Approximation of virus structure by icosahedral tilings

2015 ◽  
Vol 71 (4) ◽  
pp. 410-422 ◽  
Author(s):  
D. G. Salthouse ◽  
G. Indelicato ◽  
P. Cermelli ◽  
T. Keef ◽  
R. Twarock
Keyword(s):  
Goodness Of Fit ◽  
Virus Assembly ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Three Dimensions ◽  
Coarse Grained ◽  
Icosahedral Symmetry ◽  
Point Sets ◽  
Viral Capsids ◽  
Project Scheme

Viruses are remarkable examples of order at the nanoscale, exhibiting protein containers that in the vast majority of cases are organized with icosahedral symmetry. Janner used lattice theory to provide blueprints for the organization of material in viruses. An alternative approach is provided here in terms of icosahedral tilings, motivated by the fact that icosahedral symmetry is non-crystallographic in three dimensions. In particular, a numerical procedure is developed to approximate the capsid of icosahedral viruses by icosahedral tilesviaprojection of high-dimensional tiles based on the cut-and-project scheme for the construction of three-dimensional quasicrystals. The goodness of fit of our approximation is assessed using techniques related to the theory of polygonal approximation of curves. The approach is applied to a number of viral capsids and it is shown that detailed features of the capsid surface can indeed be satisfactorily described by icosahedral tilings. This work complements previous studies in which the geometry of the capsid is described by point sets generated as orbits of extensions of the icosahedral group, as such point sets are by construction related to the vertex sets of icosahedral tilings. The approximations of virus geometry derived here can serve as coarse-grained models of viral capsids as a basis for the study of virus assembly and structural transitions of viral capsids, and also provide a new perspective on the design of protein containers for nanotechnology applications.

Symmetry-adapted digital modeling II. The double-helix B-DNA

2016 ◽  
Vol 72 (3) ◽  
pp. 312-323 ◽  
Author(s):  
A. Janner
Keyword(s):  
Dimensional Space ◽  
Double Helix ◽  
Three Dimensional ◽  
Reduction Factor ◽  
Lattice Points ◽  
Three Dimensions ◽  
Coarse Grained ◽  
Digital Modeling ◽  
Dna Strands ◽  
Dna Double Helix

The positions of phosphorus in B-DNA have the remarkable property of occurring (in axial projection) at well defined points in the three-dimensional space of a projected five-dimensional decagonal lattice, subdividing according to the golden mean ratio τ:1:τ [with τ = (1+\sqrt {5})/2] the edges of an enclosing decagon. The corresponding planar integral indicesn1,n2,n3,n4(which are lattice point coordinates) are extended to include the axial indexn5as well, defined for each P position of the double helix with respect to the single decagonal lattice ΛP(aP,cP) withaP= 2.222 Å andcP= 0.676 Å. A finer decagonal lattice Λ(a,c), witha=aP/6 andc=cP, together with a selection of lattice points for each nucleotide with a given indexed P position (so as to define a discrete set in three dimensions) permits the indexing of the atomic positions of the B-DNA d(AGTCAGTCAG) derived by M. J. P. van Dongen. This is done for both DNA strands and the single lattice Λ. Considered first is the sugar–phosphate subsystem, and then each nucleobase guanine, adenine, cytosine and thymine. One gets in this way a digital modeling of d(AGTCAGTCAG) in a one-to-one correspondence between atomic and indexed positions and a maximal deviation of about 0.6 Å (for the value of the lattice parameters given above). It is shown how to get a digital modeling of the B-DNA double helix for any given code. Finally, a short discussion indicates how this procedure can be extended to derive coarse-grained B-DNA models. An example is given with a reduction factor of about 2 in the number of atomic positions. A few remarks about the wider interest of this investigation and possible future developments conclude the paper.

