The main goal of this paper is to examine theoretically and numerically the impact of a chosen bending model on the dynamics of elastic filaments settling in a viscous fluid under gravity at low-Reynolds-number. We use the bead-spring approximation of a filament and the Rotne-Prager mobility matrix to describe hydrodynamic interactions between the beads. We analyze the dynamics of trumbbells, for which bending angles are typically larger than for thin and long filaments. Each trumbbell is made of three beads connected by springs and it exhibits a bending resistance, described by the harmonic or - alternatively - by the 'cosine' (also called the Kratky-Porod) bending models, both often used in the literature. Using the harmonic bending potential, and coupling it to the spring potential by the Young's modulus, we find simple benchmark solutions: stable stationary configurations of a single elastic trumbbell and attraction of two elastic trumbbells towards a periodic long-lasting orbit. As the most significant result of this paper, we show that for very elastic trumbbells at the same initial conditions, the Kratky-Porod bending potential can lead to qualitatively and quantitatively different spurious dynamics, with artificially large bending angles and unrealistic shapes. We point out that for the bead models of an elastic filament, the range of applicability of the Kratky-Porod model might not go beyond bending angles smaller than π/2 for touching beads and beyond an even much lower value for beads well-separated from each other. The existence of stable stationary configurations of elastic trumbbells and a family of periodic oscillations of two elastic trumbbells are very important findings on their own.

Short read sequencing of diploid individuals does not permit the direct inference of the sequence on each of the two chromosomes. Although various phasing software packages exist, they were primarily tailored for and tested on human data, which differ from other species in factors that influence phasing, such as SNP density, amounts of linkage disequilibrium (LD) and sample sizes. Despite becoming increasingly popular for other species, the reliability of phasing in non-human data has not been evaluated to a sufficient extent.We scrutinized the phasing accuracy for Drosophila melanogaster, a species with high polymorphism levels and reduced LD relative to humans. We phased two D. melanogaster populations and compared the results to the known haplotypes. The performance increased with size of the reference panel and was highest when the reference panel and phased individuals were from the same population. Full genomic SNP data and inclusion of sequence read information also improved phasing. Despite humans and Drosophila having similar switch error rates between polymorphic sites, the distances between switch errors were much shorter in Drosophila with only fragments < 300-1500 bp being correctly phased with ≥ 95% confidence. This suggests that the higher SNP density cannot compensate for the higher recombination rate in D. melanogaster.Furthermore, we show that populations that have gone through demographic events such as bottlenecks can be phased with higher accuracy. Our results highlight that statistically phased data are particularly error prone in species with large population sizes or populations lacking suitable reference panels.

Hydrodynamic interactions between two identical elastic dumbbells settling under gravity in a viscous fluid at low-Reynolds-number are investigated within the point-particle model. Evolution of a benchmark initial configuration is studied, in which the dumbbells are vertical and their centres are aligned horizontally. Rigid dumbbells and pairs of separate beads starting from the same positions tumble periodically while settling down. We find that elasticity (which breaks time-reversal symmetry of the motion) significantly affects the system's dynamics. This is remarkable taking into account that elastic forces are always much smaller than gravity. We observe oscillating motion of the elastic dumbbells, which tumble and change their length non-periodically. Independently of the value of the spring constant, a horizontal hydrodynamic repulsion appears between the dumbbellstheir centres of mass move apart from each other horizontally. The shift is fast for moderate values of the spring constant k, and slows down when k tends to zero or to infinity; in these limiting cases we recover the periodic dynamics reported in the literature. For moderate values of the spring constant, and different initial configurations, we observe the existence of a universal time-dependent solution to which the system converges after an initial relaxation phase. The tumbling time and the width of the trajectories in the centre-of-mass frame increase with time. In addition to its fundamental significance, the benchmark solution presented here is important to understand general features of systems with larger number of elastic particles, at regular and random configurations.