论文标题
离子通道的动力学通过非铁量量子力学
Dynamics of ion channels via non-Hermitian quantum mechanics
论文作者
论文摘要
我们研究离子通道的动力学和热力学，被认为是有效的1D库仑系统。跨离子相互作用的远距离性质是由于水和脂质之间的介电常数不匹配，因此将归档的电气限制在大部分填充水通道内。这种库仑系统的统计力学主要由熵效应主导，可以通过将其映射到有效的量子力学上来准确地解释。在存在多价离子的情况下，相应的量子力学似乎是非热的。在这篇综述中，我们讨论了相应的非汉密尔顿人的半经典计算框架。非热性将WKB的动作积分从实际线提升到无法达到直接计算的复杂riemann表面上的封闭周期。我们通过应用代数拓扑的工具（例如Picard-fuchs方程）来避免此问题。我们讨论其解决方案与长水通道内多价溶液的热力学和相关函数的关系。
We study dynamics and thermodynamics of ion channels, considered as effective 1D Coulomb systems. The long range nature of the inter-ion interactions comes about due to the dielectric constants mismatch between the water and lipids, confining the electric filed to stay mostly within the water-filled channel. Statistical mechanics of such Coulomb systems is dominated by entropic effects which may be accurately accounted for by mapping onto an effective quantum mechanics. In presence of multivalent ions the corresponding quantum mechanics appears to be non-Hermitian. In this review we discuss a framework for semiclassical calculations for corresponding non-Hermitian Hamiltonians. Non-Hermiticity elevates WKB action integrals from the real line to closed cycles on a complex Riemann surfaces where direct calculations are not attainable. We circumvent this issue by applying tools from algebraic topology, such as the Picard-Fuchs equation. We discuss how its solutions relate to the thermodynamics and correlation functions of multivalent solutions within long water-filled channels.
