Theoretical Chemistry Accounts

, Volume 128, Issue 2, pp 191–206 | Cite as

Theoretical studies on model reaction pathways of prostaglandin H2 isomerization to prostaglandin D2/E2

  • Naoto Yamaguchi
  • Tatsuya Naiki
  • Takamitsu Kohzuma
  • Toshikazu Takada
  • Fumihiko Sakata
  • Seiji Mori
Regular Article

Abstract

Model reaction mechanisms in the biosynthesis of prostaglandin D2 (PGD2) and prostaglandin E2 (PGE2) from prostaglandin H2 with PGD2/E2 synthase were examined using the ab initio second-order Møller–Plesset perturbation method and density functional theory. The reaction was modeled similar to the isomerization of 2,3-dioxabicyclo[2.2.1]heptane to 3-hydroxycyclopentanone in the presence of MeS. An explicit solvation of two H2O molecules was also considered, and two probable types of reaction mechanisms were demonstrated. One mechanism starts with proton abstraction from an oxygen-bound carbon at the endoperoxide by a thiolate ion and the other is stepwise and involves attack of a thiolate anion on an oxygen of the endoperoxide group in the first step with protonation of the other oxygen, followed by deprotonation from a carbon-attached oxygen to break an O–S bond to yield PGD2 or PGE2. We also found that the mPW1LYP hybrid method was superior to the B3LYP functional for systems with respect to the state-of-the-art CCSD(T) energetics.

Keywords

Prostaglandin H2 Prostaglandin D2 Prostaglandin E2 Prostaglandin D2 synthase Prostaglandin E2 synthase Model reaction mechanisms mPW1LYP hybrid functional 

Notes

Acknowledgments

This work was supported in part by Grants-in-Aid No. 19550004 (S. M) and 22550145 (T. K.) for Scientific Research from JSPS, Scientific Research on Priority Areas No. 20038005 (S. M.) from MEXT, Project of Development of Basic Technologies for Advanced Production Methods Using Microorganism Functions by the New Energy and Industrial Technology Development Organization (NEDO) to T. K, and Japan Science and Technology agency for the Strategic Promotion of Innovative Research and Development (SPIRE) to T. K. We thank Drs. Yoshihiro Urade and Kosuke Aritake, Osaka Bioscience Institute, for stimulating discussions, Prof. Osamu Hayaishi, Osaka Bioscience Institute, for encouragement in our studies, and Prof. Takeshi Nishikawa for granting us the permission to use the TSUBAME grid cluster in the Tokyo Institute of Technology in his project supported by NEDO. The generous allotment of computational time from the Research Center for Computational Science, the National Institutes of Natural Sciences, Japan, is also gratefully acknowledged.

Supplementary material

214_2010_814_MOESM1_ESM.doc (225 kb)
Supplementary material 1 (DOC 225 kb)

