Some Patterns of Shape Change Controlled by Eigenstrain Architectures Sebastien Turcaud
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The Ordered Distribution of Natural Numbers on the Square Root Spiral
The Ordered Distribution of Natural Numbers on the Square Root Spiral - Harry K. Hahn - Ludwig-Erhard-Str. 10 D-76275 Et Germanytlingen, Germany ------------------------------ mathematical analysis by - Kay Schoenberger - Humboldt-University Berlin ----------------------------- 20. June 2007 Abstract : Natural numbers divisible by the same prime factor lie on defined spiral graphs which are running through the “Square Root Spiral“ ( also named as “Spiral of Theodorus” or “Wurzel Spirale“ or “Einstein Spiral” ). Prime Numbers also clearly accumulate on such spiral graphs. And the square numbers 4, 9, 16, 25, 36 … form a highly three-symmetrical system of three spiral graphs, which divide the square-root-spiral into three equal areas. A mathematical analysis shows that these spiral graphs are defined by quadratic polynomials. The Square Root Spiral is a geometrical structure which is based on the three basic constants: 1, sqrt2 and π (pi) , and the continuous application of the Pythagorean Theorem of the right angled triangle. Fibonacci number sequences also play a part in the structure of the Square Root Spiral. Fibonacci Numbers divide the Square Root Spiral into areas and angle sectors with constant proportions. These proportions are linked to the “golden mean” ( golden section ), which behaves as a self-avoiding-walk- constant in the lattice-like structure of the square root spiral. Contents of the general section Page 1 Introduction to the Square Root Spiral 2 2 Mathematical description of the Square Root Spiral 4 3 The distribution -
Structural Insight Into Marburg Virus Nucleoprotein-RNA Complex Formation
bioRxiv preprint doi: https://doi.org/10.1101/2021.07.13.452116; this version posted July 13, 2021. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 1 Structural insight into Marburg virus nucleoprotein-RNA complex formation 2 3 Yoko Fujita-Fujiharu1,2,3, Yukihiko Sugita1,2,4, Yuki Takamatsu1,#, Kazuya Houri1,2,3, Manabu 4 Igarashi5, Yukiko Muramoto1,2,3, Masahiro Nakano1,2,3, Yugo Tsunoda1, Stephan Becker6,7, 5 Takeshi Noda1,2,3* 6 7 1 Laboratory of Ultrastructural Virology, Institute for Frontier Life and Medical Sciences, 8 Kyoto University, 53 Shogoin Kawahara-cho, Sakyo-ku, Kyoto 606-8507, Japan 9 2 Laboratory of Ultrastructural Virology, Graduate School of Biostudies, Kyoto University, 53 10 Shogoin Kawahara-cho, Sakyo-ku, Kyoto 606-8507, Japan 11 3 CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332- 12 0012, Japan 13 4 Hakubi Center for Advanced Research, Kyoto University, Kyoto, Japan. 14 5 Division of Epidemiology, International Institute for Zoonosis Control, Hokkaido University, 15 Sapporo 001-0020, Japan 16 6 Institute of Virology, University of Marburg, 35043 Marburg, Germany. 17 7 German Center for Infection Research (DZIF), Marburg-Gießen-Langen Site, University of 18 Marburg, 35043 Marburg, Germany. 19 20 # present address: Department of Virology I, National Institute of Infectious Diseases, Gakuen 21 4-7-1, Musashimurayama-city, Tokyo 208-0011, Japan 22 *correspondence to: [email protected] 23 24 bioRxiv preprint doi: https://doi.org/10.1101/2021.07.13.452116; this version posted July 13, 2021. -
Α/Β Coiled Coils 2 3 Marcus D
1 α/β Coiled Coils 2 3 Marcus D. Hartmann, Claudia T. Mendler†, Jens Bassler, Ioanna Karamichali, Oswin 4 Ridderbusch‡, Andrei N. Lupas* and Birte Hernandez Alvarez* 5 6 Department of Protein Evolution, Max Planck Institute for Developmental Biology, 72076 7 Tübingen, Germany 8 † present address: Nuklearmedizinische Klinik und Poliklinik, Klinikum rechts der Isar, 9 Technische Universität München, Munich, Germany 10 ‡ present address: Vossius & Partner, Siebertstraße 3, 81675 Munich, Germany 11 12 13 14 * correspondence to A. N. Lupas or B. Hernandez Alvarez: 15 Department of Protein Evolution 16 Max-Planck-Institute for Developmental Biology 17 Spemannstr. 