Consistent calculations of pKa's of ionizable residues in proteins: Semi-microscopic and microscopic approaches

Journal of Physical Chemistry B

Volumn 101, Issue 22, 1997, Pages 4458-4472

  Sham, Yuk Yin ^a   Chu, Zhen Tao ^a   Warshel, Arieh ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000671518     PISSN: 15206106     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp963412w     Document Type: Article

References (93)

1. Perutz, M. F. Science 1978, 207, 1187.
2. Warshel, A. Proc. Natl. Acad. Sci. U.S.A. 1978, 75, 5250.
3. Warshel, A.; Russell, S. T. Q. Rev. Biol. 1984, 17, 283.
4. Sharp, K. A.; Honig, B. Ann. Rev. Biophys. Biophys. Chem. 1990, 19, 301.
5. Matthew, J. B. Annu. Rev. of Biophys. Biophys. Chem. 1985, 14, 387.
6. Nakamura, H. Q. Rev. Biophys. 1996, 29, 1.
7. Warshel, A. Acc. Chem. Res. 1981, 14, 284.
8. Warshel, A.; Åqvist, S. Annu. Rev. Biophys. Biophys. Chem. 1991, 20, 267.
9. Warshel, A. Biochemistry 1981, 20, 3167.
10. Linderstrom-Lang, K. C. R. Travl. Lab. Carlsberg 1924, 15, 1.
11. Tanford, C.; Kirkwood, J. G. J. Am. Chem. Soc. 1957, 79, 5333.
12. Tanford, C; Roxby, R. Biochemistry 1972, 2192.
13. Warshel, A.; Russell, S. T.; Churg, A. K. Proc. Natl. Acad. Sci. U.S.A. 1984, 81, 4785.
14. Lee, F. S.; Chu, Z. T.; Warshel, A. J. Comput. Chem. 1993, 14, 161.
15. States, D. J.; Karplus, M. J. Mol Biol. 1987, 197, 122.
16. Warshel, A.; Levitt, M. J. Mol. Biol. 1976, 103, 227.
17. Russell, S. T.; Warshel, A. J. Mol. Biol. 1985, 185, 389.
18. Warshel, A.; Naray-Szabo, G.; Sussman, F.; Hwang, J. K. Biochemistry 1989, 28, 3629.
19. King, G.; Warshel, A. J. Chem. Phys. 1989, 91, 3647.
20. Coalson, R. D.; Duncan, A. J. Phys. Chem. 1996, 100, 2612.
21. 25 when it was incorrectly suggested that the PDLD model of ref 16 did not evaluate self-energies and argued that this model is in fact macroscopic in nature and that it is physically equivalent to the use of a finite-difference grid within DC methods. These assertions are incorrect both in presentation of facts and in interpretation of the physics of dipolar solvents. A grid of dipoles with finite spacing or the equivalent system of polar molecules on a lattice is not equivalent to the numerical grid used in evaluating the electrostatic potential in DC approaches (see ref 26), although as the lattice spacing is reduced to unrealistically small values, the average behavior of simple dipole lattices predictably approaches that of macroscopic models.
22. Davis, M. E.; McCammon, J. A. Chem. Rev. 1990, 90, 509.
23. Krishtalik, L. I. Mol. Biol. (Moscow) 1984, 18, 892.
24. Yadav, A.; Jackson, R. M.; Holbrook, J. J.; Warshel, A. J. Am. Chem. Soc. 1991, 113, 4800.
25. Schaefer, M.; Karplus, M. J. Phys. Chem. 1996, 100, 1578.
26. 27). No such variation of fields exists in the continuum formulations or in the DC treatments. It may be useful in this respect to consider an example of how a microscopic grid of dipoles is used in analytically solvable cases to obtain continuum results (e.g. ref 28). Since dipolar models provide a more "realistic" description, they can be reduced to a continuum description, but the reverse is not possible. Macroscopic models involve the use of dielectric constants, while no such scaling is used in the PDLD model. The use of the dipolar model has facilitated a consistent description of protein electrostatics quite early and is probably the reason why the PDLD model did not fall into all the traps that plagued macroscopic treatments of proteins; for example looking at the microscopic interactions led immediately to the explicit consideration of the protein permanent dipoles rather than to futile attempts of representing them by a low dielectric constant.
