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FAB-MS Applications in the Elucidation of Proanthocyanidin Structures

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Abstract

Fast atom bombardment mass spectrometry (FAB-MS), which requires no chemical derivatization prior to mass spectral analysis, has become a powerful tool for studying the structures of biopolymers. FAB and similar forms of mass spectrometry have the potential for achieving the same degree of importance in the elucidation of proanthocyanidin structure currently accorded nuclear magnetic resonance. The extent and state of research on the use of FAB-MS to determine molecular weight, adduct identity, sequence, branching, and linkage type are reviewed in this paper. Experimental considerations (such as sample introduction, sample matrices, and instrument modes) and mass spectral features associated with the characterization of oligomeric proanthocyanidins are surveyed.

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References

  1. Haslam, E. Natural proanthocyanidins. In: Harborne, J.B.; Mabry, T.J.; Mabry, H. (eds.) The Flavonoids, Academic Press, New York, pp. 505–559 (1975).

    Google Scholar 

  2. Haslam, E. Proanthocyanidins. In: Harbone, J.B.; Mabry, T.J. (eds.) The Flavonoids: Advances in Research, Chapman and Hall, London, pp. 417–447 (1982).

    Google Scholar 

  3. Salunkhe, D.K.; Jadhav, S.J.; Kadam, S.S.; Chavan, J.K. Chemical, biochemical, and biological significance of polyphenols in cereals and legumes. CRC Crit. Rev. Food Sci. Nitr. 17: 277 (1982).

    Article  CAS  Google Scholar 

  4. Haslam, E. Symmetry and promiscuity in procyanidin biochemistry. Phytochemistry 16: 1625 (1977).

    Article  CAS  Google Scholar 

  5. Delcour, J.A.; Vandeberghe, M.M.; Dondeyne, P.; Schrevens, E.L.; Wijnhoven, J. Flavor and haze stability differences in unhopped and hopped all-malt Pilsner beers brewed with proanthocyanidin-free and with regular malt. J. Inst. Brew. 90: 67 (1984).

    CAS  Google Scholar 

  6. Kumar, R.; Singh, M. Tannins: their adverse role in ruminant nutrition. J. Agric. Food. Chem. 32: 447 (1984).

    Article  CAS  Google Scholar 

  7. Butler, L.G.; Riedl, D.J.; Lebryk, D.G.; Blytt, H.J. Interaction of proteins with sorghum tannin: mechanism, specificity and significance. J. Am. Oil Chem. Soc. 61: 916 (1984).

    Article  CAS  Google Scholar 

  8. Klocke, J.A.; Chan, B.C. Effects of cotton condensed tannin on feeding and digestion in the cotton pest Heliothis zea. J. Insect Physiol. 28: 911 (1982).

    Article  CAS  Google Scholar 

  9. Zucker, W.V. Tannins: does structure determine function? An ecological perspective. Am. Nat. 121: 335 (1983).

    Article  CAS  Google Scholar 

  10. Hemingway, R.W. Bark: its chemistry and prospects for chemical utilization. In: Goldestein, I.S. (ed.) Organic Chemicals from Biomass, CRC Press, Boca Raton, Florida pp. 189–248 (1981).

    Google Scholar 

  11. Pizzi, A. Tannin-based wood adhesives. In: Pizzi, A. (ed.) Wood Adhesives, Chemistry and Technology, Marcel Dekker, New York, pp. 177–246 (1983).

    Google Scholar 

  12. Hemingway, R.W.; Laks, P.E.; McGraw, G.W.; Kreibich, R.E. Reactions of condensed tannins and the development of tannin-based adhesives. In: Proceedings IUFRO Conference, Forest Products Research International - Achievements and the Future, Vol. 6, Pretoria, South Africa, pp. 17.11–17. 20 (1985).

    Google Scholar 

  13. Price, M.L.; Van Scoyoc, S.; Butler, L.G. A critical evaluation of the vanillin reaction as an assay for tannin in sorghum grain. J. Agric. Food Chem. 26: 1214 (1978).

