No Access Submitted: 18 September 1995 Accepted: 29 March 1996 Published Online: 31 August 1998
J. Chem. Phys. 105, 1902 (1996); https://doi.org/10.1063/1.472061
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  • Eyal Neria
  • Stefan Fischer
  • Martin Karplus
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. 1. J. Keck, Discuss. Faraday 33, 173 (1962). Google ScholarCrossref
  2. 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. 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. 4. C. L. BrooksIII, M. Karplus, and B. M. Pettitt, Adv. Chem. Phys. 71, 1 (1988). Google Scholar
  5. 5. S. Glasstone, K. J. Laidler, and H. Eyring, Theory of Rate Processes (McGraw-Hill, New York, 1941). Google Scholar
  6. 6. P. Hanggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990). Google ScholarCrossref, ISI
  7. 7. E. P. Wigner, Trans. Faraday Soc. 34, 29 (1938). Google ScholarCrossref
  8. 8. D. A. McQuarrie, Statistical Mechanics (Harper and Row, New York 1976). Google Scholar
  9. 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. 10. C. Pangali, M. Rao, and B. J. Berne, J. Chem. Phys. 71, 2975 (1979). Google ScholarScitation, ISI
  11. 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. 12. D. W. Robertus, B. J. Berne, and D. Chandler, J. Chem. Phys. 70, 3395 (1979). Google ScholarScitation, ISI
  13. 13. D. J. Tobias and C. L. BrooksIII, Chem. Phys. Lett. 142, 472 (1987). Google ScholarCrossref
  14. 14. E. A. Carter, G. Ciccotti, J. T. Hynes, and R. Kapral, Chem. Phys. Lett. 156, 472 (1989). Google ScholarCrossref, ISI
  15. 15. E. Paci, G. Ciccotti, M. Ferrario, and R. Kapral, Chem. Phys. Lett. 176, 581 (1991). Google ScholarCrossref
  16. 16. J. M. Depaepe, J. P. Ryckaert, E. Paci, and G. Ciccotti, Mol. Phys. 79, 515 (1993). Google ScholarCrossref
  17. 17. D. Chandler, J. Chem. Phys. 68, 2959 (1978). Google ScholarScitation, ISI
  18. 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. 19. J. E. Straub, D. A. Hsu, and B. J. Berne, J. Phys. Chem. 89, 5188 (1985). Google ScholarCrossref, ISI
  20. 20. B. J. Gertner, K. R. Wilson, and J. T. Hynes, J. Chem. Phys. 90, 3537 (1989). Google ScholarScitation, ISI
  21. 21. L. R. Pratt, J. Chem. Phys. 85, 5045 (1986). Google ScholarScitation
  22. 22. A. Ulitskey and R. Elber, J. Chem. Phys. 92, 1510 (1990). Google ScholarScitation
  23. 23. S. Fischer and M. Karplus, Chem. Phys. Lett. 194, 252 (1992). Google ScholarCrossref
  24. 24. R. Elber, J. Chem. Phys. 93, 4312 (1990). Google ScholarScitation
  25. 25. T. Lazaridis, D. J. Tobias, C. L. Brooks III, and M. Paulaitis, J. Chem. Phys. 95, 7612 (1991). Google ScholarScitation
  26. 26. P. Pechukas, Annu. Rev. Phys. Chem. 32, 159 (1981). Google ScholarCrossref, ISI
  27. 27. J. P. Ryckaert and G. Ciccotti, J. Chem. Phys. 78, 7368 (1983). Google ScholarScitation, ISI
  28. 28. C. Eckart, Phys. Rev. 47, 552 (1935). Google ScholarCrossref
  29. 29. E. B. Wilson, J. C. Decius, and P. C. Cross, Molecular Vibrations (McGraw-Hill, New York, 1955). Google Scholar
  30. 30. H. M. Pickett and H. L. Strauss, J. Am. Chem. Soc. 92, 7281 (1970). Google ScholarCrossref
  31. 31. D. R. Herschbach, H. S. Johnston, and D. Rapp, J. Chem. Phys. 31, 1652 (1959). Google ScholarScitation, ISI
  32. 32. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford, London, 1989). Google Scholar
  33. 33. S. Fischer Ph.D. thesis, Harvard University 1992; S. Fischer and M. Karplus (unpublished). Google Scholar
  34. 34. B. M. Pettitt and M. Karplus, J. Amer. Chem. Soc. 107, 1166 (1985). Google ScholarCrossref
  35. 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. 36. J. P. Ryckaert, G. Ciccotti, and H. J. C. Berensden, J. Comput. Phys. 23, 327 (1977). Google ScholarCrossref, ISI
  37. 37. A. MacKerell and M. Karplus (unpublished). Google Scholar
  38. 38. S. Fischer, S. Michnick, and M. Karplus, Biochem. 32, 13830 (1993). Google ScholarCrossref
  39. 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. 40. O. L. Beveridge and F. M. DiCapua, Annu. Rev. Biophys. Biophys. Chem. 18, 431 (1989). Google ScholarCrossref
  41. 41. T. P. Straatsma and J. A. McCammon, Annu. Rev. Phys. Chem. 43, 407 (1992). Google ScholarCrossref
  42. 42. C. L. Brooks III and D. A. Case, Chem. Rev. 93, 2487 (1993), and references therein. Google ScholarCrossref
  43. 43. J. A. McCammon, P. G. Wolynes, and M. Karplus, Biochem. 18, 927 (1979). Google ScholarCrossref
  44. 44. W. F. van Gunsteren and M. Karplus, Macromolecules 15, 1528 (1982). Google ScholarCrossref
  45. 45. W. E. Reiher, Ph.D. thesis, Harvard University, 1985. Google Scholar
  46. 46. W. L. Jorgensen, J. Chandrasekhar, and J. P. Madura, J. Chem. Phys. 79, 926 (1983). Google ScholarScitation, ISI
  47. 47. R. A. Loncharich and B. R. Brooks, Proteins 6, 32 (1989). Google ScholarCrossref
  48. 48. A. Warshel and M. Levitt, J. Mol. Biol. 103, 227 (1976). Google ScholarCrossref, ISI
  49. 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
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