Spherical harmonic molecular surfaces

Max, Nelson; Getzoff, E. D.

doi:10.1109/38.7748

Cited by 85 publications

(71 citation statements)

References 13 publications

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“…The conventional three-dimensional Fourier series (Leicester, Finney & Bywater, 1988;Max & Getzoff, 1988). These do not require the choice of an origin,…”

Section: Discussionmentioning

confidence: 99%

A resolution-sensitive procedure for comparing protein surfaces and its application to the comparison of antigen-combining sites

Gerstein¹

1992

Acta Cryst Sect A

109

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HANS GRIMMER 271 and the form of 7r given in Table 3 i.e. only the piezomagnetoelectric effect contributes to PI and P2. Also U2N2P, U2NES, Nb2C0409 and Nb2Mn409 have symmetry 3'm' according to Ole~ et al. (1976).The author is indebted to Professor H. Schmid for his suggestion to investigate the form of the piezomagnetoelectric effect and for stimulating discussions.References AIZU, K. (1970). Phys. Rev. B, 2, 754-772. GRIMMER, H. (1991a). Acta Cryst. A47, 226-232. GRIMMER, H. (1991b). Helv. Phys. Acta, 64, 187-188. KOPSKg, V. (1979 Resolution is a crucial parameter to consider in making surface comparisons. A method is presented here for the rapid, objective and automatic comparison of selected parts of protein surfaces as a function of resolution using differences and correlations of Fourier coefficients. A test-case application of this procedure to the surfaces of five immunoglobulin antigen-combining sites allowed them to be partitioned into two categories.

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“…The conventional three-dimensional Fourier series (Leicester, Finney & Bywater, 1988;Max & Getzoff, 1988). These do not require the choice of an origin,…”

Section: Discussionmentioning

confidence: 99%

A resolution-sensitive procedure for comparing protein surfaces and its application to the comparison of antigen-combining sites

Gerstein¹

1992

Acta Cryst Sect A

109

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“…Single-valued means that a ray from the origin to infinity will only intersect the surface once, which is equivalent to the definition of a star-like particle [20]. The function r(h,/) is, in principle, impossible to express explicitly for random shapes, but it can always be approximated by a summation of spherical harmonic functions for star-like shapes [21][22][23]. It is clear that almost of all sand and gravel used for concrete have star-like shapes (i.e., are star-shaped) [12,24,25].…”

Section: Mathematical Representation Of a 3d Irregular Shapementioning

confidence: 99%

Anm: a geometrical model for the composite structure of mortar and concrete using real-shape particles

Qian

Garboczi

et al. 2014

Mater Struct

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The composite geometrical structure of mortar composites can be represented by a model consisting of sand embedded in a cement paste matrix and the structure of concrete by gravel embedded in a mortar matrix. Traditionally, spheres have often been used to represent aggregates (sand and gravel), although the accuracy of properties computed for structures using spherical aggregates as inclusions can be limited when the property contrast between aggregate and matrix is large. In this paper, a new geometrical model is described, which can simulate the composite structures of mortar and concrete with real-shape aggregates. The aggregate shapes are either directly or statistically taken from real particles, using a spherical harmonic expansion, where a set of spherical harmonic coefficients, a nm , is used to describe the irregular shape. The model name of Anm is taken from this choice of notation. The takeand-place parking method is employed to put multiple irregular particles together within a pre-determined empty container, which becomes a representative volume element. This representative volume element can then be used as input into some kind of computational material model, which uses other numerical techniques such as finite elements to compute properties of the Anm composite structure.

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“…These methods are developed and applied in a wide range of fields, including computer vision, biological imaging, brain mapping, target recognition and for satellite image analysis. In molecular biology, the notion that the structure (or shape) of a protein is a major determinant of its function has led to the development of methods for representing, measuring and comparing protein structures [3][4][5]. Brain morphometry, concerned with the measurement of the brain geometric structures and the changes they undergo during development, ageing, learning, disease and evolution, has become central in neurobiology [6 -10].…”

Section: Introductionmentioning

confidence: 99%

Landmark-free geometric methods in biological shape analysis

Koehl

Hass

2015

J. R. Soc. Interface.

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In this paper, we propose a new approach for computing a distance between two shapes embedded in three-dimensional space. We take as input a pair of triangulated genus zero surfaces that are topologically equivalent to spheres with no holes or handles, and construct a discrete conformal map f between the surfaces. The conformal map is chosen to minimize a symmetric deformation energy E sd ( f ) which we introduce. This measures the distance of f from an isometry, i.e. a non-distorting correspondence. We show that the energy of the minimizing map gives a well-behaved metric on the space of genus zero surfaces. In contrast to most methods in this field, our approach does not rely on any assignment of landmarks on the two surfaces. We illustrate applications of our approach to geometric morphometrics using three datasets representing the bones and teeth of primates. Experiments on these datasets show that our approach performs remarkably well both in shape recognition and in identifying evolutionary patterns, with success rates similar to, and in some cases better than, those obtained by expert observers.

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Spherical harmonic molecular surfaces

Cited by 85 publications

References 13 publications

A resolution-sensitive procedure for comparing protein surfaces and its application to the comparison of antigen-combining sites

A resolution-sensitive procedure for comparing protein surfaces and its application to the comparison of antigen-combining sites

Anm: a geometrical model for the composite structure of mortar and concrete using real-shape particles

Landmark-free geometric methods in biological shape analysis

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