35 18 D-72076 Tübingen 19 Germany 20 Tel. –49 7071 601 356 21 Fax –49 7071 601 349 22 [email protected], [email protected] 23 1 24 Abstract 25 Coiled coils are the best-understood protein fold, as their backbone structure can uniquely be 26 described by parametric equations. This level of understanding has allowed their manipulation 27 in unprecedented detail. They do not seem a likely source of surprises, yet we describe here 28 the unexpected formation of a new type of fiber by the simple insertion of two or six residues 29 into the underlying heptad repeat of a parallel, trimeric coiled coil. These insertions strain the 30 supercoil to the breaking point, causing the local formation of short β-strands, which move the 31 path of the chain by 120° around the trimer axis. The result is an α/β coiled coil, which retains 32 only one backbone hydrogen bond per repeat unit from the parent coiled coil. -
Coverrailway Curves Book.Cdr
RAILWAY CURVES March 2010 (Corrected & Reprinted : November 2018) INDIAN RAILWAYS INSTITUTE OF CIVIL ENGINEERING PUNE - 411 001 i ii Foreword to the corrected and updated version The book on Railway Curves was originally published in March 2010 by Shri V B Sood, the then professor, IRICEN and reprinted in September 2013. The book has been again now corrected and updated as per latest correction slips on various provisions of IRPWM and IRTMM by Shri V B Sood, Chief General Manager (Civil) IRSDC, Delhi, Shri R K Bajpai, Sr Professor, Track-2, and Shri Anil Choudhary, Sr Professor, Track, IRICEN. I hope that the book will be found useful by the field engineers involved in laying and maintenance of curves. Pune Ajay Goyal November 2018 Director IRICEN, Pune iii PREFACE In an attempt to reach out to all the railway engineers including supervisors, IRICEN has been endeavouring to bring out technical books and monograms. This book “Railway Curves” is an attempt in that direction. The earlier two books on this subject, viz. “Speed on Curves” and “Improving Running on Curves” were very well received and several editions of the same have been published. The “Railway Curves” compiles updated material of the above two publications and additional new topics on Setting out of Curves, Computer Program for Realignment of Curves, Curves with Obligatory Points and Turnouts on Curves, with several solved examples to make the book much more useful to the field and design engineer. It is hoped that all the P.way men will find this book a useful source of design, laying out, maintenance, upgradation of the railway curves and tackling various problems of general and specific nature. -
Some Curves and the Lengths of Their Arcs Amelia Carolina Sparavigna
Some Curves and the Lengths of their Arcs Amelia Carolina Sparavigna To cite this version: Amelia Carolina Sparavigna. Some Curves and the Lengths of their Arcs. 2021. hal-03236909 HAL Id: hal-03236909 https://hal.archives-ouvertes.fr/hal-03236909 Preprint submitted on 26 May 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Some Curves and the Lengths of their Arcs Amelia Carolina Sparavigna Department of Applied Science and Technology Politecnico di Torino Here we consider some problems from the Finkel's solution book, concerning the length of curves. The curves are Cissoid of Diocles, Conchoid of Nicomedes, Lemniscate of Bernoulli, Versiera of Agnesi, Limaçon, Quadratrix, Spiral of Archimedes, Reciprocal or Hyperbolic spiral, the Lituus, Logarithmic spiral, Curve of Pursuit, a curve on the cone and the Loxodrome. The Versiera will be discussed in detail and the link of its name to the Versine function. Torino, 2 May 2021, DOI: 10.5281/zenodo.4732881 Here we consider some of the problems propose in the Finkel's solution book, having the full title: A mathematical solution book containing systematic solutions of many of the most difficult problems, Taken from the Leading Authors on Arithmetic and Algebra, Many Problems and Solutions from Geometry, Trigonometry and Calculus, Many Problems and Solutions from the Leading Mathematical Journals of the United States, and Many Original Problems and Solutions. -
Eukaryotic Genome Annotation
