Autophagy is activated and involved in cell death with participation of cathepsins during stress-induced microspore embryogenesis in barley

Microspores are reprogrammed towards embryogenesis by stress. Many microspores die after this stress, limiting the efficiency of microspore embryogenesis. Autophagy is a degradation pathway that plays critical roles in stress response and cell death. In animals, cathepsins have an integral role in autophagy by degrading autophagic material; less is known in plants. Plant cathepsins are papain-like C1A cysteine proteases involved in many physiological processes, including programmed cell death. We have analysed the involvement of autophagy in cell death, in relation to cathepsin activation, during stress-induced microspore embryogenesis in Hordeum vulgare. After stress, reactive oxygen species (ROS) and cell death increased and autophagy was activated, including HvATG5 and HvATG6 up-regulation and increase of ATG5, ATG8, and autophagosomes. Concomitantly, cathepsin L/F-, B-, and H-like activities were induced, cathepsin-like genes HvPap-1 and HvPap-6 were up-regulated, and HvPap-1, HvPap-6, and HvPap-19 proteins increased and localized in the cytoplasm, resembling autophagy structures. Inhibitors of autophagy and cysteine proteases reduced cell death and promoted embryogenesis. The findings reveal a role for autophagy in stress-induced cell death during microspore embryogenesis, and the participation of cathepsins. Similar patterns of activation, expression, and localization suggest a possible connection between cathepsins and autophagy. The results open up new possibilities to enhance microspore embryogenesis efficiency with autophagy and/or cysteine protease modulators.España, MINECO AGL2014-52028-R and AGL2017-82447-

Equipartitioning by a convex 3-fan

We show that for a given planar convex set K of positive area there exist three pairwise internally disjoint convex sets whose union is K such that they have equal area and equal perimeter

Maximizing the Total Resolution of Graphs

A major factor affecting the readability of a graph drawing is its resolution. In the graph drawing literature, the resolution of a drawing is either measured based on the angles formed by consecutive edges incident to a common node (angular resolution) or by the angles formed at edge crossings (crossing resolution). In this paper, we evaluate both by introducing the notion of "total resolution", that is, the minimum of the angular and crossing resolution. To the best of our knowledge, this is the first time where the problem of maximizing the total resolution of a drawing is studied. The main contribution of the paper consists of drawings of asymptotically optimal total resolution for complete graphs (circular drawings) and for complete bipartite graphs (2-layered drawings). In addition, we present and experimentally evaluate a force-directed based algorithm that constructs drawings of large total resolution

Rotation sets of billiards with one obstacle

We investigate the rotation sets of billiards on the $m$-dimensional torus with one small convex obstacle and in the square with one small convex obstacle. In the first case the displacement function, whose averages we consider, measures the change of the position of a point in the universal covering of the torus (that is, in the Euclidean space), in the second case it measures the rotation around the obstacle. A substantial part of the rotation set has usual strong properties of rotation sets

A Tverberg type theorem for matroids

Let b(M) denote the maximal number of disjoint bases in a matroid M. It is shown that if M is a matroid of rank d+1, then for any continuous map f from the matroidal complex M into the d-dimensional Euclidean space there exist t \geq \sqrt{b(M)}/4 disjoint independent sets \sigma_1,\ldots,\sigma_t \in M such that \bigcap_{i=1}^t f(\sigma_i) \neq \emptyset.Comment: This article is due to be published in the collection of papers "A Journey through Discrete Mathematics. A Tribute to Jiri Matousek" edited by Martin Loebl, Jaroslav Nesetril and Robin Thomas, due to be published by Springe

Optimal bounds for a colorful Tverberg--Vrecica type problem

We prove the following optimal colorful Tverberg-Vrecica type transversal theorem: For prime r and for any k+1 colored collections of points C^l of size |C^l|=(r-1)(d-k+1)+1 in R^d, where each C^l is a union of subsets (color classes) C_i^l of size smaller than r, l=0,...,k, there are partition of the collections C^l into colorful sets F_1^l,...,F_r^l such that there is a k-plane that meets all the convex hulls conv(F_j^l), under the assumption that r(d-k) is even or k=0. Along the proof we obtain three results of independent interest: We present two alternative proofs for the special case k=0 (our optimal colored Tverberg theorem (2009)), calculate the cohomological index for joins of chessboard complexes, and establish a new Borsuk-Ulam type theorem for (Z_p)^m-equivariant bundles that generalizes results of Volovikov (1996) and Zivaljevic (1999).Comment: Substantially revised version: new notation, improved results, additional references; 12 pages, 2 figure

Tverberg’s theorem at 50: Extensions and counterexamples

We describe how a powerful new “constraint method” yields many different extensions of the topological version of Tverberg’s 1966 Theorem in the prime power case— and how the same method also was instrumental in the recent spectacular construction of counterexamples for the general case. © 2016. All rights reserved

Continuum Surface Energy from a Lattice Model

We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with general binary interactions in two dimensions. A new bond counting approach is used, which reduces the problem to the lattice point problem of number theory. The main contribution is an explicit formula for the surface energy density as a function of the deformation gradient and boundary normal. The result is valid for a large class of domains, including faceted (polygonal) shapes and regions with piecewise smooth boundaries.Comment: V. 1: 10 pages, no fig's. V 2: 23 pages, no figures. Misprints corrected. Section 3 added, (new results). Intro expanded, refs added.V 3: 26 pages. Abstract changed. Section 2 split into 2. Section (4) added material. V 4, 28 pages, Intro rewritten. Changes in Sec.5 (presentation only). Refs added.V 5,intro changed V.6 address reviewer's comment