Three-Dimensional Navier-Stokes Computation of Turbomachinery Flows Using an Explicit Numerical Procedure and a Coupled k-ε Turbulence Model

1991 ◽  
Author(s):  
R. F. Kunz ◽  
B. Lakshminarayana
Keyword(s):  
Reynolds Number ◽  
Turbulence Model ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Secondary Flows ◽  
Three Dimensions ◽  
Quality Data ◽  
Navier Stokes ◽  
Evaluation Procedure ◽  
Pressure Probe

An explicit, three-dimensional, coupled Navier-Stokes/k-ε technique has been developed and successfully applied to complex internal flow calculations. Several features of the procedure, which enable convergent and accurate calculation of high Reynolds number two-dimensional cascade flows have been extended to three-dimensions, including a low Reynolds number compressible form of the k-ε turbulence model, local timestep specification based on hyperbolic and parabolic stability requirements, and eigenvalue and local velocity scaling of artificial dissipation operators. A flux evaluation procedure which eliminates the finite difference metric singularity, at leading and trailing edges, on H- and C-grids, is presented. The code is used to predict the pressure distribution, primary velocity and secondary flows in an incompressible, turbulent curved duct flow for which CFD validation quality data is available. Also, a subsonic compressor rotor passage, for which detailed laser, rotating hot-wire and five-hole pressure probe measurements have been made is computed. Detailed comparisons between predicted and measured core flow and near wall velocity profiles, wake profiles, and spanwise mixing effects downstream of the rotor passage are presented for this case. It is found that the technique provides accurate and convergent engineering simulation of these complex turbulent flows.

scholarly journals Exploring the Interplay between Virology and Molecular Crystallography

2008 ◽  
Vol 9 (3-4) ◽  
pp. 167-173 ◽  
Author(s):  
Aloysio Janner
Keyword(s):  
Point Group ◽  
Morphological Characterization ◽  
Three Dimensions ◽  
Icosahedral Symmetry ◽  
Coat Proteins ◽  
Viral Capsids ◽  
Icosahedral Group ◽  
Higher Dimensional ◽  
Icosahedral Viruses ◽  
The One

Polyhedra with icosahedral symmetry and vertices labelled by rational indices of points of a six-dimensional lattice left invariant by the icosahedral group allow a morphological characterization of icosahedral viruses which includes the Caspar–Klug classification as a special case. Scaling transformations relating the indexed polyhedron enclosing the surface with the one delimiting the central cavity lead to models of viral capsids observed in nature. Similar scaling relations can be obtained from projected images in three dimensions of higher-dimensional crystallographic point groups having the icosahedral group as a subgroup. This crystallographic approach can be extended to axial-symmetric clusters of coat proteins around icosahedral axes of the capsid. One then gets enclosing forms with vertices at points of lattices left invariant by the corresponding point group and having additional crystallographic properties also observed in natural crystals, but not explained by the known crystallographic laws.

Three-Dimensional Elasticity Analysis of Thick Rectangular Laminated Composite Plates Using Meshless Local Petrov-Galerkin (MLPG) Method

2006 ◽  
Vol 5-6 ◽  
pp. 331-338 ◽  
Author(s):  
S.M.R. Alavi ◽  
Mohammad Mohammadi Aghdam ◽  
A. Eftekhari
Keyword(s):  
Interpolation Method ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Plates ◽  
Three Dimensions ◽  
Elasticity Analysis ◽  
Weak Formulation ◽  
Mlpg Method

This article presents apparently the first application of Meshless local Petrov-Galerkin (MLPG) method for 3-D elasticity analysis of moderately thick rectangular laminated plates. As with other Meshless methods, the problem domain is represented by a set of spread nodes in all three dimensions of the plate without configuration of elements. The Moving Least-Squares (MLS) method is applied to construct the required shape functions. A local asymmetric weak formulation of the problem is developed and MLPG is applied to solve the governing equations. Direct interpolation method is employed to enforce essential boundary conditions. Details of formulation, numerical procedure, convergence and accuracy characteristics of the method are investigated. Results are compared, where possible, with other analytical and numerical methods and show good agreement.

