On the discrete spectrum of quantum layers

Consider a quantum particle trapped between a curved layer of constant width built over a complete, non-compact, $\mathcal C^2$ smooth surface embedded in $\mathbb{R}^3$. We assume that the surface is asymptotically flat in the sense that the second fundamental form vanishes at infinity, and that the surface is not totally geodesic. This geometric setting is known as a quantum layer. We consider the quantum particle to be governed by the Dirichlet Laplacian as Hamiltonian. Our work concerns the existence of bound states with energy beneath the essential spectrum, which implies the existence of discrete spectrum. We first prove that if the Gauss curvature is integrable, and the surface is weakly $\kappa$-parabolic, then the discrete spectrum is non-empty. This result implies that if the total Gauss curvature is non-positive, then the discrete spectrum is non-empty. We next prove that if the Gauss curvature is non-negative, then the discrete spectrum is non-empty. Finally, we prove that if the surface is parabolic, then the discrete spectrum is non-empty if the layer is sufficiently thin.Comment: Clarifications and corrections to previous version, conjecture from previous version is proven here (Theorem 1.5), additional references include

Review of battery electric vehicle propulsion systems incorporating flywheel energy storage

The development of battery electric vehicles (BEV) must continue since this can lead us towards a zero emission transport system. There has been an advent of the production BEVs in recent years; however their low range and high cost still remain the two important drawbacks. The battery is the element which strongly affects the cost and range of the BEV. The batteries offer either high specific power or high specific energy but not both. To provide the BEVs with the characteristic to compete with conventional vehicles it is beneficial to hybridize the energy storage combining a high energy battery with a high power source. This shields the battery from peak currents and improves its capacity and life. There are various devices which could qualify as a secondary storage system for the BEV such as high power battery, supercapacitor and high speed flywheel (FW). This paper aims to review a specific type of hybridisation of energy storage which combines batteries and high speed flywheels. The flywheel has been used as a secondary energy system in BEVs from the early 1970s when the oil crises triggered an interest in BEVs. Since the last decade the interest in flywheels has strengthened and their application in the kinetic energy recovery system (KERS) in Formula 1 has further bolstered the case for flywheels. With a number of automotive manufacturers getting involved in developing flywheels for road applications, the authors believe commercial flywheel based powertrains are likely to be seen in the near future. It is hence timely to produce a review of research and development in the area of flywheel assisted BEVs

The Role of Oligomerization and Cooperative Regulation in Protein Function: The Case of Tryptophan Synthase

The oligomerization/co-localization of protein complexes and their cooperative regulation in protein function is a key feature in many biological systems. The synergistic regulation in different subunits often enhances the functional properties of the multi-enzyme complex. The present study used molecular dynamics and Brownian dynamics simulations to study the effects of allostery, oligomerization and intermediate channeling on enhancing the protein function of tryptophan synthase (TRPS). TRPS uses a set of α/β–dimeric units to catalyze the last two steps of L-tryptophan biosynthesis, and the rate is remarkably slower in the isolated monomers. Our work shows that without their binding partner, the isolated monomers are stable and more rigid. The substrates can form fairly stable interactions with the protein in both forms when the protein reaches the final ligand–bound conformations. Our simulations also revealed that the α/β–dimeric unit stabilizes the substrate–protein conformation in the ligand binding process, which lowers the conformation transition barrier and helps the protein conformations shift from an open/inactive form to a closed/active form. Brownian dynamics simulations with a coarse-grained model illustrate how protein conformations affect substrate channeling. The results highlight the complex roles of protein oligomerization and the fine balance between rigidity and dynamics in protein function

Heterogeneous localisation of membrane proteins in Staphylococcus aureus

The bacterial cytoplasmic membrane is the interface between the cell and its environment, with multiple membrane proteins serving its many functions. However, how these proteins are organised to permit optimal physiological processes is largely unknown. Based on our initial findings that 2 phospholipid biosynthetic enzymes (PlsY and CdsA) localise heterogeneously in the membrane of the bacterium Staphylococcus aureus, we have analysed the localisation of other key membrane proteins. A range of protein fusions were constructed and used in conjunction with quantitative image analysis. Enzymes involved in phospholipid biosynthesis as well as the lipid raft marker FloT exhibited a heterogeneous localisation pattern. However, the secretion associated SecY protein, was more homogeneously distributed in the membrane. A FRET-based system also identified novel colocalisation between phospholipid biosynthesis enzymes and the respiratory protein CydB revealing a likely larger network of partners. PlsY localisation was found to be dose dependent but not to be affected by membrane lipid composition. Disruption of the activity of the essential cell division organiser FtsZ, using the inhibitor PC190723 led to loss of PlsY localisation, revealing a link to cell division and a possible role for FtsZ in functions not strictly associated with septum formation

Complementation of the yeast deletion mutant DeltaNCE103 by members of the beta class of carbonic anhydrases is dependent on carbonic anhydrase activity rather than on antioxidant activity.

In recent years, members of the beta class of CAs (carbonic anhydrases) have been shown to complement Delta NCE103, a yeast strain unable to grow under aerobic conditions. The activity required for complementation of Delta NCE103 by tobacco chloroplast CA was studied by site-directed mutagenesis. E196A (Glu196-->Ala), a mutated tobacco CA with low levels of CA activity, complemented Delta NCE103. To determine whether restoration of Delta NCE103 was due to residual levels of CA activity or whether it was related to previously proposed antioxidant activity of CAs [Götz, Gnann and Zimmermann (1999) Yeast 15, 855-864], additional complementation analysis was performed using human CAII, an alpha CA structurally unrelated to the beta class of CAs to which the tobacco protein belongs. Human CAII complemented Delta NCE103, strongly arguing that CA activity is responsible for the complementation of Delta NCE103. Consistent with this conclusion, recombinant NCE103 synthesized in Escherichia coli shows CA activity, and Delta NCE103 expressing the tobacco chloroplast CA exhibits the same sensitivity to H2O2 as the wild-type strain

Different GABA(A) receptor subtypes mediate the anxiolytic, abuse-related, and motor effects of benzodiazepine-like drugs in primates

Benzodiazepines exert their effects by binding to multiple subtypes of the GABA(A) receptor, the predominant subtypes in the brain being those that contain α(1)-, α(2)-, α(3)-, and α(5)-subunits. To understand the potentially different roles of these subtypes in the therapeutic and side effects of benzodiazepines, we evaluated GABA(A) receptor subtype-preferring compounds in nonhuman primate models predictive of anxiolytic, sedative, motor, subjective, and reinforcing effects of benzodiazepine-type drugs. These compounds included zolpidem, which shows preferential binding to GABA(A) receptors containing α(1)-subunits (α(1)GABA(A) receptors); L-838,417, which shows functional selectivity for α(2)GABA(A), α(3)GABA(A), and α(5)GABA(A) receptors; and nonselective conventional benzodiazepines. The results provide evidence in nonhuman primates that α(1)GABA(A) receptors do not play a key role in the anxiolytic and muscle-relaxant properties of benzodiazepine-type drugs; instead, these effects involve α(2)GABA(A), α(3)GABA(A), and/or α(5)GABA(A) subtypes. Our results also suggest that the α(1)GABA(A) receptor subtype might be critically involved in the subjective, sedative, and motor effects of benzodiazepine-type drugs. In contrast, stimulation of α(1)GABA(A) receptors is sufficient, but not necessary, for mediation of the abuse potential of these drugs