Strongly bounded groups and infinite powers of finite groups

We define a group as strongly bounded if every isometric action on a metric space has bounded orbits. This latter property is equivalent to the so-called uncountable strong cofinality, recently introduced by G. Bergman. Our main result is that G^I is strongly bounded when G is a finite, perfect group and I is any set. This strengthens a result of Koppelberg and Tits. We also prove that omega_1-existentially closed groups are strongly bounded.Comment: 10 pages, no figure. Versions 1-3 were entitled "Uncountable groups with Property (FH)". To appear in Comm. Algebr

Impact of disease-causing missense mutations on the structure and function of PHEX

X-linked hypophosphatemia (XLH), the most prevalent form of inherited rickets in humans, is caused by mutations in the PHEX gene, which encodes a protein with high homology to the M13 family of type-II integral membrane zinc metallopeptidases. We created an online mutation database, PHEXdb (http://data.mch.mcgill.ca/phexdb), to catalogue PHEX mutations identified in XLH patients, and found that missense mutations account for 22% of the 157 mutations reported to date. We also undertook to examine the effects of eight missense mutations (C85R, D237G, Y317F, G579R, G579V, S711R, A720T, and F731Y) on synthesis, glycosylation, cellular trafficking, and catalytic activity of the recombinant proteins using several approaches. The wild-type protein was resistant to endoglycosidase H (endo H), indicating that it is fully glycosylated. In addition, biotinylation and immunofluorescence studies revealed that the wild-type protein resides at the cell surface. The D237G, Y317F and F731Y mutant PHEX proteins were also endo H resistant and thus terminally glycosylated. In contrast, endo H digestion demonstrated that C85R, G579R, G579V, S711R and A720T were not terminally glycosylated. Furthermore, immunofluorescence showed that C85R, G579R and S711R were sequestered in the endoplasmic reticulum (ER). A secreted form of wild-type and mutant PHEX (secPHEX) proteins was generated to examine catalytic activity, using a synthetic fluorogenic peptide substrate. For this purpose, rescue of ER-trapped mutant proteins was attempted by growing transfected cells at 26°C. Low temperature was able to rescue three of the five trapped mutant proteins (G579V, S711R and A720T). Residual catalytic activity was observed with four mutant proteins (D237G, Y317F, A720T and F731Y) relative to the wild-type. However, the rescued S711R mutant was devoid of catalytic activity. Finally, limited proteolysis with trypsin and endoproteinase Glu-c revealed that the mutations D237G and F731Y induce confor

Chronic High Fructose Intake Reduces Serum 1,25 (OH)2D-3 Levels in Calcium-Sufficient Rodents

Excessive fructose consumption inhibits adaptive increases in intestinal Ca2+ transport in lactating and weanling rats with increased Ca2+ requirements by preventing the increase in serum levels of 1,25(OH)(2)D-3. Here we tested the hypothesis that chronic fructose intake decreases 1,25(OH)(2)D-3 levels independent of increases in Ca2+ requirements. Adult mice fed for five wk a high glucose-low Ca2+ diet displayed expected compensatory increases in intestinal and renal Ca2+ transporter expression and activity, in renal CYP27B1 (coding for 1 alpha-hydroxylase) expression as well as in serum 1,25(OH)(2)D-3 levels, compared with mice fed isocaloric glucose- or fructose-normal Ca2+ diets. Replacing glucose with fructose prevented these increases in Ca2+ transporter, CYP27B1, and 1,25(OH)(2)D-3 levels induced by a low Ca2+ diet. In adult mice fed for three mo a normal Ca2+ diet, renal expression of CYP27B1 and of CYP24A1 (24-hydroxylase) decreased and increased, respectively, when the carbohydrate source was fructose instead of glucose or starch. Intestinal and renal Ca2+ transporter activity and expression did not vary with dietary carbohydrate. To determine the time course of fructose effects, a high fructose or glucose diet with normal Ca2+ levels was fed to adult rats for three mo. Serum levels of 1,25(OH)(2)D-3 decreased and of FGF23 increased significantly over time. Renal expression of CYP27B1 and serum levels of 1,25(OH)(2)D-3 still decreased in fructose-compared to those in glucose-fed rats after three mo. Serum parathyroid hormone, Ca2+ and phosphate levels were normal and independent of dietary sugar as well as time of feeding. Thus, chronically high fructose intakes can decrease serum levels of 1,25(OH)(2)D-3 in adult rodents experiencing no Ca2+ stress and fed sufficient levels of dietary Ca2+. This finding is highly significant because fructose constitutes a substantial portion of the average diet of Americans already deficient in vitamin D