Chen D, Eisenberg R
Department of Physiology, Rush Medical Center, Chicago, Illinois 60612.
Biophys J. 1993 May;64(5):1405-21. doi: 10.1016/S0006-3495(93)81507-8.
Flux through an open ionic channel is analyzed with Poisson-Nernst-Planck (PNP) theory. The channel protein is described as an unchanging but nonuniform distribution of permanent charge, the charge distribution observed (in principle) in x-ray diffraction. Appropriate boundary conditions are derived and presented in some generality. Three kinds of charge are present: (a) permanent charge on the atoms of the protein, the charge independent of the electric field; (b) free or mobile charge, carried by ions in the pore as they flux through the channel; and (c) induced (sometimes called polarization) charge, in the pore and protein, created by the electric field, zero when the electric field is zero. The permanent charge produces an offset in potential, a built-in Donnan potential at both ends of the channel pore. The system is completely solved for bathing solutions of two ions. Graphs describe the distribution of potential, concentration, free (i.e., mobile) and induced charge, and the potential energy associated with the concentration of charge, as well as the unidirectional flux as a function of concentration of ions in the bath, for a distribution of permanent charge that is uniform. The model shows surprising complexity, exhibiting some (but not all) of the properties usually attributed to single filing and exchange diffusion. The complexity arises because the arrangement of free and induced charge, and thus of potential and potential energy, varies, sometimes substantially, as conditions change, even though the channel structure and conformation (of permanent charge) is strictly constant. Energy barriers and wells, and the concomitant binding sites and binding phenomena, are outputs of the PNP theory: they are computed, not assumed. They vary in size and location as experimental conditions change, while the conformation of permanent charge remains constant, thus giving the model much of its interesting behavior.
通过泊松-能斯特-普朗克（PNP）理论分析开放离子通道中的通量。通道蛋白被描述为永久电荷的不变但非均匀分布，这种电荷分布（原则上）可在X射线衍射中观察到。推导了适当的边界条件并进行了一定程度的概括。存在三种电荷：（a）蛋白质原子上的永久电荷，其电荷与电场无关；（b）自由或移动电荷，由离子在孔中通量通过通道时携带；（c）感应（有时称为极化）电荷，在孔和蛋白质中，由电场产生，电场为零时为零。永久电荷产生电位偏移，即通道孔两端的固有唐南电位。对于两种离子的浴液，该系统已完全求解。图表描述了电位、浓度、自由（即移动）电荷和感应电荷的分布，以及与电荷浓度相关的势能，以及单向通量作为浴液中离子浓度的函数，针对均匀的永久电荷分布。该模型显示出惊人的复杂性，展现出一些（但不是全部）通常归因于单通道填充和交换扩散的特性。这种复杂性的产生是因为即使通道结构和（永久电荷的）构象严格恒定，但自由电荷和感应电荷的排列，以及因此电位和势能的排列，会随着条件变化而有时大幅变化。能垒和势阱以及伴随的结合位点和结合现象是PNP理论的输出：它们是计算得出的，而非假设的。随着实验条件的变化，它们的大小和位置会改变，而永久电荷的构象保持不变，从而赋予模型许多有趣的行为。
