We use a lattice model to study first-passage time distributions of target finding events through complex environments with elongated fibers distributed with different anisotropies and volume occupation fractions. For isotropic systems and for low densities of aligned fibers, the three-dimensional search is a Poisson process with the first-passage time exponentially distributed with the most probable finding time at zero. At high enough densities of aligned fibers, elongated channels emerge, reducing the dynamics dimensionality to one dimension. We show how the shape and size of the channels modify the behavior of the first-passage time distribution and its short, intermediate, and long time scales. We develop an exactly solvable model for synthetic rectangular channels, which captures the effects of the tortuous local structure of the elongated channels that naturally emerge in our system. For arbitrary values of the nematic order parameter of fiber orientations, we develop a mapping to the simpler situation of fully aligned fibers at some other effective volume occupation fraction. Our results shed light on the molecular transport of biomolecules between biological cells in complex fibrous environments.

中文翻译：

---

在纤维生物环境中寻找目标

我们使用格子模型来研究目标发现事件在复杂环境中的首次通过时间分布，细长纤维分布有不同的各向异性和体积占有率。对于各向同性系统和排列纤维的低密度，三维搜索是一个泊松过程，第一通过时间呈指数分布，最可能的发现时间为零。在排列纤维的密度足够高时，会出现拉长的通道，将动力学维度降低到一维。我们展示了通道的形状和大小如何修改首通道时间分布的行为及其短、中和长时间尺度。我们为合成矩形通道开发了一个完全可解的模型，它捕捉了我们系统中自然出现的细长通道的曲折局部结构的影响。对于纤维取向的向列顺序参数的任意值，我们开发了一种映射到完全对齐的纤维在其他一些有效体积占有率下的更简单情况。我们的结果阐明了复杂纤维环境中生物细胞之间生物分子的分子运输。