Fischer W, Brickmann J, Läuger P
Biophys Chem. 1981 Apr;13(2):105-16. doi: 10.1016/0301-4622(81)80009-9.
Ion transport through biological membranes often takes place via pore-like protein channels. The elementary process of this transport can be described as a motion of the ion in a quasi-periodic multi-well potential. In this study molecular dynamics simulations of ion transport in a model channel were performed in order to test the validity of reaction-rate theory for this process. The channel is modelled as a hexagonal helix of infinite length, and the ligand groups interacting with the ion are represented by dipoles lining the central hole of the channel. The dipoles interact electrostatically with each other and are allowed to oscillate around an equilibrium orientation. The coupled equations of motion for the ion and the dipoles were solved simultaneously with the aid of a numerical integration procedure. From the calculated ion trajectories it is seen that, particularly at low temperatures, the ion oscillates back and forth in the trapping site many times before it leaves the site and jumps over the barrier. The observed oscillation frequency was found to be virtually temperature-independent (nu 0 approximately equal to 2 X 10(12) s-1) so that the strong increase of transport rate with temperature results almost exclusively from the Arrhenius-type exponential dependence of jump probability w on 1/T. At higher temperatures simultaneous jumps over several barriers occasionally occur. Although the exponential form of w(T) was in agreement with the predictions of rate theory, the activation energy Ea as determined from w(T) was different from the barrier height which was calculated from the static potential of the ion in the channel; the actual transport rate was 1 X 10(3) times higher than the rate predicted from the calculated barrier height. This observation was interpreted by the notion that ion transport in the channel is strongly influenced by thermal fluctuations in the conformation of the ligand system which in turn give rise to fluctuations of barrier height.
离子通过生物膜的运输通常经由孔状蛋白质通道进行。这种运输的基本过程可描述为离子在准周期多阱势中的运动。在本研究中，进行了模型通道中离子运输的分子动力学模拟，以检验该过程反应速率理论的有效性。通道被建模为无限长的六边形螺旋，与离子相互作用的配体基团由排列在通道中心孔周围的偶极子表示。偶极子彼此之间存在静电相互作用，并允许围绕平衡取向振荡。借助数值积分程序同时求解离子和偶极子的耦合运动方程。从计算出的离子轨迹可以看出，特别是在低温下，离子在离开阱位点并越过势垒之前，会在捕获位点来回振荡多次。观察到的振荡频率实际上与温度无关（ν0约等于2×10¹² s⁻¹），因此运输速率随温度的强烈增加几乎完全源于跳跃概率w对1/T的阿仑尼乌斯型指数依赖。在较高温度下，偶尔会发生同时越过多个势垒的跳跃。尽管w(T)的指数形式与速率理论的预测一致，但由w(T)确定的活化能Ea与根据通道中离子的静电势计算出的势垒高度不同；实际运输速率比根据计算出的势垒高度预测的速率高1×10³倍。这一观察结果可通过以下观点来解释，即通道中的离子运输受到配体系统构象热涨落的强烈影响，而这反过来又导致势垒高度的涨落。
