DOCSLIB.ORG

Biophysics of Knotting

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Biophysics of Knotting ANRV411-BB39-18 ARI 2 April 2010 11:20 Biophysics of Knotting Dario Meluzzi,1 Douglas E. Smith,2 and Gaurav Arya1 1Department of Nanoengineering and 2Department of Physics, University of California at San Diego, La Jolla, California 92093; email: [email protected], [email protected] Annu. Rev. Biophys. 2010. 39:349–66 by University of California - San Diego on 05/31/10. For personal use only. Key Words First published online as a Review in Advance on polymer physics, entanglement, DNA, proteins, topoisomerase Annu. Rev. Biophys. 2010.39:349-366. Downloaded from arjournals.annualreviews.org February 16, 2010 The Annual Review of Biophysics is online at Abstract biophys.annualreviews.org Knots appear in a wide variety of biophysical systems, ranging from This article’s doi: biopolymers, such as DNA and proteins, to macroscopic objects, such as 10.1146/annurev.biophys.093008.131412 umbilical cords and catheters. Although significant advancements have Copyright c 2010 by Annual Reviews. been made in the mathematical theory of knots and some progress has All rights reserved been made in the statistical mechanics of knots in idealized chains, the 1936-122X/10/0609-0349$20.00 mechanisms and dynamics of knotting in biophysical systems remain far from fully understood. We report on recent progress in the biophysics of knotting—the formation, characterization, and dynamics of knots in various biophysical contexts. 349 ANRV411-BB39-18 ARI 2 April 2010 11:20 variety of topics related to the biophysics of Contents knotting. The organization of these topics re- flects our attempt to address the following gen- INTRODUCTION .................. 350 eral questions: Where and how do knots form? TYPES OF KNOTS.................. 350 How likely are knots to form? What are some KNOTTING IN BIOPHYSICAL properties of knots and knotted systems? In SYSTEMS ........................ 352 what processes do knots play a role? When and PROBABILITIES OF how do knots disappear? In addressing these KNOTTING ..................... 354 questions, we aim for a qualitative presentation FEATURES OF KNOTTED of recent works, emphasizing the diversity of SYSTEMS ........................ 356 methods and results without delving extensively Size of Knots and Knotted into technical details. A more comprehensive Systems ........................ 356 treatment of specific topics can be found in Knot Localization.................. 357 books (1, 19) and in the various cited reviews. Strength and Stability of Knotted Systems ............. 357 DYNAMIC PROCESSES TYPES OF KNOTS INVOLVING KNOTS ............ 358 The ability to discern and classify different Knot Diffusion .................... 358 kinds of knots is an essential requirement for Electrophoresis .................... 359 understanding biophysical processes involving Unknotting ........................ 359 knots. The mathematical field of Knot theory CONCLUSION ..................... 361 offers powerful tools for detecting and classify- ing different knots (1). A knot is a topological state of a closed, nonintersecting curve. Two closed curves contain knots of the same type INTRODUCTION if one of the curves can be deformed in space Knots are fascinating topological objects that to match the other curve without temporarily have captured human imagination for centuries. opening either curve. In practice, a 3D knot- They find a plethora of useful applications, ted curve is mathematically analyzed by first from tying shoelaces to securing surgical su- projecting it onto a 2D plane and then exam- tures. But knots can also be a nuisance, crop- ining the points, known as crossings, where ping up in long hair, electrical cords, and other the curve crosses itself in the 2D projection inconvenient places. Equally important, knots (Figure 1a). Note that when we talk about are interesting subjects for scientific inquiry and knots in open curves, such as a linear string or by University of California - San Diego on 05/31/10. For personal use only. have attracted increasing attention from physi- DNA molecule, we are imagining that the ends cists and biophysicists: Various physically rel- of those curves are connected using a sensible, Annu. Rev. Biophys. 