    Article  CAS  Google Scholar 

  14. Price, M.L.; Butler, L.G. Rapid visual estimation and spectrophotometric determination of tannin content of sorghum grain. J. Agric. Food Chem. 25: 1268 (1977).

    Article  CAS  Google Scholar 

  15. Hagerman, A.E.; Butler, L.G. Protein precipitation method for the quantitative determination of tannins. J. Agric. Food Chem. 26: 809 (1978).

    Article  CAS  Google Scholar 

  16. Hagerman, A.E.; Butler, L.G. Condensed tannin purification and characterization of tannin-associated proteins. J. Agric. Food Chem. 28: 947 (1980).

    Article  PubMed  CAS  Google Scholar 

  17. Bate-Smith, E.C. Hemanalysis of tannins. Concept of relative astringency. Phytochemistry 12: 907 (1973).

    Article  Google Scholar 

  18. Haslam, E. Polyphenol-protein interactions. Biochem. J. 139: 285 (1974).

    PubMed  CAS  Google Scholar 

  19. Maxson, E.D.; Rooney, L.W. Evaluation of methods for tannin analysis in sorghum grain. J. Cereal Chem. 49: 719 (1972).

    CAS  Google Scholar 

  20. Weinges, K.; Kaltenhauser, W.; Marx, H.-D.; Nadar, E.; Nader, F.; Perrier, J.; Seiler, D. Proanthocyanidins. X. Procyanidins from fruit. Justus Leibigs Ann. Chem. 711: 184 (1968).

    CAS  Google Scholar 

  21. Mabry, T.J.; Markham, K.R. Mass spectrometry of flavonoids. In: Ilarborne, J.B.; Mabry, T.J.; Mabry, H. (eds.) The Flavonoids, Academic Press, New York (1975).

    Google Scholar 

  22. Mabry, T.J.; Ulubelen, A. Mass spectrometry of flavonoids and related plant phenolics. In: Waller, G.R.; Dermer, O.C. (eds.) Biochemical Applications of Mass Spectrometry, 1st Suppl. Vol. Wiley, New York (1980).

    Google Scholar 

  23. Ozawa, T.; Kobayashi, S.; Seki, R.; Imagawa, H. A new gallotannin from bark of chesnut tree Castanea crenata Sieb. et Zucc. Agric. Biol. Chem. 48: 1411 (1984).

    Article  CAS  Google Scholar 

  24. Piretti, M.V.; Pistore, R.; Razzoboni, C. On the chemical constitution of kaki tannin. Ann. Chim. 75: 137 (1985).

    CAS  Google Scholar 

  25. Kingston, D.G.I.; Fales, H.M. Methane chemical ionization mass spectrometry of flavonoids. Tetrahedron 29: 4083 (1973).

    Article  CAS  Google Scholar 

  26. Itokawa, H.; Oshida, Y.; Ikuta, A.; Shida, Y. In-beam electron impact, chemical ionization and negative ion chemical ionization of flavonoid glycosides. Chem. Lett.: 49 (1982).

    Google Scholar 

  27. Bankova, V.S.; Mollova, N.N.; Popov, S.S. Chemical ionization mass spectrometry with amines as reactant gases. Org . Mass Spectrom. 21: 109 (1986).

    Google Scholar 

  28. Karchesy, J.J.; Laver, M.L.; Barofsky, D.F.; Barofsky, E. Structure of oregonin, a natural diarylheptanoid xyloside. J. Chem. Soc. Chem. Common.: 649 (1974).

    Google Scholar 

  29. Schulten, H.R.; Games, D.E. High resolution field desorption mass spectrometry. II. Glycosides. Biomed. Mass Spectrom. 1: 120 (1974).

    Article  PubMed  CAS  Google Scholar 

  30. Karchesy, J.J.; Loveland, P.M.; Laver, M.L.; Barofsky, D.F., Barofsky, E. Condensed tannins from the barks of Aines rubra and Pseudotsuga menzies II. Phytochemistry 15: 2009 (1976).

    Google Scholar 

  31. Biswas, K.M.; Ali, M.E.; Jackson, A.H.; Games, D.E. Application of field desorption and electron impact mass spectrometry and NMR spectroscopy in the study of flavonoid O-glycosides. J. Ind. Chem. Soc. 55: 1240 (1978).

