Multistability of free spontaneously-curved anisotropic strips

Multistable structures are objects with more than one stable conformation, exemplified by the simple switch. Continuum versions are often elastic composite plates or shells, such as the common measuring tape or the slap bracelet, both of which exhibit two stable configurations: rolled and unrolled. Here we consider the energy landscape of a general class of multistable anisotropic strips with spontaneous Gaussian curvature. We show that while strips with non-zero Gaussian curvature can be bistable, strips with positive spontaneous curvature are always bistable, independent of the elastic moduli, strips of spontaneous negative curvature are bistable only in the presence of spontaneous twist and when certain conditions on the relative stiffness of the strip in tension and shear are satisfied. Furthermore, anisotropic strips can become tristable when their bending rigidity is small. Our study complements and extends the theory of multistability in anisotropic shells and suggests new design criteria for these structures.Comment: 20 pages, 10 figure

Spectral Analysis of Guanine and Cytosine Fluctuations of Mouse Genomic DNA

We study global fluctuations of the guanine and cytosine base content (GC%) in mouse genomic DNA using spectral analyses. Power spectra S(f) of GC% fluctuations in all nineteen autosomal and two sex chromosomes are observed to have the universal functional form S(f) \sim 1/f^alpha (alpha \approx 1) over several orders of magnitude in the frequency range 10^-7< f < 10^-5 cycle/base, corresponding to long-ranging GC% correlations at distances between 100 kb and 10 Mb. S(f) for higher frequencies (f > 10^-5 cycle/base) shows a flattened power-law function with alpha < 1 across all twenty-one chromosomes. The substitution of about 38% interspersed repeats does not affect the functional form of S(f), indicating that these are not predominantly responsible for the long-ranged multi-scale GC% fluctuations in mammalian genomes. Several biological implications of the large-scale GC% fluctuation are discussed, including neutral evolutionary history by DNA duplication, chromosomal bands, spatial distribution of transcription units (genes), replication timing, and recombination hot spots.Comment: 15 pages (figures included), 2 figure

Statics and Dynamics of the Wormlike Bundle Model

Bundles of filamentous polymers are primary structural components of a broad range of cytoskeletal structures, and their mechanical properties play key roles in cellular functions ranging from locomotion to mechanotransduction and fertilization. We give a detailed derivation of a wormlike bundle model as a generic description for the statics and dynamics of polymer bundles consisting of semiflexible polymers interconnected by crosslinking agents. The elastic degrees of freedom include bending as well as twist deformations of the filaments and shear deformation of the crosslinks. We show that a competition between the elastic properties of the filaments and those of the crosslinks leads to renormalized effective bend and twist rigidities that become mode-number dependent. The strength and character of this dependence is found to vary with bundle architecture, such as the arrangement of filaments in the cross section and pretwist. We discuss two paradigmatic cases of bundle architecture, a uniform arrangement of filaments as found in F-actin bundles and a shell-like architecture as characteristic for microtubules. Each architecture is found to have its own universal ratio of maximal to minimal bending rigidity, independent of the specific type of crosslink induced filament coupling; our predictions are in reasonable agreement with available experimental data for microtubules. Moreover, we analyze the predictions of the wormlike bundle model for experimental observables such as the tangent-tangent correlation function and dynamic response and correlation functions. Finally, we analyze the effect of pretwist (helicity) on the mechanical properties of bundles. We predict that microtubules with different number of protofilaments should have distinct variations in their effective bending rigidity

Hacia una pedagogía como teoría crítica en la formación de profesores en Ciencias de la Educación

El presente trabajo parte de la siguiente pregunta: ¿Qué lugar ocupa hoy y cuál debería ocupar la Pedagogía en la formación de profesores en Ciencias de la Educación?; y en la búsqueda de una respuesta a esta pregunta surge a posteriori: ¿Se puede pensar la pedagogía como teoría crítica frente a las ciencias de la educación (entendidas como ciencias que producen “Teoría Tradicional”)? Porque si esto fuera así los pedagogos tendríamos la responsabilidad de pensar una teoría de la educación de carácter emancipatorio para poder replantear la cuestión de “¿Hacia dónde va la educación?” Es decir, si la pedagogía es un saber y una reflexión sobre la práctica, debemos poder producir un saber que sea emancipatorio y propositivo que nos permita decir como apuntar al objetivo de la igualdad en la escuela. Es fundamental replantear en la formación de profesionales de la educación ¿Qué es lo que hacemos como educadores?, ¿Qué sentido tiene nuestro trabajo docente? ¿Para qué educar hoy? Habría que repensar el rol de la pedagogía posicionándola como teoría crítica en la formación de profesores en Ciencias de la Educación, teniendo en cuenta este marco actual que se nos presenta.Facultad de Humanidades y Ciencias de la Educació

