Effect of Superhelical Structure on the Secondary Structure of DNA Rings
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Engineering Curves – I
Engineering Curves – I 1. Classification 2. Conic sections - explanation 3. Common Definition 4. Ellipse – ( six methods of construction) 5. Parabola – ( Three methods of construction) 6. Hyperbola – ( Three methods of construction ) 7. Methods of drawing Tangents & Normals ( four cases) Engineering Curves – II 1. Classification 2. Definitions 3. Involutes - (five cases) 4. Cycloid 5. Trochoids – (Superior and Inferior) 6. Epic cycloid and Hypo - cycloid 7. Spiral (Two cases) 8. Helix – on cylinder & on cone 9. Methods of drawing Tangents and Normals (Three cases) ENGINEERING CURVES Part- I {Conic Sections} ELLIPSE PARABOLA HYPERBOLA 1.Concentric Circle Method 1.Rectangle Method 1.Rectangular Hyperbola (coordinates given) 2.Rectangle Method 2 Method of Tangents ( Triangle Method) 2 Rectangular Hyperbola 3.Oblong Method (P-V diagram - Equation given) 3.Basic Locus Method 4.Arcs of Circle Method (Directrix – focus) 3.Basic Locus Method (Directrix – focus) 5.Rhombus Metho 6.Basic Locus Method Methods of Drawing (Directrix – focus) Tangents & Normals To These Curves. CONIC SECTIONS ELLIPSE, PARABOLA AND HYPERBOLA ARE CALLED CONIC SECTIONS BECAUSE THESE CURVES APPEAR ON THE SURFACE OF A CONE WHEN IT IS CUT BY SOME TYPICAL CUTTING PLANES. OBSERVE ILLUSTRATIONS GIVEN BELOW.. Ellipse Section Plane Section Plane Hyperbola Through Generators Parallel to Axis. Section Plane Parallel to end generator. COMMON DEFINATION OF ELLIPSE, PARABOLA & HYPERBOLA: These are the loci of points moving in a plane such that the ratio of it’s distances from a fixed point And a fixed line always remains constant. The Ratio is called ECCENTRICITY. (E) A) For Ellipse E<1 B) For Parabola E=1 C) For Hyperbola E>1 Refer Problem nos. -
A Characterization of Helical Polynomial Curves of Any Degree
A CHARACTERIZATION OF HELICAL POLYNOMIAL CURVES OF ANY DEGREE J. MONTERDE Abstract. We give a full characterization of helical polynomial curves of any degree and a simple way to construct them. Existing results about Hermite interpolation are revisited. A simple method to select the best quintic interpolant among all possible solutions is suggested. 1. Introduction The notion of helical polynomial curves, i.e, polynomial curves which made a constant angle with a ¯xed line in space, have been studied by di®erent authors. Let us cite the papers [5, 6, 7] where the main results about the cubical and quintic cases are stablished. In [5] the authors gives a necessary condition a polynomial curve must satisfy in order to be a helix. The condition is expressed in terms of its hodograph, i.e., its derivative. If a polynomial curve, ®, is a helix then its hodograph, ®0, must be Pythagorean, i.e., jj®0jj2 is a perfect square of a polynomial. Moreover, this condition is su±cient in the cubical case: all PH cubical curves are helices. In the same paper it is also stated that not only ®0 must be Pythagorean, but also ®0^®00. Following the same ideas, in [1] it is proved that both conditions are su±cient in the quintic case. Unfortunately, this characterization is no longer true for higher degrees. It is possible to construct examples of polynomial curves of degree 7 verifying both conditions but being not a helix. The aim of this paper is just to show how a simple geometric trick can clarify the proofs of some previous results and to simplify the needed compu- tations to solve some related problems as for instance, the Hermite problem using helical polynomial curves. -
Linguistic Presentation of Objects
Zygmunt Ryznar dr emeritus Cracow Poland [email protected] Linguistic presentation of objects (types,structures,relations) Abstract Paper presents phrases for object specification in terms of structure, relations and dynamics. An applied notation provides a very concise (less words more contents) description of object. Keywords object relations, role, object type, object dynamics, geometric presentation Introduction This paper is based on OSL (Object Specification Language) [3] dedicated to present the various structures of objects, their relations and dynamics (events, actions and processes). Jay W.Forrester author of fundamental work "Industrial Dynamics”[4] considers the importance of relations: “the structure of interconnections and the interactions are often far more important than the parts of system”. Notation <!...> comment < > container of (phrase,name...) ≡> link to something external (outside of definition)) <def > </def> start-end of definition <spec> </spec> start-end of specification <beg> <end> start-end of section [..] or {..} 1 list of assigned keywords :[ or :{ structure ^<name> optional item (..) list of items xxxx(..) name of list = value assignment @ mark of special attribute,feature,property @dark unknown, to obtain, to discover :: belongs to : equivalent name (e.g.shortname) # number of |name| executive/operational object ppppXxxx name of item Xxxx with prefix ‘pppp ‘ XXXX basic object UUUU.xxxx xxxx object belonged to UUUU object class & / conjunctions ‘and’ ‘or’ 1 If using Latex editor we suggest [..] brackets -
