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Computerized Molecular Modeling of Carbohydrates

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The Plant Cell Wall

Part of the book series: Methods in Molecular Biology ((MIMB,volume 2149))

Abstract

Computerized molecular modeling continues to increase in capability and applicability to carbohydrates. This chapter covers nomenclature and conformational aspects of carbohydrates, perhaps of greater use to computational chemists who do not have a strong background in carbohydrates, and its comments on various methods and studies might be of more use to carbohydrate chemists who are inexperienced with computation. Work on the intrinsic variability of glucose, an overall theme, is described. Other areas of the authors’ emphasis, including evaluation of hydrogen bonding by the atoms-in-molecules approach, and validation of modeling methods with crystallographic results are also presented.

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References

  1. Watts HD, Mohamed MNA, Kubicki JD (2014) A DFT study of vibrational frequencies and 13C NMR chemical shifts of model cellulosic fragments as a function of size. Cellulose 21:53–70

    CAS  Google Scholar 

  2. Toukach FV, Ananikov VP (2013) Recent advances in computational predictions of NMR parameters for the structure elucidation of carbohydrates: methods and limitations. Chem Soc Rev 42:8376–8415

    CAS  PubMed  Google Scholar 

  3. Kurihara Y, Ueda K (2006) An investigation of the pyranose ring interconversion path of α-l-idose calculated using density functional theory. Carbohydr Res 341:2565–2574

    CAS  PubMed  Google Scholar 

  4. Steiner T, Saenger W (1998) Closure of the cavity in permethylated cyclodextrins through glucose inversion, flipping, and kinking. Angew Chem Int Ed 37:3404–3407

    CAS  Google Scholar 

  5. Añibarro M, Gessler K, Usón I, Sheldrick GM, Harata K, Hirayama K, Abe Y, Saenger W (2001) Effect of peracylation of β-cyclodextrin on the molecular structure and on the formation of inclusion complexes: an X-ray study. J Am Chem Soc 123:11854–11862

    PubMed  Google Scholar 

  6. Gould IR, Bettley HA-A, Bryce RA (2007) Correlated ab initio quantum chemical calculations of di- and trisaccharide conformations. J Comput Chem 28:1965–1973

    CAS  PubMed  Google Scholar 

  7. French AD (2015) Computerized models of carbohydrates, in polysaccharides bioactivity and biotechnology. In: Mérillon JM, Ramawat KG (eds) Springer, pp 1397–1440

    Google Scholar 

  8. Devarajan A, Markutsya S, Lamm MH, Cheng X, Smith JC, Baluyut JY, Kholod Y, Gordon MS, Windus TL (2013) Ab initio study of molecular interactions in cellulose Iα. J Phys Chem B 117:10430–10443

    CAS  PubMed  Google Scholar 

  9. Barnett CB, Naidoo KJ (2010) Ring puckering: a metric for evaluating the accuracy of AM1, PM3, PM3CARB-1, and SCC-DFTB carbohydrate QM/MM simulations. J Phys Chem B 114:17142–17154

    CAS  PubMed  Google Scholar 

  10. Foresman J ., Frisch AE. Exploring chemistrywith electronic structure methods, 3rd edn. http://www.gaussian.com/g_prod/explore3.htm

  11. Barrows SE, Dulles FJ, Cramer CJ, French AD, Truhlar DG (1995) Relative stability of alternative chair forms and hydroxymethyl conformations of β-glucopyranose. Carbohydr Res 276:219–251

    CAS  Google Scholar 

  12. Becke, AD (1993) Density-functional thermochemistry. III. The role of exact exchange, J Chem Phys 98:5648–5652

    Google Scholar 

  13. Zhao Y, Truhlar DG (2008) The M06 suite of density functionals for main group thermochemistry, themochemical kinetics, noncovalent intereactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals Theor Chem Acc 120:215–241

    Google Scholar 

  14. Svensson M, Humbel S, Froese RDJ, Matsubara T, Sieber S, Morokuma K (1996) ONIOM: a multilayered integrated MO + MM method for geometry optimizations and single point energy predictions. A test for Diels−Alder reactions and Pt(P(t-Bu)3)2 + H2 oxidative addition. J Phys Chem 100:19357–19363