References

  1. 1.
    Ragolia L (ed) (2007) Prostaglandin D2 synthase—a multitude of biological functions. Research Signpost, KeralaGoogle Scholar
  2. 2.
    Goodwin GM (ed) (2010) Prostaglandins: biochemistry, functions, types and roles. Nova Science Pub Inc., New YorkGoogle Scholar
  3. 3.
    Samuelsson B, Paoletti R, Folco GC, Granström E, Nicosia S (2001) Advances in prostaglandin and leukotriene research: basic science and new clinical applications. Kluwer, DordrechtGoogle Scholar
  4. 4.
    Santovito D, Mezzetti A, Cipollone F (2009) Curr Opin Lipid 20:402–408Google Scholar
  5. 5.
    Miller SB (2006) Semin Arthritis Rheum 36:37–49Google Scholar
  6. 6.
    Curtis-Prior P (ed) (2004) The eicosanoids. Wiley, USAGoogle Scholar
  7. 7.
    Corey EJ, Nicolaou KC, Machida Y, Malmsten CL, Samuelsson B (1975) Proc Natl Acad Sci 72:3355–3358Google Scholar
  8. 8.
    Goldblatt MW (1933) J Soc Chem Ind (London) 62:1056–1057Google Scholar
  9. 9.
    von Euler US (1934) Arch Exptl Pathol Pharmakol Naungn-Schmiedeberg’s 175:78–84Google Scholar
  10. 10.
    Bergström S, Ryhage R, Samuelsson B, Sjövall J (1963) J Biol Chem 238:3555–3564Google Scholar
  11. 11.
    Pace-Asciak C, Nashat M (1976) J Neurochem 27:551–556Google Scholar
  12. 12.
    Lewis RA, Soter NA, Diamond PT, Austen KF, Oates JA, Roberts LJ II (1982) J Immunol 129:1627–1631Google Scholar
  13. 13.
    Tanaka K, Ogawa K, Sugamura K, Nakamura M, Takano S, Nagata K (2000) J Immunol 164:2277–2280Google Scholar
  14. 14.
    Ueno R, Honda K, Inoue S, Hayaishi O (1983) Proc Natl Acad Sci USA 80:1735–1737Google Scholar
  15. 15.
    Onoe H, Ueno R, Fujita I, Nishino H, Oomura Y, Hayaishi O (1988) Proc Natl Acad Sci USA 85:4082–4086Google Scholar
  16. 16.
    Matsuoka T, Hirata M, Tanaka H, Takahashi Y, Murata T, Kabashima K, Sugimoto Y, Kobayashi T, Ushikubi F, Aze Y, Eguchi N, Urade Y, Yoshida N, Kimura K, Mizoguchi A, Honda Y, Nagai H, Narumiya S (2000) Science 287:2013–2017Google Scholar
  17. 17.
    Ueno R, Narumiya S, Ogorochi T, Nakayama T, Ishikawa Y, Hayaishi O (1982) Proc Natl Acad Sci USA 79:6093–6097Google Scholar
  18. 18.
    Shimizu T, Yamamoto S, Hayaishi O (1979) J Biol Chem 254:5222–5228Google Scholar
  19. 19.
    Urade Y, Kitahama K, Ohishi H, Kaneko T, Mizuno N, Hayaishi O (1993) Proc Natl Acad Sci USA 90:9070–9074Google Scholar
  20. 20.
    Beuckmann CT, Gordon WC, Kanaoka Y, Eguchi N, Marcheselli VL, Gerashchenko DY, Urade Y, Hayaishi O, Bazan NG (1996) J Neurosci 16:6119–6124Google Scholar
  21. 21.
    Tokugawa Y, Kunishige I, Kubota Y, Shimoya K, Nobunaga T, Kimura T, Saji F, Murata Y, Eguchi N, Oda H, Urade Y, Hayaishi O (1998) Biol Reprod 58:600–607Google Scholar
  22. 22.
    Eguchi Y, Eguchi N, Oda H, Seiki K, Kijima Y, Matsu-ura Y, Urade Y, Hayaishi O (1997) Proc Natl Acad Sci USA 94:14689–14694Google Scholar
  23. 23.
    Pinzar E, Kanaoka Y, Inui T, Eguchi N, Urade Y, Hayaishi O (2000) Proc Natl Acad Sci USA 97:4903–4907Google Scholar
  24. 24.
    Eguchi N, Minami T, Shirafuji N, Kanaoka Y, Tanaka T, Nagata A, Yoshida N, Urade Y, Ito S, Hayaishi O (1999) Proc Natl Acad Sci USA 96:726–730Google Scholar
