Geometry and physics of knots

KNOTS are usually categorized in terms of topological properties that are invariant under changes in a knot's spatial configuration(1-4). Here we approach knot identification from a different angle, by considering the properties of particular geometrical forms which we define as 'ideal'. For a knot with a given topology and assembled from a tube of uniform diameter, the ideal form is the geometrical configuration having the highest ratio of volume to surface area. Practically, this is equivalent to determining the shortest piece of tube that can be closed to form the knot. Because the notion of an ideal form is independent of absolute spatial scale, the length-to-diameter ratio of a tube providing an ideal representation is constant, irrespective of the tube's actual dimensions. We report the results of computer simulations which show that these ideal representations of knots have surprisingly simple geometrical properties. In particular, there is a simple linear relationship between the length-to-diameter ratio and the crossing number-the number of intersections in a two-dimensional projection of the knot averaged over all directions. We have also found that the average shape of knotted polymeric chains in thermal equilibrium is closely related to the ideal representation of the corresponding knot type. Our observations provide a link between ideal geometrical objects and the behaviour of seemingly disordered systems, and allow the prediction of properties of knotted polymers such as their electrophoretic mobility(5).

Aging and motor programming: differential effects according to the selection of action

There are controversial reports about the effect of aging on movement preparation, and it is unclear to which extent cognitive and/or motor related cerebral processes may be affected. This study examines the age effects on electro-cortical oscillatory patterns during various motor programming tasks, in order to assess potential differences according to the mode of action selection. Twenty elderly (EP, 60-84 years) and 20 young (YP, 20-29 years) participants with normal cognition underwent 3 pre-cued response tasks (S1-S2 paradigm). S1 carried either complete information on response side (Full; stimulus-driven motor preparation), no information (None; general motor alertness), or required free response side selection (Free; internally-driven motor preparation). Electroencephalogram (EEG) was recorded using 64 surface electrodes. Alpha (8-12 Hz) desynchronization (ERD)/synchronization (ERS) and motor-related amplitude asymmetries (MRAA) were analyzed during the S1-S2 interval. Reaction times (RTs) to S2 were slower in EP than YP, and in None than in the other 2 tasks. There was an Age x Task interaction due to increased RTs in Free compared to Full in EP only. Central bilateral and midline activation (alpha ERD) was smaller in EP than YP in None. In Full just before S2, readiness to move was reflected by posterior midline inhibition (alpha ERS) in both groups. In Free, such inhibition was present only in YP. Moreover, MRAA showed motor activity lateralization in both groups in Full, but only in YP in Free. The results indicate reduced recruitment of motor regions for motor alertness in the elderly. They further show less efficient cerebral processes subtending free selection of movement in elders, suggesting reduced capacity for internally-driven action with age.

Differential contribution of mitochondria, NADPH oxidases, and glycolysis to region-specific oxidant stress in the anoxic-reoxygenated embryonic heart.

The ability of the developing myocardium to tolerate oxidative stress during early gestation is an important issue with regard to possible detrimental consequences for the fetus. In the embryonic heart, antioxidant defences are low, whereas glycolytic flux is high. The pro- and antioxidant mechanisms and their dependency on glucose metabolism remain to be explored. Isolated hearts of 4-day-old chick embryos were exposed to normoxia (30 min), anoxia (30 min), and hyperoxic reoxygenation (60 min). The time course of ROS production in the whole heart and in the atria, ventricle, and outflow tract was established using lucigenin-enhanced chemiluminescence. Cardiac rhythm, conduction, and arrhythmias were determined. The activity of superoxide dismutase, catalase, gutathione reductase, and glutathione peroxidase as well as the content of reduced and oxidized glutathione were measured. The relative contribution of the ROS-generating systems was assessed by inhibition of mitochondrial complexes I and III (rotenone and myxothiazol), NADPH oxidases (diphenylene iodonium and apocynine), and nitric oxide synthases (N-monomethyl-l-arginine and N-iminoethyl-l-ornithine). The effects of glycolysis inhibition (iodoacetate), glucose deprivation, glycogen depletion, and lactate accumulation were also investigated. In untreated hearts, ROS production peaked at 10.8 ± 3.3, 9 ± 0.8, and 4.8 ± 0.4 min (means ± SD; n = 4) of reoxygenation in the atria, ventricle, and outflow tract, respectively, and was associated with arrhythmias. Functional recovery was complete after 30-40 min. At reoxygenation, 1) the respiratory chain and NADPH oxidases were the main sources of ROS in the atria and outflow tract, respectively; 2) glucose deprivation decreased, whereas glycogen depletion increased, oxidative stress; 3) lactate worsened oxidant stress via NADPH oxidase activation; 4) glycolysis blockade enhanced ROS production; 5) no nitrosative stress was detectable; and 6) the glutathione redox cycle appeared to be a major antioxidant system. Thus, the glycolytic pathway plays a predominant role in reoxygenation-induced oxidative stress during early cardiogenesis. The relative contribution of mitochondria and extramitochondrial systems to ROS generation varies from one region to another and throughout reoxygenation.

