1
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Cha M, Ma J, Kim JY, Emre EST, Kotov NA. Graph-theoretical chirality measure and chirality-property relations for chemical structures with multiscale mirror asymmetries. Chirality 2024; 36:e23678. [PMID: 38859658 DOI: 10.1002/chir.23678] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2024] [Revised: 04/23/2024] [Accepted: 04/24/2024] [Indexed: 06/12/2024]
Abstract
Chirality is an essential geometric property unifying small molecules, biological macromolecules, inorganic nanomaterials, biological microparticles, and many other chemical structures. Numerous chirality measures have attempted to quantify this geometric property of mirror asymmetry and to correlate these measures with physical and chemical properties. However, their utility has been widely limited because these correlations have been largely notional. Furthermore, chirality measures also require prohibitively demanding computations, especially for chiral structures comprised of thousands of atoms. Acknowledging the fundamental problems with quantification of mirror asymmetry, including the ambiguity of sign-variable pseudoscalar chirality measures, we revisit this subject because of the significance of quantifying chirality for quantitative biomimetics and describing the chirality of nanoscale materials that display chirality continuum and scale-dependent mirror asymmetry. We apply the concept of torsion within the framework of differential geometry to the graph theoretical representation of chiral molecules and nanostructures to address some of the fundamental problems and practical limitations of other chirality measures. Chiral gold clusters and other chiral structures are used as models to elaborate a graph-theoretical chirality (GTC) measure, demonstrating its applicability to chiral materials with different degrees of chirality at different scales. For specific cases, we show that GTC provides an adequate description of both the sign and magnitude of mirror asymmetry. The direct correlations with macroscopic properties, such as chiroptical spectra, are enhanced by using the hybrid chirality measures combining parameters from discrete mathematics and physics. Taking molecular helices as an example, we established a direct relation between GTC and optical activity, indicating that this chirality measure can be applied to chiral metamaterials and complex chiral constructs.
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Affiliation(s)
- Minjeong Cha
- Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan, USA
- Biointerfaces Institute, University of Michigan, Ann Arbor, Michigan, USA
| | - Jessica Ma
- Biointerfaces Institute, University of Michigan, Ann Arbor, Michigan, USA
- Center of Complex Particle Systems (COMPASS), University of Michigan, Ann Arbor, Michigan, USA
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan, USA
| | - Ji-Young Kim
- Biointerfaces Institute, University of Michigan, Ann Arbor, Michigan, USA
- Center of Complex Particle Systems (COMPASS), University of Michigan, Ann Arbor, Michigan, USA
| | - Emine Sumeyra Turali Emre
- Biointerfaces Institute, University of Michigan, Ann Arbor, Michigan, USA
- Center of Complex Particle Systems (COMPASS), University of Michigan, Ann Arbor, Michigan, USA
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan, USA
| | - Nicholas A Kotov
- Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan, USA
- Biointerfaces Institute, University of Michigan, Ann Arbor, Michigan, USA
- Center of Complex Particle Systems (COMPASS), University of Michigan, Ann Arbor, Michigan, USA
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan, USA
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2
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Alon G, Ben-Haim Y, Tuvi-Arad I. Continuous symmetry and chirality measures: approximate algorithms for large molecular structures. J Cheminform 2023; 15:106. [PMID: 37946281 PMCID: PMC10636902 DOI: 10.1186/s13321-023-00777-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Accepted: 10/28/2023] [Indexed: 11/12/2023] Open
Abstract
Quantifying imperfect symmetry of molecules can help explore the sources, roles and extent of structural distortion. Based on the established methodology of continuous symmetry and chirality measures, we develop a set of three-dimensional molecular descriptors to estimate distortion of large structures. These three-dimensional geometrical descriptors quantify the gap between the desirable symmetry (or chirality) and the actual one. They are global parameters of the molecular geometry, intuitively defined, and have the ability to detect even minute structural changes of a given molecule across chemistry, including organic, inorganic, and biochemical systems. Application of these methods to large structures is challenging due to countless permutations that are involved in the symmetry operations and have to be accounted for. Our approach focuses on iteratively finding the approximate direction of the symmetry element in the three-dimensional space, and the relevant permutation. Major algorithmic improvements over previous versions are described, showing increased accuracy, reliability and structure preservation. The new algorithms are tested for three sets of molecular structures including pillar[5]arene complexes with Li+, C100 fullerenes, and large unit cells of metal organic frameworks. These developments complement our recent algorithms for calculating continuous symmetry and chirality measures for small molecules as well as protein homomers, and simplify the usage of the full set of measures for various research goals, in molecular modeling, QSAR and cheminformatics.