    CAS  Google Scholar 

  15. Schnupf U, Momany FA (2011) Rapidly calculated DFT relaxed iso-potential ϕ/ψ maps: β-cellobiose. Cellulose 18:859–887

    CAS  Google Scholar 

  16. Mucs D, Bryce RA (2014) The application of quantum mechanics in structure-based drug design. Expert Opin Drug Discov 8:263–276

    Google Scholar 

  17. Ardèvol A, Rovira C (2015) Reaction mechanisms in carbohydrate-active enzymes: glycoside hydrolases and glycosyltransferases. Insights from ab initio quantum mechanics/molecular mechanics dynamic simulations. J Am Chem Soc 137:7528–7547

    PubMed  Google Scholar 

  18. Frank M, Schloissnig S (2010) Bioinformatics and molecular modeling in glycobiology. Cell Mol Life Sci 67:2749–2772

    CAS  PubMed  PubMed Central  Google Scholar 

  19. Grindley TB (2008) In: Fraser-Reid BO, Tatsuta K, Thiem J (eds) Glycosciences: structure and conformation of carbohydrates. Springer, Berlin, pp 3–55

    Google Scholar 

  20. McNaught D (1996) Nomenclature of carbohydrates (IUPAC recommendations 1996). Pure Appl Chem 68:1919–2008. http://www.chem.qmul.ac.uk/iupac/2carb/00n01.html#00

    CAS  Google Scholar 

  21. French AD, Dowd MK (1994) Analysis of the ring-form tautomers of psicose with MM3 (92). J Comput Chem 15:561–570

    CAS  Google Scholar 

  22. Boeyens JCA (1978) The conformation of six-membered rings. J Cryst Mol Struct 8:317–320

    Google Scholar 

  23. Cremer D, Pople JA (1975) A general definition of ring puckering coordinates. J Am Chem Soc 97:1354–1358

    CAS  Google Scholar 

  24. Altona C, Sundaralingam M (1972) Conformational analysis of the sugar ring in nucleosides and nucleotides. A new description using the concept of pseudorotation. J Am Chem Soc 94:8205–8212

    CAS  PubMed  Google Scholar 

  25. Haasnoot CAG (1992) The conformation of six-membered rings described by puckering coordinates derived from endocyclic torsion angles. J Am Chem Soc 114:882–887

    CAS  Google Scholar 

  26. Bérces A, Whitfield DM, Nukada T (2001) Quantitative description of six-membered ring conformations following the IUPAC conformational nomenclature. Tetrahedron 57:477–491

    Google Scholar 

  27. Joshi NV, Rao VSR (1979) Flexibility of the pyranose ring in α- and β-d-glucoses. Biopolymers 18:2993–3004

    CAS  Google Scholar 

  28. Hill D, Reilly PJ (2007) Puckering coordinates of monocyclic rings by triangular decomposition. J Chem Inf Model 47:1031–1035

    CAS  PubMed  Google Scholar 

  29. French AD, Johnson GP (2007) Linkage and pyranosyl ring twisting in cyclodextrins. Carbohydr Res 342:1223–1237

    CAS  PubMed  Google Scholar 

  30. Nishiyama Y, Langan P, Chanzy H (2002) Crystal structure and hydrogen-bonding system in cellulose Iβ from synchrotron X-ray and neutron fiber diffraction. J Am Chem Soc 124:9074–9082

    CAS  PubMed  Google Scholar 

  31. Yoneda Y, Mereiter K, Jaeger C, Brecker L, Kosma P, Rosenau T, French A (2008) van der Waals versus hydrogen-bonding forces in a crystalline analog of cellotetraose: cyclohexyl 4′-O-cyclohexyl β-d-cellobioside cyclohexane solvate. J Am Chem Soc 130:16678–16690

    CAS  PubMed  Google Scholar 

  32. Bader RFW (1990) Atoms in molecules — a quantum theory. Oxford University Press, Oxford

    Google Scholar 

  33. Csonka GI, Kolossváry I, Császár P, Éliás K, Csizmadia IG (1997) The conformational space of selected aldo-pyrano-hexoses. J Mol Struct Theochem 395-396:29–40

