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## Davydov soliton
## Additional recommended knowledge
Davydov's Hamiltonian is formally similar to the Fröhlich-Holstein Hamiltonian for the interaction of electrons with a polarizable lattice. Thus the Hamiltonian of the energy operator is
where is the quasiparticle (exciton) Hamiltonian, which describes the motion of the amide I excitations between adjacent sites; is the phonon Hamiltonian, which describes
the vibrations of the lattice; and is the interaction Hamiltonian, which describes the interaction of the amide I excitation with the lattice. The quasiparticle (exciton) Hamiltonian is:
where the index counts the peptide groups along the α-helix spine, the index α = 1,2,3 counts each α-helix spine, J is the energy of the amide I
vibration (CO stretching), J is the dipole-dipole coupling energy between a particular amide I bond and those ahead and behind along the same spine, J is the
dipole-dipole coupling energy between a particular amide I bond and those on adjacent spines in the same unit cell of the protein α-helix, and are respectively
the boson creation and annihilation operator for a quasiparticle at the peptide group. The phonon Hamiltonian is
Finally, the interaction Hamiltonian is
The mathematical techniques that are used to analyze Davydov's soliton are similar to some that have been developed in polaron theory. In this context the Davydov's soliton corresponds to a polaron that is (i) The Davydov soliton is a There are three possible fundamental approaches towards Davydov model: ## References- ^
^{a}^{b}Davydov AS (1973). "The theory of contraction of proteins under their excitation".*Journal of Theoretical Biology***38**: 559-569. - ^
^{a}^{b}Davydov AS (1974). "Quantum theory of muscular contraction".*Biophysics***19**: 684-691. - ^
^{a}^{b}Davydov AS (1977). "Solitons and energy transfer along protein molecules".*Journal of Theoretical Biology***66**: 379-387. **^**Brizhik L, Eremko A, Piette B, Zakrzewski W (2004). "Solitons in α-helical proteins".*Physical Review E***70**: 031914, 1-16.- ^
^{a}^{b}^{c}Scott AS (1992). "Davydov's soliton".*Physics Reports***217**: 1-67. - ^
^{a}^{b}Cruzeiro-Hansson L, Takeno S. (1997). "Davydov model: the quantum, mixed quantum-classical, and full classical systems".*Physical Review E***56**: 894-906. **^**Cruzeiro-Hansson L (2005). "Influence of the nonlinearity and dipole strength on the amide I band of protein α-helices".*The Journal of Chemical Physics***123**: 234909, 1-7.**^**Cruzeiro-Hansson L (1997). "Short timescale energy transfer in proteins".*Solphys '97 Proceedings*.
Categories: Biophysics | Biological matter |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Davydov_soliton". A list of authors is available in Wikipedia. |