DOCSLIB.ORG

X-Ray Scattering from the Superhelix in Circular DNA (Supercoiling/Diffraction from Solutions/Specific Linking Difference/Writhe Vs

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
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. The pitch angle a and contour length per turn c are reported for the native molecule at MATERIALS AND METHODS several concentrations of the platinum intercalating compound. From these parameters, the best-fitting toroidal helix is con- The apparatus used will be described in detail elsewhere. structed and its geometry is investigated. The specific linking dif- Briefly, it consists of a beam powered by a Rigaku 12-kW ro- ference of the native molecule is estimated to be ALk/Lk0 - tating anode source operated at 50 kV and 190 mA collimated -0.055. If the best-fitting toroidal helix is taken to be the actual by two pinholes 0.75 mm in diameter set 100 cm apart in an structure, the partitioning of superhelicity between twist and evacuated collimation chamber. The beam irradiates the sample writhe occurs in the approximate ratio of 2: 1. contained in a flat sample holder with mica windows separated by a path length of 1 mm. Its diffraction pattern is recorded on The large-scale tertiary structure ofa covalently closed, circular a PSD placed at the end ofan evacuated path 150 cm from the DNA-molecule (ccc DNA) in solution is known to be drastically sample. An extra guard pinhole, diameter 0.8 mm, is placedjust affected by the internal stresses imposed by superhelicity. The before the sample. With this arrangement, the slit scattering variations ofsedimentation velocity with increased supercoiling is effectively reduced to an insignificant value everywhere but suggest a decreasing (average) radius ofgyration as the molecule at the innermost region ofthe pattern. Because ofthe small size assumes more compact conformations (1). In addition to hydro- ofthe beam and the large sample-to-detector distance, slit cor- dynamic methods, small-angle x-ray scattering (SAS) may be rections are not necessary. The intensity loss associated with the used to investigatelarge-scale properties ofstressed DNA struc- greatly increased collimation ofthe pinholes and the large scat- ture in solution. The observed scattering intensity is related to tering radius are adequately compensated for by the much the distribution ofelectron pairs within the molecule and hence greater power output ofthe 12-kW generator. Thus, we are now provides structural information. able to obtain direct traces ofthe diffraction patterns free ofall Hydrodynamic evidence (2) indicates that dissolved super- corrections with the exception of a fairly minor one due to the helical polyoma ccc DNA may undergo an ionic strength-de- finite width ofthe main beam. This causes an overlap oftwo or pendent transition between an interwound conformation (high three channels of the PSD and is not significant. salt) and a toroidal (super)helix (Na' 0.01 M). The interwound In these experiments the DNA used was the natively super- superhelical structure observed by electron microscopy may not coiled COP608 plasmid (4,258 bp), a 179-bp deletion ofthe PT be representative of solution conformations because the sam- 181 plasmid of Staphylococcus aureus. The cells were grown ples are spread flat and dried in preparation for photography. overnight in Cy broth, harvested by centrifugation, and lysed Previous communications (3, 4) reported the x-ray scattering by the clear lysate method (5). Purification of the superhelical from two natively superhelical ccc DNAs infl solution, PM2 DNA was done according to-the acid/phenol extraction pro- [=10,600 base pairs (bp)] and PBR313 (-4,400 bp). The ob- cedure of Zasloffet aL (6). The DNA solution was freed of RNA served superhelix diffraction patterns were consistent with a and protein impurities. The DNA was precipitated, resus- noninterwound coiled coil geometry, the first (i.e., smallest) pended in low ionic strength buffer, and then twice extracted order of which had a contour length of c = 920 A per turn at with 1 vol ofredistilled phenol equilibrated with 50 mM NaOAc a pitch angle 450 < a < 55°. However, those results were pre- to a pH of4.0. As shown by Zasloff et aL (6), nicked and chro- sented as being preliminary in nature because practical limi- mosomal DNA will be selectively removed from the aqueous tations ofthe experiment precluded correcting the data for slit phase by this process, leaving a 95% pure solution of super- where the first-order scat- helical DNA. The phenol was removed by ether extraction. The effects. The intensities in the region resus- ters were measured with a Kratky camera having infinite slit solution was ethanol precipitated and the DNA was slit widths pended in the buffer used for the x-ray experiments (0.2 M geometry. Because of the low intensities involved, In certain considerably greater than optimal had to be used. This de- Tris HCl, pH 7.5/0.05 M NaCl/1.0 mM Na2EDTA). small- in part by page charge Abbreviations: ccc DNA, covalently closed circular DNA; SAS, The publication costs ofthis article were defrayed PSD, position-sensitive detector; bp, base pairs payment. This article must therefore be hereby marked "advertise- angle x-ray scattering; platinum(II). ment" in accordance with 18 U. S. C. §1734 solely to indicate this fact. (bp); PtTS, 2-hydroxyethanethiolato(2,2',2",-terpyridine) 741 