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Affiliation(s)
- Gil Alon
- Department of Mathematics and Computer Science, The Open University of Israel, Raanana, Israel.
| | - Yuval Ben-Haim
- Department of Natural Sciences, The Open University of Israel, Raanana, Israel
| | - Inbal Tuvi-Arad
- Department of Natural Sciences, The Open University of Israel, Raanana, Israel.
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3
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Tuvi-Arad I, Shalit Y. The SARS-CoV-2 spike protein structure: a symmetry tale on distortion trail. Phys Chem Chem Phys 2023; 25:14430-14439. [PMID: 37184521 DOI: 10.1039/d3cp00163f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
A preliminary step in the SARS-CoV-2 human infection process is a conformational change of the receptor binding domain (RBD) of its spike protein, characterized by a significant loss of symmetry. During this process, the residues which later on bind to the human angiotensin converting enzyme 2 (ACE2) receptor, become exposed at the surface of the protein. Symmetry analysis of a data set of 33 protein structures from experimental measurements and 32 structures from molecular dynamics simulation, show that the initial state carries clear indications on the structure of the final state, with respect to the local distortion along the sequence. This surprising finding implies that this type of analysis predicts the mechanism of change. We further show that the level of local distortion at the initial state increases with variant's transmissibility, for the wild type (WT) along with past and present variants of concern (WT ∼ alpha < beta < delta < Omicron BA.1), in accordance with the trend of their evolutionary path. In other words, the initial structure of the variant which is most infectious is also the most distorted, making its path to the final state shorter. It has been claimed that the RBD migration of the spike protein is allosterically controlled. Our analysis provides a quantitative support to a major theorem in this respect - that information about an allosteric process is encoded in the structure itself, suggesting that the path of local distortion is related to an allosteric information network.
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Affiliation(s)
- Inbal Tuvi-Arad
- Department of Natural Sciences, The Open University of Israel, Raanana, Israel.
| | - Yaffa Shalit
- Department of Natural Sciences, The Open University of Israel, Raanana, Israel.
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4
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Fecher GH, Kübler J, Felser C. Chirality in the Solid State: Chiral Crystal Structures in Chiral and Achiral Space Groups. MATERIALS (BASEL, SWITZERLAND) 2022; 15:5812. [PMID: 36079191 PMCID: PMC9457223 DOI: 10.3390/ma15175812] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Revised: 08/11/2022] [Accepted: 08/16/2022] [Indexed: 06/15/2023]
Abstract
Chirality depends on particular symmetries. For crystal structures it describes the absence of mirror planes and inversion centers, and in addition to translations, only rotations are allowed as symmetry elements. However, chiral space groups have additional restrictions on the allowed screw rotations as a symmetry element, because they always appear in enantiomorphous pairs. This study classifies and distinguishes the chiral structures and space groups. Chirality is quantified using Hausdorff distances and continuous chirality measures and selected crystal structures are reported. Chirality is discussed for bulk solids and their surfaces. Moreover, the band structure, and thus, the density of states, is found to be affected by the same crystal parameters as chirality. However, it is independent of handedness. The Berry curvature, as a topological measure of the electronic structure, depends on the handedness but is not proof of chirality because it responds to the inversion of a structure. For molecules, optical circular dichroism is one of the most important measures for chirality. Thus, it is proposed in this study that the circular dichroism in the angular distribution of photoelectrons in high symmetry configurations can be used to distinguish the handedness of chiral solids and their surfaces.