    CAS  Google Scholar 

  34. Klein RA (2002) Electron density topological analysis of hydrogen bonding in glucopyranose and hydrated glucopyranose. J Am Chem Soc 124:13931–19937

    CAS  PubMed  Google Scholar 

  35. Klein RA (2006) Lack of intramolecular hydrogen bonding in glucopyranose: vicinal hydroxyl groups exhibit negative cooperativity. Chem Phys Lett 433:165–169

    CAS  Google Scholar 

  36. Koch U, Popelier P (1995) Characterization of C-H-O hydrogen bonds on the basis of the charge density. J Phys Chem 99:9747–9754

    CAS  Google Scholar 

  37. Schrodinger, Portland, OR. www.schrodinger.com

  38. Çarçabal P, Jockusch RA, Hunig I, Snoek LC, Kroemer RT, Davis BG, Gamblin DP, Compagnon I, Oomens J, Simons JP (2005) Hydrogen bonding and cooperativity in isolated and hydrated sugars: mannose, galactose, glucose, and lactose. J Am Chem Soc 127:11414–11425

    PubMed  Google Scholar 

  39. Allinger NL, Yuh YH, Lii J-H (1989) Molecular mechanics. The MM3 force field for hydrocarbons. J Am Chem Soc 111:8551–8567

    CAS  Google Scholar 

  40. Allen FH (2002) The Cambridge structural database: a quarter of a million crystal structures and rising. Acta Crystallogr B Struct Sci 58:380–388

    Google Scholar 

  41. Naidoo KJ, Brady JW (1997) The application of simulated annealing to the conformational analysis of disaccharides. Chem Phys 224:263–273

    CAS  Google Scholar 

  42. Schmidt RK, Teo B, Brady JW (1995) Use of umbrella sampling in the calculation of the potential of mean force for maltose in vacuum from molecular dynamics simulations. J Phys Chem 99:11339–11343

    CAS  Google Scholar 

  43. Kuttel MM, Naidoo KJ (2005) Free energy surfaces for the α(1→4)-glycosidic linkage: implications for polysaccharide solution structure and dynamics. J Phys Chem B 109:7468–7474

    CAS  PubMed  Google Scholar 

  44. Sugita Y, Okamoto Y (1999) Replica-exchange molecular dynamics method for protein folding. Chem Phys Lett 314:141–151

    CAS  Google Scholar 

  45. Campen RK, Verde AV, Kubicki JD (2007) Influence of glycosidic linkage neighbors on disaccharide conformation in vacuum. J Phys Chem B 111:13775–13785

    CAS  PubMed  Google Scholar 

  46. Shen T, Langan P, French AD, Johnson GP, Gnanakaran S (2009) Conformational flexibility of soluble cellulose oligomers: Chain length and temperature dependence. J Am Chem Soc 131:14786–14794

    CAS  PubMed  Google Scholar 

  47. Voter AF (1997) Hyperdynamics: accelerated molecular dynamics of infrequent events. Phys Rev Lett 78:3908–3911

    CAS  Google Scholar 

  48. Laio A, Parrinello M (2002) Escaping free-energy minima. Proc Natl Acad Sci U S A 99:12562–12566

    CAS  PubMed  PubMed Central  Google Scholar 

  49. Grubmuller H (1995) Predicting slow structural transitions in macromolecular systems: conformational flooding. Phys Rev E 52:2893–2906

    CAS  Google Scholar 

  50. Hamelberg D, Mongan J, McCammon J (2004) Accelerated molecular dynamics: a promising and efficient simulation method for biomolecules A. J Chem Phys 120:11919–11929

    CAS  PubMed  Google Scholar 

  51. Johnson GP, Petersen L, French AD, Reilly PJ (2009) Twisting of glycosidic bonds by hydrolases. Carbohydr Res 344:2157–2166

    CAS  PubMed  Google Scholar 

  52. Mohamadi F, Richards NGJ, Guida WC, Liskamp R, Lipton M, Caufield C, Chang G, Hendrikson T, Still WC (1990) Macromodel – an integrated software system for modeling organic and bioorganic molecules using molecular mechanics. J Comput Chem 11:440–467