    CAS  Google Scholar 

  32. Geiger, H.; Schwinger, G. Field desorption mass spectrometery and thermal fragmentation of flavonoid glucosides. Phytochemistry 19: 897 (1980).

    Article  CAS  Google Scholar 

  33. Nonaka, G.-I.; Morimoto, S.; Nishioka, I. Tannins and related compounds. Part 13. Isolation and structure of trimeric, tetrameric and pentameric proanthocyanidins from cinnamen. J. Chem. Soc. Perkin Trans. 1.: 2139 (1983).

    Google Scholar 

  34. Foo, L.Y.; Porter, L.J. Prodelphinidin polymers: definition of structural units. J. Chem. Soc. Perkin Trans. 1: 1186 (1978).

    Article  Google Scholar 

  35. Foo, L.Y.; Hemingway, R.W. Condensed tannins: synthesis of the first branched procyanidin trimer. J. Chem. Soc. Chem. Commun.: 85 (1984).

    Google Scholar 

  36. Yoshida, T.; Hatano, T.; Okudo, T.; Memon, M.; Shingu, T.; Inoue, K. Spectral and chromatographic analyses of tannins. I. Carbon-13 nuclear magnetic resonance spectra of hydrolyzable tannins. Chem. Pharm. Bull. 32: 1790 (1984).

    Article  CAS  Google Scholar 

  37. Nonaka, G.-I.; Kawahara, O., Nishioka, I. Tannins and related compounds. XV. A new class of dimeric flavan-3-ol gallates from green tea leaf. Chem. Pharm. Bull. 31: 3906 (1983).

    Article  CAS  Google Scholar 

  38. Beart, J.E.; Lilley, T.H.; Haslam, E. Plant polyphenols - secondary metablolism and chemical defense: some observations. Phytochemistry 24: 33 (1985).

    Article  CAS  Google Scholar 

  39. Surman, D.J.; Vickerman, J.C. Fast atom bombardment quadrapole mass spectrometry. J. Chem. Soc. Chem. Commun.: 324 (1981).

    Google Scholar 

  40. Barber, M.; Bordoli, R.S.; Sedgwick, R.D.; Tyler, A.N. Fast atom bombardment of solids (F.A.B.): a new ion source for mass spectrometry. J. Chem. Soc. Chem. Commun.: 325 (1981).

    Google Scholar 

  41. Burlingame, A.L.; Baillie, T.A.; Derrick, P.J. Mass spectrometry. Anal. Chem. 58: 165R (1986).

    Google Scholar 

  42. Day, R.J.; Unger, S.E.; Cooks, R.G. Molecular secondary ion mass spectrometry. Anal. Chem. 52: 557A (1980).

    Google Scholar 

  43. Williams, D.H.; Findeis, A.F.; Naylor, S.; Gibson, B.W. Aspects of the production of FAB and SIMS mass spectra. J. Am. Chem. Soc. 109: 1980 (1987).

    Article  CAS  Google Scholar 

  44. Pachuta, S.J.; Cooks, R.G. Mechanisms in molecular SIMS. Chem. Rev. 87: 647 (1987).

    Article  CAS  Google Scholar 

  45. Williams, D.H.; Smith, R.J.; Santikarn, S.; Maggio, J.E.; Daley, D.J.; Bradley, C.V. FAB mass spectrometry of some biopolymers. Spectros. Int. J. 2: 232 (1983).

    CAS  Google Scholar 

  46. Fenseleau, C.; Cotter, R.J. Chemical aspects of fast atom bombardment. Chem. Rev. 87: 501 (1987).

    Article  Google Scholar 

  47. Aberth, W.; Straub, K.M.; Burlingame, A.L. Secondary ion mass spectrometry with cesium ion primary beam and liquid target matrix for analysis of bioorganic compounds. Anal. Chem. 54: 2029 (1982).