Large-scale Oscillation of Structure-Related DNA Sequence Features in Human Chromosome 21

Human chromosome 21 is the only chromosome in human genome that exhibits oscillation of (G+C)-content of cycle length of hundreds kilobases (500 kb near the right telomere). We aim at establishing the existence of similar periodicity in structure-related sequence features in order to relate this (G+C)% oscillation to other biological phenomena. The following quantities are shown to oscillate with the same 500kb periodicity in human chromosome 21: binding energy calculated by two sets of dinucleotide-based thermodynamic parameters, AA/TT and AAA/TTT bi-/tri-nucleotide density, 5'-TA-3' dinucleotide density, and signal for 10/11-base periodicity of AA/TT or AAA/TTT. These intrinsic quantities are related to structural features of the double helix of DNA molecules, such as base-pair binding, untwisting/unwinding, stiffness, and a putative tendency for nucleosome formation.Comment: submitted to Physical Review

Calculating singlet excited states: comparison with fast time-resolved infrared spectroscopy of coumarins

In contrast to the ground state, the calculation of the infrared (IR) spectroscopy of molecular singlet excited states represents a substantial challenge. Here we use the structural IR fingerprint of the singlet excited states of a range of coumarin dyes to assess the accuracy of density functional theory based methods for the calculation of excited state IR spectroscopy. It is shown that excited state Kohn-Sham density functional theory provides a high level of accuracy and represents an alternative approach to time-dependent density functional theory for simulating the IR spectroscopy of the singlet excited states

Solitons in Yakushevich-like models of DNA dynamics with improved intrapair potential

The Yakushevich (Y) model provides a very simple pictures of DNA torsion dynamics, yet yields remarkably correct predictions on certain physical characteristics of the dynamics. In the standard Y model, the interaction between bases of a pair is modelled by a harmonic potential, which becomes anharmonic when described in terms of the rotation angles; here we substitute to this different types of improved potentials, providing a more physical description of the H-bond mediated interactions between the bases. We focus in particular on soliton solutions; the Y model predicts the correct size of the nonlinear excitations supposed to model the ``transcription bubbles'', and this is essentially unchanged with the improved potential. Other features of soliton dynamics, in particular curvature of soliton field configurations and the Peierls-Nabarro barrier, are instead significantly changed

Statistical Mechanics of Torque Induced Denaturation of DNA

A unifying theory of the denaturation transition of DNA, driven by temperature T or induced by an external mechanical torque Gamma is presented. Our model couples the hydrogen-bond opening and the untwisting of the helicoidal molecular structure. We show that denaturation corresponds to a first-order phase transition from B-DNA to d-DNA phases and that the coexistence region is naturally parametrized by the degree of supercoiling sigma. The denaturation free energy, the temperature dependence of the twist angle, the phase diagram in the T,Gamma plane and isotherms in the sigma, Gamma plane are calculated and show a good agreement with experimental data.Comment: 5 pages, 3 figures, model improve

Fluctuation-Facilitated Charge Migration along DNA

We propose a model Hamiltonian for charge transfer along the DNA double helix with temperature driven fluctuations in the base pair positions acting as the rate limiting factor for charge transfer between neighboring base pairs. We compare the predictions of the model with the recent work of J.K. Barton and A.H. Zewail (Proc.Natl.Acad.Sci.USA, {\bf 96}, 6014 (1999)) on the unusual two-stage charge transfer of DNA.Comment: 4 pages, 2 figure

DNA cruciform arms nucleate through a correlated but non-synchronous cooperative mechanism

Inverted repeat (IR) sequences in DNA can form non-canonical cruciform structures to relieve torsional stress. We use Monte Carlo simulations of a recently developed coarse-grained model of DNA to demonstrate that the nucleation of a cruciform can proceed through a cooperative mechanism. Firstly, a twist-induced denaturation bubble must diffuse so that its midpoint is near the centre of symmetry of the IR sequence. Secondly, bubble fluctuations must be large enough to allow one of the arms to form a small number of hairpin bonds. Once the first arm is partially formed, the second arm can rapidly grow to a similar size. Because bubbles can twist back on themselves, they need considerably fewer bases to resolve torsional stress than the final cruciform state does. The initially stabilised cruciform therefore continues to grow, which typically proceeds synchronously, reminiscent of the S-type mechanism of cruciform formation. By using umbrella sampling techniques we calculate, for different temperatures and superhelical densities, the free energy as a function of the number of bonds in each cruciform along the correlated but non-synchronous nucleation pathways we observed in direct simulations.Comment: 12 pages main paper + 11 pages supplementary dat