2010.39:349-366. Downloaded from arjournals.annualreviews.org evant systems have an undeniable capacity to well-defined procedure to yield corresponding become entangled. Notable examples include closed curves (Figure 1b). biopolymers such as DNA and proteins. An The absence of a knot is called the unknot understanding of these knots beyond the con- or trivial knot. It can always be rearranged to fines of mathematical topology and theoretical yield a projection with zero crossings. Knots, in physics is essential to bring about new discov- contrast, give rise to projections with nonzero eries and practical applications in biology and numbers of crossings. The minimum number Knot: a topological nanotechnology. of crossings, C, is an invariant for any arrange- state of a closed 3D Here we describe some recent experimen- ment of a closed string with a given knot. C curve, also a knot-like tal and theoretical efforts in the biophysics is often used to classify knots into different conformation of an open chain of knotting. We begin with a brief introduc- types. Specifically, each knot type is denoted tion to knot classification. We then explore a as CS, where S is a sequence number within 350 Meluzzi · Smith · Arya ANRV411-BB39-18 ARI 2 April 2010 11:20 a b Projection Open curve Closed curve c d 31 q–1 + q–3 – q–4 Trefoil 4 2 –1 –2 1 q – q + 1 –q + q Figure-eight SK SP 51 q–2 + q–4 – q–5 + q–6 – q–7 S 52 q–1 – q–2 + 2q–3 – q–4 + q–5 – q–6 K SP e f g Square Granny Slipknot D knot knot SK S K Figure 1 Knot types and features. (a) Knots formally exist only in 3D curves (left). Knot projections are 2D representations of knots (right). (b) Knot-like conformations in open curves are often encountered in biophysics (left). To analyze such knots, their loose ends must be connected, according to some procedure, to obtain a closed curve (right). (c) Projections of the four simplest nontrivial knot types, with the corresponding CS denominations and Jones polynomials (see text for definition of CS) (adapted from http://katlas.math. toronto.edu/wiki/Main Page). (d ) The size of a knot, SK , in a polymer may be less than the size of the polymer, SP, containing the knot. (e) In a slip link arrangement, entropic competition between the knotted loops causes the ring to squeeze one of the knots. The size of the latter can be deduced from the position of by University of California - San Diego on 05/31/10. For personal use only. the ring. Adapted from Reference 64. ( f ) The size of a tight knot can be estimated from the volume of the ∼ 2 1/3 enclosing ideal knot representation: SK (D L) , where D and L are the diameter and length of the outer Annu. Rev. Biophys. 2010.39:349-366. Downloaded from arjournals.annualreviews.org tube. Adapted from Reference 39. ( g) Square and granny knots can tie ropes together but unravel easily at the molecular scale. Slipknots in proteins have been studied to assess the effects of knots on stability. the family of knot types having the same C Simple knots can be distinguished visually (Figure 1c). Some common knots are also re- by comparison with published tables, but ex- ferred to by name: 31 and 41 are called trefoil tensively knotted systems require mathematical and figure-eight, respectively. The number of methods of knot classification. One ingenious different knot types having the same C increases strategy for classifying knots is to transform rapidly with C: There are only 3 knots with 6 a knot projection into a special polynomial crossings, but 1,388,705 knots with 16 cross- formula, which depends on the knot type but ings (42). The number C serves as a measure of not on any particular projection. Comparing knot complexity. this polynomial with those enumerated in www.annualreviews.org • Biophysics of Knotting 351 ANRV411-BB39-18 ARI 2 April 2010 11:20 knot tables enables the identification of the chain segments, is facilitated by enzymes such as knot type from a given projection. Examples topoisomerases and recombinases. Fundamen- of such polynomials include the Alexander, tal insights into the mechanisms of these and Jones polynomial: a mathematical Jones, and HOMFLY polynomials (1). V.F.R. other enzymes have resulted from detailed anal- expression that can be Jones was awarded the famous Fields Medal in yses of knots in DNA (13, 59, 98, 115). computed by analyzing mathematics in 1990 for his groundbreaking DNA topoisomerases are classified as type I the crossings in discovery of the Jones polynomial. These or type II (93). Type I DNA topoisomerases any particular 2D pro- polynomials occasionally fail to distinguish temporarily break a single DNA strand and jection of a knot, and serves as fingerprint different knots and become computationally allow it to pass through the complementary to uniquely identify prohibitive with projections of many crossings, strand (7). Knotted dsDNA results when cir- the type of the knot but they are