On the efficient evaluation of ruin probabilities for completely monotone claim size distributions

In this paper we propose a highly accurate approximation procedure for ruin probabilities in the classical collective risk model, which is based on a quadrature/rational approximation procedure proposed in [2]. For a certain class of claim size distributions (which contains the completely monotone distributions) we give a theoretical justification for the method. We also show that under weaker assumptions on the claim size distribution, the method may still perform reasonably well in some cases. This in particular provides an efficient alternative to a related method proposed in [3]. A number of numerical illustrations for the performance of this procedure is provided for both completely monotone and other types of random variables.

Continuous-time random-walk model for financial distributions

We apply the formalism of the continuous-time random walk to the study of financial data. The entire distribution of prices can be obtained once two auxiliary densities are known. These are the probability densities for the pausing time between successive jumps and the corresponding probability density for the magnitude of a jump. We have applied the formalism to data on the U.S. dollardeutsche mark future exchange, finding good agreement between theory and the observed data.

Tuning clustering in random networks with arbitrary degree distributions

We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the clustering coefficient for each class of nodes of degree k are fixed ad hoc and a priori. The algorithm generates corresponding topologies by applying first a closure of triangles and second the classical closure of remaining free stubs. The procedure unveils an universal relation among clustering and degree-degree correlations for all networks, where the level of assortativity establishes an upper limit to the level of clustering. Maximum assortativity ensures no restriction on the decay of the clustering coefficient whereas disassortativity sets a stronger constraint on its behavior. Correlation measures in real networks are seen to observe this structural bound.

Mutations causing Liddle syndrome reduce sodium-dependent downregulation of the epithelial sodium channel in the Xenopus oocyte expression system.

Liddle syndrome is an autosomal dominant form of hypertension resulting from deletion or missense mutations of a PPPxY motif in the cytoplasmic COOH terminus of either the beta or gamma subunit of the epithelial Na channel (ENaC). These mutations lead to increased channel activity. In this study we show that wild-type ENaC is downregulated by intracellular Na+, and that Liddle mutants decrease the channel sensitivity to inhibition by intracellular Na+. This event results at high intracellular Na+ activity in 1.2-2.4-fold higher cell surface expression, and 2.8-3.5-fold higher average current per channel in Liddle mutants compared with the wild type. In addition, we show that a rapid increase in the intracellular Na+ activity induced downregulation of the activity of wild-type ENaC, but not Liddle mutants, on a time scale of minutes, which was directly correlated to the magnitude of the Na+ influx into the oocytes. Feedback inhibition of ENaC by intracellular Na+ likely represents an important cellular mechanism for controlling Na+ reabsorption in the distal nephron that has important implications for the pathogenesis of hypertension.

Free inertial processes driven by Gaussian noise: Probability distributions, anomalous diffusion and fractal behavior

We study the motion of an unbound particle under the influence of a random force modeled as Gaussian colored noise with an arbitrary correlation function. We derive exact equations for the joint and marginal probability density functions and find the associated solutions. We analyze in detail anomalous diffusion behaviors along with the fractal structure of the trajectories of the particle and explore possible connections between dynamical exponents of the variance and the fractal dimension of the trajectories.

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

A single point mutation in the pore region of the epithelial Na+ channel changes ion selectivity by modifying molecular sieving.

The epithelial Na+ channel (ENaC) belongs to a new class of channel proteins called the ENaC/DEG superfamily involved in epithelial Na+ transport, mechanotransduction, and neurotransmission. The role of ENaC in Na+ homeostasis and in the control of blood pressure has been demonstrated recently by the identification of mutations in ENaC beta and gamma subunits causing hypertension. The function of ENaC in Na+ reabsorption depends critically on its ability to discriminate between Na+ and other ions like K+ or Ca2+. ENaC is virtually impermeant to K+ ions, and the molecular basis for its high ionic selectivity is largely unknown. We have identified a conserved Ser residue in the second transmembrane domain of the ENaC alpha subunit (alphaS589), which when mutated allows larger ions such as K+, Rb+, Cs+, and divalent cations to pass through the channel. The relative ion permeability of each of the alphaS589 mutants is related inversely to the ionic radius of the permeant ion, indicating that alphaS589 mutations increase the molecular cutoff of the channel by modifying the pore geometry at the selectivity filter. Proper geometry of the pore is required to tightly accommodate Na+ and Li+ ions and to exclude larger cations. We provide evidence that ENaC discriminates between cations mainly on the basis of their size and the energy of dehydration.

