Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations

Multi-objective optimization algorithms aim at finding Pareto-optimal solutions. Recovering Pareto fronts or Pareto sets from a limited number of function evaluations are challenging problems. A popular approach in the case of expensive-to-evaluate functions is to appeal to metamodels. Kriging has been shown efficient as a base for sequential multi-objective optimization, notably through infill sampling criteria balancing exploitation and exploration such as the Expected Hypervolume Improvement. Here we consider Kriging metamodels not only for selecting new points, but as a tool for estimating the whole Pareto front and quantifying how much uncertainty remains on it at any stage of Kriging-based multi-objective optimization algorithms. Our approach relies on the Gaussian process interpretation of Kriging, and bases upon conditional simulations. Using concepts from random set theory, we propose to adapt the Vorob’ev expectation and deviation to capture the variability of the set of non-dominated points. Numerical experiments illustrate the potential of the proposed workflow, and it is shown on examples how Gaussian process simulations and the estimated Vorob’ev deviation can be used to monitor the ability of Kriging-based multi-objective optimization algorithms to accurately learn the Pareto front.

A pentasymmetric open channel blocker for Cys-loop receptor channels.

γ-Aminobutyric acid type A receptors (GABAA receptors) are chloride ion channels composed of five subunits, mediating fast synaptic and tonic inhibition in the mammalian brain. These receptors show near five-fold symmetry that is most pronounced in the second trans-membrane domain M2 lining the Cl- ion channel. To take advantage of this inherent symmetry, we screened a variety of aromatic anions with matched symmetry and found an inhibitor, pentacyanocyclopentdienyl anion (PCCP-) that exhibited all characteristics of an open channel blocker. Inhibition was strongly dependent on the membrane potential. Through mutagenesis and covalent modification, we identified the region α1V256-α1T261 in the rat recombinant GABAA receptor to be important for PCCP- action. Introduction of positive charges into M2 increased the affinity for PCCP- while PCCP- prevented the access of a positively charged molecule into M2. Interestingly, other anion selective cys-loop receptors were also inhibited by PCCP-, among them the Drosophila RDL GABAA receptor carrying an insecticide resistance mutation, suggesting that PCCP- could serve as an insecticide.

Ubiquitin-specific protease USP2-45 acts as a molecular switch to promote α2δ-1-induced downregulation of Ca v1.2 channels

Availability of voltage-gated calcium channels (Cav) at the plasma membrane is paramount to maintaining the calcium homeostasis of the cell. It is proposed that the ubiquitylation/de-ubiquitylation balance regulates the density of ion channels at the cell surface. Voltage-gated calcium channels Cav1.2 have been found to be ubiquitylated under basal conditions both in vitro and in vivo. In a previous study, we have shown that Cav1.2 channels are ubiquitylated by neuronal precursor cell-expressed developmentally downregulated 4 (Nedd4-1) ubiquitin ligases, but the identity of the counterpart de-ubiquitylating enzyme remained to be elucidated. Regarding sodium and potassium channels, it has been reported that the action of the related isoform Nedd4-2 is counteracted by the ubiquitin-specific protease (USP) 2-45. In this study, we show that USP 2-45 also de-ubiquitylates Cav channels. We co-expressed USPs and Cav1.2 channels together with the accessory subunits β2 and α2δ-1, in tsA-201 and HEK-293 mammalian cell lines. Using whole-cell current recordings and surface biotinylation assays, we show that USP2-45 specifically decreases both the amplitude of Cav currents and the amount of Cav1.2 subunits inserted at the plasma membrane. Importantly, co-expression of the α2δ-1 accessory subunit is necessary to support the effect of USP2-45. We further show that USP2-45 promotes the de-ubiquitylation of both Cav1.2 and α2δ-1 subunits. Remarkably, α2δ-1, but not Cav1.2 nor β2, co-precipitated with USP2-45. These results suggest that USP2-45 binding to α2δ-1 promotes the de-ubiquitylation of both Cav1.2 and α2δ-1 subunits, in order to regulate the expression of Cav1.2 channels at the plasma membrane.

