The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius-Perron operator $U$ of the cusp map $F:[-1,1]\to [-1,1]$, $F(x)=1-2 x^{1/2}$ (which is an approximation of the Poincare section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in (0,1)$ the spectrum of $U$ in the Hardy space in the disk $\{z\in C:|z-q|

Extended spectral decompositions of the Renyi map

We present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map.

A nonradioactive method for the assay of polyphosphate kinase activity and its application in the study of polyphosphate metabolism in Burkholderia cepacia

Studies of polyphosphate (polyP) metabolism in microorganisms have been hampered by the lack of a convenient method for the assay in cell extracts of the activity of polyphosphate kinase (PPK), the enzyme principally responsible for microbial polyP biosynthesis. We report the development of such an assay, based on the well-established metachromatic reaction, with toluidine blue, of the polyP formed during the PPK-catalyzed reaction. The method was successfully used in the characterization of PPK activity in crude extracts of an environmental Burkholderia cepacia isolate. The development of a protocol for the physical recovery of polyP from solution is also reported. (C) 2002 Elsevier Science (USA). All rights reserved.

Early alterations in serum creatine kinase and total cholesterol following high intensity eccentric muscle actions

Aim. The purpose of this experiment was to assess the levels of muscle soreness, serum total cholesterol (TC) and creatine kinase (CK) in the first 48 hours following fatiguing eccentric exercise performed with the triceps brachii.

Mapping the realm: A New Look at the Gough Map of Britain (c.1360)

The mid-fourteenth century map of Britain known as the ‘Gough’ map is the earliest extant depiction of the island in geographically recognizable form. Hitherto, however, interest in the road or route patterns marked on the map has meant that the map's extraordinarily rich settlement geography has not received the attention it merits and that, consequently, the point of the map may have been missed. The availability of a digital scan of the map coupled with the use of Geographical Information System (GIS) software provides the opportunity for a new look at the Gough map and the questions it poses. Attention in this article is directed to the settlement geography it shows, and in particular to the map's 654 cities, towns, villages, castles and monasteries. Their geographical positions as given on the manuscript are compared with their modern equivalents to shed light on some of the basic questions—the map's place of origin, the purpose or purposes for which it was made and the circumstances of its production—that have posed such a challenge for scholars. Our preliminary conclusion is that the key to understanding the original primary role of the Gough map lies in its accurate but selective depiction of the settlement geography of fourteenth-century Britain.

Protein kinase B/Akt activity is involved in renal TGF-beta 1-driven epithelial-mesenchymal transition in vitro and in vivo

The molecular pathogenesis of diabetic nephropathy (DN), the leading cause of end-stage renal disease worldwide, is complex and not fully understood. Transforming growth factor-beta (TGF-beta1) plays a critical role in many fibrotic disorders, including DN. In this study, we report protein kinase B (PKB/Akt) activation as a downstream event contributing to the pathophysiology of DN. We investigated the potential of PKB/Akt to mediate the profibrotic bioactions of TGF-beta1 in kidney. Treatment of normal rat kidney epithelial cells (NRK52E) with TGF-beta1 resulted in activation of phosphatidylinositol 3-kinase (PI3K) and PKB/Akt as evidenced by increased Ser473 phosphorylation and GSK-3beta phosphorylation. TGF-beta1 also stimulated increased Smad3 phosphorylation in these cells, a response that was insensitive to inhibition of PI3K or PKB/Akt. NRK52E cells displayed a loss of zona occludins 1 and E-cadherin and a gain in vimentin and alpha-smooth muscle actin expression, consistent with the fibrotic actions of TGF-beta1. These effects were blocked with inhibitors of PI3K and PKB/Akt. Furthermore, overexpression of PTEN, the lipid phosphatase regulator of PKB/Akt activation, inhibited TGF-beta1-induced PKB/Akt activation. Interestingly, in the Goto-Kakizaki rat model of type 2 diabetes, we also detected increased phosphorylation of PKB/Akt and its downstream target, GSK-3beta, in the tubules, relative to that in control Wistar rats. Elevated Smad3 phosphorylation was also detected in kidney extracts from Goto-Kakizaki rats with chronic diabetes. Together, these data suggest that TGF-beta1-mediated PKB/Akt activation may be important in renal fibrosis during diabetic nephropathy.

Regulation of 3-phosphoinositide-dependent protein kinase-1 (PDK1) by src involves tyrosine phosphorylation of PDK1 and Src homology 2 domain binding

3-Phosphoinositide-dependent protein kinase-1 (PDK1) appears to play a central regulatory role in many cell signalings between phosphoinositide-3 kinase and various intracellular serine/threonine kinases. In resting cells, PDK1 is known to be constitutively active and is further activated by tyrosine phosphorylation (Tyr(9) and Tyr(373/376)) following the treatment of the cell with insulin or pervanadate. However, little is known about the mechanisms for this additional activation of PDK1. Here, we report that the SH2 domain of Src, Crk, and GAP recognized tyrosine-phosphorylated PDK1 in vitro. Destabilization of PDK1 induced by geldanamycin (a Hsp90 inhibitor) was partially blocked in HEK 293 cells expressing PDK1- Y9F. Co-expression of Hsp90 enhanced PDK1-Src complex formation and led to further increased PDK1 activity toward PKB and SGK. Immunohistochemical analysis with anti- phospho-Tyr9 antibodies showed that the level of Tyr9 phosphorylation was markedly increased in tumor samples compared with normal. Taken together, these data suggest that phosphorylation of PDK1 on Tyr9, distinct from Tyr373/376, is important for PDK1/Src complex formation, leading to PDK1 activation. Furthermore, Tyr9 phosphorylation is critical for the stabilization of both PDK1 and the PDK1/Src complex via Hsp90-mediated protection of PDK1 degradation.

