A new variational radial basis function approximation for inference in multivariate diffusions

In this paper we present a radial basis function based extension to a recently proposed variational algorithm for approximate inference for diffusion processes. Inference, for state and in particular (hyper-) parameters, in diffusion processes is a challenging and crucial task. We show that the new radial basis function approximation based algorithm converges to the original algorithm and has beneficial characteristics when estimating (hyper-)parameters. We validate our new approach on a nonlinear double well potential dynamical system.

Approximating differentiable relationships between delay embedded dynamical systems with radical basis functions

This thesis is about the study of relationships between experimental dynamical systems. The basic approach is to fit radial basis function maps between time delay embeddings of manifolds. We have shown that under certain conditions these maps are generically diffeomorphisms, and can be analysed to determine whether or not the manifolds in question are diffeomorphically related to each other. If not, a study of the distribution of errors may provide information about the lack of equivalence between the two. The method has applications wherever two or more sensors are used to measure a single system, or where a single sensor can respond on more than one time scale: their respective time series can be tested to determine whether or not they are coupled, and to what degree. One application which we have explored is the determination of a minimum embedding dimension for dynamical system reconstruction. In this special case the diffeomorphism in question is closely related to the predictor for the time series itself. Linear transformations of delay embedded manifolds can also be shown to have nonlinear inverses under the right conditions, and we have used radial basis functions to approximate these inverse maps in a variety of contexts. This method is particularly useful when the linear transformation corresponds to the delay embedding of a finite impulse response filtered time series. One application of fitting an inverse to this linear map is the detection of periodic orbits in chaotic attractors, using suitably tuned filters. This method has also been used to separate signals with known bandwidths from deterministic noise, by tuning a filter to stop the signal and then recovering the chaos with the nonlinear inverse. The method may have applications to the cancellation of noise generated by mechanical or electrical systems. In the course of this research a sophisticated piece of software has been developed. The program allows the construction of a hierarchy of delay embeddings from scalar and multi-valued time series. The embedded objects can be analysed graphically, and radial basis function maps can be fitted between them asynchronously, in parallel, on a multi-processor machine. In addition to a graphical user interface, the program can be driven by a batch mode command language, incorporating the concept of parallel and sequential instruction groups and enabling complex sequences of experiments to be performed in parallel in a resource-efficient manner.

The use of ERS-1 crossovers and TOPEX/Poseidon repeat pass data for global sea surface variability studies

In previous sea-surface variability studies, researchers have failed to utilise the full ERS-1 mission due to the varying orbital characteristics in each mission phase, and most have simply ignored the Ice and Geodetic phases. This project aims to introduce a technique which will allow the straightforward use of all orbital phases, regardless of orbit type. This technique is based upon single satellite crossovers. Unfortunately the ERS-1 orbital height is still poorly resolved (due to higher air drag and stronger gravitational effects) when compared with that of TOPEX/Poseidon (T/P), so to make best use of the ERS-1 crossover data corrections to the ERS-1 orbital heights are calculated by fitting a cubic-spline to dual-crossover residuals with T/P. This correction is validated by comparison of dual satellite crossovers with tide gauge data. The crossover processing technique is validated by comparing the extracted sea-surface variability information with that from T/P repeat pass data. The two data sets are then combined into a single consistent data set for analysis of sea-surface variability patterns. These patterns are simplified by the use of an empirical orthogonal function decomposition which breaks the signals into spatial modes which are then discussed separately. Further studies carried out on these data include an analysis of the characteristics of the annual signal, discussion of evidence for Rossby wave propagation on a global basis, and finally analysis of the evidence for global mean sea level rise.