Glycosylation of TRPM4 and TRPM5 channels: molecular determinants and functional aspects

The transient receptor potential channel, TRPM4, and its closest homolog, TRPM5, are non-selective cation channels that are activated by an increase in intracellular calcium. They are expressed in many cell types, including neurons and myocytes. Although the electrophysiological and pharmacological properties of these two channels have been previously studied, less is known about their regulation, in particular their post-translational modifications. We, and others, have reported that wild-type (WT) TRPM4 channels expressed in HEK293 cells, migrated on SDS-PAGE gel as doublets, similar to other ion channels and membrane proteins. In the present study, we provide evidence that TRPM4 and TRPM5 are each N-linked glycosylated at a unique residue, Asn(992) and Asn(932), respectively. N-linked glycosylated TRPM4 is also found in native cardiac cells. Biochemical experiments using HEK293 cells over-expressing WT TRPM4/5 or N992Q/N932Q mutants demonstrated that the abolishment of N-linked glycosylation did not alter the number of channels at the plasma membrane. In parallel, electrophysiological experiments demonstrated a decrease in the current density of both mutant channels, as compared to their respective controls, either due to the Asn to Gln mutations themselves or abolition of glycosylation. To discriminate between these possibilities, HEK293 cells expressing TRPM4 WT were treated with tunicamycin, an inhibitor of glycosylation. In contrast to N-glycosylation signal abolishment by mutagenesis, tunicamycin treatment led to an increase in the TRPM4-mediated current. Altogether, these results demonstrate that TRPM4 and TRPM5 are both N-linked glycosylated at a unique site and also suggest that TRPM4/5 glycosylation seems not to be involved in channel trafficking, but mainly in their functional regulation.

Bounding Standard Gaussian Tail Probabilities

We review various inequalities for Mills' ratio (1 - Φ)= Ø, where Ø and Φ denote the standard Gaussian density and distribution function, respectively. Elementary considerations involving finite continued fractions lead to a general approximation scheme which implies and refines several known bounds.

On degeneracy and invariances of random fields paths with applications in Gaussian process modelling

We study pathwise invariances and degeneracies of random fields with motivating applications in Gaussian process modelling. The key idea is that a number of structural properties one may wish to impose a priori on functions boil down to degeneracy properties under well-chosen linear operators. We first show in a second order set-up that almost sure degeneracy of random field paths under some class of linear operators defined in terms of signed measures can be controlled through the two first moments. A special focus is then put on the Gaussian case, where these results are revisited and extended to further linear operators thanks to state-of-the-art representations. Several degeneracy properties are tackled, including random fields with symmetric paths, centred paths, harmonic paths, or sparse paths. The proposed approach delivers a number of promising results and perspectives in Gaussian process modelling. In a first numerical experiment, it is shown that dedicated kernels can be used to infer an axis of symmetry. Our second numerical experiment deals with conditional simulations of a solution to the heat equation, and it is found that adapted kernels notably enable improved predictions of non-linear functionals of the field such as its maximum.

