Dualizing complexes-The modern way

We give a survey of some recent results on Grothendieck duality. We begin with a brief reminder of the classical theory, and then launch into an overview of some of the striking developments since 2005.

Hardy-Weinberg Equilibrium and the Ternary Plot

The Hardy-Weinberg law, formulated about 100 years ago, states that under certainassumptions, the three genotypes AA, AB and BB at a bi-allelic locus are expected to occur inthe proportions p2, 2pq, and q2 respectively, where p is the allele frequency of A, and q = 1-p.There are many statistical tests being used to check whether empirical marker data obeys theHardy-Weinberg principle. Among these are the classical xi-square test (with or withoutcontinuity correction), the likelihood ratio test, Fisher's Exact test, and exact tests in combinationwith Monte Carlo and Markov Chain algorithms. Tests for Hardy-Weinberg equilibrium (HWE)are numerical in nature, requiring the computation of a test statistic and a p-value.There is however, ample space for the use of graphics in HWE tests, in particular for the ternaryplot. Nowadays, many genetical studies are using genetical markers known as SingleNucleotide Polymorphisms (SNPs). SNP data comes in the form of counts, but from the countsone typically computes genotype frequencies and allele frequencies. These frequencies satisfythe unit-sum constraint, and their analysis therefore falls within the realm of compositional dataanalysis (Aitchison, 1986). SNPs are usually bi-allelic, which implies that the genotypefrequencies can be adequately represented in a ternary plot. Compositions that are in exactHWE describe a parabola in the ternary plot. Compositions for which HWE cannot be rejected ina statistical test are typically “close" to the parabola, whereas compositions that differsignificantly from HWE are “far". By rewriting the statistics used to test for HWE in terms ofheterozygote frequencies, acceptance regions for HWE can be obtained that can be depicted inthe ternary plot. This way, compositions can be tested for HWE purely on the basis of theirposition in the ternary plot (Graffelman & Morales, 2008). This leads to nice graphicalrepresentations where large numbers of SNPs can be tested for HWE in a single graph. Severalexamples of graphical tests for HWE (implemented in R software), will be shown, using SNPdata from different human populations

Identificació i caracterització funcional dels complexes proteics dels receptors BRL1 i BRL3 en el teixit vascular d’Arabidopsis Thaliana

Els esteroids juguen papers clau en el creixement I el desenvolupament d’eucariotes multicel•lulars. En plantes, aquestes hormones, anomenades Brassinosteroides (BRs), estan involucrades en una gran varietat de processos biològics essencials per a les plantes. S’han descrit anteriorment dos receptors de BRs del tipus Leucine Rich Repeat Receptor Like Kinase LRR-RLK, BRASSINOSTEROID RECEPTOR LIKE 1 i 3 (BRL1 i BRL3 respectivalemt) que són homòlegs al receptor principal BRI1 i són necessaris pel desenvolupament vascular. Tot i que els principals components de la senyal ja han estat identificats pel seu homòleg més pròxim, el receptor BRI1, els complexes de BRL1 i BRL3 juntament amb els candidats co-receptors així com els components de la ruta de senyalització encara no han sigut identificats. Per tal d’entendre millor la funció molecular d’aquests receptors de BRs en la planta aquesta tesis doctoral planteja dues aproximacions: com a primera aproximació, vaig realitzar un estudi fenotípic del desenvolupament del teixit vascular a la planta model Arabidopsis thaliana (Arabidopsis). Disposant d'una amplia bateria de mutants de síntesis de la hormona i senyalització del receptor BRI1, vam analitzar quantitativament el seu patró vascular a la tija d'Arabidopsis. Vam establir els paràmetres en les plantes silvestres [Col-0 wild type, (WT)] i els vam analitzar a tots i cadascun dels mutants. Això conjuntament amb una col•laboració amb la Dr. Marta Ibañes, física de la Universitat de Barcelona que va construir un model matemàtic per simular la formació del patró vascular ens va permetre el•laborar una hipòtesis que vam demostrar experimentalment i va ser publicada a la revista PNAS. Posteriorment vam observar que les plantes knock-out d'aquests dos receptors BRL1 y BRL3 a diferència de BRI1, no tenien cap fenotip obvi en el teixit vascular de la planta adulta. Així, a continuació, per entendre quina necessitat té la planta de disposar de tres receptors tant altament homòlegs que poden percebre la mateixa hormona, vam utilitzar una aproximació bioquímica en col•laboració amb el Prof. de Vries de la Universitat de Wageningen (Holanda) per tal de purificar els complexes dels receptors in vivo i els seus interactors. Això ens ha permès entendre millor el paper funcional d'aquests receptors en la planta. Els resultats d’aquests experiments estan resumits en un article en preparació que aviat estarà en revisió.

