ABSTRACT
A method is presented for determining activation free energies in complex molecular systems. The method relies on knowledge of the minimum energy path and bases the activation free energy calculation on moving along this path from a minimum to a saddle point. Use is made of a local reaction coordinate which describes the advance of the reaction in each segment of the minimum energy path. The activation free energy is formulated as a sum of two terms. The first is due to the change in the local reaction coordinate between the endpoints of each segment of the path. The second is due to the change in direction of the minimum energy path between consecutive segments. Both contributions can be obtained by molecular dynamics simulations with a constraint on the local reaction coordinate. The method is illustrated by applying it to a model potential and to the C7eq to C7ax transition in the alanine dipeptide. It is found that the term due to the change of direction in the reaction path can make a substantial contribution to the activation free energy.
- 1. J. Keck, Discuss. Faraday 33, 173 (1962). Google ScholarCrossref
- 2. For a recent review that includes a wide range of applications, see J. B. Anderson, Adv. Chem. Phys. 91, 381 (1995). Google ScholarISI
- 3. C. H. Bennett, in Algorithms for Chemical Computation, edited by R. E. Christoferson (Am. Chem. Soc., Washington, D.C., 1977), p. 63. Google Scholar
- 4. C. L. BrooksIII, M. Karplus, and B. M. Pettitt, Adv. Chem. Phys. 71, 1 (1988). Google Scholar
- 5. S. Glasstone, K. J. Laidler, and H. Eyring, Theory of Rate Processes (McGraw-Hill, New York, 1941). Google Scholar
- 6. P. Hanggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990). Google ScholarCrossref, ISI
- 7. E. P. Wigner, Trans. Faraday Soc. 34, 29 (1938). Google ScholarCrossref
- 8. D. A. McQuarrie, Statistical Mechanics (Harper and Row, New York 1976). Google Scholar
- 9. J. P. Valleau and G. M. Torrie, in Statistical Mechanics, Part A edited by B. J. Berne (Plenum, New York, 1977), p. 137. Google Scholar
- 10. C. Pangali, M. Rao, and B. J. Berne, J. Chem. Phys. 71, 2975 (1979). Google ScholarScitation, ISI
- 11. S. H. Northrup, M. R. Pear, C. Y. Lee, J. A. McCammon, and M. Karplus, Proc. Natl. Acad. Sci., USA 79, 4035 (1982). Google ScholarCrossref
- 12. D. W. Robertus, B. J. Berne, and D. Chandler, J. Chem. Phys. 70, 3395 (1979). Google ScholarScitation, ISI
- 13. D. J. Tobias and C. L. BrooksIII, Chem. Phys. Lett. 142, 472 (1987). Google ScholarCrossref
- 14. E. A. Carter, G. Ciccotti, J. T. Hynes, and R. Kapral, Chem. Phys. Lett. 156, 472 (1989). Google ScholarCrossref, ISI
- 15. E. Paci, G. Ciccotti, M. Ferrario, and R. Kapral, Chem. Phys. Lett. 176, 581 (1991). Google ScholarCrossref
- 16. J. M. Depaepe, J. P. Ryckaert, E. Paci, and G. Ciccotti, Mol. Phys. 79, 515 (1993). Google ScholarCrossref
- 17. D. Chandler, J. Chem. Phys. 68, 2959 (1978). Google ScholarScitation, ISI
- 18. The term activation free energy used here is different from the standard use (see Ref. 5) and refers to the potential of mean force difference between the dividing surface and the minimum. Google Scholar
- 19. J. E. Straub, D. A. Hsu, and B. J. Berne, J. Phys. Chem. 89, 5188 (1985). Google ScholarCrossref, ISI
- 20. B. J. Gertner, K. R. Wilson, and J. T. Hynes, J. Chem. Phys. 90, 3537 (1989). Google ScholarScitation, ISI