  25. 25.
    Takeda K, Takahashi NH, Shibahara S (2007) Tohoku J Exp Med 211:201–221Google Scholar
  26. 26.
    Takeda K, Takahashi NH, Yoshizawa M, Shibahara S (2010) J Biochem (ahead of print)Google Scholar
  27. 27.
    Tanaka T, Urade Y, Kimura H, Eguchi N, Nishikawa A, Hayaishi O (1997) J Biol Chem 272:15789–15795Google Scholar
  28. 28.
    Urade Y, Tanaka T, Eguchi N, Kikuchi M, Kimura H, Toh H, Hayaishi O (1995) J Biol Chem 270:1422–1428Google Scholar
  29. 29.
    Miyano M, Ago H, Aritake K, Irikura D, Kumasaka T, Inoue T, Yamamoto M, Urade Y, Hayaishi O (2005) Acta Cryst A61:C109Google Scholar
  30. 30.
    Miyamoto Y, Nishimura S, Inoue K, Shimamoto S, Yoshida T, Fukuhara A, Yamada M, Urade Y, Yagi N, Ohkubo T, Inui T (2010) J Struct Biol 169:209–218Google Scholar
  31. 31.
    Zhou Y, Shaw N, Li Y, Zhao Y, Zhang R, Liu Z-J (2010) FASEB J 24. doi: 10.1096/fj.10-164863
  32. 32.
    Shimamoto S, Yoshida T, Inui T, Gohda K, Kobayashi Y, Fujimori K, Tsurumura T, Aritake K, Urade Y, Ohkubo T (2007) J Biol Chem 282:31373–31379Google Scholar
  33. 33.
    Kumasaka T, Aritake K, Ago H, Irikura D, Tsurumura T, Yamamoto T, Miyano M, Urade Y, Hayaishi O (2009) J Biol Chem 284:22344–22352Google Scholar
  34. 34.
    Christ-Hazelhof E, Nugteren DH (1979) Biochim Biophys Acta 572:43–51Google Scholar
  35. 35.
    Meyer DJ, Thomas M (1995) Biochem J 311:739–742Google Scholar
  36. 36.
    Urade Y, Hayaishi O (2000) Vitam Horm 58:89–120Google Scholar
  37. 37.
    Li L, Yang Y, Stevens RL (2003) J Biol Chem 278:4725–4729Google Scholar
  38. 38.
    Mahmud I, Ueda N, Yamaguchi H, Yamashita R, Yamamoto S, Kanaoka Y, Urade Y, Hayaishi O (1997) J Biol Chem 272:28263–28266Google Scholar
  39. 39.
    Urade Y, Ujihara M, Horiguchi Y, Ikai K, Hayaishi O (1989) J Immunol 143:2982–2989Google Scholar
  40. 40.
    Mohri I, Eguchi N, Suzuki K, Urade Y, Taniike M (2003) GLIA 42:263–274Google Scholar
  41. 41.
    Okinaga T, Mohri I, Fujimura H, Imai K, Ono J, Urade Y, Taniike M (2002) Acta Neuropathol 104:377–384Google Scholar
  42. 42.
    Aritake K, Kado Y, Inoue T, Miyano M, Urade Y (2006) J Biol Chem 281:15277–15286Google Scholar
  43. 43.
    Kanaoka Y, Urade Y (2003) Prostaglandins Leukot Essent Fatty Acids 69:163–167Google Scholar
  44. 44.
    Kanaoka Y, Ago H, Inagaki E, Nanayama T, Miyano M, Kikuno R, Fujii Y, Eguchi N, Toh H, Urade Y, Hayaishi O (1997) Cell 90:1085–1095Google Scholar
  45. 45.
    Inoue T, Irikura D, Okazaki N, Kinugasa S, Matsumura H, Uodome N, Yamamoto M, Kumasaka T, Miyano M, Kai Y, Urade Y (2003) Nat Struct Biol 10:291–296Google Scholar
  46. 46.
    Inoue T, Okano Y, Kado Y, Aritake K, Irikura D, Uodome N, Okazaki N, Kinugasa S, Shishitani H, Matsumura H, Kai Y, Urade Y (2004) J Biochem 135:279–283Google Scholar
  47. 47.
    Hohwy M, Spadola L, Lundquist B, Hawtin P, Dahmén J, Groth-Clausen I, Nilsson E, Persdotter S, von Wachenfeldt K, Folmer RHA, Edman K (2008) J Med Chem 51:2178–2186Google Scholar
  48. 48.
    Pinzar E, Miyano M, Kanaoka Y, Urade Y, Hayaishi O (2000) J Biol Chem 275:31239–31244Google Scholar