27. Purcell, E. M. Electricity and Magnetism; McGraw-Hill: New York, 1965.
28. Jackson, J. D. Classical Electrodynamics; Wiley: New York, 1975.
29. Warshel, A. J. Phys. Chem. 1979, 83, 1640.
30. Cramer, C. J.; Truhlar, D. G. J. Am. Chem. Soc. 1991, 113, 8305.
31. Rashin, A. A. J. Phys. Chem. 1990, 94, 1725.
32. a's of identical groups in different environments.
33. Lim, C.; Bashford, D.; Karplus, M. J. Phys. Chem. 1991, 95, 5610.
34. Warwicker, J.; Watson, H. C. J. Mol. Bio. 1982, 157, 671.
35. Rogers, N. K. Prog. Biophys. Mol. Biol. 1986, 48, 37.
36. Gilson, M.; Honig, B. Biopolymers 1986, 25, 2097.
37. Bashford, D.; Karplus, M. Biochemistry 1990, 29, 10219.
38. Yang, A. S.; Gunner, M. R.; Sampogna, R.; Sharp, K.; Honig, B. Proteins: Struct., Fund., Genet. 1993, 15, 252.
39. McPherson, P. H.; Schonfeld, M.; Paddock, M. L.; Okamura, M. Y. Biochemistry 1994, 33, 1181.
40. Warshel, A.; Sussman, F.; King, G. Biochemistry 1986, 25, 8368.
41. Merz, Ke. M. J. Am. Chem. Soc. 1991, 113, 3572.
42. Lee, F. S.; Warshel, A. J. Chem. Phys. 1992, 97, 3100.
43. Buono, G. S.; Figueirido, F. E.; Levy, R. M. Proteins: Struct., Funct., Genet. 1994, 20, 85.
44. King, G.; Lee, F. S.; Warshel, A. J. Chem. Phys. 1991, 95, 4366.
45. Dipolar models and any other explicit representation of molecular systems have to reproduce the compensating effect of opposing electrostatic interaction such as charge-charge and solvation effects by a balance of large contributions of opposite magnitude. On the other hand, macroscopic models obtain such effects by assuming the dielectric constant of the given medium rather than obtaining it microscopically. Obviously, it is more challenging to obtain precise results from microscopic models due to wellknown convergence problems, but the chances of having the incorrect physics in nonhomogenous systems are much larger when one uses macroscopic models, since the correct continuum representation of a given microscopic system is far from obvious.
46. Jorgensen, W. L.; Briggs, J. M. J. Am. Chem. Soc. 1989, 111, 4190.
47. Lancaster, C. R. D.; Michel, H.; Honig, B.; Gunner, M. R. Biophys. J. 1996, 70, 2469.
48. Beroza, P.; Okamura, M. Y.; Feher, G. Proc. Natl. Acad. U.S.A. 1991, 88, 5804.
49. Warshel, A. In Methods in Enzyntology; Packer, L., Ed.; Academic Press, Inc.: London, 1986; Vol. 127, p 578.
50. Warshel, A. Photochem. Photobiol 1979, 30, 285.
51. Daggett, V.; Kollman, P. A.; Kuntz, I, D. Biopolymers 1991, 31, 1115.
52. Muegge, I.; Qi, P. X.; Wand, A. J.; Chu, Z. T.; Warshel, A. J. Phys. Chem. B 1997, 101, 825.
53. King, G.; Warshel, A. J. Chem. Phys. 1990, 93, 8682.
54. Papazyan, A.; Warshel, A. Submitted.
55. Alden, R. G.; Parson, W. W.; Chu, Z. T.; Warshel, A.J. Am. Chem. Soc. 1995, 117, 12284.
56. L gives very similar solvation energies, as should be clear from the Born equation; and (c) many versions of our approach still include the Langevin function, including those with a publicly available source (ref 57), and it will probably be useful if those who have problems with dipolar models would try a computer program with dipoles around a charge and realize what the properties of such models are.
