Discontinuous Galerkin methods for the Multi-dimensional Vlasov-Poisson problem

We introduce and analyze two new semi-discrete numerical methods for the multi-dimensional Vlasov-Poisson system. The schemes are constructed by combing a discontinuous Galerkin approximation to the Vlasov equation together with a mixed finite element method for the Poisson problem. We show optimal error estimates in the case of smooth compactly supported initial data. We propose a scheme that preserves the total energy of the system.

Progesterone down-regulates the open probability of the amiloride-sensitive epithelial sodium channel via a Nedd4-2-dependent mechanism.

Activation of the mitogen-activated protein (MAP) kinase cascade by progesterone in Xenopus oocytes leads to a marked down-regulation of activity of the amiloride-sensitive epithelial sodium channel (ENaC). Here we have studied the signaling pathways involved in progesterone effect on ENaC activity. We demonstrate that: (i) the truncation of the C termini of the alphabetagammaENaC subunits results in the loss of the progesterone effect on ENaC; (ii) the effect of progesterone was also suppressed by mutating conserved tyrosine residues in the Pro-X-X-Tyr (PY) motif of the C termini of the beta and gamma ENaC subunits (beta(Y618A) and gamma(Y628A)); (iii) the down-regulation of ENaC activity by progesterone was also suppressed by co-expression ENaC subunits with a catalytically inactive mutant of Nedd4-2, a ubiquitin ligase that has been previously demonstrated to decrease ENaC cell-surface expression via a ubiquitin-dependent internalization/degradation mechanism; (iv) the effect of progesterone was significantly reduced by suppression of consensus sites (beta(T613A) and gamma(T623A)) for ENaC phosphorylation by the extracellular-regulated kinase (ERK), a MAP kinase previously shown to facilitate the binding of Nedd4 ubiquitin ligases to ENaC; (v) the quantification of cell-surface-expressed ENaC subunits revealed that progesterone decreases ENaC open probability (whole cell P(o), wcP(o)) and not its cell-surface expression. Collectively, these results demonstrate that the binding of active Nedd4-2 to ENaC is a crucial step in the mechanism of ENaC inhibition by progesterone. Upon activation of ERK, the effect of Nedd4-2 on ENaC open probability can become more important than its effect on ENaC cell-surface expression.

Origins and efficiency of the electric industry regulation in Spain, 1910-1936

The aim of this paper is to discover the origins of utility regulation in Spain, and to analyse, from a microeconomic perspective, its characteristics and the impact of regulation on consumers and utilities. Madrid and the Madrilenian utilities are taken as a case study. The electric industry in the period studied was a natural monopoly2. Each of the three phases of production, generation, transmission and distribution, had natural monopoly characteristics. Therefore, the most efficient form to generate, transmit and distribute electricity was the monopoly because one firm can produce a quantity at a lower cost than the sum of costs incurred by two or more firms. A problem arises because when a firm is the single provider it can charge prices above the marginal cost, at monopoly prices. When a monopolist reduces the quantity produced, price increases, causing the consumer to demand less than the economic efficiency level, incurring a loss of consumer surplus. The loss of the consumer surplus is not completely gained by the monopolist, causing a loss of social surplus, a deadweight loss. The main objective of regulation is going to be to reduce to a minimum the deadweight loss. Regulation is also needed because when the monopolist fixes prices at marginal cost equal marginal revenue there would be an incentive for firms to enter the market creating inefficiency. The Madrilenian industry has been chosen because of the availability of statistical information on costs and production. The complex industry structure and the atomised demand add interest to the analysis. This study will also provide some light on the tariff regulation of the period which has been poorly studied and will complement the literature on the US electric utilities regulation where a different type of regulation was implemented.

Repeated Interaction and the Revelation of the Monitor's Type: A Principal-Monitor-Agent Problem

This paper studies a dynamic principal-monitor-agent relation where a strategic principal delegates the task of monitoring the effort of a strategic agent to a third party. The latter we call the monitor, whose type is initially unknown. Through repeated interaction the agent might learn his type. We show that this process damages the principal's payoffs. Compensation is assumed exogenous, limiting to a great extent the provision of incentives. We go around this difficulty by introducing costly replacement strategies, i.e. the principal replaces the monitor, thus disrupting the agent's learning. We found that even when replacement costs are null, if the revealed monitor is strictly preferred by both parties, there is a loss in efficiency due to the impossibility of bene…tting from it. Nonetheless, these strategies can partially recover the principal's losses. Additionally, we establish upper and lower bounds on the payoffs that the principal and the agent can achieve. Finally we characterize the equilibrium strategies under public and private monitoring (with communication) for different cost and impatience levels.

