Quantitative Diameter Measurements of Chromatin and TMV Fibers in the Freeze-Dried State

1988 ◽  
Vol 46 ◽  
pp. 170-171
Author(s):  
B. D. Athey ◽  
A. L. Stout ◽  
M. F. Smith ◽  
J. P. Langmore
Keyword(s):  
Reliable Method ◽  
Fiber Diameter ◽  
Quantitative Agreement ◽  
One Dimension ◽  
Fiber Axis ◽  
Two Dimensional ◽  
Fiber Density ◽  
Variable Diameter ◽  
Freeze Dried ◽  
Expected Values

Although there is general agreement that Inactive chromosome fibers consist of helically packed nucleosomes, the pattern of packing is still undetermined. Only one of the proposed models, the crossed-linker model, predicts a variable diameter dependent on the length of DNA between nucleosomes. Measurements of the fiber diameter of negatively-stained and frozen- hydrated- chromatin from Thyone sperm (87bp linker) and Necturus erythrocytes (48bp linker) have been previously reported from this laboratory. We now introduce a more reliable method of measuring the diameters of electron images of fibrous objects. The procedure uses a modified version of the computer program TOTAL, which takes a two-dimensional projection of the fiber density (represented by the micrograph itself) and projects it down the fiber axis onto one dimension. We illustrate this method using high contrast, in-focus STEM images of TMV and chromatin from Thyone and Necturus. The measured diameters are in quantitative agreement with the expected values for the crossed-linker model for chromatin structure

scholarly journals The diameters of frozen-hydrated chromatin fibers increase with DNA linker length: evidence in support of variable diameter models for chromatin.

1990 ◽  
Vol 111 (3) ◽  
pp. 795-806 ◽  
Author(s):  
B D Athey ◽  
M F Smith ◽  
D A Rankert ◽  
S P Williams ◽  
J P Langmore
Keyword(s):  
Fiber Diameter ◽  
Quantitative Agreement ◽  
Fiber Structure ◽  
Linker Length ◽  
Necturus Maculosus ◽  
Variable Diameter ◽  
Computer Image Processing ◽  
Sperm Dna ◽  
Chromatin Fibers ◽  
Processing Techniques

The diameters of chromatin fibers from Thyone briareus (sea cucumber) sperm (DNA linker length, n = 87 bp) and Necturus maculosus (mudpuppy) erythrocytes (n = 48 bp) were investigated. Soluble fibers were frozen into vitrified aqueous solutions of physiological ionic strength (124 mM), imaged by cryo-EM, and measured interactively using quantitative computer image-processing techniques. Frozen-hydrated Thyone and Necturus fibers had significantly different mean diameters of 43.5 nm (SD = 4.2 nm; SEM = 0.61 nm) and 32.0 nm (SD = 3.0 nm; SEM = 0.36 nm), respectively. Evaluation of previously published EM data shows that the diameters of chromatin from a large number of sources are proportional to linker length. In addition, the inherent variability in fiber diameter suggests a relationship between fiber structure and the heterogeneity of linker length. The cryo-EM data were in quantitative agreement with space-filling double-helical crossed-linker models of Thyone and Necturus chromatin. The data, however, do not support solenoid or twisted-ribbon models for chromatin that specify a constant 30 nm diameter. To reconcile the concept of solenoidal packing with the data, we propose a variable-diameter solid-solenoid model with a fiber diameter that increases with linker length. In principle, each of the variable diameter models for chromatin can be reconciled with local variations in linker length.

scholarly journals Reducing a Class of Two-Dimensional Integrals to One-Dimension with an Application to Gaussian Transforms

Atoms ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 53
Author(s):  
Jack C. Straton
Keyword(s):  
Quantum Theory ◽  
Arbitrary Function ◽  
Plane Waves ◽  
Wave Functions ◽  
One Dimension ◽  
Two Dimensional ◽  
Transition Amplitudes ◽  
Multidimensional Integrals ◽  
Coulomb Potentials

Quantum theory is awash in multidimensional integrals that contain exponentials in the integration variables, their inverses, and inverse polynomials of those variables. The present paper introduces a means to reduce pairs of such integrals to one dimension when the integrand contains powers multiplied by an arbitrary function of xy/(x+y) multiplying various combinations of exponentials. In some cases these exponentials arise directly from transition-amplitudes involving products of plane waves, hydrogenic wave functions, and Yukawa and/or Coulomb potentials. In other cases these exponentials arise from Gaussian transforms of such functions.

