Transition-state structural refinement with GRACE and CHARMM: Flexible QM/MM modelling for lactate dehydrogenase

Abstract

Realistic simulations of chemical reactions require the use not only of methods capable of describing accurately the energy of molecules undergoing bonding changes within a particular chemical environment, but also of methods capable of exploring topographical features of significance on energy hypersurfaces spanning perhaps several thousand degrees of freedom. Hybrid quantum-mechanical/molecular-mechanical techniques show much promise for the first task, but existing computer codes are inadequate for the second. Application of these methods to real chemical problems demands new tools for location and characterisation of saddle-points, intrinsic reaction coordinates, hessians and vibrational frequencies for very large flexible systems. Algorithms capable of performing these tasks have been incorporated in a new software package, GRACE, which provides a non-invasive interface between popular codes for quantum chemistry and molecular dynamics and modelling. Transition structures (TSs) have been refined by this novel procedure, using a combined AM1/CHARMM24/TIP3P potential, involving full gradient relaxation of the positions of 1900–2000 atoms of a solvated enzyme–substrate complex (lactate dehydrogenase/NADH/pyruvate/water). Six different starting structures (arbitrarily selected from a molecular dynamics trajectory for the enzyme–substrate complex) lead to six different TSs. Although the essential features of these TSs are invariant, the relative dispositions of active-site residues differ quite significantly. The transition state for the enzymic reaction would represent an average of the properties of many, nearly degenerate TSs. This insight emerges only as a consequence of the flexible model of the active site employed in this study.

