考虑惯性效应的无序系统中的亚扩散
Finite-range viscoelastic subdiffusion in disordered systems with inclusion of inertial effects
摘要：
这项工作证明了粘弹性亚扩散在细胞生物系统的随机环境中的重要性。该模型显示了几个显着的特点，这使得它成为一个有吸引力的范式来解释生物亚扩散的物理本质。特别是，它结合了粘弹性与不同的非遍历特征。我们扩展了这个模型，使其适用于包括惯性效应后，在无序的生物膜的脂质亚扩散。对于脂质，惯性效应发生在皮秒的范围内，并且幂律衰减粘弹性记忆在几纳秒的范围内延伸。因此，在没有无序的情况下，扩散将在超过这个记忆范围的时间尺度上变得正常。然而，无论是实验还是在一些分子动力学模拟中，脂质亚扩散的时间范围都远远超出了粘弹性记忆范围。我们研究了三个一维模型的相关淬火高斯无序来解释这个难题：奇异短程（指数相关），光滑短程（高斯相关），和光滑长程（幂律相关）的障碍。对于中等无序强度，瞬态粘弹性亚扩散转变为由环境随机性引起的亚扩散。它的特点是由一个时间依赖的幂律指数的亚扩散，这可以显示非单调的行为，在最近的一些分子动力学模拟协议。此外，测试粒子在这种无序为主的制度的空间分布是一个非高斯，指数功率分布，这也与分子动力学的研究结果和实验。此外，这种subdiffusion是nonergodic与单轨迹平均值显示出广泛的分散，在协议与实验观察的subdiffusion在活细胞中的各种粒子。
英文摘要：
This work justifies the paradigmatic importance of viscoelastic subdiffusion in random environments for cellular biological systems. This model displays several remarkable features, which makes it an attractive paradigm to explain the physical nature of biological subdiffusion. In particular, it combines viscoelasticity with distinct non-ergodic features. We extend this model to make it suitable for the subdiffusion of lipids in disordered biological membranes upon including the inertial effects. For lipids, the inertial effects occur in the range of picoseconds, and a power-law decaying viscoelastic memory extends over the range of several nanoseconds. Thus, in the absence of disorder, diffusion would become normal on a time scale beyond this memory range. However, both experimentally and in some molecular-dynamical simulations, the time range of lipid subdiffusion extends far beyond the viscoelastic memory range. We study three 1d models of correlated quenched Gaussian disorder to explain the puzzle: singular short-range (exponentially correlated), smooth short-range (Gaussian-correlated), and smooth long-range (power-law correlated) disorder. For a moderate disorder strength, transient viscoelastic subdiffusion changes into the subdiffusion caused by the randomness of the environment. It is characterized by a time-dependent power-law exponent of subdiffusion, which can show nonmonotonous behavior, in agreement with some recent molecular-dynamical simulations. Moreover, the spatial distribution of test particles in this disorder-dominated regime is shown to be a non-Gaussian, exponential power distribution, which also correlates well with molecular-dynamical findings and experiments. Furthermore, this subdiffusion is nonergodic with single-trajectory averages showing a broad scatter, in agreement with experimental observations for subdiffusion of various particles in living cells.
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