Equilibrium Bundle Size of Rodlike Polyelectrolytes with Counterion-Induced Attractive Interactions

Multivalent counterions can induce an effective attraction between like-charged rodlike polyelectrolytes, leading to the formation of polelectrolyte bundles. In this paper, we calculate the equilibrium bundle size using a simple model in which the attraction between polyelectrolytes (assumed to be pairwise additive) is treated phenomenologically. If the counterions are point-like, they almost completely neutralize the charge of the bundle, and the equilibrium bundle size diverges. When the counterions are large, however, steric and short-range electrostatic interactions prevent charge neutralization of the bundle, thus forcing the equilibrium bundle size to be finite. We also consider the possibility that increasing the number of nearest neighbors for each rod in the bundle frustrates the attractive interaction between the rods. Such a frustration leads to the formation of finite size bundles as well, even when the counterions are small.Comment: 4 pages, 2 figures; v2: typos corrected, references added, minor changes made to conten

The effect of curvature and topology on membrane hydrodynamics

We study the mobility of extended objects (rods) on a spherical liquid-liquid interface to show how this quantity is modified in a striking manner by both the curvature and the topology of the interface. We present theoretical calculations and experimental measurements of the interfacial fluid velocity field around a moving rod bound to the crowded interface of a water-in-oil droplet. By using different droplet sizes, membrane viscosities, and rod lengths, we show that the viscosity mismatch between the interior and exterior fluids leads to a suppression of the fluid flow on small droplets that cannot be captured by the flat interface predictions.Comment: 4 pages, 3 figure

Setting temporal baselines for biodiversity : the limits of available monitoring data for capturing the full impact of anthropogenic pressures

Temporal baselines are needed for biodiversity, in order for the change in biodiversity to be measured over time, the targets for biodiversity conservation to be defined and conservation progress to be evaluated. Limited biodiversity information is widely recognized as a major barrier for identifying temporal baselines, although a comprehensive quantitative assessment of this is lacking. Here, we report on the temporal baselines that could be drawn from biodiversity monitoring schemes in Europe and compare those with the rise of important anthropogenic pressures. Most biodiversity monitoring schemes were initiated late in the 20th century, well after anthropogenic pressures had already reached half of their current magnitude. Setting temporal baselines from biodiversity monitoring data would therefore underestimate the full range of impacts of major anthropogenic pressures. In addition, biases among taxa and organization levels provide a truncated picture of biodiversity over time. These limitations need to be explicitly acknowledged when designing management strategies and policies as they seriously constrain our ability to identify relevant conservation targets aimed at restoring or reversing biodiversity losses. We discuss the need for additional research efforts beyond standard biodiversity monitoring to reconstruct the impacts of major anthropogenic pressures and to identify meaningful temporal baselines for biodiversity

Patterns of richness across forest beetle communities—A methodological comparison of observed and estimated species numbers

Abstract Species richness is a frequently used measure of biodiversity. The compilation of a complete species list is an often unattainable goal. Estimators of species richness have been developed to overcome this problem. While the use of these estimators is becoming increasingly popular, working with the observed number of species is still common practice. To assess whether patterns of beetle communities based on observed numbers may be compared among each other, we compared patterns from observed and estimated numbers of species for beetle communities in the canopy of the Leipzig floodplain forest. These patterns were species richness and the number of shared species among three tree species and two canopy strata. We tested the applicability of the asymptotic Chao1 estimator and the estimate provided by the nonasymptotic rarefaction–extrapolation method for all tree species and both upper canopy and lower canopy. In the majority of cases, the ranking patterns of species richness for host tree species and strata were the same for the observed and estimated number of species. The ranking patterns of the number of species shared among host tree species and strata, however, were significantly different between observed and estimated values. Our results indicate that the observed number of species under‐represents species richness and the number of shared species. However, ranking comparisons of published patterns based on the number of observed species may be acceptable for species richness but likely not reliable for the number of shared species. Further studies are needed to corroborate this conclusion. We encourage to use estimators and to provide open access to data to allow comparative assessments