References

1. A. Warshel and M. Levitt, J. Mol. Biol., 1976, 103, 227.
2. U. C. Singh and P. A. Kollman, J. Comput. Chem., 1986, 7, 718.
3. M. J. Field, P. A. Bash and M. Karplus, J. Comput. Chem., 1990, 11, 700.
4. (a) F. Maseras and K. Morokuma, J. Comput. Chem., 1995, 16, 1170; (b) M. Svensson, S. Humbel, R. D. J. Froese, T. Matsubara, S. Sieber and K. Morokuma, J. Phys. Chem., 1996, 100, 19357.
5. V. Moliner, A. J. Turner and I. H. Williams, J. Chem. Soc., Chem. Commun., 1997, 1271.
6. B. R. Brooks, R. E. Bruccoleri, B. D. Olafson, D. J. States, S. Swaminathan and M. Karplus, J. Comput. Chem., 1983, 4, 187; CHARMM24b2, M. Karplus Harvard University, 1996.
7. B. Paizs, G. Fogarasi and P. Pulay, J. Chem. Phys., 1998, 109, 6571.
8. J. Baker, J. Comput. Chem., 1986, 7, 385.
9. S. F. Fischer and M. Karplus, Chem. Phys. Lett., 1992, 194, 252.
10. M. J. D. Powell, Math. Programming, 1971, 1, 26.
11. P. Culot, G. Dive, V. H. Nguyen and J. M. Ghuysen, Theoret. Chim. Acta, 1992, 82, 189.
12. F. Jensen, in MOPAC93 Manual, J. J. P. Stewart, Fujitsu Limited, Tokyo, Japan, 1993; J. J. P. Stewart, MOPAC 7, (QCPE 455 7.0), Quantum Chem. Program Exch. Bull., 1993, 13, 42.
13. D. C. Liu and J. Nocedal, Math. Progamming, 1989, 45, 503.
14. M. J. D. Powell, Math. Programming, 1977, 12, 241.
15. T. R. Dafforn, I. G. Badcoe, R. B. Sessions, A. S. El Hawrani and J. J. Holbrook, Proteins: Struct. Funct. Genet., 1997, 29, 228.
16. D. B. Wigley, S. J. Gamblin, S. P. Turkenburg, E. J. Dodson, K. Piontek, H. Muirhead and J. J. Holbrook, J. Mol. Biol., 1992, 223, 317.
17. M. J. S. Dewar, E. G. Zoebisch, E. F. Healy and J. J. P. Stewart, J. Am. Chem. Soc., 1985, 107, 3902.
18. J. J. Pavelites, J. Gao, P. A. Bash and A. D. Mackerell, J. Comput. Chem., 1997, 18, 221.
19. A. D. MacKerell, D. Bashford, M. Bellott, R. L. Dunbrack, J. D. Evanseck, M. J. Field, S. Fischer, J. Gao, H. Guo, S. Ha, D. Joseph-McCarthy, L. Kuchnir, K. Kuczera, F. T. K. Lau, C. Mattos, S. Michnick, T. Ngo, D. T. Nguyen, B. Prodhom, W. E. Reiher, B. Roux, M. Schlenkrich, J. C. Smith, R. Stote, J. Straub, M. Watanabe, J. Wiorkiewicz-Kuczera, D. Yin and M. Karplus, J. Phys. Chem. B, 1998, 102, 3586.
20. C. L. Brooks and M. Karplus, J. Mol. Biol., 1989, 208, 159.
21. S. Nakagawa, A. H. Yu, M. Karplus and H. Umeyama, Proteins, 1993, 16, 172.
22. J. Andrés, V. Moliner, J. Krechl and E. Silla, J. Chem. Soc., Perkin Trans. 2, 1995, 1551.
23. M. W. Schmidt, M. S. Gordon and M. Dupuis, J. Am. Chem. Soc., 1985, 107, 2585; J. J. P. Stewart, MOPAC 7, (QCPE 4557.0), Quantum Chem. Program Exch. Bull., 1993, 13, 42.
24. I. H. Williams, Chem. Phys. Lett., 1982, 88, 462; J. Mol. Struct.: THEOCHEM, 1983, 11, 275.
25. C. A. Coleman, J. G. Rose and C. J. Murray, J. Am. Chem. Soc., 1992, 114, 9755.
26. A. R. Clarke and T. R. Dafforn, personal communication. Measurements at 20 °C in 50 mM bis-tris buffer at pH 6.0 with 5 mM fructose-1,6-bisphosphate.
27. J. Wilkie and I. H. Williams, J. Chem. Soc., Perkin Trans. 2, 1995, 1559.
28. J. A. Barnes and I. H. Williams, J. Chem. Soc., Chem. Commun., 1996, 193.
29. S. Ranganathan and J. E. Gready, J. Phys. Chem. B, 1997, 101, 5614.
30. P. G. Bolhuis, C. Dellago and D. Chandler, Faraday Discuss., 1998, 110, paper 110/23.
31. (a) Q. Xue and E. S. Yeung, Nature, 1995, 373, 681; (b) W. Tan and E. S. Yeung, Anal. Chem., 1997, 69, 4242.
32. J. K. Ousterhout, TCL and TK toolkit, Addison Wesley, 1994.
33. R. D. Amos, CADPAC: The Cambridge Analytical Derivatives Package, Issue 6, Cambridge, 1995; with contributions from I. L. Alberts, J. S. Andrews, S. M. Colwell, N. C. Handy, D. Jayatilaka, P. J. Knowles, R. Kobayashi, K. E. Laidig, G. Laming, A. M. Lee, P. E. Maslen, C. W. Murray, J. E. Rice, E. D. Simandiras, A. J. Stone, M.-D. Su and D. J. Tozer.
34. GAMESS-UK is a package of ab initio programs written by M. F. Guest, J. H. van Lenthe, K. Schoffel, P. Sherwood and R. J. Harrison, Daresbury Laboratory, 1995–1997, with contributions from R. D. Amos, R. J. Buenker, M. Dupuis, N. C. Handy, I. H. Hilliere, P. J. Knowles, V. Bonacic-Koutecky, W. von Niessen, V. R. Saunders and A. J. Stone. The package is derived from the original GAMESS code due to M. Dupuis, D. Spangler, J. Wendoloski.
35. R. Sayle, RasMol v2.5: A Molecular Visualisation Program, Biomolecular Structure, Glaxo Research and Development, Greenford, Middlesex, UK.
36. Xmol version 1.3.1, Minnesota Supercomputer Center Inc..