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Affiliation(s)
- Gerhard H. Fecher
- Max Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany
| | - Jürgen Kübler
- Institute of Solid State Physics, Technical University Darmstadt, D-64289 Darmstadt, Germany
| | - Claudia Felser
- Max Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany
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5
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Nguyen HVT, Jiang Y, Mohapatra S, Wang W, Barnes JC, Oldenhuis NJ, Chen KK, Axelrod S, Huang Z, Chen Q, Golder MR, Young K, Suvlu D, Shen Y, Willard AP, Hore MJA, Gómez-Bombarelli R, Johnson JA. Bottlebrush polymers with flexible enantiomeric side chains display differential biological properties. Nat Chem 2022; 14:85-93. [PMID: 34824461 PMCID: PMC9122101 DOI: 10.1038/s41557-021-00826-8] [Citation(s) in RCA: 29] [Impact Index Per Article: 14.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2020] [Accepted: 09/27/2021] [Indexed: 11/08/2022]
Abstract
Chirality and molecular conformation are central components of life: biological systems rely on stereospecific interactions between discrete (macro)molecular conformers, and the impacts of stereochemistry and rigidity on the properties of small molecules and biomacromolecules have been intensively studied. Nevertheless, how these features affect the properties of synthetic macromolecules has received comparably little attention. Here we leverage iterative exponential growth and ring-opening metathesis polymerization to produce water-soluble, chiral bottlebrush polymers (CBPs) from two enantiomeric pairs of macromonomers of differing rigidity. Remarkably, CBPs with conformationally flexible, mirror image side chains show several-fold differences in cytotoxicity, cell uptake, blood pharmacokinetics and liver clearance; CBPs with comparably rigid, mirror image side chains show no differences. These observations are rationalized with a simple model that correlates greater conformational freedom with enhanced chiral recognition. Altogether, this work provides routes to the synthesis of chiral nanostructured polymers and suggests key roles for stereochemistry and conformational rigidity in the design of future biomaterials.
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Affiliation(s)
- Hung V-T Nguyen
- Department of Chemistry and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Yivan Jiang
- Department of Chemistry and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Somesh Mohapatra
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Wencong Wang
- Department of Chemistry and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Jonathan C Barnes
- Department of Chemistry and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Nathan J Oldenhuis
- Department of Chemistry and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Kathleen K Chen
- Department of Chemistry and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Simon Axelrod
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA
| | - Zhihao Huang
- Department of Chemistry and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Qixian Chen
- Department of Chemistry and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Matthew R Golder
- Department of Chemistry and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Katherine Young
- Department of Chemistry and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Dylan Suvlu
- Department of Chemistry and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Yizhi Shen
- Department of Chemistry and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Adam P Willard
- Department of Chemistry and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Michael J A Hore
- Department of Macromolecular Science and Engineering, Case Western Reserve University, Cleveland, OH, USA
| | - Rafael Gómez-Bombarelli
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.
| | - Jeremiah A Johnson
- Department of Chemistry and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.
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6
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Tashiro M, Imamura Y, Katouda M. De novo generation of optically active small organic molecules using Monte Carlo tree search combined with recurrent neural network. J Comput Chem 2020; 42:136-143. [DOI: 10.1002/jcc.26441] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2020] [Revised: 10/10/2020] [Accepted: 10/14/2020] [Indexed: 12/21/2022]
Affiliation(s)
| | - Yutaka Imamura
- Department of Chemistry Graduate School of Science and Engineering, Tokyo Metropolitan University Hachioji Tokyo Japan
| | - Michio Katouda
- Department of Computational Science and Technology Research Organization for Information Science and Technology Minato‐ku Tokyo Japan
- Research Institute for Science and Engineering, Waseda University Shinjuku‐ku Tokyo Japan
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7
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Shalit Y, Tuvi-Arad I. Side chain flexibility and the symmetry of protein homodimers. PLoS One 2020; 15:e0235863. [PMID: 32706779 PMCID: PMC7380632 DOI: 10.1371/journal.pone.0235863] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2020] [Accepted: 06/24/2020] [Indexed: 01/22/2023] Open
Abstract
A comprehensive analysis of crystallographic data of 565 high-resolution protein homodimers comprised of over 250,000 residues suggests that amino acids form two groups that differ in their tendency to distort or symmetrize the structure of protein homodimers. Residues of the first group tend to distort the protein homodimer and generally have long or polar side chains. These include: Lys, Gln, Glu, Arg, Asn, Met, Ser, Thr and Asp. Residues of the second group contribute to protein symmetry and are generally characterized by short or aromatic side chains. These include: Ile, Pro, His, Val, Cys, Leu, Trp, Tyr, Phe, Ala and Gly. The distributions of the continuous symmetry measures of the proteins and the continuous chirality measures of their building blocks highlight the role of side chain geometry and the interplay between entropy and symmetry in dictating the conformational flexibility of proteins.