  49. 49.
    Uchida Y, Urade Y, Mori S, Kohzuma T (2010) J Inorg Biochem 104:331–340Google Scholar
  50. 50.
    Bergström S, Dressler F, Ryhage R, Samuelsson B, Sjövall J (1962) Arkiv Kemi 19:563Google Scholar
  51. 51.
    Smith WL, Marnett LJ, DeWitt DL (1991) Pharmacol Ther 49:153–179Google Scholar
  52. 52.
    Vander AJ (1968) Am J Physiol 214:218–221Google Scholar
  53. 53.
    Milton AS, Wendlandt S (1971) J Physiol 218:325–336Google Scholar
  54. 54.
    Matsumura H, Goh Y, Ueno R, Sakai T, Hayaishi O (1988) Brain Res 444:265–272Google Scholar
  55. 55.
    Milton AS, Wendlandt S (1970) J Physiol (London) 207:76P–77PGoogle Scholar
  56. 56.
    Shimizu T, Wolfe LS (1990) J Neurochem 55:1–15Google Scholar
  57. 57.
    Ben-Ami I, Freimann S, Armon L, Dantes A, Strassburger D, Friedler S, Raziel A, Seger R, Ron-El R, Amsterdam A (2006) Mol Hum Reprod 12:593–599Google Scholar
  58. 58.
    Hayaishi O (1991) FASEB J 5:2575–2581Google Scholar
  59. 59.
    Serhan CN, Levy B (2003) Proc Natl Acad Sci USA 100:8609–8611Google Scholar
  60. 60.
    Ogino N, Miyamoto T, Yamamoto S, Hayaishi O (1977) J Biol Chem 252:890–895Google Scholar
  61. 61.
    Moonen P, Buytenhek M, Nugteren DH (1982) Methods Enzymol 86:84–91Google Scholar
  62. 62.
    Jakobsson PJ, Thorén S, Morgenstern R, Samuelsson B (1999) Proc Natl Acad Sci USA 96:7220–7225Google Scholar
  63. 63.
    Thoren S, Weinander R, Saha S, Jegerschold C, Pettersson PL, Samuelsson B, Hebert H, Hamberg M, Morgenstern R, Jakobsson PJ (2003) J Biol Chem 278:22199–22209Google Scholar
  64. 64.
    Tanaka Y, Ward SL, Smith WL (1987) J Biol Chem 262:1374–1381Google Scholar
  65. 65.
    Murakami M, Naraba H, Tanioka T, Semmyo N, Nakatani Y, Kojima F, Ikeda T, Fueki M, Ueno A, Oh-Ishi S, Kudo I (2000) J Biol Chem 275:32783–32792Google Scholar
  66. 66.
    Hara S, Kamei D, Sasaki Y, Tanemoto A, Nakatani Y, Murakami M (2010) Biochimie 92:651–659Google Scholar
  67. 67.
    Xing L, Kurumbail R, Frazier R, Davies M, Fujiwara H, Weinberg R, Gierse J, Caspers N, Carter J, McDonald J, Moore W, Vazquez M (2009) J Comput Aided Mol Des 23:13–24Google Scholar
  68. 68.
    Hamza A, Tong M, AbdulHameed MDM, Liu J, Goren AC, Tai H-H, Zhan C-G (2010) J Phys Chem B 114:5605–5616Google Scholar
  69. 69.
    Hamza A, AbdulHameed MDM, Zhan C-G (2008) J Phys Chem B 112:7320–7329Google Scholar
  70. 70.
    Jegerschöld C, Pawelzik S-C, Purhonen P, Bhakat P, Gheorghe KR, Gyobu N, Mitsuoka K, Morgenstern R, Jakobsson P-J, Hebert H (2008) Proc Natl Acad Sci USA 105:11110–11115Google Scholar
  71. 71.
    Hammarberg T, Hamberg M, Wetterholm A, Hansson H, Samuelsson B, Haeggström JZ (2009) J Biol Chem 284:301–305Google Scholar
  72. 72.
    Watanabe K, Kurihara K, Tokunaga Y, Hayaishi O (1997) Biochem Biophys Res Commun 235:148–152Google Scholar
  73. 73.
    Watanabe K, Kurihara K, Suzuki T (1999) Biochim Biophys Acta 1439:406–414Google Scholar
  74. 74.
    Murakami M, Nakashima K, Kamei D, Masuda S, Ishikawa Y, Ishii T, Ohmiya Y, Watanabe K, Kudo I (2003) J Biol Chem 278:37937–37947Google Scholar
  75. 75.