Regulation of the voltage-gated sodium channel Nav1.7 by ubiquitin ligase Nedd4-2

Background and aim: Neuropathic pain (NP) is a frequent and disabling disorder occurring as a consequence of a direct lesion of the nervous system and recurrently associated with a positive shift toward nervous system excitability. Peripheral nerve activity is mainly carried by voltage-gated sodium channels (VGSC), with Nav1.7 isoform being an important candidate since loss of function mutations of its gene is associated with congenital inability to experience pain. Interestingly, ubiquitin ligases from the Nedd4 family are well known proteins that regulate the turnover of many membrane proteins such as VGSC and we showed Nedd2-2 is downregualted in experimental models of chronic pain. The aim of this study was to investigate the importance of Nedd4-2 in the modulation of Nav1.7 at the membrane. Methods: In vitro: whole cell patch clamp on HEK293 cell line stably expressing Nav1.7 was used to record sodium currents (INa), where the peak current of INa reflects the quantity of functional Nav1.7 expressed at the membrane. The possibility that Nedd4-2 modulates the currents was assessed by investigating the effect of its cotransfection on INa. Biotinylation of cell surface was used to isolate membrane-targeted Nav1.7. Furthermore, as the interaction between Nedd4-2 and Nav isoforms was previously reported to rely on an xPPxYx sequence (PY-motif), we mutated this latter to study its impact in the specific interaction between Nav1.7 and Nedd4-2. GST-fusion proteins composed of the Nav1.7 c terminal 66 amino acids (wild-type or PY mutated) and GST were used to pull-down Nedd4-2 from lysates. Results: Co-transfection of Nav1.7 with Nedd4-2 reduced the Nav1.7 current amplitude by ~80% (n = 36, p <0.001), without modifying the biophysical properties of INa. In addition, we show that the quantity of Nav1.7 at the membrane was decreased when Nedd4-2 was present. This effect was dependent on the PY-motif since mutations in this sequence abolished the down-regulatory effect of Nedd4-2. The importance of this motif was further confirmed by pull down experiments since the PY mutant completely eliminate the interaction with Nedd4-2. Perspectives: Altogether, these results point to the importance of Nedd4-2 as a Nav1.7 regulator through cell surface modulation of this sodium channel. Further experiments in freshly dissociated neurons from wild type and Scn1bflox/Nedd4-2Cre mice are needed to confirm in vivo these preliminary data.

An approximate mathematical model for solidification of a flowing liquid in a microchannel

A mathematical model is developed to analyse the combined flow and solidification of a liquid in a small pipe or two-dimensional channel. In either case the problem reduces to solving a single equation for the position of the solidification front. Results show that for a large range of flow rates the closure time is approximately constant, and the value depends primarily on the wall temperature and channel width. However, the ice shape at closure will be very different for low and high fluxes. As the flow rate increases the closure time starts to depend on the flow rate until the closure time increases dramatically, subsequently the pipe will never close.

The problem of the competitiveness of nuclear energy: a biophysical explanation

In this study I try to explain the systemic problem of the low economic competitiveness of nuclear energy for the production of electricity by carrying out a biophysical analysis of its production process. Given the fact that neither econometric approaches nor onedimensional methods of energy analyses are effective, I introduce the concept of biophysical explanation as a quantitative analysis capable of handling the inherent ambiguity associated with the concept of energy. In particular, the quantities of energy, considered as relevant for the assessment, can only be measured and aggregated after having agreed on a pre-analytical definition of a grammar characterizing a given set of finite transformations. Using this grammar it becomes possible to provide a biophysical explanation for the low economic competitiveness of nuclear energy in the production of electricity. When comparing the various unit operations of the process of production of electricity with nuclear energy to the analogous unit operations of the process of production of fossil energy, we see that the various phases of the process are the same. The only difference is related to characteristics of the process associated with the generation of heat which are completely different in the two systems. Since the cost of production of fossil energy provides the base line of economic competitiveness of electricity, the (lack of) economic competitiveness of the production of electricity from nuclear energy can be studied, by comparing the biophysical costs associated with the different unit operations taking place in nuclear and fossil power plants when generating process heat or net electricity. In particular, the analysis focuses on fossil-fuel requirements and labor requirements for those phases that both nuclear plants and fossil energy plants have in common: (i) mining; (ii) refining/enriching; (iii) generating heat/electricity; (iv) handling the pollution/radioactive wastes. By adopting this approach, it becomes possible to explain the systemic low economic competitiveness of nuclear energy in the production of electricity, because of: (i) its dependence on oil, limiting its possible role as a carbon-free alternative; (ii) the choices made in relation to its fuel cycle, especially whether it includes reprocessing operations or not; (iii) the unavoidable uncertainty in the definition of the characteristics of its process; (iv) its large inertia (lack of flexibility) due to issues of time scale; and (v) its low power level.