Reynolds stresses and mean fields generated by pure waves: applications to shear flows and convection in a rotating shell

2008 ◽  
Vol 602 ◽  
pp. 303-326 ◽  
Author(s):  
E. PLAUT ◽  
Y. LEBRANCHU ◽  
R. SIMITEV ◽  
F. H. BUSSE
Keyword(s):  
Shear Flows ◽  
Rossby Waves ◽  
Zonal Flow ◽  
Quantitative Agreement ◽  
Model Systems ◽  
Geometrical Factor ◽  
Wave Flow ◽  
Nonlinear Frequency ◽  
Two Dimensional ◽  
Reynolds Stresses

A general reformulation of the Reynolds stresses created by two-dimensional waves breaking a translational or a rotational invariance is described. This reformulation emphasizes the importance of a geometrical factor: the slope of the separatrices of the wave flow. Its physical relevance is illustrated by two model systems: waves destabilizing open shear flows; and thermal Rossby waves in spherical shell convection with rotation. In the case of shear-flow waves, a new expression of the Reynolds–Orr amplification mechanism is obtained, and a good understanding of the form of the mean pressure and velocity fields created by weakly nonlinear waves is gained. In the case of thermal Rossby waves, results of a three-dimensional code using no-slip boundary conditions are presented in the nonlinear regime, and compared with those of a two-dimensional quasi-geostrophic model. A semi-quantitative agreement is obtained on the flow amplitudes, but discrepancies are observed concerning the nonlinear frequency shifts. With the quasi-geostrophic model we also revisit a geometrical formula proposed by Zhang to interpret the form of the zonal flow created by the waves, and explore the very low Ekman-number regime. A change in the nature of the wave bifurcation, from supercritical to subcritical, is found.

Stochastic closure for nonlinear Rossby waves

1977 ◽  
Vol 82 (4) ◽  
pp. 747-765 ◽  
Author(s):  
Greg Holloway ◽  
Myrl C. Hendershott
Keyword(s):  
Rossby Waves ◽  
Functional Dependence ◽  
Quantitative Agreement ◽  
Relative Strength ◽  
Interesting Case ◽  
Test Field ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Rossby Wave Propagation

An extension of the turbulence ‘test-field model’ (Kraichnan 1971 a) is given for two-dimensional flow with Rossby-wave propagation. Such a unified treatment of waves and turbulence is necessary for flows in which the relative strength of nonlinear terms depends upon the length scale considered. We treat the geophysically interesting case in which long, fast Rossby waves propagate substantially without interaction while short Rossby waves are thoroughly dominated by advection. We recover the observations of Rhines (1975) that the tendency of two-dimensional flow to organize energy into larger scales of motion is inhibited by Rossby waves and that an initially isotropic flow develops anisotropy preferring zonal motion. The anisotropy evolves to an equilibrium functional dependence on the isotropic part of the flow spectrum. Theoretical results are found to be in quantitative agreement with numerical flow simulations.

Effect of method of conservation on the n-alkane C31 concentration of two legumes and three temperate grasses

2006 ◽  
Vol 34 ◽  
pp. 79-85
Author(s):  
M.R. Reyes-Reyes ◽  
S. E. Buntinx ◽  
F. S. Barajas-Torres ◽  
I. C. Gavilán-García ◽  
F.A. Castrejón-Pineda
Keyword(s):  
White Clover ◽  
Reliable Method ◽  
Dactylis Glomerata ◽  
Gas Chromatograph ◽  
Dry Ice ◽  
Plastic Bags ◽  
Freeze Dried ◽  
Soxhlet Method ◽  
Kikuyu Grass ◽  
Alkane Analysis

SummaryThe objective of this study was to compare five methods of forage preservation (ice, dry ice, liquid-N, drying in newspaper, and sundried) on the concentration of the n-alkane C31 in Medicago sativa cv Puebla 76 (lucerne/alfalfa), Trifolium repens latum (white clover), Lolium perenne (perennial ryegrass), Pennisetum clandestinum (kikuyu grass) and Dactylis glomerata (orchardgrass/cocksfoot). The sampled forages in ice and dry ice were kept in hermetically sealed plastic bags in a plastic cooler. The deep frozen samples were put into small plastic bags and submerged in liquid-N. The samples dried in newspaper were placed between sheets of newspaper, and put into hermetically sealed plastic bags. All these samples were taken to the laboratory and freeze-dried approximately 24 h later. The sun-dried samples were taken to the laboratory in newspaper and sun-dried for 48 h. The forage samples were ground and worked on in triplicate, extracted by the Soxhlet method (C34 n-alkane was used as standard and n-heptane as solvent), saponified, separated, purified and injected into a gas chromatograph. The data were analysed for variance as a randomised factorial (n=74). The comparison between means was by the Boneferroni test (P<0.05). The interaction between forage and method of conservation was significant P<0.0001). There were no differences between methods of conservation for white clover (mean 26mg C31/kg DM) or orchardgrass/cocksfoot (mean 31 mgC31/ kgDM). In comparison with liquid-N, (261 mgC31/kgDM), the other methods reduced the concentration of n-alkane in kikuyu grass by 27-35%. Sun and newspaper dried samples increased the concentration of C31 in alfalfa/lucerne by 6 and 15% respectively in comparison with freezing with liquid-N (291 mgC31/kgDM), while that frozen on ice reduced C31 by about 8%. This method, however, increased the ryegrass n-alkane by 12% in relation to liquid-N (169 mgC31/kgDM), but sun drying reduced it by about 40%. It is concluded that drying in liquid-N is the most reliable method for the conservation of samples for n-alkane analysis.

