Coloring decompositions of complete geometric graphs

A decomposition of a non-empty simple graph $G$ is a pair $[G,P]$, such that $P$ is a set of non-empty induced subgraphs of $G$, and every edge of $G$ belongs to exactly one subgraph in $P$. The chromatic index $\chi'([G,P])$ of a decomposition $[G,P]$ is the smallest number $k$ for which there exists a $k$-coloring of the elements of $P$ in such a way that: for every element of $P$ all of its edges have the same color, and if two members of $P$ share at least one vertex, then they have different colors. A long standing conjecture of Erd\H{o}s-Faber-Lov\'asz states that every decomposition $[K_n,P]$ of the complete graph $K_n$ satisfies $\chi'([K_n,P])\leq n$. In this paper we work with geometric graphs, and inspired by this formulation of the conjecture, we introduce the concept of chromatic index of a decomposition of the complete geometric graph. We present bounds for the chromatic index of several types of decompositions when the vertices of the graph are in general position. We also consider the particular case in which the vertices are in convex position and present bounds for the chromatic index of a few types of decompositions.Comment: 18 pages, 5 figure

The influence of molecular reach and diffusivity on the efficacy of membrane-confined reactions

Signaling by surface receptors often relies on tethered reactions whereby an enzyme bound to the cytoplasmic tail of a receptor catalyzes reactions on substrates within reach. The overall length and stiffness of the receptor tail, the enzyme, and the substrate determine a biophysical parameter termed the molecular reach of the reaction. This parameter determines the probability that the receptor-tethered enzyme will contact the substrate in the volume proximal to the membrane when separated by different distances within the membrane plane. In this work, we develop particle-based stochastic reaction-diffusion models to study the interplay between molecular reach and diffusion. We find that increasing the molecular reach can increase reaction efficacy for slowly diffusing receptors, whereas for rapidly diffusing receptors, increasing molecular reach reduces reaction efficacy. In contrast, if reactions are forced to take place within the two-dimensional plasma membrane instead of the three-dimensional volume proximal to it or if molecules diffuse in three dimensions, increasing molecular reach increases reaction efficacy for all diffusivities. We show results in the context of immune checkpoint receptors (PD-1 dephosphorylating CD28), a standard opposing kinase-phosphatase reaction, and a minimal two-particle model. The work highlights the importance of the three-dimensional nature of many two-dimensional membrane-confined interactions, illustrating a role for molecular reach in control-ling biochemical reactions.Published versio

Sibson’s formula for higher order Voronoi diagrams

Let $S$ be a set of $n$ points in general position in $\mathbb{R}^d$. The order-$k$ Voronoi diagram of $S$, $V_k(S)$, is a subdivision of $\mathbb{R}^d$ into cells whose points have the same $k$ nearest points of $S$. Sibson, in his seminal paper from 1980 (A vector identity for the Dirichlet tessellation), gives a formula to express a point $Q$ of $S$ as a convex combination of other points of $S$ by using ratios of volumes of the intersection of cells of $V_2(S)$ and the cell of $Q$ in $V_1(S)$. The natural neighbour interpolation method is based on Sibson's formula. We generalize his result to express $Q$ as a convex combination of other points of $S$ by using ratios of volumes from Voronoi diagrams of any given order.This research has been supported by projects 2021SGR00266 and PID2019-104129GB-I00/MCIN/ AEI/ 10.13039/501100011033.Award-winningPostprint (published version

Multisite Phosphorylation Modulates the T Cell Receptor ζ-Chain Potency but not the Switchlike Response

AbstractMultisite phosphorylation is ubiquitous in cellular signaling and is thought to provide signaling proteins with additional regulatory mechanisms. Indeed, mathematical models have revealed a large number of mechanisms by which multisite phosphorylation can produce switchlike responses. The T cell antigen receptor (TCR) is a multisubunit receptor on the surface of T cells that is a prototypical multisite substrate as it contains 20 sites that are distributed on 10 conserved immunoreceptor tyrosine-based activation motifs (ITAMs). The TCR ζ-chain is a homodimer subunit that contains six ITAMs (12 sites) and exhibits a number of properties that are predicted to be sufficient for a switchlike response. We have used cellular reconstitution to systematically study multisite phosphorylation of the TCR ζ-chain. We find that multisite phosphorylation proceeds by a nonsequential random mechanism, and find no evidence that multiple ITAMs modulate a switchlike response but do find that they alter receptor potency and maximum phosphorylation. Modulation of receptor potency can be explained by a reduction in molecular entropy of the disordered ζ-chain upon phosphorylation. We further find that the tyrosine kinase ZAP-70 increases receptor potency but does not modulate the switchlike response. In contrast to other multisite proteins, where phosphorylations act in strong concert to modulate protein function, we suggest that the multiple ITAMs on the TCR function mainly to amplify subsequent signaling

Pesticide use in banana plantations in Costa Rica-A review of environmental and human exposure, effects and potential risks