Rapid fluidic exchange microsystem for recording of fast ion channel kinetics in Xenopus oocytes.

We present a new lab-on-a-chip system for electrophysiological measurements on Xenopus oocytes. Xenopus oocytes are widely used host cells in the field of pharmacological studies and drug development. We developed a novel non-invasive technique using immobilized non-devitellinized cells that replaces the traditional "two-electrode voltage-clamp" (TEVC) method. In particular, rapid fluidic exchange was implemented on-chip to allow recording of fast kinetic events of exogenous ion channels expressed in the cell membrane. Reducing fluidic exchange times of extracellular reagent solutions is a great challenge with these large millimetre-sized cells. Fluidic switching is obtained by shifting the laminar flow interface in a perfusion channel under the cell by means of integrated poly-dimethylsiloxane (PDMS) microvalves. Reagent solution exchange times down to 20 ms have been achieved. An on-chip purging system allows to perform complex pharmacological protocols, making the system suitable for screening of ion channel ligand libraries. The performance of the integrated rapid fluidic exchange system was demonstrated by investigating the self-inhibition of human epithelial sodium channels (ENaC). Our results show that the response time of this ion channel to a specific reactant is about an order of magnitude faster than could be estimated with the traditional TEVC technique.

Epithelial sodium channel/degenerin family of ion channels: a variety of functions for a shared structure.

The recently discovered epithelial sodium channel (ENaC)/degenerin (DEG) gene family encodes sodium channels involved in various cell functions in metazoans. Subfamilies found in invertebrates or mammals are functionally distinct. The degenerins in Caenorhabditis elegans participate in mechanotransduction in neuronal cells, FaNaC in snails is a ligand-gated channel activated by neuropeptides, and the Drosophila subfamily is expressed in gonads and neurons. In mammals, ENaC mediates Na+ transport in epithelia and is essential for sodium homeostasis. The ASIC genes encode proton-gated cation channels in both the central and peripheral nervous system that could be involved in pain transduction. This review summarizes the physiological roles of the different channels belonging to this family, their biophysical and pharmacological characteristics, and the emerging knowledge of their molecular structure. Although functionally different, the ENaC/DEG family members share functional domains that are involved in the control of channel activity and in the formation of the pore. The functional heterogeneity among the members of the ENaC/DEG channel family provides a unique opportunity to address the molecular basis of basic channel functions such as activation by ligands, mechanotransduction, ionic selectivity, or block by pharmacological ligands.

The membrane-associated transient receptor potential vanilloid channel is the central heat shock receptor controlling the cellular heat shock response in epithelial cells.

The heat shock response (HSR) is a highly conserved molecular response to various types of stresses, including heat shock, during which heat-shock proteins (Hsps) are produced to prevent and repair damages in labile proteins and membranes. In cells, protein unfolding in the cytoplasm is thought to directly enable the activation of the heat shock factor 1 (HSF-1), however, recent work supports the activation of the HSR via an increase in the fluidity of specific membrane domains, leading to activation of heat-shock genes. Our findings support the existence of a plasma membrane-dependent mechanism of HSF-1 activation in animal cells, which is initiated by a membrane-associated transient receptor potential vanilloid receptor (TRPV). We found in various non-cancerous and cancerous mammalian epithelial cells that the TRPV1 agonists, capsaicin and resiniferatoxin (RTX), upregulated the accumulation of Hsp70, Hsp90 and Hsp27 and Hsp70 and Hsp90 respectively, while the TRPV1 antagonists, capsazepine and AMG-9810, attenuated the accumulation of Hsp70, Hsp90 and Hsp27 and Hsp70, Hsp90, respectively. Capsaicin was also shown to activate HSF-1. These findings suggest that heat-sensing and signaling in mammalian cells is dependent on TRPV channels in the plasma membrane. Thus, TRPV channels may be important drug targets to inhibit or restore the cellular stress response in diseases with defective cellular proteins, such as cancer, inflammation and aging.

