ABSTRACT Low-frequency vibrational excitations of protein macromolecules in the terahertz frequency region are suggested to contribute to many biological processes such as enzymatic catalysis, intra-protein energy/charge transport, recognition, and allostery. To explain high effectiveness of these processes, two possible mechanisms of the long-lived excitation were proposed by H. Fröhlich and A.S. Davydov, which relate to either vibrational modes or solitary waves, respectively. In this paper, we developed a quantum dynamic model of vibrational excitation in α-helical proteins interacting with the aqueous environment. In the model, we distinguished three coupled subsystems, i.e., (i) a chain of hydrogen-bonded peptide groups (PGs), interacting with (ii) the subsystem of the side-chain residuals which in turn interact with (iii) the environment, surrounding water responsible for dissipation and fluctuation in the system. It was shown that the equation of motion for phonon variables of the PG chain can be transformed to nonlinear Schrodinger equation which admits bifurcation into the solution corresponding to the weak-damped vibrational modes (Fröhlich-type regime) and Davydov solitons. A bifurcation parameter is derived through the strength of phonon–phonon interaction between the side-chains and hydration-shell water molecules. As shown, the energy of these excited states is pumped through the interaction of the side-chains with fluctuating water environment of the proteins. The suggested mechanism of the collective vibrational mode excitation is discussed in connection with the recent experiments on the long-lived collective protein excitations in the terahertz frequency region and vibrational energy transport pathways in proteins.

中文翻译：

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α-螺旋蛋白结构与水环境相互作用的集体激发

摘要 蛋白质大分子在太赫兹频率区域的低频振动激发有助于许多生物过程，如酶催化、蛋白质内能量/电荷传输、识别和变构。为了解释这些过程的高效性，H. Fröhlich 和 AS Davydov 提出了两种可能的长寿命激发机制，分别与振动模式或孤立波有关。在本文中，我们开发了 α-螺旋蛋白与水环境相互作用的振动激发的量子动力学模型。在模型中，我们区分了三个耦合子系统，即 (i) 氢键肽基 (PG) 链，与 (ii) 侧链残基子系统相互作用，后者又与 (iii) 环境相互作用, 周围的水负责系统的耗散和波动。结果表明，PG链的声子变量的运动方程可以转化为非线性薛定谔方程，该方程允许分岔进入对应于弱阻尼振动模式（Fröhlich型状态）和Davydov孤子的解。分叉参数是通过侧链和水合壳水分子之间的声子-声子相互作用的强度推导出来的。如图所示，这些激发态的能量通过侧链与蛋白质波动的水环境的相互作用被泵送。