    Article  CAS  Google Scholar 

  48. DePauw, E. Liquid matrices for secondary-ion mass spectrometry. Mass Spectrom. Rev. 5: 191 (1986).

    Article  Google Scholar 

  49. Carr, S.A.; Reinhold, V.N.; Green, B.N.; Hass, J.R. Enhancement of structural information in FAB ionized carbohydrate samples by neutral gas collision. Biomed. Mass Spectrom., 12: 288 (1985).

    Article  PubMed  CAS  Google Scholar 

  50. Barber, M.; Bordoli, R.S.; Elliott, G.J.; Tyler, A.N.; Bill, J.C.; Green, B.N. Fast atom bombardment (FAB) mass spectrometry: a mass spectal investigation of some of the insulins. Biomed. Mass Spectrom. 11: 182 (1984).

    Article  PubMed  CAS  Google Scholar 

  51. Martin, S.A.; Costello, C.E.; Biemann, K. Optimization of experimental procedures for fast atom bombardment mass spectrometery. Anal. Chem. 54: 2362 (1982).

    Article  CAS  Google Scholar 

  52. Barber, M.; Bordoli, R.S.; Elliott, G.J.; Sedgwick, R.D.; Tyler, A.N. Fast atom baombardment mass spectrometry. Anal. Chem. 59: 645A (1982).

    Google Scholar 

  53. Fenselau, C. Fast atom bombardment. In: Benninghoven, A. (ed.) Formation from Organic Solids, Springer-Verlag, Berlin (1983).

    Google Scholar 

  54. Rinehart, K.L. Fast atom bombardment mass spectrometry. Science 218: 254 (1982).

    Article  PubMed  CAS  Google Scholar 

  55. Miller, J.M. Fast-atom bombardment mass spectrometry and related techniques. Adv. Inorg. Chem. Radiochem. 28: 1 (1984).

    Article  CAS  Google Scholar 

  56. Cochran, R.L. Fast atom bombardment/mass spectrometry (FAB/MS) and its industrial applications. Appl. Spectrosc. Rev. 22: 137 (1986).

    Article  CAS  Google Scholar 

  57. Domon, B.; Hostettman, K. Mass spectrometric studies of underivatized polyphenolic glycosides. Phytochemistry 24: 575 (1985).

    Article  CAS  Google Scholar 

  58. Karchesy, J.J.; Hemingway, R.W.; Foo, Y.L.; Barofsky, E.; Barofsky, D.F. Sequencing procyanidin oligomers by fast atom bombardment mass spectrometry. Anal. Chem. 58: 2563 (1986).

    Article  CAS  Google Scholar 

  59. Karchesy, J.J.; Foo, L.Y.; Barofsky, E.; Arbogast, B.; Barofsky, D.F. Negative ion fast atom bombardment mass spectrometry of procyanidin oligomers. Wood Chem. Technol. (in press).

    Google Scholar 

  60. de Koster, C.G.; Heerma, W.; Dijkstra, G.; Niemann, G.J. Fast atom bombardment of flavonols. Biomed. Mass Spectrom. 12: 596 (1985).

    Article  Google Scholar 

  61. Hsu, F.L.; Nonaka, G.; Nishioka, I. Tannins and related compounds. XXXIII. Isolation and characterization of procyanidins in Dioscorea cirrhosa Lour. Chem. Phar. Bull. 33: 3293 (1985).

    Article  CAS  Google Scholar 

  62. Morimoto, S.; Nonaka, G.; Nishioka, I. Tannins and related compounds. XXXXV. Procyanidins with a doubly linked unit from the root bark of Cinnamomum sieboldii Meisner. Chem. Pharm. Bull. 33: 4338 (1985).

    Article  CAS  Google Scholar 

  63. Morimota, S.; Nonaka, G.; Nishioka, I. Tannins and related compounds. XXXVIII. Isolation and characterization of flavan-3-ol glucosides and procyanidin oligomers from cassia bark (Cinnamomum cassia Blume). Chem. Pharm. Bull. 34: 633 (1986).

    Article  Google Scholar 

  64. Morimoto, S.; Nonaka, G.; Nishioka, I. Tannins and related compounds. XXXIX. Procyanidin c-glucosides and acylated flavan-3-ol glucoside from barks of Cinnamomum cassia Blume and C. obtusifolium Nees. Chem. Pharm. Bull. 34: 643 (1986).