Congenital ataxia and hemiplegic migraine with cerebral edema associated with a novel gain of function mutation in the calcium channel CACNA1A.

Mutations in the CACNA1A gene, encoding the α1 subunit of the voltage-gated calcium channel CaV2.1 (P/Q-type), have been associated with three neurological phenotypes: familial and sporadic hemiplegic migraine type 1 (FHM1, SHM1), episodic ataxia type 2 (EA2), and spinocerebellar ataxia type 6 (SCA6). We report a child with congenital ataxia, abnormal eye movements and developmental delay who presented severe attacks of hemiplegic migraine triggered by minor head traumas and associated with hemispheric swelling and seizures. Progressive cerebellar atrophy was also observed. Remission of the attacks was obtained with acetazolamide. A de novo 3bp deletion was found in heterozygosity causing loss of a phenylalanine residue at position 1502, in one of the critical transmembrane domains of the protein contributing to the inner part of the pore. We characterized the electrophysiology of this mutant in a Xenopus oocyte in vitro system and showed that it causes gain of function of the channel. The mutant CaV2.1 activates at lower voltage threshold than the wild type. These findings provide further evidence of this molecular mechanism as causative of FHM1 and expand the phenotypic spectrum of CACNA1A mutations with a child exhibiting severe SHM1 and non-episodic ataxia of congenital onset.

ENaC-mediated alveolar fluid clearance and lung fluid balance depend on the channel-activating protease 1.

Sodium transport via epithelial sodium channels (ENaC) expressed in alveolar epithelial cells (AEC) provides the driving force for removal of fluid from the alveolar space. The membrane-bound channel-activating protease 1 (CAP1/Prss8) activates ENaC in vitro in various expression systems. To study the role of CAP1/Prss8 in alveolar sodium transport and lung fluid balance in vivo, we generated mice lacking CAP1/Prss8 in the alveolar epithelium using conditional Cre-loxP-mediated recombination. Deficiency of CAP1/Prss8 in AEC induced in vitro a 40% decrease in ENaC-mediated sodium currents. Sodium-driven alveolar fluid clearance (AFC) was reduced in CAP1/Prss8-deficient mice, due to a 48% decrease in amiloride-sensitive clearance, and was less sensitive to beta(2)-agonist treatment. Intra-alveolar treatment with neutrophil elastase, a soluble serine protease activating ENaC at the cell surface, fully restored basal AFC and the stimulation by beta(2)-agonists. Finally, acute volume-overload increased alveolar lining fluid volume in CAP1/Prss8-deficient mice. This study reveals that CAP1 plays a crucial role in the regulation of ENaC-mediated alveolar sodium and water transport and in mouse lung fluid balance.

Predicting future distributions of mountain plants under climate change: does dispersal capacity matter?

Many studies have investigated the impacts that climate change could potentially have on the distribution of plant species, but few have attempted to constrain projections through plant dispersal limitations. Instead, most studies published so far have been using the simplification of considering dispersal as either unlimited or null. However, depending on a species' dispersal capacity, landscape fragmentation, and the rate of climatic change, these assumptions can lead to serious over- or underestimation of a species' future distribution. To quantify the discrepancies between unlimited, realistic, and no dispersal scenarios, we carried out projections of future distribution over the 21st century for 287 mountain plant species in a study area of the Western Swiss Alps. For each species, simulations were run for four dispersal scenarios (unlimited dispersal, no dispersal, realistic dispersal and realistic dispersal with long-distance dispersal events) and under four climate change scenarios. Although simulations accounting for realistic dispersal limitations did significantly differ from those considering dispersal as unlimited or null in terms of projected future distribution, using the unlimited dispersal simplification nevertheless provided good approximations for species extinctions under more moderate climate change scenarios. Overall, simulations accounting for dispersal limitations produced, for our mountainous study area, results that were significantly closer to unlimited dispersal than to no dispersal. Finally, analyzing the temporal pattern of species extinctions over the entire 21st century showed that, due to the possibility of a large number of species shifting their distribution to higher elevation, important species extinctions for our study area might not occur before the 2080-2100 time periods.