Mathematical and Statistical Computing Laboratory, Office of Intramural Research, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA.
Section on Molecular Transport, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, USA.
J Chem Phys. 2021 Mar 21;154(11):111101. doi: 10.1063/5.0044044.
In the one-dimensional description, the interaction of a solute molecule with the channel wall is characterized by the potential of mean force U(x), where the x-coordinate is measured along the channel axis. When the molecule can reversibly bind to certain amino acid(s) of the protein forming the channel, this results in a localized well in the potential U(x). Alternatively, this binding can be modeled by introducing a discrete localized site, in addition to the continuum of states along x. Although both models may predict identical equilibrium distributions of the coordinate x, there is a fundamental difference between the two: in the first model, the molecule passing through the channel unavoidably visits the potential well, while in the latter, it may traverse the channel without being trapped at the discrete site. Here, we show that when the two models are parameterized to have the same thermodynamic properties, they automatically yield identical translocation probabilities and mean translocation times, yet they predict qualitatively different shapes of the translocation time distribution. Specifically, the potential well model yields a narrower distribution than the model with a discrete site, a difference that can be quantified by the distribution's coefficient of variation. This coefficient turns out to be always smaller than unity in the potential well model, whereas it may exceed unity when a discrete trapping site is present. Analysis of the translocation time distribution beyond its mean thus offers a way to differentiate between distinct translocation mechanisms.
在一维描述中，溶质分子与通道壁的相互作用由平均力势 U(x) 来表征，其中 x 坐标沿通道轴测量。当分子可以可逆地结合到形成通道的蛋白质的某些氨基酸上时，这会导致势 U(x) 中出现局部势阱。或者，可以通过在沿 x 的连续状态之外引入离散的局部位置来模拟这种结合。尽管这两种模型都可以预测坐标 x 的相同平衡分布，但它们之间存在根本的区别：在第一种模型中，穿过通道的分子不可避免地会访问势阱，而在后一种模型中，它可能在没有被困在离散位置的情况下穿过通道。在这里，我们表明，当两个模型被参数化为具有相同的热力学性质时，它们自动产生相同的易位概率和平均易位时间，但它们预测了易位时间分布的定性不同的形状。具体来说，势阱模型产生的分布比具有离散位置的模型更窄，这种差异可以通过分布的变异系数来量化。在势阱模型中，该系数始终小于 1，而当存在离散的捕获位置时，它可能超过 1。因此，对易位时间分布的均值进行分析提供了一种区分不同易位机制的方法。