    CAS  Google Scholar 

  53. Kaminski GA, Friesner RA, Tirado-Rives J, Jorgensen WJ (2001) Evaluation and reparametrization of the OPLS-AA force field for proteins via comparison with accurate quantum chemical calculations on peptides. J Phys Chem B 105:6474–6487

    CAS  Google Scholar 

  54. Shen T, Langan P, French AD, Johnson GP, Gnanakaran S (2009) Conformational flexibility of soluble cellulose oligomers: chain length and temperature dependence. J Amer Chem Soc 131:14786–14794

    CAS  Google Scholar 

  55. Weiner SJ, Kollman PA, Case DA, Singh UC, Ghio C, Alagona G, Profeta S Jr, Weiner P (1984) A new force field for molecular mechanical simulation of nucleic acids and proteins. J Am Chem Soc 106:765–784

    CAS  Google Scholar 

  56. Woods RJ, Dwek RA, Edge CJ, Fraser-Reid B (1995) Molecular mechanical and molecular dynamic simulations of glycoproteins and oligosaccharides. 1. GLYCAM_93 parameter development. J Phys Chem 99:3832–3846

    CAS  Google Scholar 

  57. Ferretti V, Bertolasi V, Gilli G (1984) Structure of 6-kestose monohydrate, C18H31O16.H2O. Acta Crystallogr C 40:531–535

    Google Scholar 

  58. Jeffrey GA (1997) Introduction to hydrogen bonding. Oxford University Press, New York, NY, p 12

    Google Scholar 

  59. Parthasarathi R, Elango M, Subramanian V, Sathyamurthy N (2009) Structure and stability of water chains (H2O)n, n = 5−20. J Phys Chem A 113:3744–3749

    CAS  PubMed  Google Scholar 

  60. Grabowski SJ (2006) Hydrogen bonding – new insights. Springer, Dordrecht, p 519

    Google Scholar 

  61. Lii J-H, Chen K-H, Johnson GP, French AD, Allinger NL (2005) The external-anomeric torsional effect. Carbohydr Res 340:853–862

    CAS  PubMed  Google Scholar 

  62. Jeffrey GA, Pople JA, Radom L (1972) The application of ab initio molecular orbital theory to the anomeric effect. A comparison of theoretical predictions and experimental data on conformations and bond lengths in some pyranoses and methyl pyranosides. Carbohydr Res 25:117–131

    CAS  Google Scholar 

  63. Jeffrey GA, Pople JA, Radom L (1974) The application of ab initio molecular orbital theory to structural moieties of carbohydrates. Carbohydr Res 38:81–95

    CAS  Google Scholar 

  64. Jaradat DMM, Mebs S, Chęcińska L, Luger P (2007) Experimental charge density of sucrose at 20 K: bond topological, atomic, and intermolecular quantitative properties. Carbohydr Res 342:1480–1489

    CAS  PubMed  Google Scholar 

  65. Tvaroška I, Bleha T (1979) Lone pair interactions in dimethoxymethane and anomeric effect. Can J Chem 57:424–435

    Google Scholar 

  66. Allinger NL, Schmitz LR, Motoc I, Bender C, Labanowski JK (1992) Heats of formation of organic molecules. 2. The basis for calculations using either ab initio or molecular mechanics methods. Alcohols and ethers. J Am Chem Soc 114:2880–2883

    CAS  Google Scholar 

  67. French AD, Kelterer A-M, Johnson GP, Dowd MK (2000) B3LYP/6-31G∗, RHF/6-31G∗ and MM3 heats of formation of disaccharide analogs. J Mol Struct 556:303–313

    CAS  Google Scholar 

  68. Takahashia O, Yamasakia K, Kohnob Y, Uedab K, Suezawac H, Nishio M (2009) The origin of the generalized anomeric effect: possibility of CH/n and CH/π hydrogen bonds. Carbohydr Res 344:1225–1229

    Google Scholar 

  69. Perdew JP, Ruzsinszky A, Constantin LA, Sun J, Csonka GI (2009) Some fundamental issues in ground-state density functional theory: a guide for the perplexed. J Chem Theory Comput 5:902–908