Differential expression of peroxisome proliferator-activated receptors (PPARs): tissue distribution of PPAR-alpha, -beta, and -gamma in the adult rat.

Peroxisome proliferator-activated receptors (PPARs) are members of the nuclear hormone receptor superfamily that can be activated by various xenobiotics and natural fatty acids. These transcription factors primarily regulate genes involved in lipid metabolism and also play a role in adipocyte differentiation. We present the expression patterns of the PPAR subtypes in the adult rat, determined by in situ hybridization using specific probes for PPAR-alpha, -beta and -gamma, and by immunohistochemistry using a polyclonal antibody that recognizes the three rat PPAR subtypes. In numerous cell types from either ectodermal, mesodermal, or endodermal origin, PPARs are coexpressed, with relative levels varying between them from one cell type to the other. PPAR-alpha is highly expressed in hepatocytes, cardiomyocytes, enterocytes, and the proximal tubule cells of kidney. PPAR-beta is expressed ubiquitously and often at higher levels than PPAR-alpha and -gamma. PPAR-gamma is expressed predominantly in adipose tissue and the immune system. Our results suggest new potential directions to investigate the functions of the different PPAR subtypes.

Differential distribution of tau proteins in developing cat cerebellum.

The differential distribution and phosphorylation of tau proteins in cat cerebellum was studied with two well characterized antibodies, TAU-1 and TAU-2. TAU-1 detects tau proteins in axons, and the epitope in perikarya and dendrites is masked by phosphorylation. TAU-2 detects a phosphorylation-independent epitope on tau proteins. The molecular composition of tau proteins in the range of 45 kD to 64 kD at birth changed after the first postnatal month to a set of several adult variants of higher molecular weights in the range of 59 kD to 95 kD. The appearance of tau proteins in subsets of axons corresponds to the axonal maturation of cerebellar local-circuit neurons in granular and molecular layers and confirms previous studies. Tau proteins were also identified in synapses by immunofluorescent double-staining with synapsin I, located in the pinceau around the Purkinje cells, and in glomeruli. Dephosphorylation of juvenile cerebellar tissue by alkaline phosphatase indicated indirectly the presence of differentially phosphorylated tau forms mainly in juvenile ages. Additional TAU-1 immunoreactivity was unmasked in numerous perikarya and dendrites of stellate cells, and in cell bodies of granule cells. Purkinje cell bodies were stained transiently at juvenile ages. During postnatal development, the intensity of the phosphate-dependent staining decreased, suggesting that phosphorylation of tau proteins in perikarya and dendrites may be essential for early steps in neuronal morphogenesis during cat cerebellum development.

Differential species-specific ectoparasitic mite intensities in two intimately coexisting sibling bat species: resource-mediated host attractiveness or parasite specialization?