    Ogorochi T, Ujihara M, Narumiya S (1987) J Neurochem 48:900–909Google Scholar
  76. 76.
    Meyer DJ, Muimo R, Thomas M, Coates D, Isaac RE (1996) Biochem J 313:223–227Google Scholar
  77. 77.
    Tanioka T, Nakatani Y, Semmyo N, Murakami M, Kudo I (2000) J Biol Chem 275:32775–32782Google Scholar
  78. 78.
    Yamada T, Komoto J, Watanabe K, Ohmiya Y, Takusagawa F (2005) J Mol Biol 348:1163–1176Google Scholar
  79. 79.
    Watanabe K, Ohkubo H, Niwa H, Tanikawa N, Koda N, Ito S, Ohmiya Y (2003) Biochem Biophys Res Commun 306:577–581Google Scholar
  80. 80.
    Yamada T, Takusagawa F (2007) Biochemistry 46:8414–8424Google Scholar
  81. 81.
    Vane JR (1971) Nat New Biol 231:232–235Google Scholar
  82. 82.
    Psaty BM, Furberg CD (2005) N Engl J Med 352:1133–1135Google Scholar
  83. 83.
    Takeuchi K, Araki H, Umeda M, Komoike Y, Suzuki K (2001) J Pharmacol Exp Ther 297:1160–1165Google Scholar
  84. 84.
    Halter F, Tarnawski AS, Schmassmann A, Peskar BM (2001) Gut 49:443–453Google Scholar
  85. 85.
    Samuelsson B, Morgenstern R, Jakobsson P-J (2007) Pharmacol Rev 59:207–224Google Scholar
  86. 86.
    Editorials (2003) Nat Struct Biol 10:233Google Scholar
  87. 87.
    Zagorski MG, Salomon RG (1980) J Am Chem Soc 102:2501–2503Google Scholar
  88. 88.
    Zagorski MG, Salomon RG (1982) J Am Chem Soc 104:3498–3503Google Scholar
  89. 89.
    Wlodawer P, Samuelson B (1973) J Biol Chem 248:5673–5678Google Scholar
  90. 90.
    Kornblum N, DeLaMare HE (1951) J Am Chem Soc 73:880–881Google Scholar
  91. 91.
    Blomberg LM, Blomberg MRA, Siegbahn PEM, van der Donk WA, Tsai A-L (2003) J Phys Chem B 107:3297–3308Google Scholar
  92. 92.
    Silva PJ, Fernandes PA, Ramos MJ (2003) Theor Chem Acc 110:345–351Google Scholar
  93. 93.
    Yanai TK, Mori S (2008) Chem Asian J 3:1900–1911Google Scholar
  94. 94.
    Yanai TK, Mori S (2009) Chem Eur J 15:4464–4473Google Scholar
  95. 95.
    Zheng Y-J, Ornstein RL (1997) J Am Chem Soc 119:648–655Google Scholar
  96. 96.
    Ridder L, Rietjens IMCM, Vervoort J, Mulholland AJ (2002) J Am Chem Soc 124:9926–9936Google Scholar
  97. 97.
    Sant’Anna CMR, Souza VP, Andrade DS (2002) Int J Quant Chem 87:311–321Google Scholar
  98. 98.
    Dourado DFAR, Fernandes PA, Mannervik B, Ramos MJ (2008) Chem Eur J 14:9591–9598Google Scholar
  99. 99.
    Dourado DFAR, Fernandes PA, Mannervik B, Ramos MJ (2010) J Phys Chem B 114:1690–1697Google Scholar
  100. 100.
    Li Y, Angelastro M, Shimshock S, Reiling S, Vaz RJ (2010) Bioorg Med Chem Lett 20:338–340Google Scholar
  101. 101.
    Yamaguchi N, Mori S, Kohzuma T, Takada T, Sakata F (2006) In: 11th International congress of quantum chemistry, 21–26 May, Kyoto, JapanGoogle Scholar
  102. 102.
    Mori S, Yamaguchi N, Kohzuma T, Takada T, Sakata F (2007) In: International conference on heteroatom chemistry-8, 12–16 Aug, Riverside, USAGoogle Scholar
  103. 103.
    Mori S, Yanai T, Yamaguchi N, Kohzuma T, Takada T, Sakata F (2008) In: 3rd Asian–Pacific conference of theoretical and computational chemistry, 22–25 Sep, Beijing, ChinaGoogle Scholar
  104. 104.
    Møller C, Plesset MS (1934) Phys Rev 46:618–622Google Scholar
