Search Results (13)

Endoplasmic reticulum-mediated protein quality control (ERQC) safeguards secretory pathway proteostasis by recognizing, retaining, repairing, and removing misfolded proteins, and is therefore essential for plant growth, development, and stress tolerance. This system relies on ER-associated degradation (ERAD), in which irreparably misfolded proteins are first recognized in the ER, then exported across the ER membrane to the cytosol, where they are ubiquitinated by ER membrane-anchored ubiquitin ligases, and subsequently degraded by the cytosolic proteasome. Studies in yeast and mammals have defined several conserved ERAD branches, including a multiprotein ERAD complex centered on the polytopic ER membrane E3 ligase HMG-CoA reductase degradation protein 1 (Hrd1), which integrates substrate recognition, membrane retrotranslocation, ubiquitin conjugation, and cytosolic extraction. Recent advances in Arabidopsis show that plants retain the core Hrd1 ERAD architecture while incorporating additional regulatory elements that adapt this machinery to plant-specific physiological demands. Genetic and biochemical analyses of misfolded receptor kinases and engineered substrates have uncovered conserved and plant-specific components of the plant Hrd1 complex, revealing how the plant ERAD pathway integrates ERQC with hormone signaling, stress adaptation, immune responses, and growth regulation. This review synthesizes recent advances in plant ERAD research and highlights key conceptual and mechanistic questions that remain to be resolved. Full article

In this paper, we present a method to optimize the attainable moment set (AMS) to increase the control authority for electrical vertical take-off and landing vehicles (eVTOLs). As opposed to 3D AMSs for conventional airplanes, the hover control of eVTOLs requires vertical thrust produced by the powered lift system in addition to three moments. The limits of the moments and vertical thrust are coupled due to input saturation, and, as a result, the concept of the traditional AMS is extended to the 4D generalized moment set to account for this coupling effect. Given a required moment set (RMS) derived from system requirements, the optimization is formulated as a 4D convex polytope coverage problem, i.e., the AMS coverage over the RMS, such that the system’s available control authority is maximized to fulfill the prescribed requirements. The optimization accounts for not only nominal flight, but also for one critical engine inoperative situation. To test the method, it is applied to an eVTOL with eight rotors to optimize for the rotors’ orientation with respect to the body axis. The results indicate highly improved coverage of the RMS for both failure-free and one-engine-inoperative situations. Closed-loop simulation tests are performed for both optimal and non-optimal configurations to further validate the results. Full article

This paper is part of a series that describes the Fibonacci icosagrid quasicrystal (FIG) and its relation to the $E_8$ root lattice. The FIG was originally constructed to represent the intersection points of an icosahedrally symmetric collection of planar grids in three dimensions, with the grid spacing of each following a Fibonacci chain. It was found to be closely related to a five-fold compound of 3D sections taken from the 4D Elser–Sloane quasicrystal (ESQC), which is derived via a cut-and-project process from $E_8$. More recently, a direct cut-and-project from $E_8$ has been found which yields the FIG (presented in another paper of this series). The present paper focuses not on the full quasicrystal, but on the relationship between the root polytope of $E_8$ (Gosset’s $4_{21}$ polytope) and the core polyhedron generated in the FIG, a compound of 20 tetrahedra referred to simply as a 20-Group. In particular, the $H_3$ symmetry of the FIG can be seen as a five-fold or “golden” composition of tetrahedral symmetry (referring to the characteristic appearance of the golden ratio). This is shown to mirror a connection between tetrahedral and five-fold symmetries present in the $4_{21}$. Indeed, the rotations that connect tetrahedra contained within the $4_{21}$ are shown to induce, in a certain natural way, the tetrahedron orientations in the 20-Group. Full article

Geometric realization of simplicial complexes makes them a unique representation of complex systems. The existence of local continuous spaces at the simplices level with global discrete connectivity between simplices makes the analysis of dynamical systems on simplicial complexes a challenging problem. In this work, we provide some examples of complex systems in which this representation would be a more appropriate model of real-world phenomena. Here, we generalize the concept of metaplexes to embrace that of geometric simplicial complexes, which also includes the definition of dynamical systems on them. A metaplex is formed by regions of a continuous space of any dimension interconnected by sinks and sources that works controlled by discrete (graph) operators. The definition of simplicial metaplexes given here allows the description of the diffusion dynamics of this system in a way that solves the existing problems with previous models. We make a detailed analysis of the generalities and possible extensions of this model beyond simplicial complexes, e.g., from polytopal and cell complexes to manifold complexes, and apply it to a real-world simplicial complex representing the visual cortex of a macaque. Full article