    Article  CAS  Google Scholar 

  65. Kashiwada, Y.; Nonaka, G.; Nishioka, I. Tannins and related compounds. XLV. Rhubarb. Isolation and characterization of flavan-3-ol and procyanidin glucosides. Chem. Phar. Bull. 34: 3208 (1986).

    Article  CAS  Google Scholar 

  66. Nonaka, G.; Morimoto, S.; Kinjo, J.; Nohara, T.; Nishioka, I. Tannins and related compounds. L. Structures of proanthocyanidin A-1 and related compounds. Chem. Pharm. Bull. 35: 149 (1987).

    Article  CAS  Google Scholar 

  67. Morimoto, S.; Nonaka, G.; Nishioka, I. Tannins and related compounds. LX. Isolation and characterization of proanthocyanidins with a doubly-linked unit from Vaccinium vitis-idaea L. Chem. Pharm. Bull. 36: 33 (1988).

    Article  CAS  Google Scholar 

  68. Gujer, R.; Magnolato, D.; Self, R. Glucosylated flavonoids and other phenolic compounds from sorghum. Phytochemistry 25: 1431 (1986).

    Article  CAS  Google Scholar 

  69. Galletti, G.C.; Self. R. The polyphenols (syn vegetable tannins) of grape skins and pressed fruit residues. Annali di Chimica 76: 195 (1986).

    CAS  Google Scholar 

  70. Self, R.; Eagles, J.; Galletti, G.C.; Mueller-Harvey, I.; Hartley, R.D.; Lea, A.G.H.; Magno-lato, D.; Richli, U.; Gujer, R.; Haslam, E. Fast atom bombardment mass spectrometry of polyphenols (syn. vegetable tannins). Biomed. Environ. Mass Spectrom. 13: 449 (1986).

    Article  CAS  Google Scholar 

  71. Karchesy, J.J.; Hemingway, R.W. Condensed tannins: 413 -+ 8:20–0 -* 7)-linked procyanidins in Arachis hypogea L. J. Agric. Food Chem. 34: 966 (1986).

    Article  CAS  Google Scholar 

  72. Yoshida, T.; Hatano, T.; Okuda, T.; Memon, M.V.; Shingu, T.; Inoue, K.; Fukushima, K. Nuclear magnetic resonance and mass spectral analyses of oligomeric hydrolyzable tannins and related tannins. Tenne Yuki Kagobutsu Toronkai Koen Yushishu 26: 158 (1983).

    Google Scholar 

  73. Sakushima, A.; Ilisada, S.; Nishibe, S.; Brandenberger, H. Application of fast atom bombardment mass spectrometry to chlorgenic acids. Phytochemistry 24: 325 (1985).

    Article  CAS  Google Scholar 

  74. Mueller-Harvey, I.; Hartley, R.D.; Harris, P.J.; Curzon, E.H. Linkage of p-coumaroyl and feruloyl groups to cell-wall polysaccharides of barley straw. Carbohydr. Res. 148: 71 (1986).

    Article  CAS  Google Scholar 

  75. Barber, M.; Green, B.N. The analysis of small proteins in the molecular weight range 10–24 kDa by magnetic sector mass spectrometry. Rapid Commun. Mass Spectrom. 1: 80 (1987).

    Article  PubMed  CAS  Google Scholar 

  76. Craig, A. G.; Engstrom, A.; Bennich, H.; and Kamensky I. Enhancement of molecule ion yields in plasma desorption mass spectrometry. In: 35th ASMS Conference on Mass Spectrometry and Allied Topics. Denver, Colorado, (1987).

    Google Scholar 

  77. Foo, L.Y.; Karchesy, J.J.; Arbogast, B.A.; Barofsky, D.F. +FAB of a mixture of water soluble procyanidins from the inner bark of Douglas-fir/magic bullet/oligomers up to pentamer (m/z 1441), unpublished data (1988).

