Donor–acceptor symmetric and antisymmetric tunneling matrix elements: a pathway model investigation of protein electron transfer

  • P. C. P. de AndradeEmail author
  • J. C. O. Guerra
Original Paper


In protein electron transfer reaction rate calculations, the electronic Hamiltonian is apportioned into donor–acceptor (DA) and protein bridge subspaces, and a two-state system is defined for the DA subspace. Löwdin partitioning is used to perform the two-state reductions necessary to compute the tunneling matrix element between D and A sites. Here, a method of performing donor and acceptor state analysis for a non-orthogonal basis set in both the weak and strong electronic coupling regimes is developed. The electron tunneling current and coupling are obtained in terms of DA symmetric and antisymmetric interatomic tunneling elements, and are then used to compare pathway models. These interatomic tunneling elements are both proportional to the Green’s function elements of the isolated protein bridge. To facilitate a perturbative treatment of antisymmetric interatomic tunneling currents, we found a well-known expression for the DA tunneling matrix element in terms of transformed Green’s function matrix elements of the isolated protein bridge. Also, the relationship of the tunneling matrix element to BO pathways is discussed using the symmetric interatomic coupling. Finally, the definition of the average interatomic and atomic pathway coupling allows us obtain the quantum interference between interatomic tunneling pathways.


Two-state approximation for non-orthogonal basis set Protein electron transfer Pathway models 



  1. 1.
    Marcus RA, Sutin N (1985) Biochim Biophys Acta 811:265Google Scholar
  2. 2.
    de Andrade PCP, Freire JN (2004) J Chem Phys 120:7811 (and references therein)Google Scholar
  3. 3.
    Hayashi T, Stuchebrukhov AA (2010) Proc Natl Acad Sci USA 107:19157Google Scholar
  4. 4.
    Li J, Liu Z, Tan C, Guo X, Wang L, Sancar A, Zhong D (2010) Nature 466:887Google Scholar
  5. 5.
    Jortner J (1980) Biochim Biophys Acta 594:193Google Scholar
  6. 6.
    Macconnell M (1961) J Chem Phys 35:508Google Scholar
  7. 7.
    Hopfield JJ (1974) Proc Natl Acad Sci USA 71:3640Google Scholar
  8. 8.
    Beratan DN, Onuchic JN, Hopfield JJ (1987) J Chem Phys 86:4488Google Scholar
  9. 9.
    Onuchic JN, Beratan DN (1990) J Chem Phys 92:722Google Scholar
  10. 10.
    Beratan DN, Betts JN, Onuchic JN (1991) Science 252:1285Google Scholar
  11. 11.
    Regan SM, Risser DNB, Onuchic JN (1993) J Phys Chem 97:13083Google Scholar
  12. 12.
    Kawatsu T, Kakitani T, Yamato T (2001) J Phys Chem B 105:4424Google Scholar
  13. 13.
    de Andrade PCP, Freire JN (2003) J Chem Phys 118:6733Google Scholar
  14. 14.
    Prytkova TR, Kurnikov IV, Beratan DN (2007) Science 315:622 (and references therein)Google Scholar
  15. 15.
    Larsson S (1981) J Am Chem Soc 103:4034Google Scholar
  16. 16.
    da Gama AAS (1990) J Theor Biol 142:251Google Scholar
  17. 17.
    Onuchic JN, de Andrade PCP, Beratan DN (1991) J Chem Phys 95:1131Google Scholar
  18. 18.
    Balabin IA, Onuchic JN (1996) J Phys Chem 100:11573Google Scholar
  19. 19.
    Skourtis SS, Onuchic JN, Beratan DN (1996) Inorg Chim Acta 243:167Google Scholar
  20. 20.
    Stuchebrukhov AA (1996) J Chem Phys 104:8424Google Scholar
  21. 21.
    Stuchebrukhov AA (1996) J Chem Phys 105:10819Google Scholar
  22. 22.
    Kawatsu T, Kakitani T, Yamato T (2000) Inorg Chim Acta 300:862Google Scholar
  23. 23.
    Kawatsu T, Kakitani T, Yamato T (2002) J Phys Chem B 106:5068Google Scholar
  24. 24.
    Kawatsu T, Kakitani T, Yamato T (2002) J Phys Chem B 106:11356Google Scholar
  25. 25.
    Skourtis SS, Onuchic JN (1993) Chem Phys Lett 209:171Google Scholar
  26. 26.
    Skourtis SS, Beratan DN, Onuchic JN (1993) Chem Phys 176:501Google Scholar
  27. 27.
    de Andrade PCP (2005) J Chem Phys 122:124713Google Scholar
  28. 28.
    Newton MD (1991) Chem Rev (Washington D.C.) 91:767Google Scholar
  29. 29.
    de Andrade PCP, Onuchic JN (1998) J Chem Phys 108:4292 (and references therein)Google Scholar
  30. 30.
    de Andrade PCP (2012) Int J Quantum Chem 112:3325Google Scholar
  31. 31.
    Siddarth P, Marcus RA (1990) J Phys Chem 94:2985Google Scholar
  32. 32.
    Skourtis SS, Beratan DN (1997) J Phys Chem B 101:1215Google Scholar
  33. 33.
    Nishioka H, Kakitani T (2008) J Phys Chem B 112:9948Google Scholar

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Instituto de FísicaUniversidade Federal de UberlândiaUberlândiaBrazil

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