Fluctuating Elastic Rings: Statics and Dynamics

We study the effects of thermal fluctuations on elastic rings. Analytical expressions are derived for correlation functions of Euler angles, mean square distance between points on the ring contour, radius of gyration, and probability distribution of writhe fluctuations. Since fluctuation amplitudes diverge in the limit of vanishing twist rigidity, twist elasticity is essential for the description of fluctuating rings. We find a crossover from a small scale regime in which the filament behaves as a straight rod, to a large scale regime in which spontaneous curvature is important and twist rigidity affects the spatial configurations of the ring. The fluctuation-dissipation relation between correlation functions of Euler angles and response functions, is used to study the deformation of the ring by external forces. The effects of inertia and dissipation on the relaxation of temporal correlations of writhe fluctuations, are analyzed using Langevin dynamics.Comment: 43 pages, 9 Figure

Tops and Writhing DNA

The torsional elasticity of semiflexible polymers like DNA is of biological significance. A mathematical treatment of this problem was begun by Fuller using the relation between link, twist and writhe, but progress has been hindered by the non-local nature of the writhe. This stands in the way of an analytic statistical mechanical treatment, which takes into account thermal fluctuations, in computing the partition function. In this paper we use the well known analogy with the dynamics of tops to show that when subjected to stretch and twist, the polymer configurations which dominate the partition function admit a local writhe formulation in the spirit of Fuller and thus provide an underlying justification for the use of Fuller's "local writhe expression" which leads to considerable mathematical simplification in solving theoretical models of DNA and elucidating their predictions. Our result facilitates comparison of the theoretical models with single molecule micromanipulation experiments and computer simulations.Comment: 17 pages two figure

Conformations of Linear DNA

We examine the conformations of a model for under- and overwound DNA. The molecule is represented as a cylindrically symmetric elastic string subjected to a stretching force and to constraints corresponding to a specification of the link number. We derive a fundamental relation between the Euler angles that describe the curve and the topological linking number. Analytical expressions for the spatial configurations of the molecule in the infinite- length limit were obtained. A unique configuraion minimizes the energy for a given set of physical conditions. An elastic model incorporating thermal fluctuations provides excellent agreement with experimental results on the plectonemic transition.Comment: 5 pages, RevTeX; 6 postscript figure

Optical excitations in a one-dimensional Mott insulator

The density-matrix renormalization-group (DMRG) method is used to investigate optical excitations in the Mott insulating phase of a one-dimensional extended Hubbard model. The linear optical conductivity is calculated using the dynamical DMRG method and the nature of the lowest optically excited states is investigated using a symmetrized DMRG approach. The numerical calculations agree perfectly with field-theoretical predictions for a small Mott gap and analytical results for a large Mott gap obtained with a strong-coupling analysis. Is is shown that four types of optical excitations exist in this Mott insulator: pairs of unbound charge excitations, excitons, excitonic strings, and charge-density-wave (CDW) droplets. Each type of excitations dominates the low-energy optical spectrum in some region of the interaction parameter space and corresponds to distinct spectral features: a continuum starting at the Mott gap (unbound charge excitations), a single peak or several isolated peaks below the Mott gap (excitons and excitonic strings, respectively), and a continuum below the Mott gap (CDW droplets).Comment: 12 pages (REVTEX 4), 12 figures (in 14 eps files), 1 tabl

Conformations of closed DNA

We examine the conformations of a model for a short segment of closed DNA. The molecule is represented as a cylindrically symmetric elastic rod with a constraint corresponding to a specification of the linking number. We obtain analytic expressions leading to the spatial configuration of a family of solutions representing distortions that interpolate between the circular form of DNA and a figure-eight form that represents the onset of interwinding. We are also able to generate knotted loops. We suggest ways to use our approach to produce other configurations relevant to studies of DNA structure. The stability of the distorted configurations is assessed, along with the effects of fluctuations on the free energy of the various configurations.Comment: 39 pages in REVTEX with 14 eps figures. Submitted to Phys. Rev. E. This manuscript updates, expands and revises, to a considerable extent, a previously posted manuscript, entitled "Conformations of Circular DNA," which appeared as cond-mat/970104

Scroll waves in isotropic excitable media : linear instabilities, bifurcations and restabilized states

Scroll waves are three-dimensional analogs of spiral waves. The linear stability spectrum of untwisted and twisted scroll waves is computed for a two-variable reaction-diffusion model of an excitable medium. Different bands of modes are seen to be unstable in different regions of parameter space. The corresponding bifurcations and bifurcated states are characterized by performing direct numerical simulations. In addition, computations of the adjoint linear stability operator eigenmodes are also performed and serve to obtain a number of matrix elements characterizing the long-wavelength deformations of scroll waves.Comment: 30 pages 16 figures, submitted to Phys. Rev.

Associations of physical activity and screen time with white matter microstructure in children from the general population

Physical activity and sedentary behaviors have been linked to a variety of general health benefits and problems. However, few studies have examined how physical activity during childhood is related to brain development, with the majority of work to date focusing on cardio-metabolic health. This study examines the association between physical activity and screen time with white matter microstructure in the general pediatric population. In a sample of 2532 children (10.12 ± 0.58 years; 50.04% boys) from the Generation R Study, a population-based cohort in Rotterdam, the Netherlands, we assessed physical activity and screen time using parent-reported questionnaires. Magnetic resonance imaging of white matter microstructure was conducted using diffusion tensor imaging. Total physical activity was positively associated with global fractional anisotropy (β = 0.057, 95% CI = 0.016, 0.098, p = 0.007) and negatively associated with global mean diffusivity (β = −0.079, 95% CI = −0.120, −0.038, p 0.05). This study provides new evidence that physical activity is modestly associated with white matter microstructure in children. In contrast, complementing other recent evidence on cognition, screen time was not associated with white matter microstructure. Causal inferences from these modest associations must be interpreted cautiously in the absence of longitudinal data. However, these data still offer a promising avenue for future work to explore to what extent physical activity may promote healthy white matter development

SARS-CoV-2 infection is effectively treated and prevented by EIDD-2801

All known recently emerged human coronaviruses probably originated in bats1. Here we used a single experimental platform based on human lung-only mice (LoM) to demonstrate efficient in vivo replication of all recently emerged human coronaviruses (SARS-CoV, MERS-CoV and SARS-CoV-2) and two highly relevant endogenous pre-pandemic SARS-like bat coronaviruses. Virus replication in this model occurs in bona fide human lung tissue and does not require any type of adaptation of the virus or the host. Our results indicate that bats harbour endogenous coronaviruses capable of direct transmission into humans. Further detailed analysis of pandemic SARS-CoV-2 in vivo infection of LoM human lung tissue showed predominant infection of human lung epithelial cells, including type II pneumocytes present in alveoli and ciliated airway cells. Acute SARS-CoV-2 infection was highly cytopathic and induced a robust and sustained type I interferon and inflammatory cytokine/chemokine response. Finally, we evaluated a therapeutic and pre-exposure prophylaxis strategy for coronavirus infection. Our results show that therapeutic and prophylactic administration of EIDD-2801, an oral broad spectrum antiviral currently in phase II–III clinical trials, dramatically inhibited SARS-CoV-2 replication in vivo and thus has significant potential for the prevention and treatment of COVID-19