    CAS  PubMed  Google Scholar 

  70. Csonka GI, French AD, Johnson GP, Stortz CA (2009) Evaluation of density functionals and basis sets for carbohydrates. J Chem Theory Comput 5:679–692

    CAS  PubMed  Google Scholar 

  71. French AD, Johnson GP (2004) Advanced conformational energy surfaces for cellobiose. Cellulose 11:449–462

    CAS  Google Scholar 

  72. Cocinero EJ, Gamblin DP, Davis BG, Simons JP (2009) The building blocks of cellulose: the intrinsic conformational structures of cellobiose, its epimer, lactose, and their singly hydrated complexes. J Am Chem Soc 131:11117–11123

    CAS  PubMed  Google Scholar 

  73. Strati GL, Willett JL, Momany FA (2002) Ab initio computational study of β-cellobiose conformers using B3LYP/6-311++G∗∗. Carbohydr Res 337:1851–1859

    CAS  PubMed  Google Scholar 

  74. French AD, Johnson GP, Cramer CJ, Csonka GI (2012) Conformational analysis of cellobiose by electronic structure theories. Carbohydr Res 350:68–76

    CAS  PubMed  Google Scholar 

  75. Marenich AV, Cramer CJ, Truhlar DG (2009) Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions. J Phys Chem B 113:6378–6396

    CAS  PubMed  Google Scholar 

  76. Keith TA (2013) AIMAll (version 13.02.26). http://aim.tkgristmill.com

  77. French AD, Csonka GI (2011) Hydroxyl orientations in cellobiose and other polyhydroxyl compounds: modeling versus experiment. Cellulose 18:897–909

    CAS  Google Scholar 

  78. French AD, Concha M, Dowd MK, Stevens ED (2014) Electron (charge) density studies of cellulose models. Cellulose 21:1051–1063

    CAS  Google Scholar 

  79. Biarnés X, Ardèvol A, Planas A, Rovira C, Laio A, Parrinello M (2007) The conformational free energy landscape of β-d-glucopyranose. Implications for substrate preactivation in β-glucoside hydrolases. J Am Chem Soc 129:10686–10693

    PubMed  Google Scholar 

  80. French AD, Johnson GP (2006) Quantum mechanics studies of cellobiose conformations. Can J Chem 84:603–612

    CAS  Google Scholar 

  81. Lii J-H, Chen K-H, Allinger NL (2003) Alcohols, ethers, carbohydrates, and related compounds. IV. Carbohydrates. J Comput Chem 24:1504–1513

    CAS  PubMed  Google Scholar 

  82. Kirschner KN, Yongye AB, Tschampel SM, González-Outeriño J, Daniels CR, Foley BL, Woods RJ (2008) J Comput Chem 29:622–655

    CAS  PubMed  PubMed Central  Google Scholar 

  83. Tschampel SM, Kennerty MR, Woods RJ (2007) TIP5P-consistent treatment of electrostatics for biomolecular simulations. J Chem Theory Comput 3:1721–1733

    CAS  PubMed  PubMed Central  Google Scholar 

  84. Brooks BR, Bruccoleri RE, Olafson BD, States DJ, Swaminathan S, Karplus M (1983) CHARMM: a program for macromolecular energy, minimization, and dynamics calculations. J Comput Chem 4:187–217

    CAS  Google Scholar 

  85. Ha SN, Giammona A, Field M, Brady JW (1988) A revised potential-energy surface for molecular mechanics studies of carbohydrates. Carbohydr Res 180:207–221

    CAS  PubMed  Google Scholar 

  86. Kuttel M, Brady JW, Naidoo KJ (2002) Carbohydrate solution simulations: producing a force field with experimentally consistent primary alcohol rotational frequencies and populations. J Comput Chem 23:1236–1243

    CAS  PubMed  Google Scholar 

  87. Guvench O, Greene SN, Kamath G, Brady JW, Venable RM, Pastor RW, Mackerell AD Jr (2008) Additive empirical force field for hexopyranose monosaccharides. J Comput Chem 29:2543–2564

    CAS  PubMed  PubMed Central  Google Scholar 

  88. Patel DS, He X, MacKerell AD Jr (2015) Polarizable empirical force field for hexopyranose monosaccharides based on the classical drude oscillator. J Phys Chem B 119:637–652

