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

On the equivalence of the Langevin and auxiliary field quantization methods for absorbing dielectrics

Recently two methods have been developed for the quantization of the electromagnetic field in general dispersing and absorbing linear dielectrics. The first is based upon the introduction of a quantum Langevin current in Maxwell's equations [T. Gruner and D.-G. Welsch, Phys. Rev. A 53, 1818 (1996); Ho Trung Dung, L. Kn\"{o}ll, and D.-G. Welsch, Phys. Rev. A 57, 3931 (1998); S. Scheel, L. Kn\"{o}ll, and D.-G. Welsch, Phys. Rev. A 58, 700 (1998)], whereas the second makes use of a set of auxiliary fields, followed by a canonical quantization procedure [A. Tip, Phys. Rev. A 57, 4818 (1998)]. We show that both approaches are equivalent.Comment: 7 pages, RevTeX, no figure

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

Fluctuating Filaments I: Statistical Mechanics of Helices

We examine the effects of thermal fluctuations on thin elastic filaments with non-circular cross-section and arbitrary spontaneous curvature and torsion. Analytical expressions for orientational correlation functions and for the persistence length of helices are derived, and it is found that this length varies non-monotonically with the strength of thermal fluctuations. In the weak fluctuation regime, the local helical structure is preserved and the statistical properties are dominated by long wavelength bending and torsion modes. As the amplitude of fluctuations is increased, the helix ``melts'' and all memory of intrinsic helical structure is lost. Spontaneous twist of the cross--section leads to resonant dependence of the persistence length on the twist rate.Comment: 5 figure

Statistical mechanics of triangulated ribbons

We use computer simulations and scaling arguments to investigate statistical and structural properties of a semiflexible ribbon composed of isosceles triangles. We study two different models, one where the bending energy is calculated from the angles between the normal vectors of adjacent triangles, the second where the edges are viewed as semiflexible polymers so that the bending energy is related to the angles between the tangent vectors of next-nearest neighbor triangles. The first model can be solved exactly whereas the second is more involved. It was recently introduced by Liverpool and Golestanian Phys.Rev.Lett. 80, 405 (1998), Phys.Rev.E 62, 5488 (2000) as a model for double-stranded biopolymers such as DNA. Comparing observables such as the autocorrelation functions of the tangent vectors and the bond-director field, the probability distribution functions of the end-to-end distance, and the mean squared twist we confirm the existence of local twist correlation, but find no indications for other predicted features such as twist-stretch coupling, kinks, or oscillations in the autocorrelation function of the bond-director field.Comment: 10 pages, 13 figures. submitted to PRE, revised versio

Virtual discovery of melatonin receptor ligands to modulate circadian rhythms

The neuromodulator melatonin synchronizes circadian rhythms and related physiological functions through the actions of two G-protein-coupled receptors: MT1 and MT2. Circadian release of melatonin at night from the pineal gland activates melatonin receptors in the suprachiasmatic nucleus of the hypothalamus, synchronizing the physiology and behaviour of animals to the light–dark cycle1–4. The two receptors are established drug targets for aligning circadian phase to this cycle in disorders of sleep5,6 and depression1–4,7–9. Despite their importance, few in vivo active MT1-selective ligands have been reported2,8,10–12, hampering both the understanding of circadian biology and the development of targeted therapeutics. Here we docked more than 150 million virtual molecules to an MT1 crystal structure, prioritizing structural fit and chemical novelty. Of these compounds, 38 high-ranking molecules were synthesized and tested, revealing ligands with potencies ranging from 470 picomolar to 6 micromolar. Structure-based optimization led to two selective MT1 inverse agonists—which were topologically unrelated to previously explored chemotypes—that acted as inverse agonists in a mouse model of circadian re-entrainment. Notably, we found that these MT1-selective inverse agonists advanced the phase of the mouse circadian clock by 1.3–1.5 h when given at subjective dusk, an agonist-like effect that was eliminated in MT1- but not in MT2-knockout mice. This study illustrates the opportunities for modulating melatonin receptor biology through MT1-selective ligands and for the discovery of previously undescribed, in vivo active chemotypes from structure-based screens of diverse, ultralarge libraries. © 2020, The Author(s), under exclusive licence to Springer Nature Limited

Photonic band gaps in materials with triply periodic surfaces and related tubular structures

We calculate the photonic band gap of triply periodic bicontinuous cubic structures and of tubular structures constructed from the skeletal graphs of triply periodic minimal surfaces. The effect of the symmetry and topology of the periodic dielectric structures on the existence and the characteristics of the gaps is discussed. We find that the C(I2-Y**) structure with Ia3d symmetry, a symmetry which is often seen in experimentally realized bicontinuous structures, has a photonic band gap with interesting characteristics. For a dielectric contrast of 11.9 the largest gap is approximately 20% for a volume fraction of the high dielectric material of 25%. The midgap frequency is a factor of 1.5 higher than the one for the (tubular) D and G structures

Micromechanics of Single Supercoiled DNA Molecules

Abstract. The theory of the mechanical response of single DNA molecules un-der stretching and twisting stresses is reviewed. Using established results for the the semiflexible polymer including the effect of torsional stress, and for the free energy of plectonemic supercoils, a theory of coexisting plectonemic and extended DNA is con-structed and shown to produce phenomena observed experimentally. Analytical results for DNA extension and torque are presented, and effects of anharmonicities in the plec-tonemic free energy are described. An application of the theory to the problem of torsional-stress-induced cruciform extrusion is also discussed. Key words. DNA, molecular biology, statistical mechanics, polymer physics. AMS(MOS) subject classifications. 82D60, 92C05, 92C40