American Journal of Quantum Chemistry and Molecular Spectroscopy

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3-Sphere Torsional Angles and Six Membered Ring Conformation

Received: 16 March 2023    Accepted: 4 April 2023    Published: 24 April 2023
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Abstract

The conformation of six membered ring, 1,3,4-tri-o-acetyl-2-azido-6-bromo-2,6-dideoxy-D-galactose α-1 and β-1, and 2,6-dideoxy-2,6-imino- D-talonic acid 2D and L-talonic acid 2L, is analyzed inscribing two five membered ring on six membered ring. Altona’s five membered ring conformational parameters, phase angles of the pseudorotation P1, P2 [deg] and angle of deviation from planarity θm [deg] = f(P [deg]), are calculated with Java Script program using 3-Sphere torsional angles. The correlation between Altona map and six membered ring Stoddart’s diagram conformations was confirmed with VISION molecular models. 3-Sphere torsional angles θnn+1 [deg] for all cis, trans-ee, -aa stereochemistry are disclosed from trigonometric point of view, Hopf fibration confirmed by Lie algebra. The cis, trans stereochemistry on two units with six sets angles ensure relationships between dihedral θHnHn+1 [deg]/vicinal angles ϕ [deg] (θBn + A = θAn, θAn = θHnHn+1, θBn = ϕ), and between dihedral θHnHn+1 [deg]/torsional angles θnn+1 [deg] (θnn+1 = A +/- θHnHn+1); in first case A = 150 for trans-aa6,1 and A = 90 for trans-aa5,2 and trans-ee stereochemistry, in last case A = 180 [deg] for cis and trans-aa stereochemistry and A = 120 [deg] for trans-ee stereochemistry. The number of dihedral angles with positive and negative sign results from 3-sphere approach for only one vicinal coupling constant 3JHnHn+1 [Hz] are restricted by the VISION molecular models.

DOI 10.11648/j.ajqcms.20230701.12
Published in American Journal of Quantum Chemistry and Molecular Spectroscopy (Volume 7, Issue 1, June 2023)
Page(s) 9-15
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

3-Sphere, Hopf Fibration, Lie Algebra, 6 Membered Ring Conformation, Altona Map, Stoddart’s Diagrams, Carbasugar