Dystrophic cardiomyopathy: role of TRPV2 channels in stretch-induced cell damage

Aims Duchenne muscular dystrophy (DMD), a degenerative pathology of skeletal muscle, also induces cardiac failure and arrhythmias due to a mutation leading to the lack of the protein dystrophin. In cardiac cells, the subsarcolemmal localization of dystrophin is thought to protect the membrane from mechanical stress. The absence of dystrophin results in an elevated stress-induced Ca2+ influx due to the inadequate functioning of several proteins, such as stretch-activated channels (SACs). Our aim was to investigate whether transient receptor potential vanilloid channels type 2 (TRPV2) form subunits of the dysregulated SACs in cardiac dystrophy. Methods and results We defined the role of TRPV2 channels in the abnormal Ca2+ influx of cardiomyocytes isolated from dystrophic mdx mice, an established animal model for DMD. In dystrophic cells, western blotting showed that TRPV2 was two-fold overexpressed. While normally localized intracellularly, in myocytes from mdx mice TRPV2 channels were translocated to the sarcolemma and were prominent along the T-tubules, as indicated by immunocytochemistry. Membrane localization was confirmed by biotinylation assays. Furthermore, in mdx myocytes pharmacological modulators suggested an abnormal activity of TRPV2, which has a unique pharmacological profile among TRP channels. Confocal imaging showed that these compounds protected the cells from stress-induced abnormal Ca2+ signals. The involvement of TRPV2 in these signals was confirmed by specific pore-blocking antibodies and by small-interfering RNA ablation of TRPV2. Conclusion Together, these results establish the involvement of TRPV2 in a stretch-activated calcium influx pathway in dystrophic cardiomyopathy, contributing to the defective cellular Ca2+ handling in this disease.

Subunit composition of VRAC channels determines substrate specificity and cellular resistance to Pt-based anti-cancer drugs

Although platinum-based drugs are widely used chemotherapeutics for cancer treatment, the determinants of tumor cell responsiveness remain poorly understood. We show that the loss of subunits LRRC8A and LRRC8D of the heteromeric LRRC8 volume-regulated anion channels (VRACs) increased resistance to clinically relevant cisplatin/carboplatin concentrations. Under isotonic conditions, about 50% of cisplatin uptake depended on LRRC8A and LRRC8D, but neither on LRRC8C nor on LRRC8E. Cell swelling strongly enhanced LRRC8-dependent cisplatin uptake, bolstering the notion that cisplatin enters cells through VRAC. LRRC8A disruption also suppressed drug-induced apoptosis independently from drug uptake, possibly by impairing VRAC-dependent apoptotic cell volume decrease. Hence, by mediating cisplatin uptake and facilitating apoptosis, VRAC plays a dual role in the cellular drug response. Incorporation of the LRRC8D subunit into VRAC substantially increased its permeability for cisplatin and the cellular osmolyte taurine, indicating that LRRC8 proteins form the channel pore. Our work suggests that LRRC8D-containing VRACs are crucial for cell volume regulation by an important organic osmolyte and may influence cisplatin/carboplatin responsiveness of tumors.

Supramolecular Organization of Dye Molecules in Zeolite L Channels: Synthesis, Properties, and Composite Materials

Sequential insertion of different dyes into the 1D channels of zeolite L (ZL) leads to supramolecular sandwich structures and allows the formation of sophisticated antenna composites for light harvesting, transport, and trapping. The synthesis and properties of dye molecules, host materials, composites, and composites embedded in polymer matrices, including two- and three-color antenna systems, are described. Perylene diimide (PDI) dyes are an important class of chromophores and are of great interest for the synthesis of artificial antenna systems. They are especially well suited to advancing our understanding of the structure–transport relationship in ZL because their core fits tightly through the 12-ring channel opening. The substituents at both ends of the PDIs can be varied to a large extent without influencing their electronic absorption and fluorescence spectra. The intercalation/insertion of 17 PDIs, 2 terrylenes, and 1 quaterrylene into ZL are compared and their interactions with the inner surface of the ZL nanochannels discussed. ZL crystals of about 500 nm in size have been used because they meet the criteria that must be respected for the preparation of antenna composites for light harvesting, transport, and trapping. The photostability of dyes is considerably improved by inserting them into the ZL channels because the guests are protected by being confined. Plugging the channel entrances, so that the guests cannot escape into the environment is a prerequisite for achieving long-term stability of composites embedded in an organic matrix. Successful methods to achieve this goal are described. Finally, the embedding of dye–ZL composites in polymer matrices, while maintaining optical transparency, is reported. These results facilitate the rational design of advanced dye–zeolite composite materials and provide powerful tools for further developing and understanding artificial antenna systems, which are among the most fascinating subjects of current photochemistry and photophysics.