Department of Physics, University of Prince Edward Island, 550 University Ave., Charlottetown, Prince Edward Island C1A 4P3, Canada.
J Chem Phys. 2013 May 7;138(17):174902. doi: 10.1063/1.4803022.
Monte Carlo (MC) simulations are used to study the dynamics of polymer translocation through a nanopore in the limit where the translocation rate is sufficiently slow that the polymer maintains a state of conformational quasi-equilibrium. The system is modeled as a flexible hard-sphere chain that translocates through a cylindrical hole in a hard flat wall. In some calculations, the nanopore is connected at one end to a spherical cavity. Translocation times are measured directly using MC dynamics simulations. For sufficiently narrow pores, translocation is sufficiently slow that the mean translocation time scales with polymer length N according to <τ> ∝ (N - N(p))(2), where N(p) is the average number of monomers in the nanopore; this scaling is an indication of a quasi-static regime in which polymer-nanopore friction dominates. We use a multiple-histogram method to calculate the variation of the free energy with Q, a coordinate used to quantify the degree of translocation. The free energy functions are used with the Fokker-Planck formalism to calculate translocation time distributions in the quasi-static regime. These calculations also require a friction coefficient, characterized by a quantity N(eff), the effective number of monomers whose dynamics are affected by the confinement of the nanopore. This was determined by fixing the mean of the theoretical distribution to that of the distribution obtained from MC dynamics simulations. The theoretical distributions are in excellent quantitative agreement with the distributions obtained directly by the MC dynamics simulations for physically meaningful values of N(eff). The free energy functions for narrow-pore systems exhibit oscillations with an amplitude that is sensitive to the nanopore length. Generally, larger oscillation amplitudes correspond to longer translocation times.
蒙特卡罗（MC）模拟用于研究聚合物通过纳米孔的动力学，在这种情况下，迁移率足够慢，以至于聚合物保持构象准平衡状态。该系统被建模为柔性硬球链，通过硬平板上的圆柱形孔进行迁移。在一些计算中，纳米孔的一端连接到一个球形腔。使用 MC 动力学模拟直接测量迁移时间。对于足够窄的孔，迁移速度足够慢，使得平均迁移时间根据<τ>∝(N-N(p))(2)与聚合物长度 N 成正比，其中 N(p)是纳米孔中单体的平均数量；这种标度是准静态区域的一个指示，其中聚合物-纳米孔摩擦占主导地位。我们使用多直方图方法来计算自由能随 Q 的变化，Q 是用于量化迁移程度的坐标。自由能函数与福克-普朗克形式主义一起用于计算准静态区域中的迁移时间分布。这些计算还需要一个摩擦系数，由一个有效数量 N(eff)来表示，该数量表示受纳米孔限制影响的动力学的有效单体数量。这是通过将理论分布的平均值固定为从 MC 动力学模拟获得的分布的平均值来确定的。对于物理上有意义的 N(eff)值，理论分布与通过 MC 动力学模拟直接获得的分布具有极好的定量一致性。对于窄孔系统，自由能函数表现出与纳米孔长度敏感的振幅的振荡。一般来说，较大的振荡幅度对应于较长的迁移时间。
