Mamonov Artem B, Coalson Rob D, Nitzan Abraham, Kurnikova Maria G
Chemistry Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA.
Biophys J. 2003 Jun;84(6):3646-61. doi: 10.1016/S0006-3495(03)75095-4.
A composite continuum theory for calculating ion current through a protein channel of known structure is proposed, which incorporates information about the channel dynamics. The approach is utilized to predict current through the Gramicidin A ion channel, a narrow pore in which the applicability of conventional continuum theories is questionable. The proposed approach utilizes a modified version of Poisson-Nernst-Planck (PNP) theory, termed Potential-of-Mean-Force-Poisson-Nernst-Planck theory (PMFPNP), to compute ion currents. As in standard PNP, ion permeation is modeled as a continuum drift-diffusion process in a self-consistent electrostatic potential. In PMFPNP, however, information about the dynamic relaxation of the protein and the surrounding medium is incorporated into the model of ion permeation by including the free energy of inserting a single ion into the channel, i.e., the potential of mean force along the permeation pathway. In this way the dynamic flexibility of the channel environment is approximately accounted for. The PMF profile of the ion along the Gramicidin A channel is obtained by combining an equilibrium molecular dynamics (MD) simulation that samples dynamic protein configurations when an ion resides at a particular location in the channel with a continuum electrostatics calculation of the free energy. The diffusion coefficient of a potassium ion within the channel is also calculated using the MD trajectory. Therefore, except for a reasonable choice of dielectric constants, no direct fitting parameters enter into this model. The results of our study reveal that the channel response to the permeating ion produces significant electrostatic stabilization of the ion inside the channel. The dielectric self-energy of the ion remains essentially unchanged in the course of the MD simulation, indicating that no substantial changes in the protein geometry occur as the ion passes through it. Also, the model accounts for the experimentally observed saturation of ion current with increase of the electrolyte concentration, in contrast to the predictions of standard PNP theory.
提出了一种用于计算通过已知结构蛋白质通道的离子电流的复合连续介质理论，该理论纳入了有关通道动力学的信息。该方法用于预测通过短杆菌肽A离子通道的电流，短杆菌肽A离子通道是一种狭窄的孔道，传统连续介质理论在其中的适用性存在疑问。所提出的方法利用了泊松-能斯特-普朗克（PNP）理论的修正版本，即平均力势-泊松-能斯特-普朗克理论（PMFPNP）来计算离子电流。与标准PNP一样，离子渗透被建模为在自洽静电势中的连续漂移-扩散过程。然而，在PMFPNP中，通过纳入将单个离子插入通道的自由能，即沿渗透途径的平均力势，将有关蛋白质和周围介质动态弛豫的信息纳入离子渗透模型。通过这种方式，大致考虑了通道环境的动态灵活性。通过将平衡分子动力学（MD）模拟与自由能的连续静电计算相结合，获得离子沿短杆菌肽A通道的PMF分布，其中MD模拟在离子位于通道中特定位置时对动态蛋白质构型进行采样。还使用MD轨迹计算通道内钾离子的扩散系数。因此，除了合理选择介电常数外，该模型没有直接的拟合参数。我们的研究结果表明，通道对渗透离子的响应会在通道内产生显著的离子静电稳定作用。在MD模拟过程中，离子的介电自能基本保持不变，这表明当离子通过时，蛋白质几何结构没有发生实质性变化。此外，与标准PNP理论的预测相反，该模型解释了实验观察到的离子电流随电解质浓度增加而饱和的现象。
