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The Heilbronn triangle problem is a classical geometrical problem that asks for a placement of n points in the unit-square [0; 1]², that maximizes the smallest area of a triangle formed by those points. This problem has natural generalizations to higher dimensions. For integers k; d ≥ 2 and a set P of n points in [0; 1]d, let s = minf(k-1); dg and Vk(d) (P) be the minimum s-dimensional volume of the convex hull of k points in P. Here, instead of considering the supremum of V(d)k (P), we consider its average value, Δ(d)k (n), when the n points in P are chosen independently and uniformly at random in [0; 1]d. We prove that Δ(d)k (n) = ⊝n-k 1+jd-k+1|), for every fixed k; d ≥ 2. [ABSTRACT FROM AUTHOR]

Copper chaperones of the ATX1 family are found in a wide range of organisms where these essential soluble carriers strictly control the transport of monovalent copper across the cytoplasm to various targets in diverse cellular compartments thereby preventing detrimental radical formation catalyzed by the free metal ion. Notably, the ATX1 family in plants contains two distinct forms of the cellular copper carrier. In addition to ATX1 having orthologs in other species, they also contain the copper chaperone CCH. The latter features an extra C-terminal extension whose function is still unknown. The secondary structure of this extension was predicted to be disordered in previous studies, although this has not been experimentally confirmed. Solution NMR studies on purified CCH presented in this study disclose that this region is intrinsically disordered regardless of the chaperone's copper loading state. Further biophysical analyses of the purified metallochaperone provide evidence that the C-terminal extension stabilizes chaperone dimerization in the copper-free and copper-bound states. A variant of CCH lacking the C-terminal extension, termed CCHΔ, shows weaker dimerization but similar copper binding. Computational studies further corroborate the stabilizing role of the C-terminal extension in chaperone dimerization and identify key residues that are vital to maintaining dimer stability., (© 2024. The Author(s).)

The plant hormone ethylene is a key regulator of growth, development and stress adaptation at all stages of the plant life cycle. Signal perception and response to the plant hormone are mediated by a family of receptor kinases localized at the ER-Golgi network which gain their high affinity and specificity for the chemically simple ethylene molecule by an essential copper cofactor bound at their transmembrane domain. Transfer of this cofactor from the plant plasma membrane to the ER-localized receptors requires secured cellular transport of the reactive transition metal. In a recent study, we disclosed the transport proteins involved in the copper transfer to the receptors and identified that cytoplasmic chaperones of the ATX1-family and a membrane-bound P -type ATPase are involved in copper routing. Strictly speaking, our data show that receptors can acquire their copper load by different routes and adopt the metal ion from the plasma membrane either by sequential transfer from soluble chaperones of the ATX1-family via the ER-bound copper-transporting ATPase RAN1 or by direct transfer from the soluble chaperones. Here, we have studied the properties of the soluble plant copper chaperone isoforms, ATX1 and CCH, in more detail. Our data support different cellular functions of these isoforms on copper mobilization.

The plant hormone ethylene is a key regulator of plant growth, development and stress adaption. Ethylene perception and response are mediated by a family of integral membrane receptors (ETRs) localized at the ER-Golgi network. The biological function of these receptors relies on a protein-bound copper cofactor. Nonetheless, molecular processes and structures controlling assembly and integration of the metal into the functional plant hormone receptor are still unknown. Here, we have explored the molecular pathways of copper transfer from the plant cytosol to the ethylene receptor family by analyzing protein-protein interactions of receptors with soluble and membrane-bound plant copper carriers. Our results suggest that receptors primarily acquire their metal cofactor from copper transporter RESPONSIVE-TO-ANTAGONIST-1 (RAN1) which has been loaded with the transition metal beforehand by soluble copper carriers of the ATX1-family. In addition, we found evidence for a direct interaction of ETRs with soluble chaperones ANTIOXIDANT-1 (ATX1) and COPPER TRANSPORT PROTEIN (CCH) raising the possibility of a direct copper exchange between soluble chaperones and receptors.

The plant hormone ethylene was identified as important triggering factor and primary regulator of flower senescence in many species. Consequently, application of chemical inhibitors of ethylene biosynthesis and action is used to extend the longevity of ethylene-sensitive flowers. Here, we show that the peptide NOP-1, a biological derived from the nuclear localization signal of ethylene regulator EIN2 tightly binds to the ethylene receptor of carnation plants - a model to study flower senescence. When applied on cut flowers the peptide biological delays petal senescence similar to previously identified and currently used chemical inhibitors, but offers significant advances to these chemicals in biodegradability, sustainability and ecotoxicity. Our bioinformatic analysis of a wide range of ethylene receptors indicates complete sequence conservation of the anticipated NOP-1 binding site in flower species supporting a widespread use of the peptide on flowering ornamentals to delay senescence and decay in cut flowers. We anticipate our innovative approach to extend flower longevity by a new class of biomolecules such as peptides, peptide analogues and peptide mimetics will significantly advance our technological capability to delay flower senescence and expand vase-life of cut flowers in a sustainable and environmentally friendly manner.

Background: Organ transplantation in Brazil is increasing, but one of its current obstacles is the negative response of the population to organ donation. Therefore, to make the process viable, it is essential that people are educated in organ donation and transplantation. The purpose of this research was to evaluate the main doubts on this subject and to clarify these issues by educating the respondents on the basis of their questions., Methods: Handout questionnaires about organ donation and transplantation were distributed in public schools. The public targets were parents, teachers, and students. The interviewers were trained medical students., Results: In this pilot study with 293 subjects, 97% of respondents had already heard about organ donation; 81% said they would donate their organs, whereas 76% said they would donate the organs of family members and 78% said they believe in the existence of organ trafficking in Brazil., Conclusions: The high percentage of respondents believing in the existence of an organ trade highlights the urgency in clarifying this topic. To do so, the population must be educated about the ethics of the process of donation, emphasizing the fact that there is no organ trade in Brazil., (Copyright © 2015 Elsevier Inc. All rights reserved.)