Comparative Features of Multicellular Eukaryotic Genomes (2017) (First three statistics from www.ensembl.org; other from original papers) C. elegans A. thaliana D. melanogaster M. musculus H. sapiens Species name Nematode Thale Cress Fruit Fly Mouse Human Size (Mb) 103 136 143 3,482 3,555 # Protein-coding genes 20,362 27,655 13,918 22,598 20,338 (25,498 (13,601 original (30,000 (30,000 original est.) original est.) original est.) est.) Transcripts 58,941 55,157 34,749 131,195 200,310 Gene density (#/kb) 1/5 1/4.5 1/8.8 1/83 1/97 LINE/SINE (%) 0.4 0.5 0.7 27.4 33.6 LTR (%) 0.0 4.8 1.5 9.9 8.6 DNA Elements 5.3 5.1 0.7 0.9 3.1 Total repeats 6.5 10.5 3.1 38.6 46.4 Exons % genome size 27 28.8 24.0 per gene 4.0 5.4 4.1 8.4 8.7 average size (bp) 250 506 Introns % genome size 15.6 average size (bp) 168 Arabidopsis Chromosome Structures Sorghum Whole Genome Details Characterizing the Proteome The Protein World • Sequencing has defined o Many, many proteins • How can we use this data to: o Define genes in new genomes o Look for evolutionarily related genes o Follow evolution of genes ▪ Mixing of domains to create new proteins o Uncover important subsets of genes that ▪ That deep phylogenies • Plants vs. animals • Placental vs. non-placental animals • Monocots vs. dicots plants • Common nomenclature needed o Ensure consistency of interpretations InterPro (http://www.ebi.ac.uk/interpro/) Classification of Protein Families • Intergrated documentation resource for protein super families, families, domains and functional sites o Mitchell AL, Attwood TK, Babbitt PC, et al. -
Archimedean Spirals ∗
Archimedean Spirals ∗ An Archimedean Spiral is a curve defined by a polar equation of the form r = θa, with special names being given for certain values of a. For example if a = 1, so r = θ, then it is called Archimedes’ Spiral. Archimede’s Spiral For a = −1, so r = 1/θ, we get the reciprocal (or hyperbolic) spiral. Reciprocal Spiral ∗This file is from the 3D-XploreMath project. You can find it on the web by searching the name. 1 √ The case a = 1/2, so r = θ, is called the Fermat (or hyperbolic) spiral. Fermat’s Spiral √ While a = −1/2, or r = 1/ θ, it is called the Lituus. Lituus In 3D-XplorMath, you can change the parameter a by going to the menu Settings → Set Parameters, and change the value of aa. You can see an animation of Archimedean spirals where the exponent a varies gradually, from the menu Animate → Morph. 2 The reason that the parabolic spiral and the hyperbolic spiral are so named is that their equations in polar coordinates, rθ = 1 and r2 = θ, respectively resembles the equations for a hyperbola (xy = 1) and parabola (x2 = y) in rectangular coordinates. The hyperbolic spiral is also called reciprocal spiral because it is the inverse curve of Archimedes’ spiral, with inversion center at the origin. The inversion curve of any Archimedean spirals with respect to a circle as center is another Archimedean spiral, scaled by the square of the radius of the circle. This is easily seen as follows. If a point P in the plane has polar coordinates (r, θ), then under inversion in the circle of radius b centered at the origin, it gets mapped to the point P 0 with polar coordinates (b2/r, θ), so that points having polar coordinates (ta, θ) are mapped to points having polar coordinates (b2t−a, θ). -
Limits of Pgl(3)-Translates of Plane Curves, I
LIMITS OF PGL(3)-TRANSLATES OF PLANE CURVES, I PAOLO ALUFFI, CAREL FABER Abstract. We classify all possible limits of families of translates of a fixed, arbitrary complex plane curve. We do this by giving a set-theoretic description of the projective normal cone (PNC) of the base scheme of a natural rational map, determined by the curve, 8 N from the P of 3 × 3 matrices to the P of plane curves of degree d. In a sequel to this paper we determine the multiplicities of the components of the PNC. The knowledge of the PNC as a cycle is essential in our computation of the degree of the PGL(3)-orbit closure of an arbitrary plane curve, performed in [5]. 