Human papillomaviruses (HPVs) are a large family of viruses with a capsid composed of the L1 and L2 proteins, which bind to receptors of the basal epithelial cells and promote virus entry. The majority of sexually active people become exposed to HPV and the virus is the most common cause of cervical cancer. Vaccines are available based on the L1 protein, which self-assembles and forms virus-like particles (VLPs) when expressed in yeast and insect cells. Although very effective, these vaccines are HPV type-restricted and their costs limit broad vaccination campaigns. Recently, vaccine candidates based on the conserved L2 epitope from serotypes 16, 18, 31, 33, 35, 6, 51, and 59 were shown to elicit broadly neutralizing anti-HPV antibodies. In this study, we tested whether E. coli outer membrane vesicles (OMVs) could be successfully decorated with L2 polytopes and whether the engineered OMVs could induce neutralizing antibodies. OMVs represent an attractive vaccine platform owing to their intrinsic adjuvanticity and their low production costs. We show that strings of L2 epitopes could be efficiently expressed on the surface of the OMVs and a polypeptide composed of the L2 epitopes from serotypes 18, 33, 35, and 59 provided a broad cross-protective activity against a large panel of HPV serotypes as determined using pseudovirus neutralization assay. Considering the simplicity of the OMV production process, our work provides a highly effective and inexpensive solution to produce universal anti-HPV vaccines. Full article

When we apply comparative phylogenetic analyses to genome data, it poses a significant problem and challenge that some of the given species (or taxa) often have missing genes (i.e., data). In such a case, we have to impute a missing part of a gene tree from a sample of gene trees. In this short paper, we propose a novel method to infer the missing part of a phylogenetic tree using an analogue of a classical linear regression in the setting of tropical geometry. In our approach, we consider a tropical polytope, a convex hull with respect to the tropical metric closest to the data points. We show a condition that we can guarantee that an estimated tree from the method has at most a Robinson–Foulds (RF) distance of four from the ground truth, and computational experiments with simulated data and empirical data from Clavicipitaceae, which contains more than 4000 genes, show the method works well. Full article

In 1974, the author proved that the codimension of the ideal $(g_1,g_2,\dots ,g_d)$ generated in the group algebra $\mathbb{K}\left[{\mathbb{Z}}^d\right]$ over a field $\mathbb{K}$ of characteristic 0 by generic Laurent polynomials having the same Newton polytope $\mathsf{\Gamma }$ is equal to $d!\times Volume\left(\mathsf{\Gamma }\right)$. Assuming that Newtons polytope is simplicial and super-convenient (that is, containing some neighborhood of the origin), the author strengthens the 1974 result by explicitly specifying the set ${\mathbb{B}}^{sh}$ of monomials of cardinality $d!\times Volume\left(\mathsf{\Gamma }\right)$, whose equivalence classes form a basis of the quotient algebra $\mathbb{K}\left[{\mathbb{Z}}^d\right]/(g_1,g_2,\dots ,g_d)$. The set ${\mathbb{B}}^{sh}$ is constructed inductively from any shelling $sh$ of the polytope $\mathsf{\Gamma }$. Using the ${\mathbb{B}}^{sh}$ structure, we prove that the associated graded $\mathbb{K}$ -algebra $g{r}^{\mathsf{\Gamma }}\left(\mathbb{K}\left[{\mathbb{Z}}^d\right]\right)$ constructed from the Arnold–Newton filtration of $\mathbb{K}$ -algebra $\mathbb{K}\left[{\mathbb{Z}}^d\right]$ has the Cohen–Macaulay property. This proof is a generalization of B. Kind and P. Kleinschmitt’s 1979 proof that Stanley–Reisner rings of simplicial complexes admitting shelling are Cohen–Macaulay. Finally, we prove that for generic Laurent polynomials $(f_1,f_2,\dots ,f_d)$ with the same Newton polytope $\mathsf{\Gamma }$, the set ${\mathbb{B}}^{sh}$ defines a monomial basis of the quotient algebra $\mathbb{K}\left[{\mathbb{Z}}^d\right]/(g_1,g_2,\dots ,g_d)$. Full article