Enhanced sensitivity of protein kinase B/Akt to insulin in hypoxia is independent of HIF1 alpha and promotes cell viability

Maintenance of oxygen homeostasis is a key requirement to ensure normal mammalian cell growth and differentiation. Hypoxia arises when oxygen demand exceeds supply, and is a feature of multiple human diseases including stroke, cancer and renal fibrosis. We have investigated the effect of hypoxia on kidney cells, and observed that insulin-induced cell viability is increased in hypoxia. We have characterized the role of protein kinase B (PKB/ Akt) in these cells as a potential mediator of this effect. PKB/Akt activity was increased by low oxygen concentrations in kidney cells, and insulin-stimulated activation of PKB/Akt was stronger, more rapid and more sustained in hypoxia. Reduction of HIF1 alpha levels using antimycin-A or siRNA targeting HlF1 alpha did not affect PKB/Akt activation in hypoxia. Pharmacologic stabilization of HIF1 alpha independent of hypoxia did not increase insulin-stimulated PKB/Akt activation. Although increased insulin-stimulated cell viability was observed in hypoxia, no differences in the degree of insulin-stimulated glucose uptake were observed in L6 muscle cells in hypoxia compared to normoxia. Thus, PKB/Akt may regulate specific cellular responses to growth factors such as insulin under adverse conditions such as hypoxia. alpha 2007 Elsevier GmbH. All rights reserved.

Stabilization of Mdm2 via decreased ubiquitination is mediated by protein kinase B/Akt-dependent phosphorylation

The tumor suppressor p53 is commonly inhibited under conditions in which the phosphatidylinositide 3'-OH kinase/protein kinase B (PKB) Akt pathway is activated. Intracellular levels of p53 are controlled by the E3 ubiquitin ligase Mdm2. Here we show that PKB inhibits Mdm2 self-ubiquitination via phosphorylation of Mdm2 on Ser(166) and Ser(188). Stimulation of human embryonic kidney 293 cells with insulin-like growth factor-1 increased Mdm2 phosphorylation on Ser(166) and Ser(188) in a phosphatidylinositide 3'-OH kinase-dependent manner, and the treatment of both human embryonic kidney 293 and COS-1 cells with phosphatidylinositide 3'-OH kinase inhibitor LY-294002 led to proteasome-mediated Mdm2 degradation. Introduction of a constitutively active form of PKB together with Mdm2 into cells induced phosphorylation of Mdm2 at Ser(166) and Ser(188) and stabilized Mdm2 protein. Moreover, mouse embryonic fibroblasts lacking PKBalpha displayed reduced Mdm2 protein levels with a concomitant increase of p53 and p21(Cip1), resulting in strongly elevated apoptosis after UV irradiation. In addition, activation of PKB correlated with Mdm2 phosphorylation and stability in a variety of human tumor cells. These findings suggest that PKB plays a critical role in controlling of the Mdm2.p53 signaling pathway by regulating Mdm2 stability.

Advances in protein kinase B signalling: AKTion on multiple fronts

The role of the serine/threonine protein kinase B (PKB, also known as Akt) is becoming increasingly more evident to researchers investigating diverse cellular processes such as glucose uptake, cell-cycle progression, apoptosis and transcriptional regulation. New roles for PKB/Akt have been described in various organisms and biological processes. From the regulation of ovarian ecdysteroid production in the humble mosquito (Aedes aegypti), through the seasonal, tissue-specific regulation of PKB/Akt during the hibernation of yellow-bellied marmots (Marmota flaviventris), to the control of glucose metabolism and insulin signalling in the mouse (Mus musculus), our knowledge of the function of this protein kinase has expanded greatly in recent years. Significant advances in all aspects of PKB/Akt signalling have occurred in the past 2 years, including biological insights, novel substrates and newly discovered regulatory mechanisms of PKB/Akt. Collectively, these data expand the current models of PKB/Akt signalling and highlight potential directions for PKB/Akt research in the future.

Ten years of protein kinase B signalling: a hard Akt to follow

It is ten years since the publication of three papers describing the cloning of a new proto-oncogene serine/threonine kinase termed protein kinase B (PKB)/Akt. Key roles for this protein kinase in cellular processes such as glucose metabolism, cell proliferation, apoptosis, transcription and cell migration are now well established. The explosion of publications involving PKB/Akt in the past three years emphasizes the high level of current interest in this signalling molecule. This review focuses on tracing the characterization of this kinase, through the elucidation of its mechanism of regulation, to its role in regulating physiological and pathophysiological processes,to our current understanding of the biology of PKB/Akt, and prospects for the future.