Feuilletages par variétés complexes et problèmes d'uniformisation

Ce texte est une introduction aux feuilletages par variétés complexes et aux problèmes d'uniformisation de tels feuilletages. Nous donnons en introduction une liste fondamentale de questions naturelles sur ces objets ainsi qu'un aperçcu des résultats connus.

Basis set superposition error-counterpoise corrected potential energy surfaces : application to hydrogen peroxide ... X (X=F-, Cl-, Br-, Li+, Na+) complexes

Møller-Plesset (MP2) and Becke-3-Lee-Yang-Parr (B3LYP) calculations have been used to compare the geometrical parameters, hydrogen-bonding properties, vibrational frequencies and relative energies for several X- and X+ hydrogen peroxide complexes. The geometries and interaction energies were corrected for the basis set superposition error (BSSE) in all the complexes (1-5), using the full counterpoise method, yielding small BSSE values for the 6-311 + G(3df,2p) basis set used. The interaction energies calculated ranged from medium to strong hydrogen-bonding systems (1-3) and strong electrostatic interactions (4 and 5). The molecular interactions have been characterized using the atoms in molecules theory (AIM), and by the analysis of the vibrational frequencies. The minima on the BSSE-counterpoise corrected potential-energy surface (PES) have been determined as described by S. Simón, M. Duran, and J. J. Dannenberg, and the results were compared with the uncorrected PES

Effect of basis set superposition error on the electron density of molecular complexes

The effect of basis set superposition error (BSSE) on molecular complexes is analyzed. The BSSE causes artificial delocalizations which modify the first order electron density. The mechanism of this effect is assessed for the hydrogen fluoride dimer with several basis sets. The BSSE-corrected first-order electron density is obtained using the chemical Hamiltonian approach versions of the Roothaan and Kohn-Sham equations. The corrected densities are compared to uncorrected densities based on the charge density critical points. Contour difference maps between BSSE-corrected and uncorrected densities on the molecular plane are also plotted to gain insight into the effects of BSSE correction on the electron density

C-H···O H-bonded complexes: how does basis set superposition error change their potential-energy surfaces?

Geometries, vibrational frequencies, and interaction energies of the CNH⋯O3 and HCCH⋯O3 complexes are calculated in a counterpoise-corrected (CP-corrected) potential-energy surface (PES) that corrects for the basis set superposition error (BSSE). Ab initio calculations are performed at the Hartree-Fock (HF) and second-order Møller-Plesset (MP2) levels, using the 6-31G(d,p) and D95++(d,p) basis sets. Interaction energies are presented including corrections for zero-point vibrational energy (ZPVE) and thermal correction to enthalpy at 298 K. The CP-corrected and conventional PES are compared; the unconnected PES obtained using the larger basis set including diffuse functions exhibits a double well shape, whereas use of the 6-31G(d,p) basis set leads to a flat single-well profile. The CP-corrected PES has always a multiple-well shape. In particular, it is shown that the CP-corrected PES using the smaller basis set is qualitatively analogous to that obtained with the larger basis sets, so the CP method becomes useful to correctly describe large systems, where the use of small basis sets may be necessary

Stable complexes involving acetylcholinesterase and amyloid-ß-peptide change the biochemical properties of the enzyme and increase the neurotoxicity of Alzheimer's fibrils

Brain acetylcholinesterase (AChE) forms stable complexes with amyloid-beta peptide (Abeta) during its assembly into filaments, in agreement with its colocalization with the Abeta deposits of Alzheimer's brain. The association of the enzyme with nascent Abeta aggregates occurs as early as after 30 min of incubation. Analysis of the catalytic activity of the AChE incorporated into these complexes shows an anomalous behavior reminiscent of the AChE associated with senile plaques, which includes a resistance to low pH, high substrate concentrations, and lower sensitivity to AChE inhibitors. Furthermore, the toxicity of the AChE-amyloid complexes is higher than that of the Abeta aggregates alone. Thus, in addition to its possible role as a heterogeneous nucleator during amyloid formation, AChE, by forming such stable complexes, may increase the neurotoxicity of Abeta fibrils and thus may determine the selective neuronal loss observed in Alzheimer's brain.