Biodiversity is declining on a global scale. Especially tropical ecosystems, containing most of the planetary biodiversity, are at risk. Agricultural monocrop systems contribute to this decline as they replace original hab-itats and depend on extensive use of synthetic pesticides that impact ecosystems. In this review we use large-scale banana production for export purposes in Costa Rica as an example for pesticide impacts, as it is in production for over a century and uses pesticides extensively for more than fifty years. We summarise the research on pesticide exposure, effects and risks for aquatic and terrestrial environment, as well as for human health. We show that exposure to pesticides is high and relatively well-studied for aquatic systems and humans, but hardly any data are available for the terrestrial compartment including adjacent non target ecosystems such as rainforest fragments. Ecological effects are demonstrated on an organismic level for various aquatic species and processes but are not available at the population and community level. For human health studies exposure evaluation is crucial and recognised effects include various types of cancer and neurobiological dysfunctions particularly in children. With the many synthetic pesticides involved in banana production, the focus on insecticides, revealing highest aquatic risks, and partly herbicides should be extended to fungicides, which are applied aerially over larger areas. The risk assessment and regulation of pesticides so far relies on temperate models and test species and is therefore likely underestimating the risk of pesticide use in tropical ecosystems, with crops such as banana. We highlight further research approaches to improve risk assessment and, in parallel, urge to follow other strategies to reduce pesticides use and especially hazardous substances

Metabolic Profiling of S-praziquantel: Structure Elucidation Using the Crystalline Sponge Method in Combination with Mass Spectrometry and Nuclear Magnetic Resonance

Praziquantel (PZQ) is the drug of choice for treatment of the neglected tropical disease schistosomiasis. Although the drug has been extensively used over several decades and its metabolism well studied (several oxidative metabolites are known from literature), the knowledge of the complete structure of some of its metabolites remains elusive. Conventional techniques, such as nuclear magnetic resonance or liquid chromatography mass spectrometry were used in the past to investigate phase I and phase II metabolites of PZQ. These techniques are either limited to provide the complete molecular structure (liquid chromatography mass spectrometry) or require large amount of sample material (NMR), which are not always available when in vitro systems are used for investigation of the metabolites. In this study, we describe new structures of S-PZQ metabolites generated in vitro from human liver microsomes using the crystalline sponge method. After chromatographic separation and purification of the oxidative metabolites, ultra-performance liquid chromatography-quadrupole time-of-flight mass spectrometry analysis was conducted to narrow down the position of oxidation to a certain part of the molecule. To determine the exact position of hydroxylation, singe-crystal X-ray diffraction analysis of the crystalline sponges and absorbed analyte was used to identify the structure of S-PZQ and its metabolites. The crystalline sponge method allowed for complete structure elucidation of the known metabolites S-trans-4'-hydroxy-PZQ (M1), S-cis-4'-hydroxy-PZQ (M2) and S-/R-11b-hydroxy-PZQ (M6) as well as the unknown metabolites S-9-hydroxy-PZQ (M3) and S-7-hydroxy-S-PZQ (M4). For comparison of structural elucidation techniques, one metabolite (M3) was additionally analyzed using NMR. SIGNIFICANCE STATEMENT: The information content of the metabolic pathway of praziquantel is still limited. The crystalline sponge method allowed the complete structural elucidation of three known and two unknown metabolites of S-praziquantel, using only trace amounts of analyte material, as demonstrated in this study

Contemplative mental training reduces hair glucocorticoid levels in a randomized clinical trial

Objective To investigate the effect of regular contemplative mental training on endocrine and psychological indices of long-term stress. Methods An open-label efficacy trial that comprised three distinct 3-month modules targeting attention and interoception, socio-affective or socio-cognitive abilities through dyadic exercises and secularised meditation practices was conducted with healthy adults. Participants underwent the training for three months, nine months, or were assigned to a retest control cohort. Chronic stress indices were assayed at four timepoints: pre-training and after three, six and nine months. The main outcome measures were cortisol (HC) and cortisone (HE) concentrations in hair and self-reported long-term stress. Results Of 362 initially randomized individuals, 30 dropped out before study initiation (N = 332; mean age-40. 7 ± SD = 9.2 years; 197 women). Hair-based glucocorticoid assays were available from n = 227, and questionnaire data from n = 326. Results from three separate training cohorts (TCs) revealed consistent decreases in HC and HE levels over the first three (TC3) to six months (TC1 and TC2) of training, with no further reduction at the final 9-month mark (baseline to end-of-training, HC: TC1, t(355) = 2.59, p = .010; est.:0.35[0.14]; TC2, t(363) = 4.06, p < .001; est.:0.48[0.12]; TC3: t(368) = 3.18, p = .002; est.:0.41[0.13]; HE: TC1, t(435) = 3.23, p = .001; est.:0.45[0.14]; TC2: t(442) = 2.60, p = .010; est.:0.33[0.13]; TC3: t(446) = 4.18, p < .001; est.:0.57[0.14]). Training effects on HC increased with practice frequency, and effects on both HC and HE were independent of training content and unrelated to change in self-reported chronic stress. Self-reported stress, and cortisol to dehydroepiandrosterone ratios as an exploratory endpoint, were also reduced, albeit less consistently. Conclusions Our results point to the reduction of long-term cortisol exposure as a mechanism through which contemplative mental training may exert positive effects on practitioners' health. Trial registration: ClinicalTrials.gov identifier: NCT0183310