Structural characterization of CD81-Claudin-1 hepatitis C virus receptor complexes

Tetraspanins are thought to exert their biological function(s) by co-ordinating the lateral movement and trafficking of associated molecules into tetraspanin-enriched microdomains. A second four-TM (transmembrane) domain protein family, the Claudin superfamily, is the major structural component of cellular TJs (tight junctions). Although the Claudin family displays low sequence homology and appears to be evolutionarily distinct from the tetraspanins, CD81 and Claudin-1 are critical molecules defining HCV (hepatitis C virus) entry; we recently demonstrated that CD81-Claudin-1 complexes have an essential role in this process. To understand the molecular basis of CD81-Claudin-1 complex formation, we produced and purified milligram quantities of full-length CD81 and Claudin-1, alone and in complex, in both detergent and lipid contexts. Structural characterization of these purified proteins will allow us to define the mechanism(s) underlying virus-cell interactions and aid the design of therapeutic agents targeting early steps in the viral life cycle.

Astrocytic GABA transporter GAT-1 dysfunction in experimental absence seizures

An enhanced tonic GABA-A inhibition in the thalamus plays a crucial role in experimental absence seizures, and has been attributed, on the basis of indirect evidence, to a dysfunction of the astrocytic GABA transporter-1 (GAT-1). Here, the GABA transporter current was directly investigated in thalamic astrocytes from a well-established genetic model of absence seizures, the Genetic Absence Epilepsy Rats from Strasbourg (GAERS), and its non-epileptic control (NEC) strain. We also characterized the novel form of GABAergic and glutamatergic astrocyte-to-neuron signalling by recording slow outward currents (SOCs) and slow inward currents (SICs), respectively, in thalamocortical (TC) neurons of both strains. In patch-clamped astrocytes, the GABA transporter current was abolished by combined application of the selective GAT-1 and GAT-3 blocker, NO711 (30µM) and SNAP5114 (60µM), respectively, to GAERS and NEC thalamic slices. NO711 alone significantly reduced (41%) the transporter current in NEC, but had no effect in GAERS. SNAP5114 alone reduced by half the GABA transporter current in NEC, whilst it abolished it in GAERS. SIC properties did not differ between GAERS and NEC TC neurons, whilst moderate changes in SOC amplitude and kinetics were observed. These data provide the first direct demonstration of a malfunction of the astrocytic thalamic GAT-1 transporter in absence epilepsy and support an abnormal astrocytic modulation of thalamic ambient GABA levels. Moreover, while the glutamatergic astrocyte-neuron signalling is unaltered in the GAERS thalamus, the changes in some properties of the GABAergic astrocyte-neuron signaling in this epileptic strain may contribute to the generation of absence seizures.

Production, purification and characterization of recombinant, full-length human claudin-1

The transmembrane domain proteins of the claudin superfamily are the major structural components of cellular tight junctions. One family member, claudin-1, also associates with tetraspanin CD81 as part of a receptor complex that is essential for hepatitis C virus (HCV) infection of the liver. To understand the molecular basis of claudin-1/CD81 association we previously produced and purified milligram quantities of functional, full-length CD81, which binds a soluble form of HCV E2 glycoprotein (sE2). Here we report the production, purification and characterization of claudin-1. Both yeast membrane-bound and detergent-extracted, purified claudin-1 were antigenic and recognized by specific antibodies. Analytical ultracentrifugation demonstrated that extraction with n-octyl-ß-d-glucopyranoside yielded monodispersed, dimeric pools of claudin-1 while extraction with profoldin-8 or n-decylphosphocholine yielded a dynamic mixture of claudin-1 oligomers. Neither form bound sE2 in line with literature expectations, while further functional analysis was hampered by the finding that incorporation of claudin-1 into proteoliposomes rendered them intractable to study. Dynamic light scattering demonstrated that claudin-1 oligomers associate with CD81 in vitro in a defined molar ratio of 1:2 and that complex formation was enhanced by the presence of cholesteryl hemisuccinate. Attempts to assay the complex biologically were limited by our finding that claudin-1 affects the properties of proteoliposomes. We conclude that recombinant, correctly-folded, full-length claudin-1 can be produced in yeast membranes, that it can be extracted in different oligomeric forms that do not bind sE2 and that a dynamic preparation can form a specific complex with CD81 in vitro in the absence of any other cellular components. These findings pave the way for the structural characterization of claudin-1 alone and in complex with CD81.

