Angular Momentum in Quantum Physics

Biedenharn, L. C.

doi:10.1017/cbo9780511759888

Cited by 639 publications

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“…The knowledge gathered about icosahedral virus capsids points towards this kind of simple organization in these systems. In the present work further evidence of this behaviour is revealed by finding the simplest form of a two-body interaction, when this is written as an expansion in the complete basis set of the angular terms of the standard multipolar expansions 29 , that incorporates the most relevant geometrical features of the real capsomer-capsomer interaction. This form will turn out to be universal and will unveil the important physical factors that determine the energetic stability of the capsid and its relationship with its geometrical structure.…”

Section: Introductionmentioning

confidence: 56%

A minimal representation of the self-assembly of virus capsids

2014

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Viruses are biological nanosystems with a capsid of protein-made capsomer units that encloses and protects the genetic material responsible for their replication. Here we show how the geometrical constraints of the capsomer-capsomer interaction in icosahedral capsids fix the form of the shortest and universal truncated multipolar expansion of the two-body interaction between capsomers. The structures of many of the icosahedral and related virus capsids are located as single lowest energy states of this potential energy surface. Our approach unveils relevant features of the natural design of the capsids and can be of interest in fields of nanoscience and nanotechnology where similar hollow convex structures are relevant.

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Section: Introductionmentioning

confidence: 56%

A minimal representation of the self-assembly of virus capsids

2014

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“…These can be constructed by a method that has been applied t o SU(2) (see for example [3]) and can, in principle, be used for SU(n). Here it is done explicitly for SU(3).…”

Section: The Lie Algebra Of Su(3)mentioning

confidence: 99%

“…Since Xg commutes with this SU(2) subgroup, this can be written as Then we may decompose P. Of the four elements of P , we can pick one, say As, analogous to the Jy = J 2 of SU (2) and write any element of P as 1 where K' is another copy of K . Dropping the redundancies, we arrive at the following product for SU (3). As stated above, this method could, in principle, be used to decompose SU(n) into an Euler angle type parameterization.…”

Section: "Euler Angle" Decompositionmentioning

confidence: 99%

“…It's important to particle physics not only due to the now famous Eight-fold way developed by Gell-Mann and Ne'eman [l], which has become known as flavor SU(3), but also due t o the color SU(3) of QCD ([2] contains an excellent review along with a meticulous set of references). Color SU (3) was introduced for consistency in the quark model to give the quark wave functions their observed fermionic nature within the flavor framework. The color SU(3) is believed to be an exact gauge symmetry) whereas the flavor symmetry is broken by the quark masses.…”

Section: Introductionmentioning

confidence: 99%

“…This is based on the SU(3) symmetry group of the 3-d isotropic harmonic oscillator. Until now the algebra of SU (3) has been 'mbyrdQphysics.utexas.edu studied extensively but the geometry of the group manifold has had much less attention. Hopefully that will eventually change.…”

Section: Introductionmentioning

confidence: 99%

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The geometry of SU(3)

Byrd¹

1997

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Protein docking using spherical polar Fourier correlations

2000

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We present a new computational method of docking pairs of proteins by using spherical polar Fourier correlations to accelerate the search for candidate low-energy conformations. Interaction energies are estimated using a hydrophobic excluded volume model derived from the notion of "overlapping surface skins," augmented by a rigorous but "soft" model of electrostatic complementarity. This approach has several advantages over former three-dimensional grid-based fast Fourier transform (FFT) docking correlation methods even though there is no analogue to the FFT in a spherical polar representation. For example, a complete search over all six rigid-body degrees of freedom can be performed by rotating and translating only the initial expansion coefficients, many unfeasible orientations may be eliminated rapidly using only low-resolution terms, and the correlations are easily localized around known binding epitopes when this knowledge is available. Typical execution times on a single processor workstation range from 2 hours for a global search (5 x 10(8) trial orientations) to a few minutes for a local search (over 6 x 10(7) orientations). The method is illustrated with several domain dimer and enzyme-inhibitor complexes and 20 large antibody-antigen complexes, using both the bound and (when available) unbound subunits. The correct conformation of the complex is frequently identified when docking bound subunits, and a good docking orientation is ranked within the top 20 in 11 out of 18 cases when starting from unbound subunits. Proteins 2000;39:178-194.

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Angular Momentum in Quantum Physics

Abstract: This 1985 text develops the theory of angular momentum from the viewpoint of a fundamental symmetry in nature and shows how this concept relates to applied areas of research in modern quantum physics.

Cited by 639 publications

References 0 publications

A minimal representation of the self-assembly of virus capsids

A minimal representation of the self-assembly of virus capsids

The geometry of SU(3)

Protein docking using spherical polar Fourier correlations

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