scholarly journals Computational wrapping: A universal method to wrap 3D-curved surfaces with nonstretchable materials for conformal devices

2020 ◽  
Vol 6 (15) ◽  
pp. eaax6212 ◽  
Author(s):  
Yu-Ki Lee ◽  
Zhonghua Xi ◽  
Young-Joo Lee ◽  
Yun-Hyeong Kim ◽  
Yue Hao ◽  
...  
Keyword(s):  
Computer Aided Design ◽  
Reliable Method ◽  
Design Method ◽  
Universal Method ◽  
Curved Surfaces ◽  
Two Dimensional ◽  
Steel Sheets ◽  
Computer Aided ◽  
Conformal Structures ◽  
Aided Design

This study starts from the counterintuitive question of how we can render conventional stiff, nonstretchable, and even brittle materials sufficiently conformable to fully wrap curved surfaces, such as spheres, without failure. Here, we extend the geometrical design method of computational origami to wrapping. Our computational wrapping approach provides a robust and reliable method for fabricating conformal devices for arbitrary curved surfaces with a computationally designed nonpolyhedral developable net. This computer-aided design transforms two-dimensional (2D)–based materials, such as Si wafers and steel sheets, into various targeted conformal structures that can fully wrap desired 3D structures without fracture or severe plastic deformation. We further demonstrate that our computational wrapping approach enables a design platform that can transform conventional nonstretchable 2D-based devices, such as electroluminescent lighting and flexible batteries, into conformal 3D curved devices.

scholarly journals ON TWO-DIMENSIONAL QUASITOPOLOGICAL FIELD THEORIES

2009 ◽  
Vol 24 (32) ◽  
pp. 6105-6121 ◽  
Author(s):  
P. TEOTONIO-SOBRINHO ◽  
C. MOLINA ◽  
N. YOKOMIZO
Keyword(s):  
Hopf Algebras ◽  
Gauge Theories ◽  
Local Symmetry ◽  
Two Dimensions ◽  
Field Theories ◽  
Partition Functions ◽  
Wilson Loops ◽  
Two Dimensional ◽  
Lattice Field ◽  
Expected Values

We study a class of lattice field theories in two dimensions that includes gauge theories. We show that in these theories it is possible to implement a broader notion of local symmetry, based on semisimple Hopf algebras. A character expansion is developed for the quasitopological field theories, and partition functions are calculated with this tool. Expected values of generalized Wilson loops are defined and studied with the character expansion.

scholarly journals Averaging over Narain moduli space

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Alexander Maloney ◽  
Edward Witten
Keyword(s):  
Einstein Gravity ◽  
Two Dimensions ◽  
Three Dimensions ◽  
One Dimension ◽  
Simons Theory ◽  
Two Dimensional ◽  
Dual Theory ◽  
Recent Developments ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract Recent developments involving JT gravity in two dimensions indicate that under some conditions, a gravitational path integral is dual to an average over an ensemble of boundary theories, rather than to a specific boundary theory. For an example in one dimension more, one would like to compare a random ensemble of two-dimensional CFT’s to Einstein gravity in three dimensions. But this is difficult. For a simpler problem, here we average over Narain’s family of two-dimensional CFT’s obtained by toroidal compactification. These theories are believed to be the most general ones with their central charges and abelian current algebra symmetries, so averaging over them means picking a random CFT with those properties. The average can be computed using the Siegel-Weil formula of number theory and has some properties suggestive of a bulk dual theory that would be an exotic theory of gravity in three dimensions. The bulk dual theory would be more like U(1)2D Chern-Simons theory than like Einstein gravity.

On two dimensional electrohydrostatic stability

1976 ◽  
Vol 349 (1657) ◽  
pp. 231-243 ◽  
Keyword(s):  
Approximate Solution ◽  
Numerical Solution ◽  
Edge Effects ◽  
Complex Variable ◽  
Equilibrium Configuration ◽  
Quantitative Agreement ◽  
Two Dimensional ◽  
Equilibrium Conditions ◽  
Conducting Membranes ◽  
Special Case

Complex variable techniques are used for the study of the electrohydrostatic stability of two dimensional charged conducting membranes, which are assumed to be fixed along their edges. The formulation of the problem is quite general, but the numerical solution presented refers to the case when the membranes are symmetrical with respect to the plane bisecting their width and carry equal and opposite charges. It is found, as expected, that for a given set of data the equilibrium configuration breaks down if the membranes are sufficiently charged. When the membranes are sufficiently apart the breakdown occurs at their edges and is manifested as inability of the system to satisfy the equilibrium conditions there. When the membranes are sufficiently close together and are charged to a certain level, they touch at their mid-points and the equilibrium breaks down. Our results are compared with an approximate solution of this problem, presented by two other authors. The approximate solution ignores the edge effects of the membranes and overestimates the amount of charge that the membranes can carry before breakdown occurs. In the special case when the gap between the membranes is much less than their width, our results are in quantitative agreement with the approximate solution but as the gap between the membranes increases, the accuracy of the approximate solution decreases.

Sign in / Sign up

Export Citation Format

Share Document