invaluable tools for analyzing the cular dsDNA is nicked or gapped and the en- dsDNA: vast majority of simpler knots. zyme breaks a strand at a location opposite double-stranded DNA the nick (23). In contrast, type II topoisom- DNA erases temporarily break both strands in one topoisomerases: KNOTTING IN BIOPHYSICAL segment of dsDNA, allowing one segment to enzymes that allow SYSTEMS pass through another intact segment before the single or double Knots can form via two general mechanisms: strands are chemically rejoined (72, 93). Type strands of DNA to pass through other single threading of loose ends or breaking and re- II DNA topoisomerases introduce knots into or double strands of joining of segments. Linear double-stranded supercoiled circular DNA in vitro (114), pro- DNA to change the DNA (dsDNA) molecules undergoing random viding a way to assess the DNA supercoiling topology of a closed cyclization in solution exemplify the first mech- activity of other enzymes, such as condensins dsDNA molecule anism.
Load more

Recommended publications
  • Molecular Knots in Biology and Chemistry
    Molecular Knots in Biology and Chemistry Nicole C. H. Lim1,2 and Sophie E. Jackson1 1Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom 2Faculty of Sciences, Universiti Brunei Darussalam, Gadong BE 1410, Brunei Darussalam E-mails: [email protected] and [email protected] Abstract Knots and entanglements are ubiquitous. Beyond their aesthetic appeal, these fascinating topological entities can be either useful or cumbersome. In recent decades, the importance and prevalence of molecular knots have been increasingly recognised by scientists from different disciplines. In this review, we provide an overview on the various molecular knots found in naturally occurring biological systems (DNA, RNA and proteins), and those created by synthetic chemists. We discuss the current knowledge in these fields, including recent developments in experimental and, in some cases, computational studies which are beginning to shed light into the complex interplay between the structure, formation and properties of these topologically intricate molecules. 2 1. Introduction Knots and entanglements are common topological features observed not only in the macroscopic world, but also at the molecular level (Figure 1). In everyday life, they can be found in various useful applications, from applying surgical sutures to tying shoelaces. However, in some cases, knots can be a nuisance, for example, they can form spontaneously in electrical cables, headphones and garden pipes. They can also lead to undesirable outcomes such as the obstruction of blood circulation to the fetus when tight knots form in the umbilical cord during human pregnancy [1]. Recently, the importance and prevalence of knots at a molecular level have become truly apparent and this has attracted increasing interest from scientists in different fields.
    [Show full text]
  • Making Molecular Machines
    CONVERSATIONS WITH SCIENTISTS David A. Leigh: Making Molecular Machines "In the field of molecular machines I think the most important development of the last 20 years is the understanding of how to get directional motion from random Brownian motion. It is the key to making molecular motors and, ultimately, all sophisticated molecular machines." University of Manchester David A. Leigh is a Royal Society Research Professor and, since 2014, the Sir Samuel Hall Chair of Chemistry at the University of Manchester in the United Kingdom. Born in 1963 in Birmingham, England, Leigh earned a bachelor's degree in chemistry from the UK's University of Sheffield in 1984 and received a Ph.D from the same institution in 1987. For the next two years, Leigh worked as a postdoctoral research associate at the National Research Council of Canada in Ottawa. He returned to Britain in 1989 to lecture in organic chemistry at the University of Manchester Institute of Science and Technology. In 1998, Leigh moved on to a chair in synthetic chemistry at the University of Warwick and, in 2001 accepted a chair in organic chemistry at the University of Edinburgh. In 2012, Leigh joined the University of Manchester faculty. Leigh is the recipient of numerous honors and awards. He has received research fellowships from the Engineering and Physical Science Research Council and from the European Research Council. His awards include the Feynman Prize for Nanotechnology, the Descartes Prize for Research, and several awards from the Royal Society of Chemistry. He is a fellow of such prestigious associations as the Royal Society of London and the Academia Europaea.
