Cluster density functional theory for lattice models based on the theory of Mobius functions

Rosenfeld's fundamental measure theory for lattice models is given a rigorous formulation in terms of the theory of Mobius functions of partially ordered sets. The free-energy density functional is expressed as an expansion in a finite set of lattice clusters. This set is endowed a partial order, so that the coefficients of the cluster expansion are connected to its Mobius function. Because of this, it is rigorously proven that a unique such expansion exists for any lattice model. The low-density analysis of the free-energy functional motivates a redefinition of the basic clusters (zero-dimensional cavities) which guarantees a correct zero-density limit of the pair and triplet direct correlation functions. This new definition extends Rosenfeld's theory to lattice model with any kind of short-range interaction (repulsive or attractive, hard or soft, one- or multi-component...). Finally, a proof is given that these functionals have a consistent dimensional reduction, i.e. the functional for dimension d' can be obtained from that for dimension d (d'<d) if the latter is evaluated at a density profile confined to a d'-dimensional subset.Comment: 21 pages, 2 figures, uses iopart.cls, as well as diagrams.sty (included

Fundamental measure theory for lattice fluids with hard core interactions

We present the extension of Rosenfeld's fundamental measure theory to lattice models by constructing a density functional for d-dimensional mixtures of parallel hard hypercubes on a simple hypercubic lattice. The one-dimensional case is exactly solvable and two cases must be distinguished: all the species with the same lebgth parity (additive mixture), and arbitrary length parity (nonadditive mixture). At the best of our knowledge, this is the first time that the latter case is considered. Based on the one-dimensional exact functional form, we propose the extension to higher dimensions by generalizing the zero-dimensional cavities method to lattice models. This assures the functional to have correct dimensional crossovers to any lower dimension, including the exact zero-dimensional limit. Some applications of the functional to particular systems are also shown.Comment: 22 pages, 7 figures, needs IOPP LaTeX styles file

Lattice density-functional theory of surface melting: the effect of a square-gradient correction

I use the method of classical density-functional theory in the weighted-density approximation of Tarazona to investigate the phase diagram and the interface structure of a two-dimensional lattice-gas model with three phases -- vapour, liquid, and triangular solid. While a straightforward mean-field treatment of the interparticle attraction is unable to give a stable liquid phase, the correct phase diagram is obtained when including a suitably chosen square-gradient term in the system grand potential. Taken this theory for granted, I further examine the structure of the solid-vapour interface as the triple point is approached from low temperature. Surprisingly, a novel phase (rather than the liquid) is found to grow at the interface, exhibiting an unusually long modulation along the interface normal. The conventional surface-melting behaviour is recovered only by artificially restricting the symmetries being available to the density field.Comment: 16 pages, 6 figure

Density functional theory for nearest-neighbor exclusion lattice gasses in two and three dimensions

To speak about fundamental measure theory obliges to mention dimensional crossover. This feature, inherent to the systems themselves, was incorporated in the theory almost from the beginning. Although at first it was thought to be a consistency check for the theory, it rapidly became its fundamental pillar, thus becoming the only density functional theory which possesses such a property. It is straightforward that dimensional crossover connects, for instance, the parallel hard cube system (three-dimensional) with that of squares (two-dimensional) and rods (one-dimensional). We show here that there are many more connections which can be established in this way. Through them we deduce from the functional for parallel hard (hyper)cubes in the simple (hyper)cubic lattice the corresponding functionals for the nearest-neighbor exclusion lattice gases in the square, triangular, simple cubic, face-centered cubic, and body-centered cubic lattices. As an application, the bulk phase diagram for all these systems is obtained.Comment: 13 pages, 13 figures; needs revtex

Rosenfeld functional for non-additive hard spheres

The fundamental measure density functional theory for hard spheres is generalized to binary mixtures of arbitrary positive and moderate negative non-additivity between unlike components. In bulk the theory predicts fluid-fluid phase separation into phases with different chemical compositions. The location of the accompanying critical point agrees well with previous results from simulations over a broad range of non-additivities and both for symmetric and highly asymmetric size ratios. Results for partial pair correlation functions show good agreement with simulation data.Comment: 8 pages with 4 figure

Gramine derivatives targeting Ca2+ channels and Ser/Thr phosphatases: A new dual strategy for the treatment of neurodegenerative diseases