1. Introduction In this paper we determine the possible limits of a fixed, arbitrary complex plane curve C , obtained by applying to it a family of translations α(t) centered at a singular transformation of the plane. In other words, we describe the curves in the boundary of the PGL(3)-orbit closure of a given curve C . Our main motivation for this work comes from enumerative geometry. In [5] we have determined the degree of the PGL(3)-orbit closure of an arbitrary (possibly singular, re- ducible, non-reduced) plane curve; this includes as special cases the determination of several characteristic numbers of families of plane curves, the degrees of certain maps to moduli spaces of plane curves, and isotrivial versions of the Gromov-Witten invariants of the plane. A description of the limits of a curve, and in fact a more refined type of information is an essential ingredient of our approach. -
STACK: a Toolkit for Analysing Β-Helix Proteins
STACK: a toolkit for analysing ¯-helix proteins Master of Science Thesis (20 points) Salvatore Cappadona, Lars Diestelhorst Abstract ¯-helix proteins contain a solenoid fold consisting of repeated coils forming parallel ¯-sheets. Our goal is to formalise the intuitive notion of a ¯-helix in an objective algorithm. Our approach is based on first identifying residues stacks — linear spatial arrangements of residues with similar conformations — and then combining these elementary patterns to form ¯-coils and ¯-helices. Our algorithm has been implemented within STACK, a toolkit for analyzing ¯-helix proteins. STACK distinguishes aromatic, aliphatic and amidic stacks such as the asparagine ladder. Geometrical features are computed and stored in a relational database. These features include the axis of the ¯-helix, the stacks, the cross-sectional shape, the area of the coils and related packing information. An interface between STACK and a molecular visualisation program enables structural features to be highlighted automatically. i Contents 1 Introduction 1 2 Biological Background 2 2.1 Basic Concepts of Protein Structure ....................... 2 2.2 Secondary Structure ................................ 2 2.3 The ¯-Helix Fold .................................. 3 3 Parallel ¯-Helices 6 3.1 Introduction ..................................... 6 3.2 Nomenclature .................................... 6 3.2.1 Parallel ¯-Helix and its ¯-Sheets ..................... 6 3.2.2 Stacks ................................... 8 3.2.3 Coils ..................................... 8 3.2.4 The Core Region .............................. 8 3.3 Description of Known Structures ......................... 8 3.3.1 Helix Handedness .............................. 8 3.3.2 Right-Handed Parallel ¯-Helices ..................... 13 3.3.3 Left-Handed Parallel ¯-Helices ...................... 19 3.4 Amyloidosis .................................... 20 4 The STACK Toolkit 24 4.1 Identification of Structural Elements ....................... 24 4.1.1 Stacks ................................... -
Stapled Peptides—A Useful Improvement for Peptide-Based Drugs
molecules Review Stapled Peptides—A Useful Improvement for Peptide-Based Drugs Mattia Moiola, Misal G. Memeo and Paolo Quadrelli * Department of Chemistry, University of Pavia, Viale Taramelli 12, 27100 Pavia, Italy; [email protected] (M.M.); [email protected] (M.G.M.) * Correspondence: [email protected]; Tel.: +39-0382-987315 Received: 30 July 2019; Accepted: 1 October 2019; Published: 10 October 2019 Abstract: Peptide-based drugs, despite being relegated as niche pharmaceuticals for years, are now capturing more and more attention from the scientific community. The main problem for these kinds of pharmacological compounds was the low degree of cellular uptake, which relegates the application of peptide-drugs to extracellular targets. In recent years, many new techniques have been developed in order to bypass the intrinsic problem of this kind of pharmaceuticals. One of these features is the use of stapled peptides. Stapled peptides consist of peptide chains that bring an external brace that force the peptide structure into an a-helical one. The cross-link is obtained by the linkage of the side