Shared action spaces:a basis function framework for social re-calibration of sensorimotor representations supporting joint action

The article explores the possibilities of formalizing and explaining the mechanisms that support spatial and social perspective alignment sustained over the duration of a social interaction. The basic proposed principle is that in social contexts the mechanisms for sensorimotor transformations and multisensory integration (learn to) incorporate information relative to the other actor(s), similar to the "re-calibration" of visual receptive fields in response to repeated tool use. This process aligns or merges the co-actors' spatial representations and creates a "Shared Action Space" (SAS) supporting key computations of social interactions and joint actions; for example, the remapping between the coordinate systems and frames of reference of the co-actors, including perspective taking, the sensorimotor transformations required for lifting jointly an object, and the predictions of the sensory effects of such joint action. The social re-calibration is proposed to be based on common basis function maps (BFMs) and could constitute an optimal solution to sensorimotor transformation and multisensory integration in joint action or more in general social interaction contexts. However, certain situations such as discrepant postural and viewpoint alignment and associated differences in perspectives between the co-actors could constrain the process quite differently. We discuss how alignment is achieved in the first place, and how it is maintained over time, providing a taxonomy of various forms and mechanisms of space alignment and overlap based, for instance, on automaticity vs. control of the transformations between the two agents. Finally, we discuss the link between low-level mechanisms for the sharing of space and high-level mechanisms for the sharing of cognitive representations. © 2013 Pezzulo, Iodice, Ferraina and Kessler.

Quinols as novel therapeutic agents. 2.1 4-(1-arylsulfonylindol- 2-yl)-4-hydroxycyclohexa-2,5-dien-1-ones and related agents as potent and selective antitumor agents

A series of substituted 4-(1-arylsulfonylindol-2-yl)-4-hydroxycyclohexa-2, 5-dien-1-ones (indolylquinols) has been synthesized on the basis of the discovery of lead compound 1a and screened for antitumor activity. Synthesis of this novel series was accomplished via the "one-pot" addition of lithiated (arylsulfonyl)indoles to 4,4-dimethoxycyclohexa-2,5-dienone followed by deprotection under acidic conditions. Similar methodology gave rise to the related naphtho-, 1H-indole-, and benzimidazole-substituted quinols. A number of compounds in this new series were found to possess in vitro human tumor cell line activity substantially more potent than the recently reported antitumor 4-substituted 4-hydroxycyclohexa-2,5-dien-1-ones1 with similar patterns of selectivity against colon, renal, and breast cell lines. The most potent compound in the series in vitro, 4-(1-benzenesulfonyl-6-fluoro-1H-indol- 2-yl)-4-hydroxycyclohexa-2,5-dienone (1h), exhibits a mean GI50 value of 16 nM and a mean LC50 value of 2.24 μM in the NCI 60-cell-line screen, with LC50 activity in the HCT 116 human colon cancer cell line below 10 nM. The crystal structure of the unsubstituted indolylquinol 1a exhibits two independent molecules, both participating in intermolecular hydrogen bonds from quinol OH to carbonyl O, but one OH group also interacts intramolecularly with a sulfonyl O atom. This interaction, which strengthens upon ab initio optimization, may influence the chemical environment of the bioactive quinol moiety. In vivo, significant antitumor activity was recorded (day 28) in mice bearing subcutaneously implanted MDA-MB-435 xenografts, following intraperitoneal treatment of mice with compound 1a at 50 mg/kg.

BCLA Pioneers Lecture - evidence basis for patient selection:how to predict contact lens success

Editorial

X-ray crystallographic and theoretical studies of an anticonvulsant enaminone:methyl 4-(4'-bromophenyl)amino-6-methyl-2-oxocyclohex-3-en-1-oate

