Homology of the three flag Hilbert Scheme

We prove the existence of an affine paving for the three-step flag Hilbert scheme that parametrizes flag of three 0-dimensional subschemes of length, respectively, n, n+1 and n+2 that are supported at the origin of the affine plane. This is done by showing that the space stratifies in smooth subvarieties, the Hilbert-Samuel's strata, each of which has an affine paving with cells of known dimension, indexed by marked Young diagrams. The affine pavings of the Hilbert-Samuel's strata allow us to prove that the Poincaré polynomials for our spaces satisfy a generating function. In the process of proving the formula for the generating function we relate combinatorially the homology of our spaces with that of known smooth subspaces of another Hilbert scheme of flags, this time of length n and n+2. As a corollary we find an affine paving and a combinatorial formula for the Poincaré of these last ambient spaces

Protection from cigarette smoke-induced vascular injury by recombinant human relaxin-2 (serelaxin)

Smoking is regarded as a major risk factor for the development of cardiovascular diseases (CVD). This study investigates whether serelaxin (RLX, recombinant human relaxin‐2) endowed with promising therapeutic properties in CVD, can be credited of a protective effect against cigarette smoke (CS)‐induced vascular damage and dysfunction. Guinea pigs exposed daily to CS for 8 weeks were treated with vehicle or RLX, delivered by osmotic pumps at daily doses of 1 or 10 μg. Controls were non‐smoking animals. Other studies were performed on primary guinea pig aortic endothelial (GPAE) cells, challenged with CS extracts (CSE) in the absence and presence of 100 ng/ml (17 nmol/l) RLX. In aortic specimens from CS‐exposed guinea pigs, both the contractile and the relaxant responses to phenylephrine and acetylcholine, respectively, were significantly reduced in amplitude and delayed, in keeping with the observed adverse remodelling of the aortic wall, endothelial injury and endothelial nitric oxide synthase (eNOS) down‐regulation. RLX at both doses maintained the aortic contractile and relaxant responses to a control‐like pattern and counteracted aortic wall remodelling and endothelial derangement. The experiments with GPAE cells showed that CSE significantly decreased cell viability and eNOS expression and promoted apoptosis by sparkling oxygen free radical‐related cytotoxicity, while RLX counterbalanced the adverse effects of CSE. These findings demonstrate that RLX is capable of counteracting CS‐mediated vascular damage and dysfunction by reducing oxidative stress, thus adding a tile to the growing mosaic of the beneficial effects of RLX in CVD

A Sparse Reformulation of the Green's Function Formalism Allows Efficient Simulations of Morphological Neuron Models

We prove that when a class of partial differential equations, generalized from the cable equation, is defined on tree graphs and the inputs are restricted to a spatially discrete, well chosen set of points, the Green's function (GF) formalism can be rewritten to scale as O (n) with the number n of inputs locations, contrary to the previously reported O (n(2)) scaling. We show that the linear scaling can be combined with an expansion of the remaining kernels as sums of exponentials to allow efficient simulations of equations from the aforementioned class. We furthermore validate this simulation paradigm on models of nerve cells and explore its relation with more traditional finite difference approaches. Situations in which a gain in computational performance is expected are discussed.Peer reviewedFinal Accepted Versio

A sparse reformulation of the Green's function formalism allows efficient simulations of morphological neuron models

Neurons are spatially extended structures with an elaborate dendritic tree that integrates spatio-temporal input patterns. Traditionally, this integration is analysed using compartmental simulations of the cable equation [1]. However, this approach is computationally expensive and renders it hard to understand the extent of interactions between spatially distant synapses. The Green's function (GF) formalism is conceptually simple and could potentially solve these issues: It summarizes the complicated spatio-temporal dynamics in a system of temporal kernels, facilitating the study of interactions among distant synapses, and its complexity is independent of the morphology [2]. Historically however, the GF formalism was abandoned because of three perceived disadvantages [3]: (i) its complexity scales quadratically with the number of synapses, (ii) it requires computationally costly convolutions, and (iii) it appears to be restricted to linear membranes. In this work, we show that all three perceived disadvantages can be overcome. First, we prove mathematically that for the cable equation – and for a more general class of partial differential equations – a transformation exists so that the complexity can be reduced to a linear scaling. We term this reduced system of temporal kernels the sparse GF (SGF) formalism. Second, we show, by using vector fitting algorithms [4], that the convolutions associated with both the GF and SGF formalisms can be re-expressed as simple, linear differential equations. In the GF formalism, this system of equations is diagonal, and hence can be integrated in a straightforward way. In the SGF formalism, this system is not diagonal, but can be expanded in eigen modes. We show that surprisingly few modes suffice to accurately describe the full spatio-temporal dynamics in this case. This results in a conceptually simple and computationally efficient neuron model. Finally, we argue that the speed gains associated with these innovations allow the restriction to linear membranes to be circumvented by including many input locations, and by distributing non-linear currents among those locations. We implemented a prototype of this new simulation paradigm that we validated and compared against the gold standard, the NEURON compartmental model simulator [5]. The comparison indicates that, in common simulation cases, the SGF formalism can result in a drastic reduction of simulation time compared to NEURON, while maintaining accuracy and conceptual simplicity. Furthermore, our paradigm allows modelers to make informed decision about the complexity. Indeed, decreasing the number of eigen modes leads to a neuron model that is essentially a point neuron extended to incorporate basic dendritic computations, whereas increasing the number of eigen modes allows for an accurate approximation of the intricate spatio-temporal dynamics. In the former form, the formalism is well suited to study the effect of dendritic integration on network function, aided further by the fact that it is well adapted for implementation into network-oriented simulators such as NEST [6]

Model lipid bilayers mimic non-specific interactions of gold nanoparticles with macrophage plasma membranes

Understanding the interaction between nanomaterials and biological interfaces is a key unmet goal that still hampers clinical translation of nanomedicine. Here we investigate and compare non-specific interaction of gold nanoparticles (AuNPs) with synthetic lipid and wild type macrophage membranes. A comprehensive data set was generated by systematically varying the structural and physicochemical properties of the AuNPs (size, shape, charge, surface functionalization) and of the synthetic membranes (composition, fluidity, bending properties and surface charge), which allowed to unveil the matching conditions for the interaction of the AuNPs with macrophage plasma membranes in vitro. This effort directly proved for the first time that synthetic bilayers can be set to mimic and predict with high fidelity key aspects of nanoparticle interaction with macrophage eukaryotic plasma membranes. It then allowed to model the experimental observations according to classical interface thermodynamics and in turn determine the paramount role played by non-specific contributions, primarily electrostatic, Van der Waals and bending energy, in driving nanoparticle-plasma membrane interactions