    [Show full text]
  • Tying the Knot: Applications of Topology to Chemistry
    Colby College Digital Commons @ Colby Honors Theses Student Research 2017 Tying the Knot: Applications of Topology to Chemistry Tarini S. Hardikar Follow this and additional works at: https://digitalcommons.colby.edu/honorstheses Part of the Geometry and Topology Commons, and the Other Chemistry Commons Colby College theses are protected by copyright. They may be viewed or downloaded from this site for the purposes of research and scholarship. Reproduction or distribution for commercial purposes is prohibited without written permission of the author. Recommended Citation Hardikar, Tarini S., "Tying the Knot: Applications of Topology to Chemistry" (2017). Honors Theses. Paper 857. https://digitalcommons.colby.edu/honorstheses/857 This Honors Thesis (Open Access) is brought to you for free and open access by the Student Research at Digital Commons @ Colby. It has been accepted for inclusion in Honors Theses by an authorized administrator of Digital Commons @ Colby. Tying the Knot: Applications of Topology to Chemistry TARINI S. HARDIKAR A Thesis Presented to the Department of Mathematics, Colby College, Waterville, ME In Partial Fulfillment of the Requirements for Graduation With Honors in Mathematics SUBMITTED MAY 2017 Tying the Knot: Applications of Topology to Chemistry TARINI S. HARDIKAR Approved: (Mentor: Professor Scott A. Taylor, Associate Professor of Mathematics) (Reader: Professor Jan E. Holly, Professor of Mathematics) “YOU HAVE TO SPEND SOME ENERGY AND EFFORT TO SEE THE BEAUTY OF MATH” - Maryam Mirzakhani “I WISH THE FIGURE EIGHT KNOT WAS THE EIGHTH FIGURE, BUT IT IS KNOT.” Acknowledgements I would like to begin by thanking my mentor, Professor Scott Taylor. Scott has been an incredible pillar of support, advice, and encouragement since my very first year at Colby.
    [Show full text]
  • Molecular Catenanes, Rotaxanes and Knots
    Molecular Catenanes, Rotaxanes and Knots A Journey Through the World of Molecular Topology Edited by J.-P. Sauvage and C. Dietrich-Buchecker Weinheim - New York * Chichester Brisbane - Singapore Toronto This Page Intentionally Left Blank Molecular Catenanes, Rotaxanes and Knots Edited by J.-P. Sauvage and C. Dietrich-Buchecker Further Titles of Interest N. V. Gerbeleu, V. B. Arion, J. Burgess Template Synthesis of Macrocyclic Compounds 1999, ISBN 3-527-29559-3 K. Riick-Braun, H. Kunz Chiral Auxiliaries in Cycloadditions 1999, ISBN 3-527-29386-8 F. T. Edelmann, I. Haiduc Supramolecular Organometallic Chemistry 1999, ISBN 3-527-29533-X 0. I. Kolodiazhnyi Phosphorus Ylides Chemistry and Application in Organic Synthesis 1999, ISBN 3-527-29531-3 Molecular Catenanes, Rotaxanes and Knots A Journey Through the World of Molecular Topology Edited by J.-P. Sauvage and C. Dietrich-Buchecker Weinheim - New York * Chichester Brisbane - Singapore Toronto Prof. Dr. Jean-Pierre Sauvage Prof. Dr. Christiane Dietrich-Buchecker Facult6 de Chimie Universit6 Louis Pasteur 4, rue Blaise Pascal F-67070 Strasbourg CCdex France This book was carefully produced. Nevertheless, authors, editors and publisher do not warrant the information contained therein to be free of errors. Readers are advised to keep in mind that state- ments, data, illustrations, procedural details or other items may inadvertently be inaccurate. Cover Illustration: Prof. Dr. J. S. Siegel, La Jolla, USA / Dr. K. Baldridge, San Diego, USA Library of Congress Card No. applied for. A catalogue record for this book is available from the British Library. Deutsche Bibliothek Cataloging-in-PublicationData: Molecular catanes, mtaxanes and knots : a journey through the world of molecular topology I E.
