707 research outputs found

    Some Fundamental Properties of a Multivariate von Mises Distribution

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    In application areas like bioinformatics multivariate distributions on angles are encountered which show significant clustering. One approach to statistical modelling of such situations is to use mixtures of unimodal distributions. In the literature (Mardia et al., 2011), the multivariate von Mises distribution, also known as the multivariate sine distribution, has been suggested for components of such models, but work in the area has been hampered by the fact that no good criteria for the von Mises distribution to be unimodal were available. In this article we study the question about when a multivariate von Mises distribution is unimodal. We give sufficient criteria for this to be the case and show examples of distributions with multiple modes when these criteria are violated. In addition, we propose a method to generate samples from the von Mises distribution in the case of high concentration.Comment: fixed a typo in the article title, minor fixes throughou

    Helical states of nonlocally interacting molecules and their linear stability: geometric approach

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    The equations for strands of rigid charge configurations interacting nonlocally are formulated on the special Euclidean group, SE(3), which naturally generates helical conformations. Helical stationary shapes are found by minimizing the energy for rigid charge configurations positioned along an infinitely long molecule with charges that are off-axis. The classical energy landscape for such a molecule is complex with a large number of energy minima, even when limited to helical shapes. The question of linear stability and selection of stationary shapes is studied using an SE(3) method that naturally accounts for the helical geometry. We investigate the linear stability of a general helical polymer that possesses torque-inducing non-local self-interactions and find the exact dispersion relation for the stability of the helical shapes with an arbitrary interaction potential. We explicitly determine the linearization operators and compute the numerical stability for the particular example of a linear polymer comprising a flexible rod with a repeated configuration of two equal and opposite off-axis charges, thereby showing that even in this simple case the non-local terms can induce instability that leads to the rod assuming helical shapes.Comment: 34 pages, 9 figure

    Elastic energy of proteins and the stages of protein folding

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    We propose a universal elastic energy for proteins, which depends only on the radius of gyration RgR_{g} and the residue number NN. It is constructed using physical arguments based on the hydrophobic effect and hydrogen bonding. Adjustable parameters are fitted to data from the computer simulation of the folding of a set of proteins using the CSAW (conditioned self-avoiding walk) model. The elastic energy gives rise to scaling relations of the form RgNνR_{g}\sim N^{\nu} in different regions. It shows three folding stages characterized by the progression with exponents ν=3/5,3/7,2/5\nu = 3/5, 3/7, 2/5, which we identify as the unfolded stage, pre-globule, and molten globule, respectively. The pre-globule goes over to the molten globule via a break in behavior akin to a first-order phase transition, which is initiated by a sudden acceleration of hydrogen bonding

    A systematically coarse-grained model for DNA, and its predictions for persistence length, stacking, twist, and chirality

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    We introduce a coarse-grained model of DNA with bases modeled as rigid-body ellipsoids to capture their anisotropic stereochemistry. Interaction potentials are all physicochemical and generated from all-atom simulation/parameterization with minimal phenomenology. Persistence length, degree of stacking, and twist are studied by molecular dynamics simulation as functions of temperature, salt concentration, sequence, interaction potential strength, and local position along the chain, for both single- and double-stranded DNA where appropriate. The model of DNA shows several phase transitions and crossover regimes in addition to dehybridization, including unstacking, untwisting, and collapse which affect mechanical properties such as rigidity and persistence length. The model also exhibits chirality with a stable right-handed and metastable left-handed helix.Comment: 30 pages, 20 figures, Supplementary Material available at http://www.physics.ubc.ca/~steve/publications.htm

    Mean-field methods in evolutionary duplication-innovation-loss models for the genome-level repertoire of protein domains

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    We present a combined mean-field and simulation approach to different models describing the dynamics of classes formed by elements that can appear, disappear or copy themselves. These models, related to a paradigm duplication-innovation model known as Chinese Restaurant Process, are devised to reproduce the scaling behavior observed in the genome-wide repertoire of protein domains of all known species. In view of these data, we discuss the qualitative and quantitative differences of the alternative model formulations, focusing in particular on the roles of element loss and of the specificity of empirical domain classes.Comment: 10 Figures, 2 Table

    Liquid-Sensing Probe and Methods for Using the Same

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    A sensor assembly includes a main body, a sensor, and a filler. The main body includes an outer surface having a continuously-variable radius of curvature in at least one portion. A sensor in thermal communication with a region of that surface having relatively low radius of curvature is disposed in the assembly recessed from the outer surface. Liquid droplets adhered to the outer surface in this region tend to migrate to a distant location having a higher radius of curvature. The main body has low thermal conductivity. The filler has a relatively higher thermal conductivity and, in embodiments, fills an opening in the outer surface of the main body, providing a thermally-conductive pathway between the sensor and the surrounding environment via the opening. A probe having a plurality of such sensors, and methods of detecting the presence of liquid and phase transitions in a predetermined space are also disclosed

    Hierarchical Chain Model of Spider Capture Silk Elasticity

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    Spider capture silk is a biomaterial with both high strength and high elasticity, but the structural design principle underlying these remarkable properties is still unknown. It was revealed recently by atomic force microscopy that, an exponential force--extension relationship holds both for capture silk mesostructures and for intact capture silk fibers [N. Becker et al., Nature Materials 2, 278 (2003)]. In this Letter a simple hierarchical chain model was proposed to understand and reproduce this striking observation. In the hierarchical chain model, a polymer is composed of many structural motifs which organize into structural modules and supra-modules in a hierarchical manner. Each module in this hierarchy has its own characteristic force. The repetitive patterns in the amino acid sequence of the major flagelliform protein of spider capture silk is in support of this model.Comment: 4 pages, 3 figures. Will be formally published in PR

    Valorizing Sewage Sludge: Using Nature-Inspired Architecture to Overcome Intrinsic Weaknesses of Waste-Based Materials

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    Sewage sludge, a biosolid product of wastewater processing, is an often-overlooked source of rich organic waste. Hydrothermal processing (HTP), which uses heat and pressure to convert biomass into various solid, liquid, and gaseous products, has shown promise in converting sewage sludge into new materials with potential application in biofuels, asphalt binders, and bioplastics. In this study we focus on hydrochar, the carbonaceous HTP solid phase, and investigate its use as a bio-based filler in additive manufacturing technologies. We explore the impact of HTP and subsequent thermal activation on chemical and structural properties of sewage sludge and discuss the role of atypical metallic and metalloid dopants in organic material processing. In additive manufacturing composites, although the addition of hydrochar generally decreases mechanical performance, we show that toughness and strain can be recovered with hierarchical microstructures, much like biological materials that achieve outstanding properties by architecting relatively weak building blocks

    Energy Storage in a Hamiltonian System in Partial Contact with a Heat Bath

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    To understand the mechanism allowing for the long-term storage of excess energy in proteins, we study a Hamiltonian system consisting of several coupled pendula in partial contact with a heat bath. It is found that energy storage is possible when the motion of each pendulum switches between oscillatory (vibrational) and rotational (phase-slip) modes. The storage time increases almost exponentially to the square root of the injected energy. The relevance of our mechanism to protein motors is discussed.Comment: 8 pages, 4 figures, to appear in J.Phys.Soc.Jp
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