ENaC and its regulatory proteins as drug targets for blood pressure control.

Hypertension is a serious medical problem affecting millions of people worldwide. A key protein regulating blood pressure is the Epithelial Na(+) Channel (ENaC). In accord, loss of function mutations in ENaC (PHA1) cause hypotension, whereas gain of function mutations (Liddle syndrome) result in hypertension. The region mutated in Liddle syndrome, called the PY motif (L/PPxY), serves as a binding site for the ubiquitin ligase Nedd4-2, a C2-WW-Hect E3 ubiquitin ligase. Nedd4-2 binds the ENaC-PY motif via it WW domains, ubiquitylates the channel and targets it for endocytosis, a process impaired in Liddle syndrome due to poor binding of the channel to Nedd4-2. This leads to accumulation of active channels at the cell surface and increased Na(+) (and fluid) absorption in the distal nephron, resulting in elevated blood volume and blood pressure. Compounds that destabilize cell surface ENaC, or enhance Nedd4-2 activity in the kidney, could potentially serve as drug targets for hypertension. In addition, recent discoveries of regulation of activation of ENaC by proteases such as furin, prostasin and elastase, which cleave the extracellular domain of this channel leading to it activation, as well as the identification of inhibitors that block the activity of these proteases, provide further avenues for drug targeting of ENaC and the control of blood pressure.

The fou2 mutation in the major vacuolar cation channel TPC1 confers tolerance to inhibitory luminal calcium.

The SV channel encoded by the TPC1 gene represents a Ca(2+)- and voltage-dependent vacuolar cation channel. Point mutation D454N within TPC1, named fou2 for fatty acid oxygenation upregulated 2, results in increased synthesis of the stress hormone jasmonate. As wounding causes Ca2+ signals and cytosolic Ca2+ is required for SV channel function, we here studied the Ca(2+)-dependent properties of this major vacuolar cation channel with Arabidopsis thaliana mesophyll vacuoles. In patch clamp measurements, wild-type and fou2 SV channels did not exhibit differences in cytosolic Ca2+ sensitivity and Ca2+ impermeability. K+ fluxes through wild-type TPC1 were reduced or even completely faded away when vacuolar Ca2+ reached the 0.1-mm level. The fou2 protein under these conditions, however, remained active. Thus, D454N seems to be part of a luminal Ca2+ recognition site. Thereby the SV channel mutant gains tolerance towards elevated luminal Ca2+. A three-fold higher vacuolar Ca/K ratio in the fou2 mutant relative to wild-type plants seems to indicate that fou2 can accumulate higher levels of vacuolar Ca(2+) before SV channel activity vanishes and K(+) homeostasis is impaired. In response to wounding fou2 plants might thus elicit strong vacuole-derived cytosolic Ca2+ signals resulting in overproduction of jasmonate.

Cell surface expression of the epithelial Na channel and a mutant causing Liddle syndrome: a quantitative approach.

The epithelial amiloride-sensitive sodium channel (ENaC) controls transepithelial Na+ movement in Na(+)-transporting epithelia and is associated with Liddle syndrome, an autosomal dominant form of salt-sensitive hypertension. Detailed analysis of ENaC channel properties and the functional consequences of mutations causing Liddle syndrome has been, so far, limited by lack of a method allowing specific and quantitative detection of cell-surface-expressed ENaC. We have developed a quantitative assay based on the binding of 125I-labeled M2 anti-FLAG monoclonal antibody (M2Ab*) directed against a FLAG reporter epitope introduced in the extracellular loop of each of the alpha, beta, and gamma ENaC subunits. Insertion of the FLAG epitope into ENaC sequences did not change its functional and pharmacological properties. The binding specificity and affinity (Kd = 3 nM) allowed us to correlate in individual Xenopus oocytes the macroscopic amiloride-sensitive sodium current (INa) with the number of ENaC wild-type and mutant subunits expressed at the cell surface. These experiments demonstrate that: (i) only heteromultimeric channels made of alpha, beta, and gamma ENaC subunits are maximally and efficiently expressed at the cell surface; (ii) the overall ENaC open probability is one order of magnitude lower than previously observed in single-channel recordings; (iii) the mutation causing Liddle syndrome (beta R564stop) enhances channel activity by two mechanisms, i.e., by increasing ENaC cell surface expression and by changing channel open probability. This quantitative approach provides new insights on the molecular mechanisms underlying one form of salt-sensitive hypertension.

Minimum Kinship Care Standards (PDF 400KB)

May 2012 (amended March 2014)

Estimating the Prevalence of Problem Opiate and Problem Cocaine Use in Northern Ireland (PDF 213 KB)

Apr-06