- 21. L. R. Pratt, J. Chem. Phys. 85, 5045 (1986). Google ScholarScitation
- 22. A. Ulitskey and R. Elber, J. Chem. Phys. 92, 1510 (1990). Google ScholarScitation
- 23. S. Fischer and M. Karplus, Chem. Phys. Lett. 194, 252 (1992). Google ScholarCrossref
- 24. R. Elber, J. Chem. Phys. 93, 4312 (1990). Google ScholarScitation
- 25. T. Lazaridis, D. J. Tobias, C. L. Brooks III, and M. Paulaitis, J. Chem. Phys. 95, 7612 (1991). Google ScholarScitation
- 26. P. Pechukas, Annu. Rev. Phys. Chem. 32, 159 (1981). Google ScholarCrossref, ISI
- 27. J. P. Ryckaert and G. Ciccotti, J. Chem. Phys. 78, 7368 (1983). Google ScholarScitation, ISI
- 28. C. Eckart, Phys. Rev. 47, 552 (1935). Google ScholarCrossref
- 29. E. B. Wilson, J. C. Decius, and P. C. Cross, Molecular Vibrations (McGraw-Hill, New York, 1955). Google Scholar
- 30. H. M. Pickett and H. L. Strauss, J. Am. Chem. Soc. 92, 7281 (1970). Google ScholarCrossref
- 31. D. R. Herschbach, H. S. Johnston, and D. Rapp, J. Chem. Phys. 31, 1652 (1959). Google ScholarScitation, ISI
- 32. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford, London, 1989). Google Scholar
- 33. S. Fischer Ph.D. thesis, Harvard University 1992; S. Fischer and M. Karplus (unpublished). Google Scholar
- 34. B. M. Pettitt and M. Karplus, J. Amer. Chem. Soc. 107, 1166 (1985). Google ScholarCrossref
- 35. B. R. Brooks, R. E. Bruccoleri, B. D. Olafson, D. J. States, S. Swamintha, and M. Karplus, J. Comput. Chem. 4, 187 (1983). Google ScholarCrossref, ISI
- 36. J. P. Ryckaert, G. Ciccotti, and H. J. C. Berensden, J. Comput. Phys. 23, 327 (1977). Google ScholarCrossref, ISI
- 37. A. MacKerell and M. Karplus (unpublished). Google Scholar
- 38. S. Fischer, S. Michnick, and M. Karplus, Biochem. 32, 13830 (1993). Google ScholarCrossref
- 39. (a)B. R. Gelin and M. Karplus, Proc. Natl. Acad. Sci. USA 72, 2002 (1975); Google ScholarCrossref
(b)J. A. McCammon and M. Karplus, 76, 3585 (1979); , Proc. Natl. Acad. Sci. U.S.A. , Google ScholarCrossref
(c)J. A. McCammon and M. Karplus, Biopolym. 19, 1375 (1980). , Google ScholarCrossref - 40. O. L. Beveridge and F. M. DiCapua, Annu. Rev. Biophys. Biophys. Chem. 18, 431 (1989). Google ScholarCrossref
- 41. T. P. Straatsma and J. A. McCammon, Annu. Rev. Phys. Chem. 43, 407 (1992). Google ScholarCrossref
- 42. C. L. Brooks III and D. A. Case, Chem. Rev. 93, 2487 (1993), and references therein. Google ScholarCrossref
- 43. J. A. McCammon, P. G. Wolynes, and M. Karplus, Biochem. 18, 927 (1979). Google ScholarCrossref
- 44. W. F. van Gunsteren and M. Karplus, Macromolecules 15, 1528 (1982). Google ScholarCrossref
- 45. W. E. Reiher, Ph.D. thesis, Harvard University, 1985. Google Scholar
- 46. W. L. Jorgensen, J. Chandrasekhar, and J. P. Madura, J. Chem. Phys. 79, 926 (1983). Google ScholarScitation, ISI
- 47. R. A. Loncharich and B. R. Brooks, Proteins 6, 32 (1989). Google ScholarCrossref
- 48. A. Warshel and M. Levitt, J. Mol. Biol. 103, 227 (1976). Google ScholarCrossref, ISI
- 49. Further details can be found in the CHARMM program, which can be obtained for a nominal fee by not-for-profit institutions from the CHARMM Development Project, 12 Oxford St., Harvard University, Cambridge, MA 02138. E-mail [email protected], Google Scholar
Please Note: The number of views represents the full text views from December 2016 to date. Article views prior to December 2016 are not included.