    [Show full text]
  • CV De Jean-Pierre Sauvage, Membre De L'académie Des Sciences
    Jean-Pierre Sauvage Élu Correspondant le 26 mars 1990, puis membre le 24 novembre 1997, dans la section de chimie ISIS, 8 allée Gaspard Monge F-67000 Strasbourg tel. +33(0)3 68 85 51 43 [email protected] Professional Career : 2009 ~present Professor Emeritus (University of Strasbourg), CNRS Director of Research Emeritus, Distinguished Visiting Scholar at Northwestern University (2010-2012) and Visiting Professor at University of Zurich (2009-2010) 1979~2009 CNRS Director of Research 1981~1984 University Professor 1971~1979 CNRS Research Fellow 20 Representative Publications : 1) C.O. Dietrich-Buchecker, J.-P. Sauvage, J.-P. Kintzinger, "Une Nouvelle Famille de Molécules : les Métallo-Caténanes", Tet. Letters, 24, 5095 (1983). 2) C.O. Dietrich-Buchecker, J.-P. Sauvage, J.-M. Kern, "Templated Synthesis of Interlocked Macrocyclic Ligands : The Catenands", J. Am. Chem. Soc., 106, 3043 (1984). 3) M. Beley, J.-P. Collin, R. Ruppert, J.-P. Sauvage, "Nickel(II)-cyclam : An Extremely Selective Electrocatalyst for Reduction of CO2 in Water", Chem. Comm., 1315 (1984). 1 4) M. Cesario, C.O. Dietrich-Buchecker, J. Guilhem, C. Pascard, J.-P. Sauvage, "Molecular Structure of a Catenand and its Copper(I) Catenate : Complete Rearrangement of the Interlocked Macrocyclic Ligands by Complexation", Chem. Comm., 244 (1985). 2+ 5) J.-C. Chambron, J.-P. Sauvage, E. Amouyal, P. Koffi, "Ru(bipy)2(dipyridophénazine) : A Complex with a Long Range Directed Charge Transfer Excited State", Nouv. J. Chim., 9, 527 (1985). 6) C.O. Dietrich-Buchecker, A. Khemiss, J.-P. Sauvage, "High Yield Synthesis of Multiring Copper(I) Catenates by Acetylenic Oxidative Coupling", Chem.
    [Show full text]
  • Knots and Links
    GENERAL I ARTICLE Knots and Links K L Sebastian Knots appear in a variety of contexts in physics, chemistry and biology. This article is an intro­ duction to the science of knots and links for the uninitiated and it outlines why scientists find them fascinating. 1. Knotted Fish Think of an organism that has four hearts, one nostril, K L Sebastian is a no stomach but with teeth on its tongue! This may seem Professor in the Depart­ like creature out of a science fiction story, but a fish with ment of Inorganic and Physical Chemistry, all these attributes exists. It is the hagfish, which is one Indian Institute of of the lowest forms of fish and is an archaic (very old) Science, Bangalore. His form of life. It can secrete a thick slime on its skin, which area of interest is makes the fish very slippery to hold. Because of this, theoretical chemistry. it is also known as the slime eel. The hagfish usually burrows into either dead or live fish and eats the flesh and internal organs. It takes hold of the flesh using its teeth and pulls it out. The most surprising thing about the hagfish is that, if it needs extra leverage to pull the flesh out, it loops itself into a knot and presses the knot against the body of the prey, as shown in Figure 1. The knot that it makes is known as the half hitch. If you take hold of the hagfish, it would then secrete the slime and use the knot mechanism to pull itself out.