References
[1] C. Altona, M. Sundaralingam, Conformational analysis of the sugar ring in nucleosides and nucleotides. A new description using the concept of pseudorotation, J. Am. Chem. Soc. 1972, 94, 8205; doi.org/10.1021/ja00778a043.
[2] A. Navarro-Vazquez, J. C. Cobas, F. J. Sardina, A graphical tool for the prediction of vicinal proton-proton 3JHH coupling constants, J. Chem. Inf. Comput. Sci. 2004, 44, 1690; doi.10.1021/ci049913f.
[3] E. Bartha, C.-I. Mitan, C. Draghici, M. T. Caproiu, P. Filip, R. Moriarty, Program for prediction dihedral angle from vicinal coupling constant with 3-sphere approach, Rev. Roum. Chim. 2021, 66, 178-183; DOI: 10.33224/rrch.2021.66.2.08 (Eng).
[4] C.-I. Mitan, E. Bartha, P. Filip, C. Draghici, M. T. Caproiu, R. M. Moriarty, Two isomers with trans-aa5,2 stereochemistry are calculated with 3-sphere trigonometric equations approach at circle inversion motion from NMR data. ACS National Meeting in Chicago, IL, August 21- 25, 2022, CARB 3717658, 22 august 2022; doi.org/10.1021/scimeetings.2c00523.
[5] C.-I. Mitan, E. Bartha, C. Draghici, M. T. Caproiu, P. Filip, R. M. Moriarty, Hopf fibration on relationship between dihedral angle θHnHn+1 [deg] and vicinal angle ϕ [deg], angles calculated from NMR data with 3-sphere approach and Java Script, Science Journal of Chemistry, SciencePG 2022, 10, 21; DOI: 10.11648/j.sjc.20221001.13 (Eng).
[6] J. B. Houseknecht, C. Altona, C. M. Hadad, T. L. Lowary, Conformational Analysis of Furanose Rings with PSEUROT:  Parametrization for Rings Possessing the Arabino, Lyxo, Ribo, and Xylo Stereochemistry and Application to Arabinofuranosides, J. Org. Chem. 2002, 67, 4647; doi.org/10.1021/jo025635q.
[7] P. MS Hendrickx, J. C. Martins, A new friendly Matlab program and GUI for the pseudorotation analysis of saturated five membered ring system based on scalar coupling constants, Chemistry Central Journal 2008, 2, 20; doi: 10.1186/1752-153X-2-4.
[8] F. H. Cano, C. Forces-Forces, S. Garcia-Blanco, A model for describing the conformation of flexible 6-membered rings. I. Tetrahedron 1977, 33, 797; doi.org/10.1016/0040-4020(77)80195-6.
[9] J. C. A. Boeyens, The conformation of six membered rings, J. Cryst. Molec. Struct., 1978, 8 (6), 317; doi 10.1007/BF01200485.
[10] C.-I. Mitan, E. Bartha, P. Filip, C. Draghici, M. T. Caproiu, R. M. Moriarty, NMR data on conformational analysis of five and six membered ring under 3-sphere approach. Vicinal constant coupling 3JHH on relationships between dihedral angles and tetrahedral angles. “Sustainability in a changing world” ACS National Meeting in Chicago, IL, August 21- 25, 2022, CARB 3717557, 22 august 2022; doi.org/10.1021/scimeetings.2c00876.
[11] X. Biarnés, A. Ardeval, A. Planas, C. Rovira, A. Laio, M. Parrinello, The conformational free energy landscape of β-glucopyranose. Implications for substrate preactivation in β-glucoside hydrolases, J. Am. Chem. Soc. 2007, 129, 10686; Doi: 10.1021/ja068411a.
[12] A. R. Ionescu, A. Bérces, M. Z. Zgierski, D. M. Whitfield, T. Nukada, Conformational pathways of saturated six-membered rings. A static and dynamical density functional study, J. Phys. Chem. A 2005, 109, 8096; doi.10.1021/jp052197t.
[13] E. Lescrinier, M. Froeyen, P. Herdewijn, Difference in conformational diversity between nucleic acids with a six-membered “sugar” unit and natural “furanose” nucleic acids, Nucleic Acids Research 2003, 31 (12), 2975; Doi: 10.1093/nor/gkg407.
[14] Wikipedia: Root system, cube tesseract, Schlafi Hess polygon.
[15] C.-I. Mitan, E. Bartha, P. Filip, C. Draghici, M. T. Caproiu, R. M. Moriarty, Manifold inversion on prediction dihedral angle from vicinal coupling constant with 3-sphere approach, Rev. Roum. Chim. 2023, in press.
[16] E. Bartha, C.-I. Mitan, C. Draghici, M. T. Caproiu, P. Filip, R. Moriarty, Rectangle as manifold on relationships between vicinal constant couplings 3JHH, 1H and 13C-chemical shifts and dihedral angles, Rev. Roum. Chim., 2022, 67 (3), 167 – 172; DOI: 10.33224/rrch.2022.67.3.05 (Eng).
[17] B. M. Malle, I. Lundt, T. M. Wrodnigg, Regioselective intramolecular ring closure of 2-amino-6-bromo-2,6-dideoxyhexano-1,4-lactones to 5- or 6-membered iminuroic acid analogues: synthesis of 1-deoxymannojirimycin and 2.5-dideoxy-2,5-imino-D-glucitol, Organic&Biomolecular Chemistry, 2008, 6, 1779; doi.org/10.1039/B719631H.
[18] C.-I. Mitan, E. Bartha, P. Filip, C. Draghici, M. T. Caproiu, R. M. Moriarty, Dihedral angles calculated with 3-sphere approach as integer in conformational analysis on D-, L- ribitol series, Rev. Roum. Chim. 2022, 66 (21), 941, DOI: 10.33224/rrch.2021.66.12.07 (Eng).
[19] J. Iglesias-Fernández, L. Raich, A. Ardèval, C. Rovira, The complete conformational free energy landscape of β-xylose reveals a two fold catalytic itinerary for β-xylanases, Chemical Science, 2015, 6, 1167; DOI: 10.1039/c4sc02240h.
[20] P. E. Marszalek, Y-P. Pang, H. Li, J. El Yazal, A. F. Oberhauser, J. M. Fernandez, Atomic levers control pyranose ring conformations, Proc. Natl. Acad. Sci. USA, 1999, 96, 7894; doi.org/10.1073/pnas96.14.7894.
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  • APA Style

    Emerich Bartha, Carmen-Irena Mitan, Petru Filip. (2023). 3-Sphere Torsional Angles and Six Membered Ring Conformation. American Journal of Quantum Chemistry and Molecular Spectroscopy, 7(1), 9-15. https://doi.org/10.11648/j.ajqcms.20230701.12

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    ACS Style

    Emerich Bartha; Carmen-Irena Mitan; Petru Filip. 3-Sphere Torsional Angles and Six Membered Ring Conformation. Am. J. Quantum Chem. Mol. Spectrosc. 2023, 7(1), 9-15. doi: 10.11648/j.ajqcms.20230701.12

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    AMA Style

    Emerich Bartha, Carmen-Irena Mitan, Petru Filip. 3-Sphere Torsional Angles and Six Membered Ring Conformation. Am J Quantum Chem Mol Spectrosc. 2023;7(1):9-15. doi: 10.11648/j.ajqcms.20230701.12