1. The mechanisms underlying host choice strategies by parasites remain poorly understood. We address two main questions: (i) do parasites prefer vulnerable or well-fed hosts, and (ii) to what extent is a parasite species specialized towards a given host species? 2. To answer these questions, we investigated, both in the field and in the lab, a host-parasite system comprising one ectoparasitic mite (Spinturnix myoti) and its major hosts, two sibling species of bats (Myotis myotis and M blythii), which coexist intimately in colonial nursery roosts. We exploited the close physical associations between host species in colonial roosts as well as naturally occurring annual variation in food abundance to investigate the relationships between parasite intensities and (i) host species and (ii) individual nutritional status. 3. Although horizontal transmission of parasites was facilitated by the intimate aggregation of bats within their colonial clusters, we found significant interspecific differences in degree of infestation throughout the 6 years of the study, with M. myotis always more heavily parasitized than M. blythii. This pattern was replicated in a laboratory experiment in which any species-specific resistance induced by exploitation of different trophic niches in nature was removed. 4. Within both host species, S. myoti showed a clear preference for individuals with higher nutritional status. In years with high resource abundance, both bat hosts harboured more parasites than in low-resource years, although the relative difference in parasite burden across species was maintained. This pattern of host choice was also replicated in the laboratory. When offered a choice, parasites always colonized better-fed individuals. 5. These results show first that host specialization in our study system occurred. Second, immediate parasite choice clearly operated towards the selection of hosts in good nutritional state.

Differential allocation and deployment of direct and indirect defences by Vicia sepium along elevation gradients

Dissecting drivers of plant defence investment remains central for understanding the assemblage of communities across different habitats. There is increasing evidence that direct defence strategies against herbivores, including secondary metabolites production, differ along ecological gradients in response to variation in biotic and abiotic conditions. In contrast, intraspecific variation in indirect defences remains unexplored. Here, we investigated variation in herbivory rate, resistance to herbivores, and indirect defences in ant-attracting Vicia species along the elevation gradient of the Alps. Specifically, we compared volatile organic compounds (VOCs) and ant attraction in high and low elevation ecotypes. Consistent with adaptation to the lower herbivory conditions that we detected at higher elevations in the field, high elevation plants were visited by fewer ants and were more susceptible to herbivore attack. In parallel, constitutive volatile organic compound production and subsequent ant attraction were lower in the high elevation ecotypes. We observed an elevation-driven trade-off between constitutive and inducible production of VOCs and ant attraction along the environmental cline. At higher elevations, inducible defences increased, while constitutive defence decreased, suggesting that the high elevation ecotypes compensate for lower indirect constitutive defences only after herbivore attack. Synthesis. Overall, direct and indirect defences of plants vary along elevation gradients. Our findings show that plant allocation to defences are subject to trade-offs depending on local conditions, and point to a feedback mechanism linking local herbivore pressure, predator abundance and the defence investment of plants.

Differential involvement of peroxisome-proliferator-activated receptors alpha and delta in fibrate and fatty-acid-mediated inductions of the gene encoding liver fatty-acid-binding protein in the liver and the small intestine.

Liver fatty-acid-binding protein (L-FABP) is a cytoplasmic polypeptide that binds with strong affinity especially to long-chain fatty acids (LCFAs). It is highly expressed in both the liver and small intestine, where it is thought to have an essential role in the control of the cellular fatty acid (FA) flux. Because expression of the gene encoding L-FABP is increased by both fibrate hypolipidaemic drugs and LCFAs, it seems to be under the control of transcription factors, termed peroxisome-proliferator-activated receptors (PPARs), activated by fibrate or FAs. However, the precise molecular mechanism by which these regulations take place remain to be fully substantiated. Using transfection assays, we found that the different PPAR subtypes (alpha, gamma and delta) are able to mediate the up-regulation by FAs of the gene encoding L-FABP in vitro. Through analysis of LCFA- and fibrate-mediated effects on L-FABP mRNA levels in wild-type and PPARalpha-null mice, we have found that PPARalpha in the intestine does not constitute a dominant regulator of L-FABP gene expression, in contrast with what is known in the liver. Only the PPARdelta/alpha agonist GW2433 is able to up-regulate the gene encoding L-FABP in the intestine of PPARalpha-null mice. These findings demonstrate that PPARdelta can act as a fibrate/FA-activated receptor in tissues in which it is highly expressed and that L-FABP is a PPARdelta target gene in the small intestine. We propose that PPARdelta contributes to metabolic adaptation of the small intestine to changes in the lipid content of the diet.

