Chiu S W, Novotny J A, Jakobsson E
Biotechnology Center, University of Illinois, Urbana 61801.
Biophys J. 1993 Jan;64(1):98-109. doi: 10.1016/S0006-3495(93)81344-4.
Using a combination of techniques, including molecular dynamics, time-correlation analysis, stochastic dynamics, and fitting of continuum diffusion theory to electrophysiological data, a characterization is made of thermally driven sodium, water, and D2O motion within the gramicidin A channel. Since the channel contents are constrained to move in a single-file fashion, the motion that corresponds to experimentally measurable rates of permeation of the membrane is the motion of the center of mass of the channel contents. We therefore emphasize channel contents center-of-mass motion in our analysis of molecular dynamics computations. The usual free energy calculation techniques would be of questionable validity when applied to such motion. As an alternative to those techniques, we postulate a periodic sinusoidal free energy profile (related to the periodic structure of the helical channel) and deduce the fluid dynamic diffusion coefficient and the height and spacing of the free energy barriers from the form of the mean-square-deviation function, using stochastic computations. The fluid dynamic friction in each case appears similar to that for aqueous solution. However, the diffusive motions are modulated by a spatially periodic free energy profile with a periodicity characteristic of an L-D pair of amino acids in the gramicidin helix, approximately 1.7 A in the model we use. The barrier height depends on which substance is moving in the channel, but in each case is several times thermal energy. For barriers of this width and height, the motion is intermediate between the low-friction (transition-state) and high-friction (Brownian) limits. Thus, neither of these formalisms that have been used commonly to describe membrane permeation gives an accurate picture of the underlying physical process (although the Brownian description seems closer to correct). The non-Markovian Langevin equation must be solved to describe properly the statistics of the process. The "channel state of matter" characteristic of the channel contents appears to have some properties typical of the solid and some typical of the liquid state. The magnitude of the local friction and nature of the ion solvation are similar to the liquid state, but the periodicities of structure, free energy, and dynamics are somewhat solid-like. The alignment of water dipoles in the channel bears some resemblance to the orientational ordering of a nematic liquid crystal, but unlike a nematic liquid crystal, the waters have a degree of translational order as well. Thus, the "channel state" is not adequately described by analogy to either the solid or liquid states or to liquid crystals but must be dealt with as its own characteristic type of condensed matter.
通过结合多种技术，包括分子动力学、时间关联分析、随机动力学以及将连续介质扩散理论拟合到电生理数据，对短杆菌肽A通道内热驱动的钠、水和重水的运动进行了表征。由于通道内的物质被限制以单列方式移动，与实验可测量的膜渗透速率相对应的运动是通道内物质质心的运动。因此，在我们对分子动力学计算的分析中，我们强调通道内物质的质心运动。当应用于这种运动时，通常的自由能计算技术的有效性是值得怀疑的。作为这些技术的替代方法，我们假设一个周期性的正弦自由能分布（与螺旋通道的周期性结构相关），并使用随机计算从均方位移函数的形式推导出流体动力学扩散系数以及自由能垒的高度和间距。在每种情况下，流体动力学摩擦力似乎与水溶液中的相似。然而，扩散运动受到空间周期性自由能分布的调制，其周期性具有短杆菌肽螺旋中L - D氨基酸对的特征，在我们使用的模型中约为1.7埃。势垒高度取决于通道中移动的是哪种物质，但在每种情况下都是热能的几倍。对于这种宽度和高度的势垒，运动介于低摩擦（过渡态）和高摩擦（布朗）极限之间。因此，通常用于描述膜渗透的这两种形式体系都没有准确描述潜在的物理过程（尽管布朗描述似乎更接近正确）。必须求解非马尔可夫朗之万方程才能正确描述该过程的统计特性。通道内物质的“通道物质状态”似乎具有一些固态的典型性质和一些液态的典型性质。局部摩擦力的大小和离子溶剂化的性质与液态相似，但结构、自由能和动力学的周期性有点像固态。通道中水偶极的排列与向列型液晶的取向有序有一些相似之处，但与向列型液晶不同，水也有一定程度的平移有序。因此，“通道状态”不能通过类比固态或液态或液晶来充分描述，而必须作为其自身特有的凝聚态物质来处理。