This document is the unedited author's version of a Submitted Work that was subsequently accepted for publication in Journal of Medicinal Chemistry , copyright © American Chemical Society after peer review. To access the final edited and published work, see http://pubs.acs.org/doi/abs/10.1021/acs.jmedchem.6b00478We describe the synthesis of gramine derivatives and their pharmacological evaluation as multipotent drugs for the treatment of Alzheimer’s disease. An innovative multitarget approach is presented, targeting both voltage-gated Ca2+ channels, classically studied for neurodegenerative diseases, and Ser/Thr phosphatases, which have been marginally aimed, even despite their key role in protein τ dephosphorylation. Twenty-five compounds were synthesized, and mostly their neuroprotective profile exceeded that offered by the head compound gramine. In general, these compounds reduced the entry of Ca2+ through VGCC, as measured by Fluo-4/AM and patch clamp techniques, and protected in Ca2+ overload-induced models of neurotoxicity, like glutamate or veratridine exposures. Furthermore, we hypothesize that these compounds decrease τ hyperphosphorylation based on the maintenance of the Ser/Thr phosphatase activity and their neuroprotection against the damage caused by okadaic acid. Hence, we propose this multitarget approach as a new and promising strategy for the treatment of neurodegenerative diseasesThis work was supported by the following grant: Proyectos de Investigación en Salud (PI13/00789, IS Carlos III). R.L.C is granted by Universidad Autónoma de Madri

PP2A ligand ITH12246 protects against memory impairment and focal cerebral ischemia in mice

ITH12246 (ethyl 5-amino-2-methyl-6,7,8,9-tetrahydrobenzo[b][1,8] naphthyridine-3-carboxylate) is a 1,8-naphthyridine described to feature an interesting neuroprotective profile in in vitro models of Alzheimer's disease. These effects were proposed to be due in part to a regulatory action on protein phosphatase 2A inhibition, as it prevented binding of its inhibitor okadaic acid. We decided to investigate the pharmacological properties of ITH12246, evaluating its ability to counteract the memory impairment evoked by scopolamine, a muscarinic antagonist described to promote memory loss, as well as to reduce the infarct volume in mice suffering phototrombosis. Prior to conducting these experiments, we confirmed its in vitro neuroprotective activity against both oxidative stress and Ca2+ overload-derived excitotoxicity, using SH-SY5Y neuroblastoma cells and rat hippocampal slices. Using a predictive model of blood-brain barrier crossing, it seems that the passage of ITH12246 is not hindered. Its potential hepatotoxicity was observed only at very high concentrations, from 0.1 mM. ITH12246, at the concentration of 10 mg/kg i.p., was able to improve the memory index of mice treated with scopolamine, from 0.22 to 0.35, in a similar fashion to the well-known Alzheimer's disease drug galantamine 2.5 mg/kg. On the other hand, ITH12246, at the concentration of 2.5 mg/kg, reduced the phototrombosis-triggered infarct volume by 67%. In the same experimental conditions, 15 mg/kg melatonin, used as control standard, reduced the infarct volume by 30%. All of these findings allow us to consider ITH12246 as a new potential drug for the treatment of neurodegenerative diseases, which would act as a multifactorial neuroprotectant.Peer Reviewe

New insights into the genetic etiology of Alzheimer's disease and related dementias

Characterization of the genetic landscape of Alzheimer's disease (AD) and related dementias (ADD) provides a unique opportunity for a better understanding of the associated pathophysiological processes. We performed a two-stage genome-wide association study totaling 111,326 clinically diagnosed/'proxy' AD cases and 677,663 controls. We found 75 risk loci, of which 42 were new at the time of analysis. Pathway enrichment analyses confirmed the involvement of amyloid/tau pathways and highlighted microglia implication. Gene prioritization in the new loci identified 31 genes that were suggestive of new genetically associated processes, including the tumor necrosis factor alpha pathway through the linear ubiquitin chain assembly complex. We also built a new genetic risk score associated with the risk of future AD/dementia or progression from mild cognitive impairment to AD/dementia. The improvement in prediction led to a 1.6- to 1.9-fold increase in AD risk from the lowest to the highest decile, in addition to effects of age and the APOE ε4 allele

Multiancestry analysis of the HLA locus in Alzheimer’s and Parkinson’s diseases uncovers a shared adaptive immune response mediated by HLA-DRB1*04 subtypes

Across multiancestry groups, we analyzed Human Leukocyte Antigen (HLA) associations in over 176,000 individuals with Parkinson’s disease (PD) and Alzheimer’s disease (AD) versus controls. We demonstrate that the two diseases share the same protective association at the HLA locus. HLA-specific fine-mapping showed that hierarchical protective effects of HLA-DRB1*04 subtypes best accounted for the association, strongest with HLA-DRB1*04:04 and HLA-DRB1*04:07, and intermediary with HLA-DRB1*04:01 and HLA-DRB1*04:03. The same signal was associated with decreased neurofibrillary tangles in postmortem brains and was associated with reduced tau levels in cerebrospinal fluid and to a lower extent with increased Aβ42. Protective HLA-DRB1*04 subtypes strongly bound the aggregation-prone tau PHF6 sequence, however only when acetylated at a lysine (K311), a common posttranslational modification central to tau aggregation. An HLA-DRB1*04-mediated adaptive immune response decreases PD and AD risks, potentially by acting against tau, offering the possibility of therapeutic avenues