Helical Curves and Double Pythagorean Hodographs
Helical polynomial curves and “double” Pythagorean-hodograph curves Rida T. Farouki Department of Mechanical & Aeronautical Engineering, University of California, Davis — synopsis — • introduction: properties of Pythagorean-hodograph curves • computing rotation-minimizing frames on spatial PH curves • helical polynomial space curves — are always PH curves • standard quaternion representation for spatial PH curves • “double” Pythagorean hodograph structure — requires both |r0(t)| and |r0(t) × r00(t)| to be polynomials in t • Hermite interpolation problem: selection of free parameters Pythagorean-hodograph (PH) curves r(ξ) = PH curve ⇐⇒ coordinate components of r0(ξ) comprise a “Pythagorean n-tuple of polynomials” in Rn PH curves incorporate special algebraic structures in their hodographs (complex number & quaternion models for planar & spatial PH curves) • rational offset curves rd(ξ) = r(ξ) + d n(ξ) Z ξ • polynomial arc-length function s(ξ) = |r0(ξ)| dξ 0 Z 1 • closed-form evaluation of energy integral E = κ2 ds 0 • real-time CNC interpolators, rotation-minimizing frames, etc. helical polynomial space curves several equivalent characterizations of helical curves • tangent t maintains constant inclination ψ with fixed vector a • a · t = cos ψ, where ψ = pitch angle and a = axis vector of helix • fixed curvature/torsion ratio, κ/τ = tan ψ (Theorem of Lancret) • curve has a circular tangent indicatrix on the unit sphere (small circle for space curve, great circle for planar curve) • (r(2) × r(3)) · r(4) ≡ 0 — where r(k) = kth arc–length derivative -
Chapter 2. Parameterized Curves in R3
Chapter 2. Parameterized Curves in R3 Def. A smooth curve in R3 is a smooth map σ :(a, b) → R3. For each t ∈ (a, b), σ(t) ∈ R3. As t increases from a to b, σ(t) traces out a curve in R3. In terms of components, σ(t) = (x(t), y(t), z(t)) , (1) or x = x(t) σ : y = y(t) a < t < b , z = z(t) dσ velocity at time t: (t) = σ0(t) = (x0(t), y0(t), z0(t)) . dt dσ speed at time t: (t) = |σ0(t)| dt Ex. σ : R → R3, σ(t) = (r cos t, r sin t, 0) - the standard parameterization of the unit circle, x = r cos t σ : y = r sin t z = 0 σ0(t) = (−r sin t, r cos t, 0) |σ0(t)| = r (constant speed) 1 Ex. σ : R → R3, σ(t) = (r cos t, r sin t, ht), r, h > 0 constants (helix). σ0(t) = (−r sin t, r cos t, h) √ |σ0(t)| = r2 + h2 (constant) Def A regular curve in R3 is a smooth curve σ :(a, b) → R3 such that σ0(t) 6= 0 for all t ∈ (a, b). That is, a regular curve is a smooth curve with everywhere nonzero velocity. Ex. Examples above are regular. Ex. σ : R → R3, σ(t) = (t3, t2, 0). σ is smooth, but not regular: σ0(t) = (3t2, 2t, 0) , σ0(0) = (0, 0, 0) Graph: x = t3 y = t2 = (x1/3)2 σ : y = t2 ⇒ y = x2/3 z = 0 There is a cusp, not because the curve isn’t smooth, but because the velocity = 0 at the origin. -
Topography of the Histone Octamer Surface: Repeating Structural Motifs Utilized in the Docking of Nucleosomal
Proc. Natl. Acad. Sci. USA Vol. 90, pp. 10489-10493, November 1993 Biochemistry Topography of the histone octamer surface: Repeating structural motifs utilized in the docking of nucleosomal DNA (histone fold/helix-strand-helix motif/parallel fi bridge/binary DNA binding sites/nucleosome) GINA ARENTS* AND EVANGELOS N. MOUDRIANAKIS*t *Department of Biology, The Johns Hopkins University, Baltimore, MD 21218; and tDepartment of Biology, University of Athens, Athens, Greece Communicated by Christian B. Anfinsen, August 5, 1993 ABSTRACT The histone octamer core of the nucleosome is interactions. The model offers strong predictive criteria for a protein superhelix offour spirally arrayed histone dimers. The structural and genetic biology. cylindrical face of this superhelix is marked by intradimer and interdimer pseudodyad axes, which derive from the nature ofthe METHODS histone fold. The histone fold appears as the result of a tandem, parallel duplication of the "helix-strand-helix" motif. This The determination of the structure of the histone octamer at motif, by