Objective: The aims of this study were to establish the structure of the potent anticonvulsant enaminone methyl 4-(4′-bromophenyl)amino-6-methyl-2- oxocyclohex-3-en-1-oate (E139), and to determine the energetically preferred conformation of the molecule, which is responsible for the biological activity. Materials and Methods: The structure of the molecule was determined by X-ray crystallography. Theoretical ab initio calculations with different basis sets were used to compare the energies of the different enantiomers and to other structurally related compounds. Results: The X-ray crystal structure revealed two independent molecules of E139, both with absolute configuration C11(S), C12(R), and their inverse. Ab initio calculations with the 6-31G, 3-21G and STO-3G basis sets confirmed that the C11(S), C12(R) enantiomer with both substituents equatorial had the lowest energy. Compared to relevant crystal structures, the geometry of the theoretical structures shows a longer C-N and shorter C=O distance with more cyclohexene ring puckering in the isolated molecule. Conclusion: Based on a pharmacophoric model it is suggested that the enaminone system HN-C=C-C=O and the 4-bromophenyl group in E139 are necessary to confer anticonvulsant property that could lead to the design of new and improved anticonvulsant agents. Copyright © 2003 S. Karger AG, Basel.

CuII chain compound showing a ferromagnetic coupling through triple N1,N2-1,2,4-triazole bridges

[Cu(hyetrz)3](CF3SO3)2·H2O [hyetrz = 4-(2′-hydroxyethyl)-1,2,4-triazole] represents the first structurally characterised ferromagnetically coupled CuII chain compound containing triple N1,N2-1,2,4-triazole bridges. catena-[μ-Tris{4-(2′-hydroxyethyl)-1,2,4-triazole-N1,N2}copper(II)] bis(trifluoromethanesulfonate) hydrate (C14H23F6S2O10CuN9) crystallises in the triclinic space group Pl, a = 13.54(3), b = 14.37(3), c = 15.61(4) Å, α = 95.9(1), β = 104.9(1), γ = 106.5(1)°, V = 2763(11) Å3, Z = 4 (CuII units). The CuII ions are linked by triple N1,N2-1,2,4-triazole bridges yielding an alternating chain with Cu1−Cu2 = 3.8842(4) Å and Cu2−Cu3 = 3.9354(4) Å. Analysis of the magnetic data according to a high-temperature series expansion gives a J value of +1.45(3) cm−1. The nature and the magnitude of the ferromagnetic exchange have been discussed on the basis of the structural features. (© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2003).

Compactness in the First Baire Class and Baire-1 Operators

For a polish space M and a Banach space E let B1 (M, E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1 (M, E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy, in case E = R, also hold true in the general case. For instance: a subset of B1 (M, E) is compact iff it is sequentially (resp. countably) compact, the convex hull of a compact bounded subset of B1 (M, E) is relatively compact, etc. We also show that our class includes Gulko compact. In the second part of the paper we examine under which conditions a bounded linear operator T : X ∗ → Y so that T |BX ∗ : (BX ∗ , w∗ ) → Y is a Baire-1 function, is a pointwise limit of a sequence (Tn ) of operators with T |BX ∗ : (BX ∗ , w∗ ) → (Y, · ) continuous for all n ∈ N. Our results in this case are connected with classical results of Choquet, Odell and Rosenthal.

Automata–based Method for Solving Systems of Linear Constraints in {0,1}

We consider a finite state automata based method of solving a system of linear Diophantine equations with coefficients from the set {-1,0,1} and solutions in {0,1}.

Structural basis for receptor activity-modifying protein-dependent selective peptide recognition by a G protein-coupled receptor

Association of receptor activity-modifying proteins (RAMP1-3) with the G protein-coupled receptor (GPCR) calcitonin receptor-like receptor (CLR) enables selective recognition of the peptides calcitonin gene-related peptide (CGRP) and adrenomedullin (AM) that have diverse functions in the cardiovascular and lymphatic systems. How peptides selectively bind GPCR:RAMP complexes is unknown. We report crystal structures of CGRP analog-bound CLR:RAMP1 and AM-bound CLR:RAMP2 extracellular domain heterodimers at 2.5 and 1.8 Å resolutions, respectively. The peptides similarly occupy a shared binding site on CLR with conformations characterized by a β-turn structure near their C termini rather than the α-helical structure common to peptides that bind related GPCRs. The RAMPs augment the binding site with distinct contacts to the variable C-terminal peptide residues and elicit subtly different CLR conformations. The structures and accompanying pharmacology data reveal how a class of accessory membrane proteins modulate ligand binding of a GPCR and may inform drug development targeting CLR:RAMP complexes.