chains of opportune-modified amino acids posed at the right distance inside the peptide chain. In this account, we report the main stapling methodologies currently employed or under development and the synthetic pathways involved in the amino acid modifications. Moreover, we report the results of two comparative studies upon different kinds of stapled-peptides, evaluating the properties given from each typology of staple to the target peptide and discussing the best choices for the use of this feature in peptide-drug synthesis. Keywords: stapled peptide; structurally constrained peptide; cellular uptake; helicity; peptide drugs 1. -
Calculating the Structure-Based Phylogenetic Relationship
CALCULATING THE STRUCTURE-BASED PHYLOGENETIC RELATIONSHIP OF DISTANTLY RELATED HOMOLOGOUS PROTEINS UTILIZING MAXIMUM LIKELIHOOD STRUCTURAL ALIGNMENT COMBINATORICS AND A NOVEL STRUCTURAL MOLECULAR CLOCK HYPOTHESIS A DISSERTATION IN Molecular Biology and Biochemistry and Cell Biology and Biophysics Presented to the Faculty of the University of Missouri-Kansas City in partial fulfillment of the requirements for the degree Doctor of Philosophy by SCOTT GARRETT FOY B.S., Southwest Baptist University, 2005 B.A., Truman State University, 2007 M.S., University of Missouri-Kansas City, 2009 Kansas City, Missouri 2013 © 2013 SCOTT GARRETT FOY ALL RIGHTS RESERVED CALCULATING THE STRUCTURE-BASED PHYLOGENETIC RELATIONSHIP OF DISTANTLY RELATED HOMOLOGOUS PROTEINS UTILIZING MAXIMUM LIKELIHOOD STRUCTURAL ALIGNMENT COMBINATORICS AND A NOVEL STRUCTURAL MOLECULAR CLOCK HYPOTHESIS Scott Garrett Foy, Candidate for the Doctor of Philosophy Degree University of Missouri-Kansas City, 2013 ABSTRACT Dendrograms establish the evolutionary relationships and homology of species, proteins, or genes. Homology modeling, ligand binding, and pharmaceutical testing all depend upon the homology ascertained by dendrograms. Regardless of the specific algorithm, all dendrograms that ascertain protein evolutionary homology are generated utilizing polypeptide sequences. However, because protein structures superiorly conserve homology and contain more biochemical information than their associated protein sequences, I hypothesize that utilizing the structure of a protein instead -
And Beta-Helical Protein Motifs
Soft Matter Mechanical Unfolding of Alpha- and Beta-helical Protein Motifs Journal: Soft Matter Manuscript ID SM-ART-10-2018-002046.R1 Article Type: Paper Date Submitted by the 28-Nov-2018 Author: Complete List of Authors: DeBenedictis, Elizabeth; Northwestern University Keten, Sinan; Northwestern University, Mechanical Engineering Page 1 of 10 Please doSoft not Matter adjust margins Soft Matter ARTICLE Mechanical Unfolding of Alpha- and Beta-helical Protein Motifs E. P. DeBenedictis and S. Keten* Received 24th September 2018, Alpha helices and beta sheets are the two most common secondary structure motifs in proteins. Beta-helical structures Accepted 00th January 20xx merge features of the two motifs, containing two or three beta-sheet faces connected by loops or turns in a single protein. Beta-helical structures form the basis of proteins with diverse mechanical functions such as bacterial adhesins, phage cell- DOI: 10.1039/x0xx00000x puncture devices, antifreeze proteins, and extracellular matrices. Alpha helices are commonly found in cellular and extracellular matrix components, whereas beta-helices such as curli fibrils are more common as bacterial and biofilm matrix www.rsc.org/ components. It is currently not known whether it may be advantageous to use one helical motif over the other for different structural and mechanical functions. To better understand the mechanical implications of using different helix motifs in networks, here we use Steered Molecular Dynamics (SMD) simulations to mechanically unfold multiple alpha- and beta- helical proteins at constant velocity at the single molecule scale. We focus on the energy dissipated during unfolding as a means of comparison between proteins and work normalized by protein characteristics (initial and final length, # H-bonds, # residues, etc.).