    CAS  PubMed  Google Scholar 

  89. French AD, Kelterer A-M, Cramer CJ, Johnson GP, Dowd MK (2000) A QM/MM analysis of the conformations of crystalline sucrose moieties. Carbohydr Res 326:305–322

    CAS  PubMed  Google Scholar 

  90. French AD, Kelterer A-M, Johnson GP, Dowd MK, Cramer CJ (2001) HF/6-31G∗ energy surfaces for disaccharide analogs. J Comput Chem 22:65–78

    CAS  Google Scholar 

  91. Oostenbrink C, Soares TA, van der Vegt NFA, van Gusteren WF (2005) Validation of the 53A6 GROMOS force field. Eur Biophys J 34:273–284

    CAS  PubMed  Google Scholar 

  92. Stortz CA, Johnson GP, French AD, Csonka GI (2009) Comparison of different force fields for the study of disaccharides. Carbohydr Res 344:2217–2228

    CAS  PubMed  Google Scholar 

  93. Jorgensen WL, Chandrasekhar J, Madura JD, Impey RW, Klein ML (1983) Comparison of simple potential functions for simulating liquid water. J Chem Phys 79:926–935

    CAS  Google Scholar 

  94. DeMarco ML, Woods RJ (2008) Structural glycobiology: a game of snakes and ladders. Glycobiology 18:426–440

    CAS  PubMed  PubMed Central  Google Scholar 

  95. Foley BL, Tessier MB, Woods RJ (2012) Carbohydrate force fields WIREs. Comput Mol Sci 2:652–697

    CAS  Google Scholar 

  96. Krupička M, Tvaroška I (2009) Hybrid quantum mechanical/molecular mechanical investigation of the β-1,4-galactosyltransferase-I mechanism. J Phys Chem B 113(32):11314–11319

    PubMed  Google Scholar 

  97. Zhang Y, Luo M, Schramm VL (2009) Transition states of plasmodium falciparum and human orotate phosphoribosyltransferases. J Am Chem Soc 131:4685–4694

    CAS  PubMed  PubMed Central  Google Scholar 

  98. French AD (2012) Combining computational chemistry and crystallography for a better understanding of the structure of cellulose. Adv Carbohydr Chem Biochem 67:19–93

    CAS  PubMed  Google Scholar 

  99. Bu L, Beckham GT, Crowley MF, Chang CH, Matthews JF, Bomble YJ, Adney WA, Himmel ME, Nimlos MR (2009) The energy landscape for the interaction of the family 1 carbohydrate-binding module and the cellulose surface is altered by hydrolyzed glycosidic bonds. J Phys Chem B 113:10994–11002

    CAS  PubMed  Google Scholar 

  100. Zugenmaier P (2008) Crystalline cellulose and derivatives. Characterization and structrures. Springer, Berlin, pp 8–38

    Google Scholar 

  101. Matthews JF, Skopec CE, Mason PE, Zuccato P, Torget RW, Sugiyama J, Himmel ME, Brady JW (2006) Computer simulation studies of microcrystalline cellulose Iβ. Carbohydr Res 341:138–152

    CAS  PubMed  Google Scholar 

  102. Yui T, Hayashi S (2009) Structural stability of the solvated cellulose IIII crystal models: a molecular dynamics study. Cellulose 16:151–165

    CAS  Google Scholar 

  103. Shen T, Gnanakaran S (2001) The stability of cellulose: a statistical perspective from a coarse-grained model of hydrogen-bond networks. Biophys J 96:3032–3040

    Google Scholar 

  104. Wohlert J, Berglund LA (2011) A coarse-grained model for molecular dynamics simulations of native cellulose. J Chem Theory Comput 7:753–760

    CAS  Google Scholar 

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French, A.D., Johnson, G.P. (2020). Computerized Molecular Modeling of Carbohydrates. In: Popper, Z. (eds) The Plant Cell Wall. Methods in Molecular Biology, vol 2149. Humana, New York, NY. https://doi.org/10.1007/978-1-0716-0621-6_29

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  • DOI: https://doi.org/10.1007/978-1-0716-0621-6_29

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