    [Show full text]
  • Molecular Catenanes, Rotaxanes and Knots
    Molecular Catenanes, Rotaxanes and Knots A Journey Through the World of Molecular Topology Edited by J.-P. Sauvage and C. Dietrich-Buchecker WILEY-VCH Weinheim • New York • Chichester Brisbane • Singapore • Toronto Contents 1 Chemical Topology - Statistical Musings 1 1.1 Catenanes 1 1.2 Olefin Metathesis 3 1.3 Knots 4 References 6 2 A Knot Theoretic Approach to Molecular Chirality 7 2.1 Topological Chirality of Knots and Links 7 2.2 Topological Chirality of Embedded Graphs 14 2.3 Topological Chirality of Molecular Knots and Links 16 2.4 Topological Chirality of Molecular Cell Complexes 18 2.5 Molecular Möbius Ladders and Related Molecules 21 2.6 Using Automorphisms to Prove Intrinsic Chirality 31 References 34 3 Soft and Hard Molecule-Based Magnets with a Fully Interlocked Three-Dimensional Structure 37 3.1 Introduction 37 3.2 Molecular Magnetism 37 3.3 Magnetic Bricks 39 3.4 A Game of Bricks and Pieces of Mortar 40 3.5 Structure of Molecule-Based Magnets Containing Three Spin Carriers, with a Fully Interlocked Structure 44 3.6 Magnetic Properties 48 3.6.1 The Temperature Dependence of Magnetic Susceptibility 48 3.6.2 Field Dependencies of the Magnetization 51 3.7 Some Further Considerations 53 3.8 A Few Words to Conclude 54 References 55 Contents 4 Transition Metal-Incorporating Catenanes 57 4.1 Introduction 57 4.2 Interlocked Compounds Containing Metals 58 4.2.1 Metal-Containing Rotaxanes 59 4.2.2 Metal-Templated Synthesis of Catenanes 59 4.2.3 Organometallic Catenanes and Rotaxanes 60 4.2.4 Self-Assembly of a [2]Catenane Incorporating (en)Pd(H) Units ...
    [Show full text]
  • Effects of Knot Tightness at the Molecular Level
    Effects of knot tightness at the molecular level Liang Zhanga,b, Jean-François Lemonnierb, Angela Acocellac, Matteo Calvaresic, Francesco Zerbettoc,1, and David A. Leigha,b,1 aSchool of Chemistry and Molecular Engineering, East China Normal University, 200062 Shanghai, China; bSchool of Chemistry, University of Manchester, M13 9PL Manchester, United Kingdom; and cDipartimento di Chimica “G. Ciamician”, Università di Bologna, 40126 Bologna, Italy Edited by Michael L. Klein, Institute of Computational Molecular Science, Temple University, Philadelphia, PA 19122, and approved December 18, 2018 (received for review September 8, 2018) Three 819 knots in closed-loop strands of different lengths (∼20, by analogy to that previously used to prepare 1 (29). Treatment of 23, and 26 nm) were used to experimentally assess the conse- the ligands with equimolar amounts of FeCl2, followed by ring- quences of knot tightness at the molecular level. Through the closing metathesis (30), gave the corresponding 819 knot com- 1 use of H NMR, diffusion-ordered spectroscopy (DOSY), circular plexes [Fe4Knot](PF6)8 (Knot = 1–3; Fig. 1) which were isolated dichroism (CD), collision-induced dissociation mass spectrometry and characterized by electrospray ionization mass spectrometry (CID-MS) and molecular dynamics (MD) simulations on the different- and 1H NMR spectroscopy (SI Appendix, Figs. S1–S8). The 1H sized knots, we find that the structure, dynamics, and reactivity of NMR spectra of the three knotted complexes are essentially su- the molecular chains are dramatically affected by the tightness of perimposable (SI Appendix, Figs. S14 and S15), other than the the knotting. The tautness of entanglement causes differences in alkyl region due to the differences in chain length, indicating that conformation, enhances the expression of topological chirality, metal coordination of the knotted ligands holds the three com- weakens covalent bonds, inhibits decomplexation events, and plexes in similar conformations.