Downloaded by guest on October 4, 2021 74-2 Biophysics: Brady et aL Proc. Natl. Acad. Sci. USA 80 (1983) cases the appropriate concentration of the intercalating agent 2-hydroxyethanethiolato(2,2',2"-terpyridine)platinum(II) (PtTS) was added. For comparison, calf thymus DNA (type I, Sigma) was dissolved in buffer (0.2 M Tris HCl, pH 7.5/0.05 M NaCl/ 1 mM NaEDTA), ethanol precipitated, and dialyzed against the same buffer. RESULTS AND ANALYSIS Fig. 1 shows a plot of the superhelical scattering from a solu- I-0 tion of plasmid COP608 DNA (11.6 mg/ml), Mr 2.8 X 106, U, along with the background scattering (lower curve) from the 3 buffer solution (0.2 M Tris-HCI, pH 7.5/0.05 M NaCl/1 mM 0-4 Na2EDTA). Both curves are the actual output from the detector without smoothing. The counting time was 4 hr. Comparison of the two shows that- the rapidly rising portion of the back- _ ~~~~~~0-3 ground is confined to channel numbers less than 52. Beyond this it levels offto a smoothly decreasing curve ofvery favorable I signal-to-background ratio which can beaveraged over a5-chan- 0 I}0.10' 0.15 0.20 0.25' 0.30 nel interval by a least squares program and then directly sub- 41 tracted from the DNA curves. S-= SIN Ox10 Fig. 2 shows the scattering curves, corrected for background, of calf thymus DNA (curve 1), of DNA FIG. 2. Scattering curves (corrected for background) of calf thy- superhelical (curve 2), mus DNA and superhelical DNA at various intercalator ratios. The and ofsuperhelical DNA (curves 3, 4, and 5) in which PtTS had abscissa origins for curves 3 and 4 have been displaced upward. -Con- been intercalated in the mol ratios of 0, 1:30, 1:25 and 1:20 centrations and counting times were as inFig. 1. The heavy continuous (mol PtTS intercalated/mol bp). The calfthymus curve is com- lines are calculated curves for noninterwound molecules. pletely featureless. In contrast, the superhelical curves show pronounced maxima which decrease in magnitude with increas- equation (4, 7, 8) ing PtTS/DNA ratios. This shows that the diffraction maxima are attributable to the superhelical conformation ofthe circular I(s) = 2 L L sin 2. plasmid DNA. Curves taken at lower concentrations reproduce 2 Jo '0 sr(ljj12sr(, [1] this behavior, so intermolecular scattering plays no part. The maximum for the nonintercalated DNA is particularly pro- Here, 11 and 12 are two copies of the length parameter, p is the nounced. Intercalation results in displacement ofthe curves out effective electron density of the filament, and s = 41T/A sin 6; to larger s values, consistent with a decrease in contour length A is the wavelength (CuKa, A = 1.54 A) and 0 is one-half the per turn, c, ofthe unwinding superhelix. (This latter effect will scattering angle. The variable r (l1, 12) is the distance in space be demonstrated below, where the measured curves are com- between two points on the scattering filament and L is the fil- pared with those calculated for both interwound and noninter- ament length.
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.
    [Show full text]
  • 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.
    [Show full text]
  • 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
    [Show full text]
  • 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
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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
    [Show full text]
  • 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.
    [Show full text]
  • 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.).
    [Show full text]
  • Effect of Superhelical Structure on the Secondary Structure of DNA Rings
    VOL. 5, PP. 691-696 (1967) Effect of Superhelical Structure on the Secondary Structure of DNA Rings DANIEL GLAUBIGER and JOHN E. HEARST, Departnient of Chemistry, University of California, Berkeley, California Synopsis A quantity, called the linking number, is defined, which specifies the total number of t,wists in a circular helix. The linking number is invariant under continuous deforma- tions of the ring and therefore enables one to calculate the influence of superhelical structures on the secondary helix of a circular molecule. The linking number can be determined by projecting the helix into a plane and counting strand crosses in the projection as described. For example, it has been shown that for each 180" twist in a left-handed superhelix, a right-handed 360" twist is removed from the secondary helix, thus allowing local unwinding. Introduction It is of interest to relate superhelical structure of helical molecules to their secondary structure.' By defining a quantity characteristic of two- stranded circular helical niolecules, related to the helical structure, and in- variant under continuous deformations of the molecule, we are able to evaluate the changes in helical structure brought about by the imposition of superhelical configurations on such molecules. The quantity of interest, called the linking number, is related to the number of turns/cycle for a circular helical molecule.* It will be shown that superhelical structures which are made from helical polymers con- tribute to this number and alter the contribution made by the secondary structure of the molecule to this number. This is made manifest as a change in the number of turns/cycle or as a change in the number of turns/ unit length.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]