Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany.
Soft Matter. 2014 Mar 14;10(10):1591-601. doi: 10.1039/c3sm52846d.
We study the thermal Markovian diffusion of tracer particles in a 2D medium with spatially varying diffusivity D(r), mimicking recently measured, heterogeneous maps of the apparent diffusion coefficient in biological cells. For this heterogeneous diffusion process (HDP) we analyse the mean squared displacement (MSD) of the tracer particles, the time averaged MSD, the spatial probability density function, and the first passage time dynamics from the cell boundary to the nucleus. Moreover we examine the non-ergodic properties of this process which are important for the correct physical interpretation of time averages of observables obtained from single particle tracking experiments. From extensive computer simulations of the 2D stochastic Langevin equation we present an in-depth study of this HDP. In particular, we find that the MSDs along the radial and azimuthal directions in a circular domain obey anomalous and Brownian scaling, respectively. We demonstrate that the time averaged MSD stays linear as a function of the lag time and the system thus reveals a weak ergodicity breaking. Our results will enable one to rationalise the diffusive motion of larger tracer particles such as viruses or submicron beads in biological cells.
我们研究了示踪粒子在二维介质中的热马尔可夫扩散，该介质的扩散率 D(r) 随空间变化，模拟了最近在生物细胞中测量到的表观扩散系数的不均匀图谱。对于这种不均匀扩散过程 (HDP)，我们分析了示踪粒子的均方位移 (MSD)、时间平均 MSD、空间概率密度函数以及从细胞边界到核的首次通过时间动力学。此外，我们还研究了该过程的非遍历性质，这对于从单粒子跟踪实验中获得的可观测物理量的时间平均的正确物理解释非常重要。通过对二维随机朗之万方程的广泛计算机模拟，我们对这种 HDP 进行了深入研究。特别是，我们发现，在圆形区域中沿径向和角向方向的 MSD 分别遵循反常和布朗缩放。我们证明了时间平均 MSD 作为滞后时间的函数保持线性，因此系统表现出弱遍历性破坏。我们的结果将能够合理化较大示踪粒子（如病毒或亚微米珠）在生物细胞中的扩散运动。