    [Show full text]
  • Open Questions in Functional Molecular Topology
    COMMENT https://doi.org/10.1038/s42004-020-00433-7 OPEN Open questions in functional molecular topology ✉ Fredrik Schaufelberger 1 1234567890():,; Molecular knots are evolving from academic curiosities to a practically useful class of mechanically interlocked molecules, capable of performing unique tasks at the nanoscale. In this comment, the author discusses the properties of molecular knots, and highlights future challenges for chemical topology. Everyone is familiar with macroscopic knots, be they bow knots in shoelaces or stopper knots used to secure sewing threads. Since it is well known that specific knots can be tied for a desired function, it is perhaps surprising it took chemists so long to realize that knotting leads to functional advantages at the molecular level as well. Mathematicians define all closed loops as knots, and characterize them by the number of persistent crossing points in their reduced 2D projection. In mathematical terms, a common – non-interlocked macrocycle is an unknot (01 in Alexander Briggs notation, also called a 1 topologically trivial knot), while the simplest prime knot is the three-crossing trefoil knot (31) . Molecular topology concerns molecules with non-planar graphs, i. e. structures that remains entangled even when the physical limitations of molecules such as bond lengths, strain and sterics are ignored. When considering the three main classes of mechanically interlocked molecules, catenanes and knots are thus topologically non-trivial, while rotaxanes are trivial (because hypothetically, stretching a macrocycle wide enough will always enable slippage)2. Since the seminal synthesis of a metal-templated molecular trefoil knot by Sauvage in 19893, the field has evolved immensely.
    [Show full text]
  • Molecular Catenanes,Rotaxanes and Knots, a Journey Through The
    Molecular Catenanes, Rotaxanes and Knots Edited by J.-P. Sauvage and C. Dietrich-Buchecker Further Titles of Interest N. V. Gerbeleu, V. B. Arion, J. Burgess Template Synthesis of Macrocyclic Compounds 1999, ISBN 3-527-29559-3 K. Riick-Braun, H. Kunz Chiral Auxiliaries in Cycloadditions 1999, ISBN 3-527-29386-8 F. T. Edelmann, I. Haiduc Supramolecular Organometallic Chemistry 1999, ISBN 3-527-29533-X 0. I. Kolodiazhnyi Phosphorus Ylides Chemistry and Application in Organic Synthesis 1999, ISBN 3-527-29531-3 Molecular Catenanes, Rotaxanes and Knots A Journey Through the World of Molecular Topology Edited by J.-P. Sauvage and C. Dietrich-Buchecker Weinheim - New York * Chichester Brisbane - Singapore Toronto Prof. Dr. Jean-Pierre Sauvage Prof. Dr. Christiane Dietrich-Buchecker Facult6 de Chimie Universit6 Louis Pasteur 4, rue Blaise Pascal F-67070 Strasbourg CCdex France This book was carefully produced. Nevertheless, authors, editors and publisher do not warrant the information contained therein to be free of errors. Readers are advised to keep in mind that state- ments, data, illustrations, procedural details or other items may inadvertently be inaccurate. Cover Illustration: Prof. Dr. J. S. Siegel, La Jolla, USA / Dr. K. Baldridge, San Diego, USA Library of Congress Card No. applied for. A catalogue record for this book is available from the British Library. Deutsche Bibliothek Cataloging-in-PublicationData: Molecular catanes, mtaxanes and knots : a journey through the world of molecular topology I E. Wassermann . Ed. by J.-P. Sauvage and C. Dietrich-Buchecker.- Weinheim ; New York ; Chichester ; Brisbane ; Singapore ; Toronto : Wiley-VCH, 1999 ISBN 3-527-29572-0 0 WILEY-VCH Verlag GmbH, D-69469 Weinheim (Federal Republic of Germany), 1999 Printed on acid-free and chlorine-free paper.