Reliability and Sources of Validity Evidence of the Oviedo Schizotypy Assessment Questionnaire-Abbreviated (ESQUIZO-Q-A)

2012 ◽  
Vol 15 (2) ◽  
pp. 840-849 ◽  
Author(s):  
Eduardo Fonseca-Pedrero ◽  
Serafín Lemos-Giráldez ◽  
Mercedes Paino ◽  
Marta Santarén-Rosell ◽  
Susana Sierra-Baigrie ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Computerized Adaptive Testing ◽  
Factor Model ◽  
Three Dimensional ◽  
Self Report ◽  
Three Dimensions ◽  
Future Research ◽  
Validity Evidence ◽  
Dimensional Solution ◽  
Assessment Questionnaire

The main goal of this research was to examine the reliability and different sources of validity evidence of the Oviedo Schizotypy Assessment Questionnaire-Abbreviated (ESQUIZO-Q-A) in nonclinical adolescents. The final sample was made up of 1,455 participants, 705 males (48.5%), with a mean age of 15.92 years (SD = 1.18). The internal consistency of the subscales ranged from .62 to .75. The analysis of its internal structure yielded a three-dimensional solution based on the dimensions: Reality Distortion, Anhedonia, and Interpersonal Disorganization. Likewise, the goodness-of-fit indices derived from the Confirmatory Factor Analysis for the hypothesized three-factor model were adequate. The three dimensions of the ESQUIZO-Q-A were significantly correlated with the subscales of the Strengths and Difficulties Questionnaire. The ESQUIZO-Q is a brief and simple self-report with adequate psychometric properties for the assessment of schizotypal traits in nonclinical adolescent populations. Future research should continue to explore the metric quality of the ESQUIZO-Q-A (e.g., sensitivity and specificity) and incorporate the new advances in psychological and educational assessment such as Computerized Adaptive Testing.

convergent-beam diffraction from surfaces

1987 ◽  
Vol 45 ◽  
pp. 30-33
Author(s):  
J. A. Eades ◽  
A. E. Smith ◽  
D. F. Lynch
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Plane Figure ◽  
Transmission Electron ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

It is quite simple (in the transmission electron microscope) to obtain convergent-beam patterns from the surface of a bulk crystal. The beam is focussed onto the surface at near grazing incidence (figure 1) and if the surface is flat the appropriate pattern is obtained in the diffraction plane (figure 2). Such patterns are potentially valuable for the characterization of surfaces just as normal convergent-beam patterns are valuable for the characterization of crystals.There are, however, several important ways in which reflection diffraction from surfaces differs from the more familiar electron diffraction in transmission.GeometryIn reflection diffraction, because of the surface, it is not possible to describe the specimen as periodic in three dimensions, nor is it possible to associate diffraction with a conventional three-dimensional reciprocal lattice.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

scholarly journals The Everyday Life of Security: Capturing Space, Practice, and Affect

2021 ◽  
Author(s):  
Jonna Nyman
Keyword(s):  
Everyday Life ◽  
Research Methods ◽  
Lived Experiences ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Conceptual Clarity ◽  
The Everyday ◽  
Participatory Photography ◽  
High Politics ◽  
Ordinary Citizens

Abstract Security shapes everyday life, but despite a growing literature on everyday security there is no consensus on the meaning of the “everyday.” At the same time, the research methods that dominate the field are designed to study elites and high politics. This paper does two things. First, it brings together and synthesizes the existing literature on everyday security to argue that we should think about the everyday life of security as constituted across three dimensions: space, practice, and affect. Thus, the paper adds conceptual clarity, demonstrating that the everyday life of security is multifaceted and exists in mundane spaces, routine practices, and affective/lived experiences. Second, it works through the methodological implications of a three-dimensional understanding of everyday security. In order to capture all three dimensions and the ways in which they interact, we need to explore different methods. The paper offers one such method, exploring the everyday life of security in contemporary China through a participatory photography project with six ordinary citizens in Beijing. The central contribution of the paper is capturing—conceptually and methodologically—all three dimensions, in order to develop our understanding of the everyday life of security.

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