微管中偶极子的非线性动力学：赝自旋模型
Nonlinear Dynamics of Dipoles in Microtubules: Pseudo-Spin Model
摘要：
我们进行了理论研究的电场激发在微管中的动力学考虑到现实的圆柱形几何形状，偶极-偶极相互作用的微管蛋白为基础的蛋白质异二聚体，径向电场产生的溶剂，和可能的简并个别异二聚体的能量状态。在经典的赝自旋模型框架下进行了考虑。我们推导出相互作用偶极子的非线性动力学常微分方程组，以及这些方程的连续形式。我们得到了这些方程的解的形式snoidal波，孤子，扭结，和本地化尖峰。我们的研究结果将有助于更好地理解微管的功能特性，包括运动蛋白动力学和信息传递过程。我们的考虑是基于经典动力学。对可能的量子效应的作用也作了一些推测。
英文摘要：
We perform a theoretical study of the dynamics of the electric field excitations in a microtubule by taking into consideration the realistic cylindrical geometry, dipole-dipole interactions of the tubulin-based protein heterodimers, the radial electric field produced by the solvent, and a possible degeneracy of energy states of individual heterodimers. The consideration is done in the frames of the classical pseudo-spin model. We derive the system of nonlinear dynamical ordinary differential equations of motion for interacting dipoles, and the continuum version of these equations. We obtain the solutions of these equations in the form of snoidal waves, solitons, kinks, and localized spikes. Our results will help to a better understanding of the functional properties of microtubules including the motor protein dynamics and the information transfer processes. Our considerations are based on classical dynamics. Some speculations on the role of possible quantum effects are also made.
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