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Affiliation(s)
- Yaffa Shalit
- Department of Natural Sciences, The Open University of Israel, Raanana, Israel
| | - Inbal Tuvi-Arad
- Department of Natural Sciences, The Open University of Israel, Raanana, Israel
- * E-mail:
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8
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Chiral Dualism as an Instrument of Hierarchical Structure Formation in Molecular Biology. Symmetry (Basel) 2020. [DOI: 10.3390/sym12040587] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
The origin of chiral asymmetry in biology has attracted the attention of the research community throughout the years. In this paper we discuss the role of chirality and chirality sign alternation (L–D–L–D in proteins and D–L–D–L in DNA) in promoting self-organization in biology, starting at the level of single molecules and continuing to the level of supramolecular assemblies. In addition, we also discuss chiral assemblies in solutions of homochiral organic molecules. Sign-alternating chiral hierarchies created by proteins and nucleic acids are suggested to create the structural basis for the existence of selected mechanical degrees of freedom required for conformational dynamics in enzymes and macromolecular machines.
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9
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Tuvi-Arad I, Alon G. Improved algorithms for quantifying the near symmetry of proteins: complete side chains analysis. J Cheminform 2019; 11:39. [PMID: 31172379 PMCID: PMC6551912 DOI: 10.1186/s13321-019-0360-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2018] [Accepted: 05/28/2019] [Indexed: 12/12/2022] Open
Abstract
Symmetry of proteins, an important source of their elegant structure and unique functions, is not as perfect as it may seem. In the framework of continuous symmetry, in which symmetry is no longer a binary yes/no property, such imperfections can be quantified and used as a global descriptor of the three-dimensional structure. We present an improved algorithm for calculating the continuous symmetry measure for proteins that takes into account their complete set of atoms including all side chains. Our method takes advantage of the protein sequence and the division into peptides in order to improve the accuracy and efficiency of the calculation over previous methods. The Hungarian algorithm is applied to solve the assignment problem and find the permutation that defines the symmetry operation. Analysis of the symmetry of several sets of protein homomers, with various degrees of rotational symmetry is presented. The new methodology lays the foundations for accurate, efficient and reliable large scale symmetry analysis of protein structure and can be used as a collective variable that describes changes of the protein geometry along various processes, both at the backbone level and for the complete protein structure.
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Affiliation(s)
- Inbal Tuvi-Arad
- Department of Natural Sciences, The Open University of Israel, 4353701, Raanana, Israel.
| | - Gil Alon
- Department of Mathematics and Computer Science, The Open University of Israel, 4353701, Raanana, Israel.
