A Smooth Discretization Bridging Finite Element and Mesh-free Methods Using Polynomial Reproducing Simplex Splines

This work sets forth a `hybrid' discretization scheme utilizing bivariate simplex splines as kernels in a polynomial reproducing scheme constructed over a conventional Finite Element Method (FEM)-like domain discretization based on Delaunay triangulation. Careful construction of the simplex spline knotset ensures the success of the polynomial reproduction procedure at all points in the domain of interest, a significant advancement over its precursor, the DMS-FEM. The shape functions in the proposed method inherit the global continuity (Cp-1) and local supports of the simplex splines of degree p. In the proposed scheme, the triangles comprising the domain discretization also serve as background cells for numerical integration which here are near-aligned to the supports of the shape functions (and their intersections), thus considerably ameliorating an oft-cited source of inaccuracy in the numerical integration of mesh-free (MF) schemes. Numerical experiments show the proposed method requires lower order quadrature rules for accurate evaluation of integrals in the Galerkin weak form. Numerical demonstrations of optimal convergence rates for a few test cases are given and the method is also implemented to compute crack-tip fields in a gradient-enhanced elasticity model.

N-Terminal Disordered Domain of Saccharomyces cerevisiae Hop1 Protein Is Dispensable for DNA Binding, Bridging, and Synapsis of Double-Stranded DNA Molecules But Is Necessary for Spore Formation

The cytological architecture of the synaptonemal complex (SC), a meiosis-specific proteinaceous structure, is evolutionarily conserved among eukaryotes. However, little is known about the biochemical properties of SC components or the mechanisms underlying their roles in meiotic chromosome synapsis and recombination. Functional analysis of Saccharomyces cerevisiae Hop1, a key structural component of SC, has begun to reveal important insights into its function in interhomolog recombination. Previously, we showed that Hop1 is a structure-specific DNA-binding protein, exhibits higher binding affinity for the Holliday junction, and induces structural distortion at the core of the junction. Furthermore, Hop1 promotes DNA condensation and intra- and intermolecular synapsis between duplex DNA molecules. Here, we show that Hop1 possesses a modular domain organization, consisting of an intrinsically disordered N-terminal domain and a protease-resistant C-terminal domain (Hop1CTD). Furthermore, we found that Hop1CTD exhibits strong homotypic as well as heterotypic protein protein interactions, and its biochemical activities were similar to those of the full-length Hop1 protein. However, Hop1CTD failed to complement the meiotic recombination defects of the Delta hop1 strain, indicating that both N- and C-terminal domains of Hop1 are essential for meiosis and spore formation. Altogether, our findings reveal novel insights into the structure-function relationships of Hop1 and help to further our understanding of its role in meiotic chromosome synapsis and recombination.

Atomistic Simulation of Stacked Nucleosome Core Particles: Tail Bridging, the H4 Tail, and Effect of Hydrophobic Forces

We report the first atomistic simulation of two stacked nucleosome core particles (NCPs), with an aim to understand, in molecular detail, how they interact, the effect of salt concentration, and how different histone tails contribute to their interaction, with a special emphasis on the H4 tail, known to have the largest stabilizing effect on the NCP-NCP interaction. We do not observe specific K16-mediated interaction between the H4 tail and the H2A-H2B acidic patch, in contrast with the findings from crystallographic studies, but find that the stacking was stable even in the absence of this interaction. We perform simulations with the H4 tail (partially/completely) removed and find that the region between LYS-16 and LYS-20 of the H4 tail holds special importance in mediating the inter-NCP interaction. Performing similar tail-clipped simulations with the H3 tail removed, we compare the roles of the H3 and H4 tails in maintaining the stacking. We discuss the relevance of our simulation results to the bilayer and other liquid-crystalline phases exhibited by NCPs in vitro and, through an analysis of the histone-histone interface, identify the interactions that could possibly stabilize the inter-NCP interaction in these columnar mesophases. Through the mechanical disruption of the stacked nucleosome system using steered molecular dynamics, we quantify the strength of inter-NCP stacking in the presence and absence of salt. We disrupt the stacking at some specific sites of internucleosomal tail-DNA contact and perform a comparative quantification of the binding strengths of various tails in stabilizing the stacking. We also examine how hydrophobic interactions may contribute to the overall stability of the stacking and find a marked difference in the role of hydrophobic forces as compared with electrostatic forces in determining the stability of the stacked nucleosome system.

Unilateral vs. Bilateral link-formation: Bridging the gap

We provide a model that bridges the gap between two benchmark models of strategic network formation: Jackson and Wolinsky' s model based on bilateral formation of links, and Bala and Goyal's two-way fl ow model, where links can be unilaterally formed. In the model introduced and studied here a link can be created unilaterally. When it is only supported by one of the two players the fl ow through the link suffers a certain decay, but when it is supported by both the fl ow runs without friction. When the decay in links supported by only one player is maximal (i.e. there is no flow) we have Jackson and Wolinsky 's connections model without decay, while when flow in such links is perfect we have Bala and Goyal' s two-way flow model. We study Nash, strict Nash and pairwise stability for the intermediate models. Efficiency and dynamics are also examined.

Studying conscious and unconscious vision with functional Magnetic Resonance Imaging : the BOLD promise

Waking up from a dreamless sleep, I open my eyes, recognize my wife’s face and am filled with joy. In this thesis, I used functional Magnetic Resonance Imaging (fMRI) to gain insights into the mechanisms involved in this seemingly simple daily occurrence, which poses at least three great challenges to neuroscience: how does conscious experience arise from the activity of the brain? How does the brain process visual input to the point of recognizing individual faces? How does the brain store semantic knowledge about people that we know? To start tackling the first question, I studied the neural correlates of unconscious processing of invisible faces. I was unable to image significant activations related to the processing of completely invisible faces, despite existing reports in the literature. I thus moved on to the next question and studied how recognition of a familiar person was achieved in the brain; I focused on finding invariant representations of person identity – representations that would be activated any time we think of a familiar person, read their name, see their picture, hear them talk, etc. There again, I could not find significant evidence for such representations with fMRI, even in regions where they had previously been found with single unit recordings in human patients (the Jennifer Aniston neurons). Faced with these null outcomes, the scope of my investigations eventually turned back towards the technique that I had been using, fMRI, and the recently praised analytical tools that I had been trusting, Multivariate Pattern Analysis. After a mostly disappointing attempt at replicating a strong single unit finding of a categorical response to animals in the right human amygdala with fMRI, I put fMRI decoding to an ultimate test with a unique dataset acquired in the macaque monkey. There I showed a dissociation between the ability of fMRI to pick up face viewpoint information and its inability to pick up face identity information, which I mostly traced back to the poor clustering of identity selective units. Though fMRI decoding is a powerful new analytical tool, it does not rid fMRI of its inherent limitations as a hemodynamics-based measure.