Polytopic organic ligands with hydrazone moiety are at the forefront of new drug research among many others due to their unique and versatile functionality and ease of strategic ligand design. Quantum chemical calculations of these polyfunctional ligands can be carried out in silico to determine the thermodynamic parameters. In this study two new tritopic dihydrazide ligands, N’2, N’6-bis[(1E)-1-(thiophen-2-yl) ethylidene] pyridine-2,6-dicarbohydrazide (L1) and N’2, N’6-bis[(1E)-1-(1H-pyrrol-2-yl) ethylidene] pyridine-2,6-dicarbohydrazide (L2) were successfully prepared by the condensation reaction of pyridine-2,6-dicarboxylic hydrazide with 2-acetylthiophene and 2-acetylpyrrole. The FT-IR, ¹H, and ¹³C NMR, as well as mass spectra of both L1 and L2, were recorded and analyzed. Quantum chemical calculations were performed at the DFT/B3LYP/cc-pvdz/6-311G+(d,p) level of theory to study the molecular geometry, vibrational frequencies, and thermodynamic properties including changes of ∆H, ∆S, and ∆G for both the ligands. The optimized vibrational frequency and (¹H and ¹³C) NMR obtained by B3LYP/cc-pvdz/6-311G+(d,p) showed good agreement with experimental FT-IR and NMR data. Frontier molecular orbital (FMO) calculations were also conducted to find the HOMO, LUMO, and HOMO–LUMO gaps of the two synthesized compounds. To investigate the biological activities of the ligands, L1 and L2 were tested using in vitro bioassays against some Gram-negative and Gram-positive bacteria and fungus strains. In addition, molecular docking was used to study the molecular behavior of L1 and L2 against tyrosinase from Bacillus megaterium. The outcomes revealed that both L1 and L2 can suppress microbial growth of bacteria and fungi with variable potency. The antibacterial activity results demonstrated the compound L2 to be potentially effective against Bacillus megaterium with inhibition zones of 12 mm while the molecular docking study showed the binding energies for L1 and L2 to be −7.7 and −8.8 kcal mol⁻¹, respectively, with tyrosinase from Bacillus megaterium. Full article

Location detection is studied for many scenarios, such as pointing out the flaws in multiprocessors, invaders in buildings and facilities, and utilizing wireless sensor networks for monitoring environmental processes. The system or structure can be illustrated as a graph in each of these applications. Sensors strategically placed at a subset of vertices can determine and identify irregularities within the network. The open locating-dominating set S of a graph $G=(V,E)$ is the set of vertices that dominates G, and for any $i,j\in$ V(G) $N\left(i\right)\cap S\ne N\left(j\right)\cap S$ is satisfied. The set S is called the OLD-set of G. The cardinality of the set S is called open locating-dominating number and denoted by ${\gamma }^{old}\left(G\right)$. In this paper, we computed exact values of the prism and prism-related graphs, and also the exact values of convex polytopes of ${\mathcal{R}}_n$ and ${\mathcal{H}}_n$. The upper bound is determined for other classes of convex polytopes. The graphs considered here are well-known from the literature. Full article

Computer-aided methods, based on the entropic linear program framework, have been shown to be effective in assisting the study of information theoretic fundamental limits of information systems. One key element that significantly impacts their computation efficiency and applicability is the reduction of variables, based on problem-specific symmetry and dependence relations. In this work, we propose using the disjoint-set data structure to algorithmically identify the reduction mapping, instead of relying on exhaustive enumeration in the equivalence classification. Based on this reduced linear program, we consider four techniques to investigate the fundamental limits of information systems: (1) computing an outer bound for a given linear combination of information measures and providing the values of information measures at the optimal solution; (2) efficiently computing a polytope tradeoff outer bound between two information quantities; (3) producing a proof (as a weighted sum of known information inequalities) for a computed outer bound; and (4) providing the range for information quantities between which the optimal value does not change, i.e., sensitivity analysis. A toolbox, with an efficient JSON format input frontend, and either Gurobi or Cplex as the linear program solving engine, is implemented and open-sourced. Full article

We consider certain $E_n$ -type root lattices embedded within the standard Lorentzian lattice ${\mathbb{Z}}^{n+1}(3\le n\le 8)$ and study their discrete geometry from the point of view of del Pezzo surface geometry. The lattice ${\mathbb{Z}}^{n+1}$ decomposes as a disjoint union of affine hyperplanes which satisfy a certain periodicity. We introduce the notions of line vectors, rational conic vectors, and rational cubics vectors and their relations to E-polytopes. We also discuss the relation between these special vectors and the combinatorics of the Gosset polytopes of type ${(n-4)}_{21}$ . Full article

A vertex v is a peripheral vertex in G if its eccentricity is equal to its diameter, and periphery $P\left(G\right)$ is a subgraph of G induced by its peripheral vertices. Further, a vertex v in G is a central vertex if $e\left(v\right)=rad\left(G\right)$ , and the subgraph of G induced by its central vertices is called center $C\left(G\right)$ of $G.$ Average eccentricity is the sum of eccentricities of all of the vertices in a graph divided by the total number of vertices, i.e., $avec\left(G\right)=\{\frac{1}{n}\sum e_G\left(u\right);u\in V\left(G\right)\}.$ If every vertex in G is central vertex, then $C\left(G\right)=G$ , and hence, G is self-centered. In this report, we find the center, periphery and average eccentricity for the convex polytopes. Full article

In this article, we introduce special divisors (root, line, ruling, exceptional system and rational quartic) in smooth rational surfaces and study their correspondences to subpolytopes in Gosset polytopes $k_{21}$ . We also show that the sets of rulings and exceptional systems correspond equivariantly to the vertices of $2_{k1}$ and $1_{k2}$ via E-type Weyl action. Full article