Solution of the relativistic Schrödinger equation for the δ ′ -Function potential in one dimension using cutoff regularization

We study the relativistic version of the Schrödinger equation for a point particle in one dimension with the potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultraviolet divergent, and the resultant expression cannot be renormalized in the usual sense, where the divergent terms can just be omitted. Therefore, a general procedure has been developed to derive different physical properties of the system. The procedure is used first in the nonrelativistic case for the purpose of clarification and comparisons. For the relativistic case, the results show that this system behaves exactly like the delta function potential, which means that this system also shares features with quantum filed theories, like being asymptotically free. In addition, in the massless limit, it undergoes dimensional transmutation, and it possesses an infrared conformal fixed point. The comparison of the solution with the relativistic delta function potential solution shows evidence of universality.

Use of concatamers to study GABAA receptor architecture and function: application to delta-subunit-containing receptors and possible pitfalls

Many membrane proteins, including the GABA(A) [GABA (gamma-aminobutyric acid) type A] receptors, are oligomers often built from different subunits. As an example, the major adult isoform of the GABA(A) receptor is a pentamer built from three different subunits. Theoretically, co-expression of three subunits may result in many different receptor pentamers. Subunit concatenation allows us to pre-define the relative arrangement of the subunits. This method may thus be used to study receptor architecture, but also the nature of binding sites. Indeed, it made possible the discovery of a novel benzodiazepine site. We use here subunit concatenation to study delta-subunit-containing GABA(A) receptors. We provide evidence for the formation of different functional subunit arrangements in recombinant alpha(1)beta(3)delta and alpha(6)beta(3)delta receptors. As with all valuable techniques, subunit concatenation has also some pitfalls. Most of these can be avoided by carefully titrating and minimizing the length of the linker sequences joining the two linked subunits and avoiding inclusion of the signal sequence of all but the N-terminal subunit of a multi-subunit construct. Maybe the most common error found in the literature is that low expression can be overcome by simply overloading the expression system with genetic information. As some concatenated constructs result by themselves in a low level of expression, this erroneous assembly leading to receptor function may be promoted by overloading the expression system and leads to wrong conclusions.

Diversity of structure and function of alpha1alpha6beta3delta GABAA receptors: comparison with alpha1beta3delta and alpha6beta3delta receptors

delta subunit-containing gamma-aminobutyric acid, type A (GABA(A))receptors are expressed extrasynaptically and mediate tonic inhibition. In cerebellar granule cells, they often form receptors together with alpha(1) and/or alpha(6) subunits. We were interested in determining the architecture of receptors containing both subunits. We predefined the subunit arrangement of several different GABA(A) receptor pentamers by concatenation. These receptors composed of alpha(1), alpha(6), beta(3), and delta subunits were expressed in Xenopus oocytes. Currents elicited in response to GABA were determined in the presence and absence of 3alpha,21-dihydroxy-5alpha-pregnan-20-one (THDOC) or ethanol, or currents were elicited by 4,5,6,7-tetrahydroisoxazolo[5,4-c]-pyridin-3-ol (THIP). Several subunit configurations formed active channels. We therefore conclude that delta can assume multiple positions in a receptor pentamer made up of alpha(1), alpha(6), beta(3), and delta subunits. The different receptors differ in their functional properties. Functional expression of one receptor type was only evident in the combined presence of the neurosteroid THDOC with the channel agonist GABA. Most, but not all, receptors active with GABA/THDOC responded to THIP. None of the receptors was modulated by ethanol concentrations up to 30 mm. Several observations point to a preferred position of delta subunits between two alpha subunits in alpha(1)alpha(6)beta(3)delta receptors. This property is shared by alpha(1)beta(3)delta and alpha(6)beta(3)delta receptors, but there are differences in the additionally expressed isoforms.

Sediment dynamics in the subaquatic channel of the Rhone delta (Lake Geneva, France/Switzerland)

bstract With its smaller size, well-known boundary conditions, and the availability of detailed bathymetric data, Lake Geneva’s subaquatic canyon in the Rhone Delta is an excellent analogue to understand sedimentary pro- cesses in deep-water submarine channels. A multidisciplinary research effort was undertaken to unravel the sediment dynamics in the active canyon. This approach included innovative coring using the Russian MIR sub- mersibles, in situ geotechnical tests, and geophysical, sedimentological, geochemical and radiometric analysis techniques. The canyon floor/levee complex is character- ized by a classic turbiditic system with frequent spillover events. Sedimentary evolution in the active canyon is controlled by a complex interplay between erosion and sedimentation processes. In situ profiling of sediment strength in the upper layer was tested using a dynamic penetrometer and suggests that erosion is the governing mechanism in the proximal canyon floor while sedimen- tation dominates in the levee structure. Sedimentation rates progressively decrease down-channel along the levee structure, with accumulation exceeding 2.6 cm/year in the proximal levee. A decrease in the frequency of turbidites upwards along the canyon wall suggests a progressive confinement of the flow through time. The multi-proxy methodology has also enabled a qualitative slope-stability assessment in the levee structure. The rapid sediment loading, slope undercutting and over-steepening, and increased pore pressure due to high methane concentrations hint at a potential instability of the proximal levees. Fur- thermore, discrete sandy intervals show very high methane concentrations and low shear strength and thus could cor- respond to potentially weak layers prone to scarp failures.

Exercise efficiency relates with mitochondrial content and function in older adults

Chronic aerobic exercise has been shown to increase exercise efficiency, thus allowing less energy expenditure for a similar amount of work. The extent to which skeletal muscle mitochondria play a role in this is not fully understood, particularly in an elderly population. The purpose of this study was to determine the relationship of exercise efficiency with mitochondrial content and function. We hypothesized that the greater the mitochondrial content and/or function, the greater would be the efficiencies. Thirty-eight sedentary (S, n = 23, 10F/13M) or athletic (A, n = 15, 6F/9M) older adults (66.8 ± 0.8 years) participated in this cross sectional study. V˙O2peak was measured with a cycle ergometer graded exercise protocol (GXT). Gross efficiency (GE, %) and net efficiency (NE, %) were estimated during a 1-h submaximal test (55% V˙O2peak). Delta efficiency (DE, %) was calculated from the GXT. Mitochondrial function was measured as ATPmax (mmol/L/s) during a PCr recovery protocol with (31)P-MR spectroscopy. Muscle biopsies were acquired for determination of mitochondrial volume density (MitoVd, %). Efficiencies were 17% (GE), 14% (NE), and 16% (DE) higher in A than S. MitoVD was 29% higher in A and ATPmax was 24% higher in A than in S. All efficiencies positively correlated with both ATPmax and MitoVd. Chronically trained older individuals had greater mitochondrial content and function, as well as greater exercise efficiencies. GE, NE, and DE were related to both mitochondrial content and function. This suggests a possible role of mitochondria in improving exercise efficiency in elderly athletic populations and allowing conservation of energy at moderate workloads.