its occurrence in the four dimers, gives rise torepetitive 3.1 A has been described (3). The overall shape and volume structural elements-i.e., the "parallel 13 bridges" and the of this tripartite structure is in agreement with the results of "paired ends of helix I" motifs. A preponderance of positive three independent studies based on differing methodolo- charges on the surface of the octamer appears as a left-handed gies-i.e., x-ray diffraction, neutron diffraction, and electron spiral situated at the expected path of the DNA. We have microscopic image reconstruction (4-6). Furthermore, the matched a subset of DNA pseudodyads with the octamer identification of the histone fold, a tertiary structure motif of pseudodyads and thus have built a model of the nucleosome. -
Chapter 6 Protein Structure and Folding
Chapter 6 Protein Structure and Folding 1. Secondary Structure 2. Tertiary Structure 3. Quaternary Structure and Symmetry 4. Protein Stability 5. Protein Folding Myoglobin Introduction 1. Proteins were long thought to be colloids of random structure 2. 1934, crystal of pepsin in X-ray beam produces discrete diffraction pattern -> atoms are ordered 3. 1958 first X-ray structure solved, sperm whale myoglobin, no structural regularity observed 4. Today, approx 50’000 structures solved => remarkable degree of structural regularity observed Hierarchy of Structural Layers 1. Primary structure: amino acid sequence 2. Secondary structure: local arrangement of peptide backbone 3. Tertiary structure: three dimensional arrangement of all atoms, peptide backbone and amino acid side chains 4. Quaternary structure: spatial arrangement of subunits 1) Secondary Structure A) The planar peptide group limits polypeptide conformations The peptide group ha a rigid, planar structure as a consequence of resonance interactions that give the peptide bond ~40% double bond character The trans peptide group The peptide group assumes the trans conformation 8 kJ/mol mire stable than cis Except Pro, followed by cis in 10% Torsion angles between peptide groups describe polypeptide chain conformations The backbone is a chain of planar peptide groups The conformation of the backbone can be described by the torsion angles (dihedral angles, rotation angles) around the Cα-N (Φ) and the Cα-C bond (Ψ) Defined as 180° when extended (as shown) + = clockwise, seen from Cα Not -
On Helices and Bertrand Curves in Euclidean 3-Space
ON HELİCES AND BERTRAND CURVES IN EUCLİDEAN 3-SPACE Murat Babaarslan Department of Mathematics, Faculty of Science and Arts Bozok University, Yozgat, Turkey [email protected] Yusuf Yaylı Department of Mathematics, Faculty of Science Ankara University, Tandoğan, Ankara, Turkey [email protected] Abstract- In this article, we investigate Bertrand curves corresponding to spherical images of the tangent indicatrix, binormal indicatrix, principal normal indicatrix and Darboux indicatrix of a space curve in Euclidean 3-space. As a result, in case of a space curve is general helix, we show that curve corresponding to spherical images of its tangent indicatrix and binormal indicatrix are circular helices and Bertrand curves. Similarly, in case of a space curve is slant helix, we demonstrate that the curve corresponding to spherical image of its principal normal indicatrix is circular helix and Bertrand curve. Key Words- Helix, Bertrand curve, Spherical Images 1. INTRODUCTION In the differential geometry of a regular curve in Euclidean 3-space E3 , it is well known that, one of the important problems is characterization of a regular curve. The curvature and the torsion of a regular curve play an important role to determine the shape and size of the curve 1,2. Natural scientists have long held a fascination, sometimes bordering on mystical obsession for helical structures in nature. Helices arise in nanosprings, carbon nonotubes, helices, DNA double and collagen triple helix, the double helix shape is commonly associated with DNA, since the double helix is structure of DNA 3 . This fact was published for the first time by Watson and Crick in 1953 4. -
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.). -
Influence of the Sequence-Dependent Flexure of DNA on Transcription in E.Coli