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10
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Carreras A, Bernuz E, Marugan X, Llunell M, Alemany P. Effects of Temperature on the Shape and Symmetry of Molecules and Solids. Chemistry 2018; 25:673-691. [DOI: 10.1002/chem.201801682] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2018] [Revised: 07/17/2018] [Indexed: 01/22/2023]
Affiliation(s)
- Abel Carreras
- Donostia International Physics Center (DIPC) Paseo Manuel de Lardizabal 4 20018 Donostia, Euskadi Spain
| | - Efrem Bernuz
- Departament de Ciència dels Materials i Química Física andInstitut de Química Teòrica i Computacional (IQTCUB)Universitat de Barcelona Diagonal 647 08028 Barcelona, Catalunya Spain
| | - Xavier Marugan
- Departament de Ciència dels Materials i Química Física andInstitut de Química Teòrica i Computacional (IQTCUB)Universitat de Barcelona Diagonal 647 08028 Barcelona, Catalunya Spain
| | - Miquel Llunell
- Departament de Ciència dels Materials i Química Física andInstitut de Química Teòrica i Computacional (IQTCUB)Universitat de Barcelona Diagonal 647 08028 Barcelona, Catalunya Spain
| | - Pere Alemany
- Departament de Ciència dels Materials i Química Física andInstitut de Química Teòrica i Computacional (IQTCUB)Universitat de Barcelona Diagonal 647 08028 Barcelona, Catalunya Spain
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11
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Pagès G, Grudinin S. Analytical symmetry detection in protein assemblies. II. Dihedral and cubic symmetries. J Struct Biol 2018; 203:185-194. [PMID: 29902523 DOI: 10.1016/j.jsb.2018.05.005] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2018] [Accepted: 05/18/2018] [Indexed: 01/10/2023]
Abstract
Protein assemblies are often symmetric, as this organization has many advantages compared to individual proteins. Complex protein structures thus very often possess high-order symmetries. Detection and analysis of these symmetries has been a challenging problem and no efficient algorithms have been developed so far. This paper presents the extension of our cyclic symmetry detection method for higher-order symmetries with multiple symmetry axes. These include dihedral and cubic, i.e., tetrahedral, octahedral, and icosahedral, groups. Our method assesses the quality of a particular symmetry group and also determines all of its symmetry axes with a machine precision. The method comprises discrete and continuous optimization steps and is applicable to assemblies with multiple chains in the asymmetric subunits or to those with pseudo-symmetry. We implemented the method in C++ and exhaustively tested it on all 51,358 symmetric assemblies from the Protein Data Bank (PDB). It allowed us to study structural organization of symmetric assemblies solved by X-ray crystallography, and also to assess the symmetry annotation in the PDB. For example, in 1.6% of the cases we detected a higher symmetry group compared to the PDB annotation, and we also detected several cases with incorrect annotation. The method is available at http://team.inria.fr/nano-d/software/ananas. The graphical user interface of the method built for the SAMSON platform is available at http://samson-connect.net.
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Affiliation(s)
- Guillaume Pagès
- Inria, Univ. Grenoble Alpes, CNRS, Grenoble INP, LJK, Grenoble 38000, France
| | - Sergei Grudinin
- Inria, Univ. Grenoble Alpes, CNRS, Grenoble INP, LJK, Grenoble 38000, France.
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12
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Pagès G, Kinzina E, Grudinin S. Analytical symmetry detection in protein assemblies. I. Cyclic symmetries. J Struct Biol 2018; 203:142-148. [PMID: 29705493 DOI: 10.1016/j.jsb.2018.04.004] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2018] [Revised: 04/18/2018] [Accepted: 04/19/2018] [Indexed: 12/30/2022]
Abstract
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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Affiliation(s)
- Guillaume Pagès
- Inria, Univ. Grenoble Alpes, CNRS, Grenoble INP, LJK, Grenoble 38000, France
| | - Elvira Kinzina
- Moscow Institute of Physics and Technology, Dolgoprudny 141701, Russia
| | - Sergei Grudinin
- Inria, Univ. Grenoble Alpes, CNRS, Grenoble INP, LJK, Grenoble 38000, France.