57. The LD model has been used in a recent work (J. Florian and A. Warshel, submitted) that provides a reliable way of obtaining solvation free energies from the Gaussian program package. This program can be obtained from the authors.
58. Smith, P. E.; van Gunsteren, W. F. In Computer Simulation of Biomolecular Systems; van Gunsteren, W. F.; Weiner, P. K.; Wilkinson, A. J.; Eds.; Escom: Leiden, 1993; Vol. 2; p 182.
59. Langen, R.; Brayer, G. D.; Berghuis, A. M.; McLendon, G.; Sherman, F.; Warshel, A. J. Mol Biol. 1992, 224, 589.
60. Sharp, K. J. Comput. Chem. 1991, 12, 454.
61. Warshel, A. Computer Modeling of Chemical Reactions in Enzymes and Solutions; John Wiley & Sons: New York, 1991.
62. Kollman, P. Chem. Rev. 1993, 93, 2395.
63. Warshel, A. J. Phys. Chem. 1982, 86, 2218.
64. Hwang, J. K.; Warshel, A. Biochemistry 1987, 26, 2669.
65. Levy, R. M.; Belhadj, M.; Kitchen, D. B. J. Chem. Phys. 1991, 95, 3627.
66. Åqvist, J.; Medina, C.; Samuelsson, J.-E. Protein Eng. 1994, 7, 385.
67. Lee, F. S.; Chu, Z. T.; Bolger, M. B.; Warshel, A. Protein Eng. 1992, 5, 215.
68. Warshel, A.; Hwang, J. K. J. Chem. Phys. 1986, 84, 4938.
69. Warshel, A.; Chu, Z. T.; Parson, W. W. Science 1989, 246, 112.
70. Brooks, C. L.; Karplus, M. Biopolymers 1985, 24, 843.
71. Gilson, M. K. Curr. Opin. Struct. Biol. 1995, 5, 216.
72. Klein, B. J.; Pack, G. R. Biopolymers 1983, 22, 2331.
73. Yang, A. S.; Honig, B. J. Mol. Biol. 1993, 231, 459.
74. Ramanadham, M.; Sieker, L. C.; Jensen, L. H. Acta Crystallogr. Sect. A 1981, 37c, 33.
75. Wilson, K. P.; Malcolm, B. A.; Matthews, B. W. J. Biol. Chem. 1992, 267, 10842.
76. Cutler, R. L; Davies, A. M.; Creighton, S.; Warshel, A.; Moore, G. R.; Smith, M.; Mauk, A. G. Biochemistry 1989, 28, 3188.
77. Thoma, J. A. J. Theor. Biol. 1974, 44, 305.
78. Hwang, J. K.; Warshel, A. Nature 1988, 334, 270.
79. Simonson, T.; Perahia. D. J. Am. Chem. Soc. 1995, 117, 7987.
80. Simonson, T.; Perahia, D. Proc. Natl. Acad. Sci. U.S.A. 1995, 92, 1082.
81. Smith, P. E.; Brunne, R. M.; Mark, A. E. J. Phys. Chem. 1993, 97, 2009.
82. p = 1 when the whole system is treated explicitly), but that has nothing to do with the ability of a continuum description to reconcile the microscopic solvation in a heterogenous environment with the macroscopic ∈̄.
83. Antosiewicz, J.; McCammon, J. A.; Gilson, M. K. J. Mol. Biol. 1994, 238, 415.
84. Gunner, M. R.; Alexov, E.; Torres, E.; Lipovaca, S. J. Biol. Inorg. Chem. 1997, 2, 126.
85. Warshel, A.; Papazyan, A.; Muegge, I. J. Biol. Inorg. Chem. 1997, 2, 143.
86. - (a typical rather than a "small" ionizable group) in solution exactly. Thus, any correct estimate of the energetics of moving an ionizable acid to the center of a protein would reproduce our results, confirming the primary importance of the solvation term in the energetics of proteins.
87. You, T. J.; Bashford, D. Biophys. J. 1995, 69, 1721.
88. Allewell, N. M.; Oberoi, H, Methods Enzymol. 1991, 202, 3.
89. Jensen, G. M.; Warshel, A.; Stephens, P. J. Biochemistry 1994, 33, 10911.
90. Stevens, P. J.; Jollie, D. R.; Warshel, A. Chem. Rev. 1996, 96, 2491.
91. Muegge, I.; Schweins, T.; Langen, R.; Warshel, A. Structure 1996, 4, 475.
92. Gibas, C. J.; Subramaniam, S. Biophys. J. 1996, 71, 138.
93. Kuramitsu, S.; Hamaguchi, K. J. Biochem. 1980, 87, 1215.