Volume 17 Number 22 1989 Nucleic Acids Research Influence of the sequence-dependent flexure of DNA on transcription in E.coli Christina M.Collis, Peter L.Molloy, Gerald W.Both and Horace R.Drew* CSIRO Division of Biotechnology, Laboratory for Molecular Biology, PO Box 184, North Ryde, NSW 2113, Australia Received August 11, 1989; Revised and Accepted October 20, 1989 ABSTRACT In order to study the effects of DNA structure on cellular processes such as transcription, we have made a series of plasmids that locate several different kinds of DNA structure (stiff, flexible or curved) near the sites of cleavage by commonly-used restriction enzymes. One can use these plasmids to place any DNA region of interest (e.g., promoter, operator or enhancer) close to certain kinds of DNA structure that may influence its ability to work in a living cell. In the present example, we have placed a promoter from T7 virus next to the special DNA structures; the T7 promoter is then linked to a gene for a marker protein (chloramphenicol acetyl transferase). When plasmids bearing the T7 promoter are grown in cells of E. coli that contain T7 RNA polymerase, the special DNA structures seem to have little or no influence over the activity of the T7 promoter, contrary to our expectations. Yet when the same plasmids are grown in cells of E. coli that do not contain T7 RNA polymerase, some of the DNA structures show a surprising promoter activity of their own. In particular, the favourable flexibility or curvature of DNA, in the close vicinity of potential -35 and -10 promoter regions, seems to be a significant factor in determining where E. -
The Helix and the Heart
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector The Journal of BSR Thoracic and Cardiovascular Surgery Vol 124, No. 5, November 2002 Basic science review: The helix and the heart Gerald D. Buckberg, MD t is an enormous privilege and honor to be asked to give the basic science See related editorials on pages lecture. Please join me on an adventure that I have taken over the past three 884 and 886. years. I described this type of voyage to my daughters many years ago as “discovery,” in which you walk down certain common pathways but always see something different on that journey. I will tell you about my concept of how the helix and the heart affect nature, the heart, and the human. ITo pursue this new route, I select a comment from my hero, Albert Einstein, who said, “All our science, measured against reality, is primitive and childlike, and yet www.mosby.com/jtcvs is the most precious thing we have.” We all have to be students, who are often wrong and always in doubt, while a professor is sometimes wrong and never in doubt. Please join me on my student pathway to see something I discovered recently and will now share with you. The object of our affection is the heart, which is, in reality, a helix that contains an apex. The cardiac helix form, in Figure 1, was described in the 1660s by Lower as having an apical vortex, in which the muscle fibers go from outside in, in a clockwise way, and from inside out, in a counterclockwise direction. -
X-Ray Scattering from the Superhelix in Circular DNA (Supercoiling/Diffraction from Solutions/Specific Linking Difference/Writhe Vs
Proc. Nati Acad. Sci. USA Vol. 80, pp. 741-744, February 1983 Biophysics X-ray scattering from the superhelix in circular DNA (supercoiling/diffraction from solutions/specific linking difference/writhe vs. twist) G. W. BRADY*, D. B. FEIN*, H. LAMBERTSONt, V. GRASSIANt, D. Foost, AND C. J. BENHAMt Institute, Troy, New York 12181; *Center for Laboratories and Research, New York State Department of Health, Albany, New York 12222; tRensselaer Polytechnic and tDepartment of Mathematics, University of Kentucky, Lexington, Kentucky 40506 Communicated by Bruno H. Zimm, October 25, 1982 ABSTRACT This communication presents measurements, creased the lower angle limit of resolution of the instrument made with a newly constructed position-sensitive detector, of the because the inner portion of the scattering curve was super- small-angle x-ray scattering from the first-order superhelix ofna- imposed on a risingbackground resultingfrom parasitic slit scat- tive COP608 plasmid DNA. This instrument measures intensities tering. In consequence, the resulting data could not be de- free of slit effects and provides good resolution in the region of smeared, so a direct comparison with theory was precluded. interest. The reported observations, made both in the presence This paper presents measurements of SAS from the first-or- and in the absence of intercalator, closely fit the scattering pat- der ccc DNA superhelix made with a new position-sensitive terns calculated for noninterwound helical first-order superhel- detector (PSD). The resulting profiles are free of slit effects, ices. These results are consistent with a toroidal helical structure permitting direct and unambiguous comparisons with theory. but not with interwound conformations.