A first-principles analysis of the magnetism of CuII polynuclear coordination complexes: the case of [Cu4(bpy)4(aspartate)2(H2O)3](ClO4)4·2.5H2O

The magnetic structure of the [Cu4(bpy)4(aspartate)2(H2O)3](ClO4)4·2.5 H2Ocrystal - using fractional coordinates determined at room-temperature ¿ has beenanalysed in detail. This analysis has been carried out by extending our first principlesbottom-up theoretical approach, which was initially designed to study through-spacemagnetic interactions, to handle through-bond magnetic interactions. The only input datarequired by this approach are the values of the computed JAB exchange parameters for allthe unique pairs of spin-containing centres. The results allow the magnetic structure ofthe crystal, which presents two types of isolated tetranuclear CuII clusters, to be definedin quantitative terms. Each of these clusters presents ferro and antiferromagneticinteractions, the former being stronger, although outnumbered by the latter. Thecomputed magnetic susceptibility curve shows the same qualitative features as theexperimental data. However, there are small differences that are presumed to beassociated with the use of room-temperature crystal coordinates.

A first-principles analysis of the magnetism of CuII polynuclear coordination complexes: the case of [Cu4(bpy)4(aspartate)2(H2O)3](ClO4)4·2.5H2O

The magnetic structure of the [Cu4(bpy)4(aspartate)2(H2O)3](ClO4)4·2.5 H2Ocrystal - using fractional coordinates determined at room-temperature ¿ has beenanalysed in detail. This analysis has been carried out by extending our first principlesbottom-up theoretical approach, which was initially designed to study through-spacemagnetic interactions, to handle through-bond magnetic interactions. The only input datarequired by this approach are the values of the computed JAB exchange parameters for allthe unique pairs of spin-containing centres. The results allow the magnetic structure ofthe crystal, which presents two types of isolated tetranuclear CuII clusters, to be definedin quantitative terms. Each of these clusters presents ferro and antiferromagneticinteractions, the former being stronger, although outnumbered by the latter. Thecomputed magnetic susceptibility curve shows the same qualitative features as theexperimental data. However, there are small differences that are presumed to beassociated with the use of room-temperature crystal coordinates.

Somatostatin Subtype‑2 Receptor-Targeted Metal-Based Anticancer Complexes

Conjugates of a dicarba analogue of octreotide, a potent somatostatin agonist whose receptors are overexpressed on tumor cells, with [PtCl2(dap)] (dap = 1-(carboxylic acid)-1,2-diaminoethane) (3), [(η6-bip)Os(4-CO2-pico)Cl] (bip = biphenyl, pico = picolinate) (4), [(η6-p-cym)RuCl(dap)]+ (p-cym = p-cymene) (5), and [(η6-p-cym)RuCl(imidazole-CO2H)(PPh3)]+ (6), were synthesized by using a solid-phase approach. Conjugates 35 readily underwent hydrolysis and DNA binding, whereas conjugate 6 was inert to ligand substitution. NMR spectroscopy and molecular dynamics calculations showed that conjugate formation does not perturb the overall peptide structure. Only 6 exhibited antiproliferative activity in human tumor cells (IC50 = 63 ± 2 μM in MCF-7 cells and IC50 = 26 ± 3 μM in DU-145 cells) with active participation of somatostatin receptors in cellular uptake. Similar cytotoxic activity was found in a normal cell line (IC50 = 45 ± 2.6 μM in CHO cells), which can be attributed to a similar level of expression of somatostatin subtype-2 receptor. These studies provide new insights into the effect of receptor-binding peptide conjugation on the activity of metal-based anticancer drugs, and demonstrate the potential of such hybrid compounds to target tumor cells specifically.

Structures of ethylenediaminetetraacetato (3-) metal complexes. I complexes with Co, Mg and Cd metals

(I): Hexaaquacobalt(II) aqua[ethylenediaminetetraacetato(3-)]cobaltate(II) dihydrate, [Co(H2O)6][Co(C10H13N2O8)(H2O)]2.2H2O (Ibis): Hexaaquamagnesium(II) aqua[ethylenediaminetetraacetato(3-)]magnesiate(II) dihydrate, [Mg(H2O)6][Mg(C10H13N2O8)(H2O)]2.2H2O (II):Tetraaquabis{aqua[ethylenediaminetetraacetato(3-)]cadmium(II)-O-O'}Cadmium(II) tetrahydrate