DIFFERENTIAL EXPRESSION OF GLUTARYL-CoA DEHYDROGENASE IN ADULT RAT CNS, PERIPHERAL TISSUES AND DURING EMBRYONIC DEVELOPMENT

Glutaryl-CoA dehydrogenase (GCDH, EC 1.3.99.7) deficiency, known as glutaric acidemia type I, is one of the more common organic acidurias. To investigate the role of this pathway in different organs we studied the tissue-specific expression pattern of rat Gcdh. The open reading frame cDNA of the rat Gcdh gene was cloned from rat brain mRNA by RT-PCR, allowing the synthesis of digoxigenin-labeled in situ hybridization (ISH) riboprobes. Gcdh mRNA expression was analyzed by ISH on cryosections of adult rat brain, kidney, liver, spleen and heart muscle, as well as on E15 and E18 rat embryos. Gcdh was found expressed in the whole rat brain, almost exclusively in neurons. Gcdh was absent from astrocytes but expressed in rare oligodendrocytes. Strong Gcdh expression was found in liver and spleen, where expression appears predominant to lymphatic nodules. In kidney, the highest Gcdh expression is found in the juxtamedullar cortex (but not in glomerula), and at lower levels in medulla. Heart muscle was negative. During embryonic development, Gcdh was found well expressed in liver, intestinal mucosa and skin, as well as at lower levels in CNS. Further studies are ongoing to provide evidence on the presence of the entire pathway in CNS in order to understand the mechanisms leading to neurotoxicity in glutaric aciduria. The high expression of Gcdh in kidney may explain why certain patients with residual enzyme activity are low excretors at the urine metabolite level.

Differential regulation of the Hippo pathway by adherens junctions and apical-basal cell polarity modules.

Adherens junctions (AJs) and cell polarity complexes are key players in the establishment and maintenance of apical-basal cell polarity. Loss of AJs or basolateral polarity components promotes tumor formation and metastasis. Recent studies in vertebrate models show that loss of AJs or loss of the basolateral component Scribble (Scrib) cause deregulation of the Hippo tumor suppressor pathway and hyperactivation of its downstream effectors Yes-associated protein (YAP) and Transcriptional coactivator with PDZ-binding motif (TAZ). However, whether AJs and Scrib act through the same or independent mechanisms to regulate Hippo pathway activity is not known. Here, we dissect how disruption of AJs or loss of basolateral components affect the activity of the Drosophila YAP homolog Yorkie (Yki) during imaginal disc development. Surprisingly, disruption of AJs and loss of basolateral proteins produced very different effects on Yki activity. Yki activity was cell-autonomously decreased but non-cell-autonomously elevated in tissues where the AJ components E-cadherin (E-cad) or α-catenin (α-cat) were knocked down. In contrast, scrib knockdown caused a predominantly cell-autonomous activation of Yki. Moreover, disruption of AJs or basolateral proteins had different effects on cell polarity and tissue size. Simultaneous knockdown of α-cat and scrib induced both cell-autonomous and non-cell-autonomous Yki activity. In mammalian cells, knockdown of E-cad or α-cat caused nuclear accumulation and activation of YAP without overt effects on Scrib localization and vice versa. Therefore, our results indicate the existence of multiple, genetically separable inputs from AJs and cell polarity complexes into Yki/YAP regulation.

Differential Regulation of Granuloma Size and Hepatic Fibrosis in Schistosome Infections

Granuloma size is the variable most frequently used to evaluate the immunopathogenesis of schistosome infections. However, hepatic fibrosis is at the least an equally relevant variable. Hepatic fibrosis and the size of circumoval granulomas are frequently dissociated in experimental murine Schistosoma mansoni and S. japonicum infections. Virtually nothing is known of the immunoregulation of schistosomal hepatic fibrosis. This review notes many of the studies which have found discrepancies in granuloma volume and hepatic fibrosis, attempts to put them in perspective and to evaluate different methods of calculating changes in collagen synthesis or content