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13
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Alemany P, Casanova D, Alvarez S, Dryzun C, Avnir D. Continuous Symmetry Measures: A New Tool in Quantum Chemistry. REVIEWS IN COMPUTATIONAL CHEMISTRY 2017. [DOI: 10.1002/9781119356059.ch7] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Pere Alemany
- Departament de Química Física and Institut de Química Teòrica i Computacional (IQTCUB); Universitat de Barcelona; Barcelona Spain
| | - David Casanova
- Donostia International Physics Center (DIPC); Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU); Donostia Spain
- IKERBASQUE, Basque Foundation for Science; Bilbao Spain
| | - Santiago Alvarez
- Departament de Química Inorgànica and Institut de Química Teòrica i Computacional (IQTCUB); Universitat de Barcelona; Barcelona Spain
| | - Chaim Dryzun
- Institute of Chemistry and The Lise Meitner Minerva Center for Computational Quantum Chemistry; The Hebrew University of Jerusalem; Jerusalem Israel
| | - David Avnir
- Institute of Chemistry and The Lise Meitner Minerva Center for Computational Quantum Chemistry; The Hebrew University of Jerusalem; Jerusalem Israel
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14
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Brancatelli G, Nicosia C, Barboza T, Guy L, Dutasta JP, De Zorzi R, Demitri N, Dalcanale E, Geremia S, Pinalli R. Enantiospecific recognition of 2-butanol by an inherently chiral cavitand in the solid state. CrystEngComm 2017. [DOI: 10.1039/c7ce00557a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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15
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Bonjack-Shterengartz M, Avnir D. The near-symmetry of proteins. Proteins 2015; 83:722-34. [PMID: 25354765 DOI: 10.1002/prot.24706] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2014] [Revised: 10/06/2014] [Accepted: 10/18/2014] [Indexed: 11/07/2022]
Abstract
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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Affiliation(s)
- Maayan Bonjack-Shterengartz
- Institute of Chemistry and the Lise Meitner Minerva Center for Computational Quantum Chemistry, the Hebrew University of Jerusalem, Jerusalem, 91904, Israel
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16
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Dryzun C. Continuous symmetry measures for complex symmetry group. J Comput Chem 2014; 35:748-55. [PMID: 24590424 DOI: 10.1002/jcc.23548] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2013] [Revised: 12/29/2013] [Accepted: 01/02/2014] [Indexed: 12/14/2022]
Abstract
Symmetry is a fundamental property of nature, used extensively in physics, chemistry, and biology. The Continuous symmetry measures (CSM) is a method for estimating the deviation of a given system from having a certain perfect symmetry, which enables us to formulate quantitative relation between symmetry and other physical properties. Analytical procedures for calculating the CSM of all simple cyclic point groups are available for several years. Here, we present a methodology for calculating the CSM of any complex point group, including the dihedral, tetrahedral, octahedral, and icosahedral symmetry groups. We present the method and analyze its performances and errors. We also introduce an analytical method for calculating the CSM of the linear symmetry groups. As an example, we apply these methods for examining the symmetry of water, the symmetry maps of AB4 complexes, and the symmetry of several Lennard-Jones clusters.
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Affiliation(s)
- Chaim Dryzun
- Department of Natural Sciences, The Open University of Israel, Raanana, 43107, Israel
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17
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Beruski O, Vidal LN. Algorithms for computer detection of symmetry elements in molecular systems. J Comput Chem 2013; 35:290-9. [DOI: 10.1002/jcc.23493] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2013] [Revised: 10/02/2013] [Accepted: 11/05/2013] [Indexed: 12/17/2022]
Affiliation(s)
- Otávio Beruski
- Department of Physical Chemistry; Institute of Chemistry of São Carlos, University of São Paulo - São Carlos; Brazil
| | - Luciano N. Vidal
- Chemistry and Biology Department; Federal University of Technology - Paraná; Brazil
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Ostrowski S, Jamróz MH, Dobrowolski JC. A study on the stability, chirality, and theoretical spectra of the heterofullerenes C69X (X=N, P, As, B, Si, Ge). ACTA ACUST UNITED AC 2013. [DOI: 10.1016/j.tetasy.2013.07.022] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Pinsky M, Zait A, Bonjack M, Avnir D. Continuous symmetry analyses:CnvandDnmeasures of molecules, complexes, and proteins. J Comput Chem 2012; 34:2-9. [DOI: 10.1002/jcc.23092] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2012] [Revised: 07/22/2012] [Accepted: 07/24/2012] [Indexed: 11/08/2022]
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Tuvi-Arad I, Avnir D. Symmetry-Enthalpy Correlations in Diels-Alder Reactions. Chemistry 2012; 18:10014-20. [DOI: 10.1002/chem.201200927] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2012] [Indexed: 11/09/2022]
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Wheeler KA, Malehorn SH, Egan AE. Valine sulfonamidecinnamic acid asymmetric crystal reactions. Chem Commun (Camb) 2012; 48:519-21. [DOI: 10.1039/c1cc15068e] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Alemany P, Casanova D, Álvarez S. Continuous symmetry measures of irreducible representations: application to molecular orbitals. Phys Chem Chem Phys 2012; 14:11816-23. [DOI: 10.1039/c2cp41506b] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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