Molecular Docking study of Receptor Binding Domain of SARS-CoV-2 Spike Glycoprotein with Saikosaponin, a Triterpenoid Natural Product

The appearance of SARS-CoV-2 has resulted ~19000 deaths and ~423000 infections worldwide as of March 24, 2020. Coronavirus spike (S) glycoproteins hooks on target cells and binds to the angiotensin-converting enzyme 2 (ACE2) receptor. Recent researches speculated that residues 331 to 524 of the S glycoprotein of the receptor binding domain (RDB) of the spike is the most crucial target and this side was very important for computational docking. In the present study we have considered a series of saikosaponins and molecular docking was performed. Most of the docked molecules bind favorably to the RDB region of the spike glycoprotein and among them Saikosaponin B4 is the best inhibitor

Delaunay Triangulations Approximate Anchor Hulls

Recent results establish that a subset of the Voronoi diagram of a point set that is sampled from the smooth boundary of a shape approximates the medial axis. The corresponding question for the dual Delaunay triangulation is not addressed in the literature. We show that, for two dimensional shapes, the Delaunay triangulation approximates a specific structure which we call anchor hulls. Since similar shapes have similar anchor hulls, they provide an useful tool in matching shapes. We demonstrate that our approximation result is useful in this application. 1

Identifying flat and tubular regions of a shape by unstable manifolds

Figure 1: The steps of the algorithm are shown on an example dataset CLUB. Starting with an input set of points sampled from the surface (a), the medial axis in the interior of the shape is computed (b). The algorithm then detects the set of index 1 and index 2 saddle points lying on the interior medial axis and computes the unstable manifold of these saddle points (c). The unstable manifold of an index 1 saddle point is two dimensional (green) and the unstable manifold of an index 2 saddle point is one dimensional (red). The algorithm then collects the local maxima lying on the boundaries of these two types of unstable manifolds and tag them as falling into two different categories. The stable manifolds of these maxima are then used to map the 2-dimensional and 1-dimensional part of the medial axis back to the surface. The flat portion on the surface is colored cyan and the tubular region is colored golden (e). We present an algorithm to identify the flat and tubular regions of a three dimensional shape from its point sample. We consider the distance function to the input point cloud and the Morse structure induced by it on R 3. Specifically we focus on the index 1 and index 2 saddle points and their unstable manifolds. The unstable manifolds of index 2 saddles are one dimensional whereas those of index 1 saddles are two dimensional. Mapping these unstable manifolds back onto the surface, we get the tubular and flat regions. The computations are carried out on the Voronoi diagram of the input points by approximating the unstable manifolds with Voronoi faces. We demonstrate the performance of our algorithm on several point sampled objects

On magnon mediated Cooper pair formation in ferromagnetic superconductors

Identification of pairing mechanism leading to ferromagnetic superconductivity is one of the most challenging issues in condensed matter physics. Although different models have been proposed to explain this phenomenon, a quantitative understanding about this pairing is yet to be achieved. Using the localized-itinerant model, we find that in ferromagnetic superconducting materials both triplet pairing and singlet pairing of electrons are possible through magnon exchange depending upon whether the Debye cut off frequency of magnons is greater or lesser than the Hund's coupling (J) multiplied by average spin (S) per site. Taking into account the repulsive interaction due to the existence of paramagnons, we also find an expression for effective interaction potential between a pair of electrons with opposite spins. We apply the developed formalism in case of UGe2 and URhGe. The condition of singlet pairing is found to be fulfilled in these cases, as was previously envisaged by Suhl [Suhl, Phys. Rev. Lett. 87, 167007 (2001)]. We compute the critical temperatures of URhGe at ambient pressure and of UGe2 under different pressures for the first time through BCS equation. Thus, this work outlines a very simple way to evaluate critical temperature in case of a superconducting system. A close match with the available experimental results strongly supports our theoretical treatment

Shape Dimension and Approximation from Samples

There are many scientific and engineering applications where an automatic detection of shape dimension from sample data is necessary. Topological dimensions of shapes constitute an important global feature of them. We present a Voronoi based dimension detection algorithm that assigns a dimension to a sample point which is the topological dimension of the manifold it belongs to. Based on this dimension detection, we also present an algorithm to approximate shapes of arbitrary dimension from their samples. Our empirical results with data sets in three dimensions support our theory