    [Show full text]
  • DNA Knotting: Occurrences, Consequences & Resolution Jennifer Katherine Mann
    Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2007 DNA Knotting: Occurrences, Consequences & Resolution Jennifer Katherine Mann Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] THE FLORIDA STATE UNIVERSITY COLLEGE OF ARTS & SCIENCES DNA KNOTTING: OCCURRENCES, CONSEQUENCES & RESOLUTION By JENNIFER KATHERINE MANN A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy Degree Awarded: Spring Semester, 2007 Copyright © 2007 Jennifer K. Mann All Rights Reserved The members of the Committee approve the Dissertation of Jennifer Katherine Mann defended on February 28, 2007. De Witt L. Sumners Professor Co-Directing Dissertation E. Lynn Zechiedrich Professor Co-Directing Dissertation Nancy L. Greenbaum Outside Committee Member Wolfgang Heil Committee Member Jack Quine Committee Member Approved: Philip L. Bowers, Chair, Mathematics Joseph Travis, Dean, Arts & Sciences The Office of Graduate Studies has verified and approved the above named committee members. ii The dissertation is dedicated to Nicholas R. Cozzarelli, Ph.D. (1938 – 2006). iii ACKNOWLEDGEMENTS I sincerely thank my advisor Dr. De Witt L. Sumners for being a motivating, fair, encouraging, honest, challenging, supportive, and involved mentor. Dr. Sumners’ work led me into biomedical mathematics, and he made possible for me many unique educational experiences. I especially thank Dr. Lynn Zechiedrich for allowing a mathematician to move into her lab and do experiments for five years. In Dr. Zechiedrich’s lab I was allowed to continue to be a mathematician as I also became a molecular biologist and biochemist.
    [Show full text]
  • Knot Theory in Modern Chemistry
    Chemical Society Reviews Knot Theory in Modern Chemistry Journal: Chemical Society Reviews Manuscript ID CS-TRV-06-2016-000448.R1 Article Type: Tutorial Review Date Submitted by the Author: 10-Aug-2016 Complete List of Authors: Horner, Kate; Durham University, Department of Mathematical Sciences Miller, Mark; Durham University, Department of Chemistry Steed, Jonathan; Durham University, Department of Chemistry Sutcliffe, Paul; Durham University, Department of Mathematical Sciences Page 1 of 16 Chemical Society Reviews Journal Name RSC Publishing ARTICLE Knot Theory in Modern Chemistry a b b a Cite this: DOI: 10.1039/x0xx00000x Kate E. Horner,* Mark A. Miller, Jonathan W. Steed and Paul M. Sutcliffe Knot theory is a branch of pure mathematics, but it is increasingly being applied in a variety of sciences. Knots appear in chemistry, not only in synthetic molecular design, but also in an Received 00th January 2012, array of materials and media, including some not traditionally associated with knots. Accepted 00th January 2012 Mathematics and chemistry can now be used synergistically to identify, characterise and create DOI: 10.1039/x0xx00000x knots, as well as to understand and predict their physical properties. This tutorial review provides a brief introduction to the mathematics of knots and related topological concepts in www.rsc.org/ the context of the chemical sciences. We then survey the broad range of applications of the theory to contemporary research in the field. Key Learning Points development of modern knot theory, which today is an area of mathematics within the field of topology. In 1867, Sir William • Some fundamentals of knot theory. Thomson (later to become Lord Kelvin) proposed that atoms • Knot theory and closely related ideas in topology can are composed of knotted vortices of the aether.
    [Show full text]