Quantum and temperature effects on Davydov soliton dynamics: Averaged Hamiltonian method

  • Forner W
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Abstract

Ahstract. The dynamics of Davydov solitons within the so-called ID,) state which allows quantum effects in the lattice are studied at physiological temperatues using Davydov's averaged Hamiltonian method. For this purpose the Euler-Lagrange method is used to obtain approximate equations of motion from a thermally averaged Hamiltonian. Within ID,)dynamicsat T = OKand forparameiervaluesappropriate for proteins.nosolitonsare found. It is demonstrated that temperature effects at 300K shift the stability window for travelling solitons into regions of the parameter space which might be realistic for proteins. 1. Introduction For the mechanism of energy transport through proteins, Davydov [l, 21 suggested that the energy of about 0.4 eV released by the hydrolysis of adenosine-triphosphate (ATP) could be transported in quanta of the amide-I (mainly C==O stretch) vibration (about 0.2 eV). The CO groups participate in hydrogen bonds which form chains parallel to the axisof a-helical proteins. Thus the amide-I vibration interacts with the acousticphonons in these chains. The excitation of an amide-I oscillator 11.21 causes a distortion in the lattice which in turn stabilizes the amide-I excitation. It was found that for certain regions of the parameter spaceofthe model thiseffect canprevent the excitation from dispersion via the dipole-dipole coupling between neighbouring CO groups in the lattice. The region in which the vibrational energy is localized can travel as a soliton along the chain. In his original theory, Davydov and co-workers [l] used an ansatz for the wave-function (IDz)) which treats the lattice classically. At zero temperature it has been confirmed that Davydov solitons exist for parameter values appropriate for proteins [3]. Also their stability against disorder along the chain was studied [4]. The investigation of temperature led to controversial results. Halding and Lomdahl [SI found stable pulses

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  • W. Forner

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