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.

中文翻译：

---

包含惯性效应的无序系统中的有限范围粘弹性再扩散

这项工作证明了粘弹性子扩散在细胞生物系统随机环境中的典型重要性。该模型显示了几个显着的特征，这使其成为解释生物亚扩散的物理性质的一个有吸引力的范例。特别是，它将粘弹性与独特的非遍历特征相结合。我们扩展了这个模型，使其适用于脂质在无序生物膜中的再扩散，包括惯性效应。对于脂质，惯性效应发生在皮秒范围内，并且幂律衰减的粘弹性记忆扩展到几纳秒的范围内。因此，在没有紊乱的情况下，扩散将在超出这个记忆范围的时间尺度上变得正常。然而，无论是在实验上还是在一些分子动力学模拟中，脂质亚扩散的时间范围远远超出了粘弹性记忆范围。我们研究了三个相关淬灭高斯障碍的一维模型来解释这个难题：奇异短程（指数相关）、平滑短程（高斯相关）和平滑长程（幂律相关）障碍。对于中等无序强度，瞬态粘弹性子扩散变为由环境随机性引起的子扩散。它的特点是亚扩散的时间依赖幂律指数，可以表现出非单调行为，与最近的一些分子动力学模拟一致。此外，在这种以无序为主的情况下，测试粒子的空间分布显示为非高斯指数幂分布，这也与分子动力学发现和实验密切相关。此外，这种亚扩散是非遍历的，单轨迹平均值显示出广泛的散射，这与活细胞中各种粒子的亚扩散的实验观察一致。