsG-I) grew very poorly on fructose (Vmax ≈7 h 20 min), even though they were rich in Mak activity. A mutant of E. coli also rich in Mak but unable to grow on glucose by virtue of transposon-mediated inactivations both of ptsG and of the genes specifying enzyme IIMan (manXYZ) was restored to growth on glucose by plasmids containing either ptsG-F or ptsG-I, but only the former restored growth on fructose. Sequence analysis showed that the difference between these two forms of ptsG, which was reflected also by differences in the rates at which they translocated mannose and glucose analogs such as methyl α-glucoside and 2-deoxyglucose, resided in a substitution of G in ptsG-I by T in ptsG-F in the first position of codon 12, with consequent replacement of valine by phenylalanine in the deduced amino acid sequence.

Mapping the parameters of prion-induced neuropathology

We present a theoretical framework that enables us to dissect out the parametric dependencies of the pathogenesis of prion diseases. We are able to determine the influence of both host-dependent factors (connectivity, cell density, protein synthesis rate, and cell death) and strain-dependent factors (cell tropism, virulence, and replication rate). We use a model based on a linked system of differential equations on a lattice to explore how the regional distribution of central nervous system pathology in Creutzfeldt-Jakob disease, Gerstmann-Sträussler-Scheinker syndrome, and fatal familial insomnia relates to each of these factors. The model then is used to make qualitative predictions about the pathology for two possible hypothetical triggers of neuronal loss in prion diseases. Pathological progression in overexpressing mouse models has been shown to depend on the site of initial infection. The model allows us to compare the pathologies resulting from different inoculation routes.

Participation of Mitochondrial Metabolism in Photorespiration1 : Reconstituted System of Peroxisomes and Mitochondria from Spinach Leaves

In this study the interplay of mitochondria and peroxisomes in photorespiration was simulated in a reconstituted system of isolated mitochondria and peroxisomes from spinach (Spinacia oleracea L.) leaves. The mitochondria oxidizing glycine produced serine, which was reduced in the peroxisomes to glycerate. The required reducing equivalents were provided by the mitochondria via the malate-oxaloacetate (OAA) shuttle, in which OAA was reduced in the mitochondrial matrix by NADH generated during glycine oxidation. The rate of peroxisomal glycerate formation, as compared with peroxisomal protein, resembled the corresponding rate required during leaf photosynthesis under ambient conditions. When the reconstituted system produced glycerate at this rate, the malate-to-OAA ratio was in equilibrium with a ratio of NADH/NAD of 8.8 × 10−3. This low ratio is in the same range as the ratio of NADH/NAD in the cytosol of mesophyll cells of intact illuminated spinach leaves, as we had estimated earlier. This result demonstrates that in the photorespiratory cycle a transfer of redox equivalents from the mitochondria to peroxisomes, as postulated from separate experiments with isolated mitochondria and peroxisomes, can indeed operate under conditions of the very low reductive state of the NADH/NAD system prevailing in the cytosol of mesophyll cells in a leaf during photosynthesis.

Sensitive detection of bacterial transcription initiation sites and differentiation from RNA processing sites in the pheromone-induced plasmid transfer system of Enterococcus faecalis.

A method was developed to detect 5' ends of bacterial RNAs expressed at low levels and to differentiate newly initiated transcripts from processed transcripts produced in vivo. The procedure involves use of RNA ligase to link a specific oligoribonucleotide to the 5' ends of cellular RNAs, followed by production of cDNA and amplification of the gene of interest by PCR. The method was used to identify the precise sites of transcription initiation within a 10-kb region of the pheromone-inducible conjugative plasmid pCF10 of Enterococcus faecalis. Results confirmed the 5' end of a very abundant, constitutively produced transcript (from prgQ) that had been mapped previously by primer extension and defined the initiation point of a less abundant, divergently transcribed message (from prgX). The method also showed that the 5' end of a pheromone-inducible transcript (prgB) that had been mapped by primer extension was generated by processing rather than new initiation. In addition, the results provided evidence for two promoters, 3 and 5 kb upstream of prgB, and indicated that only the transcripts originating 5 kb upstream may be capable of extending to prgB.

The invariant system of coordinates of antibody molecules: prediction of the "standard" C alpha framework of VL and VH domains.

A new approach of comparing protein structures that does not involve the procedure of superposition is suggested. An invariant system of coordinates for immunoglobulin molecules that is based on the geometrical symmetry inherent to the variable domain light-chain (VL)-heavy-chain (VH) complex is described. The coordinates of the Calpha atoms in 22 immunoglobulin structures are calculated in the invariant system of coordinates. We found that 76 identical positions in this Calpha framework are symmetrical about the twofold axis. Comparison of the identical positions in these molecules allows us to select 96 positions in the light chains and 87 positions in the heavy chains whose Calpha atom coordinates are approximately the same. To check whether the average coordinates of Calpha atoms in these positions complies with the stereochemical requirements, we calculated Calpha-Calpha distances. Seventy-three positions of the light chains and 72 positions of the heavy chains satisfy the Calpha-Calpha distance criterion. The Calpha atoms in these positions are used for constructing the "standard" Calpha framework of VL and VH complexes. The average coordinates of Calpha atoms are presented.

The Ste locus, a component of the parasitic cry-Ste system of Drosophila melanogaster, encodes a protein that forms crystals in primary spermatocytes and mimics properties of the beta subunit of casein kinase 2.

Males of Drosophila melanogaster lacking the Y chromosome-linked crystal locus show multiple meiotic alterations including chromosome disorganization and prominent crystal formation in primary spermatocytes. These alterations are due to the derepression of the X chromosome-linked Stellate sequences. To understand how the derepression of the Stellate elements gives rise to these abnormalities, we have expressed the protein encoded by the Stellate sequences in bacteria and produced an antibody against the fusion protein. Immunostaining of crystal- testes has clearly shown that the Stellate protein is a major component of the crystals. Moreover, in vitro experiments have shown that this protein can interact with the catalytic alpha subunit of casein kinase 2 enzyme, altering its activity.