  105. 105.
    Becke AD (1993) J Chem Phys 98:5648–5652Google Scholar
  106. 106.
    Lee C, Yang W, Parr RG (1988) Phys Rev B 37:785–789Google Scholar
  107. 107.
    Adamo C, Barone V (1998) J Chem Phys 108:664–675Google Scholar
  108. 108.
    Raghavachari K, Trucks GW, Pople JA, Head-Gordon M (1989) Chem Phys Lett 157:479–483Google Scholar
  109. 109.
    Roothaan CCJ (1951) Rev Mod Phys 23:69–89Google Scholar
  110. 110.
    Hehre WJ, Radom L, Schleyer PvR, Pople JA (1986) Ab initio molecular orbital theory. Wiley, New York, and referenced cited thereinGoogle Scholar
  111. 111.
    Schmidt MW, Baldridge KK, Boatz JA, Elbert ST, Gordon MS, Jensen JH, Koseki S, Matsunaga N, Nguyen KA, Su SJ, Windus TL, Dupuis M, Montgomery JA (1993) J Comput Chem 14:1347–1363Google Scholar
  112. 112.
    Gaussian 03 Revision D02: Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JA Jr, Vreven T, Kudin KN, Burant JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Klene M, Li X, Knox JE, Hratchian HP, Cross JB, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA Gaussian Inc Wallingford CT (2004)Google Scholar
  113. 113.
    Fukui K (1970) J Phys Chem 74:4161–4163Google Scholar
  114. 114.
    Fukui K (1981) Acc Chem Res 14:363–368Google Scholar
  115. 115.
    Gonzalez C, Schlegel HB (1989) J Chem Phys 90:2154–2161Google Scholar
  116. 116.
    Gonzalez C, Schlegel HB (1990) J Phys Chem 94:5523–5527Google Scholar
  117. 117.
    Boys SF (1960) Rev Mod Phys 32:296–299Google Scholar
  118. 118.
    Truong TN, Stefanovich EV (1995) J Phys Chem 99:14700–14706Google Scholar
  119. 119.
    Caccuri AM, Antonini G, Nicotra M, Battistoni A, Bello ML, Boardi PG, Parker MW, Ricci G (1997) J Biol Chem 272:29681–29686Google Scholar
  120. 120.
    Morris GM, Huey R, Hart WE, Lindstron W, Gillet A, Goodsell DS, Olso AJ (2007) AutoDock 4.00Google Scholar
  121. 121.
    Morris GM, Goodsell DS, Huey R, Olson AJ (1996) J Comput Aided Mol Des 10:293–304Google Scholar
  122. 122.
    Huey R, Morris GM, Olson AJ, Goodsell DS (2007) J Comput Chem 28:1145–1152Google Scholar
  123. 123.
    Paragi-Vedanthi P, Doble M (2010) BMC Bioinformatics 11(Suppl 1):S51Google Scholar
  124. 124.
    Fersht FR (1999) Structure and mechanism in protein science: a guide to enzyme catalysis and protein folding. Freeman, New YorkGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Naoto Yamaguchi
    • 1
    • 2
    • 6
  • Tatsuya Naiki
    • 1
    • 3
  • Takamitsu Kohzuma
    • 1
    • 4
  • Toshikazu Takada
    • 5
    • 7
  • Fumihiko Sakata
    • 1
  • Seiji Mori
    • 1
    • 3
    • 4
  1. 1.Graduate School of Science and EngineeringIbaraki UniversityMitoJapan
  2. 2.VALWAY Technology CenterNEC Soft, LtdTokyoJapan
  3. 3.Faculty of ScienceIbaraki UniversityMitoJapan
  4. 4.Frontier Research Center for Applied Atomic SciencesIbaraki UniversityTokaiJapan
  5. 5.NEC CorporationTsukubaJapan
  6. 6.National Security Solutions DivisionNEC CorporationTokyoJapan
  7. 7.Research and Development Program for Next-Generation Computational ResearchRIKENTokyoJapan

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