Continuous symmetry measures for complex symmetry group

Dryzun, Chaim

doi:10.1002/jcc.23548

Cited by 16 publications

(14 citation statements)

References 87 publications

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“…All these have a common idea of comparing a protein structure with a rotated version of itself. Another set of methods for the continuous chirality and symmetry analysis has been developed by David Avnir and colleagues [17,18,19] and also by Michel Petitjean [20], however these do not seem computationally suitable for processing large amounts of macromolecular data, specifically those from PDB. On the other hand, determining a symmetry group of a molecular assembly, finding its axes of symmetry, and assessing the quality of this symmetry are the essential steps in analysis of structural molecular data.…”

Section: Introductionmentioning

confidence: 99%

Analytical symmetry detection in protein assemblies. I. Cyclic symmetries

Pagès

Kinzina

Grudinin

2018

Journal of Structural Biology

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Symmetry in protein, and, more generally, in macromolecular assemblies is a key point to understand their structure, stability and function. Many symmetrical assemblies are currently present in the Protein Data Bank (PDB) and some of them are among the largest solved structures, thus an efficient computational method is needed for the exhaustive analysis of these. The cyclic symmetry groups represent the most common assemblies in the PDB. These are also the building blocks for higher-order symmetries. This paper presents a mathematical formulation to find the position and the orientation of the symmetry axis in a cyclic symmetrical protein assembly, and also to assess the quality of this symmetry. Our method can also detect symmetries in partial assemblies. We provide an efficient C++ implementation of the method and demonstrate its efficiency on several examples including partial assemblies and pseudo symmetries. We also compare the method with two other published techniques and show that it is significantly faster on all the tested examples. Our method produces results with a machine precision, its cost function is solely based on 3D Euclidean geometry, and most of the operations are performed analytically. The method is available athttp://team.inria.fr/nano-d/software/ananas. The graphical user interface of the method built for the SAMSON platform is available athttp://samson-connect.net.

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Section: Introductionmentioning

confidence: 99%

Analytical symmetry detection in protein assemblies. I. Cyclic symmetries

Pagès

Kinzina

Grudinin

2018

Journal of Structural Biology

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“…; and so on. The use of quantitative descriptors of symmetry—the Continuous Symmetry Measure (CSM)—has already proven very useful in identifying and understanding a host of symmetry‐related phenomena, and some encouraging indications for its usefulness in protein structure analyses exist. For instance, Keinan et al .…”

Section: Introductionmentioning

confidence: 99%

The near‐symmetry of proteins

Bonjack-Shterengartz

Avnir

2015

Proteins

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The majority of protein oligomers form clusters which are nearly symmetric. Understanding of that imperfection, its origins, and perhaps also its advantages requires the conversion of the currently used vague qualitative descriptive language of the near-symmetry into an accurate quantitative measure that will allow to answer questions such as: "What is the degree of symmetry deviation of the protein?," "how do these deviations compare within a family of proteins?," and so on. We developed quantitative methods to answer this type of questions, which are capable of analyzing the whole protein, its backbone or selected portions of it, down to comparison of symmetry-related specific amino-acids, and which are capable of visualizing the various levels of symmetry deviations in the form of symmetry maps. We have applied these methods on an extensive list of homomers and heteromers and found that apparently all proteins never reach perfect symmetry. Strikingly, even homomeric protein clusters are never ideally symmetric. We also found that the main burden of symmetry distortion is on the amino-acids near the symmetry axis; that it is mainly the more hydrophilic amino-acids that take place in symmetry-distortive interactions; and more. The remarkable ability of heteromers to preserve near-symmetry, despite the different sequences, was also shown and analyzed. The comprehensive literature on the suggested advantages symmetric oligomerizations raises a yet-unsolved key question: If symmetry is so advantageous, why do proteins stop shy of perfect symmetry? Some tentative answers to be tested in further studies are suggested in a concluding outlook.

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“…The symmetry deviation value, σideal, is computed using our AlignIt approach. 33,34 The method builds on the Continuous Symmetry Measure approach and its incorporation into the program SHAPE, [40][41][42][43][44][45][46][47][48] and was developed to compare the coordination geometry of ten-coordinated lanthanide complexes. The symmetry deviation value, σideal, is calculated using equation 1, following the detailed methodology described in the ESI.…”

Section: Symmetry Deviationmentioning

confidence: 99%

Long Story Short: Donor Set Symmetry in Eu(DOTA) Crystals Determines the Electronic Structure

Thomsen

Andersen

Sørensen

2022

Preprint

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Lanthanide complexes of 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid DOTA have been studied in great detail due to their use as MRI contrast agents. Since the first report from Desreux in 1980, the Ln.DOTA complexes of gadolium(III) in particular have been thouroughly investigated. The forms of the nine-coordinated [Ln(DOTA)(H2O)]- complexes are well known, and the ligand backbone has been used extensively to create functional MRI contrast agents, luminescent probes, and as a model system for studying the properties of lanthanide(III) ions. In solution, the photophysical properties have been mapped, but as the structures are not known, direct structure property relationships have not been created. Here, the electronic properties of two Eu.DOTA compounds (1 and 2) and a Eu.DOTA-like compound (3) were studied using single-crystal luminescence spectroscopy. The donor set in the three compounds is identical (4N 4O 1O), and using the symmetry deviation value σideal it was shown that the coordination geomtry is close to identical. Nevertheless, the electronic properties evaluted using the luminescece spectrum was found to differ significantly between the three compounds. The magnitude of the crystal field splitting was found not to scale with the symmetry of the coordination geometry. It was concluded that the donor set dictates the splitting, yet the structure-property relationships governing the electronic properties of europium(III) ions still elude us.

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Continuous symmetry measures for complex symmetry group

Cited by 16 publications

References 87 publications

Analytical symmetry detection in protein assemblies. I. Cyclic symmetries

Analytical symmetry detection in protein assemblies. I. Cyclic symmetries

The near‐symmetry of proteins

Long Story Short: Donor Set Symmetry in Eu(DOTA) Crystals Determines the Electronic Structure

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