    Google Scholar 

  78. Porter, L.J. Condensed tannins, In:Rowe, J.W. (ed.) Natural Products Extraneous to the Lignocellulosic Cell Wall of Woody Plants. Springer-Verlag, New York, (in press).

    Google Scholar 

  79. Caprioli, R. Analysis of biochemical reactions with molecular specificity using fast atom bombardment mass spectrometry. Biochemistry 27: 513 (1988).

    Article  PubMed  CAS  Google Scholar 

  80. McLafferty, F. W. (ed.) Tandem Mass Spectrometry. Wiley-Interscience, New York (1983).

    Google Scholar 

  81. Gross, M.L.; Jensen, N.J.; Lippstreu-Fisher, D.L.; Tomer, K.B. Tandem mass spectrometry and fourier transform mass spectrometry for analysis of biomolecules, In: Burlingame, A.L.; Castagnoli, N. Sr. (eds.) Mass Spectrometry in the Health and Life Sciences. Elsevier, New York (1985).

    Google Scholar 

  82. Pelter, A.; Stainton, P.; Johnson, A.P.; Barber, M. The mass spectra of oxygen heterocycles. I. The 4-hydroxy-3-phenylcoumarins (isoflavonols). J. Heterocyclic Chem. 2: 256 (1965).

    Article  CAS  Google Scholar 

  83. Pelter, A.; Staintor, P.; Barber, M. The mass spectra of oxygen heterocydes. II. The mass spectra of some flavonoids. J. Heterocyclic Chem. 2: 262 (1965).

    Article  CAS  Google Scholar 

  84. Watson, J.T. Introduction to Mass Spectrometry, Raven Press, New York (1985).

    Google Scholar 

  85. Thompson, R.S.; Jacques, D.; Haslam, E.; Tanner, R.J.N. Plant proanthocyanidins. I. Introduction, isolation, structure, and distribution in nature of plant procyanidins. J. Chem. Soc. Perkin Trans. 1: 1387 (1972).

    Article  Google Scholar 

  86. Jacques, D.; Haslam, E.; Bedford, G.R.; Greatbanks, D. Plant proanthocyanidins. II. Proanthocyanidin A2 and its derivatives. J. Chem. Soc. Perkin Trans. 1: 2663 (1974).

    Article  Google Scholar 

  87. Attwood, M.R.; Brown, B.R.; Lisseter, S.G.; Torrero, C.L.; Weaver, P.M. Spectral evidence for the formation of quinone methide intermediates from 5- and 7-hydroxyflavonoids. J. Chem. Soc. Chem. Commun.: 177 (1984).

    Google Scholar 

  88. Foo, L.Y.; Wong, H. Diastereoisomeric leucoanthocyanidins from the heartwood of Acacia melanoxylon. Phytochemistry 25: 1961 (1986).

    Article  CAS  Google Scholar 

  89. Laks, P.E.; Hemingway, R.W. Condensed tannins: base-catalyzed reactions of polymeric procyanidins with toluene-a-thiol. Stability of the interflavanoid bond and pyran ring. J. Chem. Soc. Perkin Trans. 1: 465 (1987).

    Article  Google Scholar 

  90. Hemingway, R.W.; Foo, L.Y. Condensed tannins: quinone methide intermediates in procyanidin synthesis. J. Chem. Soc. Chem. Commun.: 1035 (1983).

    Google Scholar 

  91. Delcour, J.A.; Tuytens, G.M. Structure elucidation of three dimeric proanthocyanidins isolated from a commercial Belgian pilsner beer. J. Inst. Brew. 90: 153 (1984).

    CAS  Google Scholar 

  92. Karchesy, J.J.; Foo, L.Y.; Hemingway, R.W.; Barofsky, E.; Barofsky, D.R. Fast atom bombardment mass spectrometry of condensed tannin sulfonate derivatives. Wood Fiber Sci. 21: 155 (1989).

    CAS  Google Scholar 

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Barofsky, D.F. (1989). FAB-MS Applications in the Elucidation of Proanthocyanidin Structures. In: Hemingway, R.W., Karchesy, J.J., Branham, S.J. (eds) Chemistry and Significance of Condensed Tannins. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-7511-1_11

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