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  • @article{10.11648/j.ajqcms.20230701.12,
      author = {Emerich Bartha and Carmen-Irena Mitan and Petru Filip},
      title = {3-Sphere Torsional Angles and Six Membered Ring Conformation},
      journal = {American Journal of Quantum Chemistry and Molecular Spectroscopy},
      volume = {7},
      number = {1},
      pages = {9-15},
      doi = {10.11648/j.ajqcms.20230701.12},
      url = {https://doi.org/10.11648/j.ajqcms.20230701.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajqcms.20230701.12},
      abstract = {The conformation of six membered ring, 1,3,4-tri-o-acetyl-2-azido-6-bromo-2,6-dideoxy-D-galactose α-1 and β-1, and 2,6-dideoxy-2,6-imino- D-talonic acid 2D and L-talonic acid 2L, is analyzed inscribing two five membered ring on six membered ring. Altona’s five membered ring conformational parameters, phase angles of the pseudorotation P1, P2 [deg] and angle of deviation from planarity θm [deg] = f(P [deg]), are calculated with Java Script program using 3-Sphere torsional angles. The correlation between Altona map and six membered ring Stoddart’s diagram conformations was confirmed with VISION molecular models. 3-Sphere torsional angles θnn+1 [deg] for all cis, trans-ee, -aa stereochemistry are disclosed from trigonometric point of view, Hopf fibration confirmed by Lie algebra. The cis, trans stereochemistry on two units with six sets angles ensure relationships between dihedral θHnHn+1 [deg]/vicinal angles ϕ [deg] (θBn + A = θAn, θAn = θHnHn+1, θBn = ϕ), and between dihedral θHnHn+1 [deg]/torsional angles θnn+1 [deg] (θnn+1 = A +/- θHnHn+1); in first case A = 150 for trans-aa6,1 and A = 90 for trans-aa5,2 and trans-ee stereochemistry, in last case A = 180 [deg] for cis and trans-aa stereochemistry and A = 120 [deg] for trans-ee stereochemistry. The number of dihedral angles with positive and negative sign results from 3-sphere approach for only one vicinal coupling constant 3JHnHn+1 [Hz] are restricted by the VISION molecular models.},
     year = {2023}
    }
    

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  • TY  - JOUR
    T1  - 3-Sphere Torsional Angles and Six Membered Ring Conformation
    AU  - Emerich Bartha
    AU  - Carmen-Irena Mitan
    AU  - Petru Filip
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    DO  - 10.11648/j.ajqcms.20230701.12
    T2  - American Journal of Quantum Chemistry and Molecular Spectroscopy
    JF  - American Journal of Quantum Chemistry and Molecular Spectroscopy
    JO  - American Journal of Quantum Chemistry and Molecular Spectroscopy
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    EP  - 15
    PB  - Science Publishing Group
    SN  - 2994-7308
    UR  - https://doi.org/10.11648/j.ajqcms.20230701.12
    AB  - The conformation of six membered ring, 1,3,4-tri-o-acetyl-2-azido-6-bromo-2,6-dideoxy-D-galactose α-1 and β-1, and 2,6-dideoxy-2,6-imino- D-talonic acid 2D and L-talonic acid 2L, is analyzed inscribing two five membered ring on six membered ring. Altona’s five membered ring conformational parameters, phase angles of the pseudorotation P1, P2 [deg] and angle of deviation from planarity θm [deg] = f(P [deg]), are calculated with Java Script program using 3-Sphere torsional angles. The correlation between Altona map and six membered ring Stoddart’s diagram conformations was confirmed with VISION molecular models. 3-Sphere torsional angles θnn+1 [deg] for all cis, trans-ee, -aa stereochemistry are disclosed from trigonometric point of view, Hopf fibration confirmed by Lie algebra. The cis, trans stereochemistry on two units with six sets angles ensure relationships between dihedral θHnHn+1 [deg]/vicinal angles ϕ [deg] (θBn + A = θAn, θAn = θHnHn+1, θBn = ϕ), and between dihedral θHnHn+1 [deg]/torsional angles θnn+1 [deg] (θnn+1 = A +/- θHnHn+1); in first case A = 150 for trans-aa6,1 and A = 90 for trans-aa5,2 and trans-ee stereochemistry, in last case A = 180 [deg] for cis and trans-aa stereochemistry and A = 120 [deg] for trans-ee stereochemistry. The number of dihedral angles with positive and negative sign results from 3-sphere approach for only one vicinal coupling constant 3JHnHn+1 [Hz] are restricted by the VISION molecular models.
    VL  - 7
    IS  - 1
    ER  - 

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Author Information
  • Department of Chemistry, “C. D. Nenitescu” Institute of Organic and Supramolecular Chemistry, Bucharest, Romania

  • Department of Chemistry, “C. D. Nenitescu” Institute of Organic and Supramolecular Chemistry, Bucharest, Romania

  • Department of Chemistry, “C. D. Nenitescu” Institute of Organic and Supramolecular Chemistry, Bucharest, Romania

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