Department of Biomedical Engineering; Lorry I. Lokey Interdisciplinary Center for Life Sciences and Engineering.
Department of Biomedical Engineering; Lorry I. Lokey Interdisciplinary Center for Life Sciences and Engineering; Department of Electrical Engineering, Technion - Israel Institute of Technology, Haifa, Israel.
Biophys J. 2019 Jul 23;117(2):185-192. doi: 10.1016/j.bpj.2019.06.015. Epub 2019 Jun 22.
Diffusion plays a crucial role in many biological processes including signaling, cellular organization, transport mechanisms, and more. Direct observation of molecular movement by single-particle-tracking experiments has contributed to a growing body of evidence that many cellular systems do not exhibit classical Brownian motion but rather anomalous diffusion. Despite this evidence, characterization of the physical process underlying anomalous diffusion remains a challenging problem for several reasons. First, different physical processes can exist simultaneously in a system. Second, commonly used tools for distinguishing between these processes are based on asymptotic behavior, which is experimentally inaccessible in most cases. Finally, an accurate analysis of the diffusion model requires the calculation of many observables because different transport modes can result in the same diffusion power-law α, which is typically obtained from the mean-square displacements (MSDs). The outstanding challenge in the field is to develop a method to extract an accurate assessment of the diffusion process using many short trajectories with a simple scheme that is applicable at the nonexpert level. Here, we use deep learning to infer the underlying process resulting in anomalous diffusion. We implement a neural network to classify single-particle trajectories by diffusion type: Brownian motion, fractional Brownian motion and continuous time random walk. Further, we demonstrate the applicability of our network architecture for estimating the Hurst exponent for fractional Brownian motion and the diffusion coefficient for Brownian motion on both simulated and experimental data. These networks achieve greater accuracy than time-averaged MSD analysis on simulated trajectories while only requiring as few as 25 steps. When tested on experimental data, both net and ensemble MSD analysis converge to similar values; however, the net needs only half the number of trajectories required for ensemble MSD to achieve the same confidence interval. Finally, we extract diffusion parameters from multiple extremely short trajectories (10 steps) using our approach.
扩散在许多生物学过程中起着至关重要的作用，包括信号转导、细胞组织、运输机制等。通过单粒子跟踪实验对分子运动的直接观察为越来越多的证据做出了贡献，即许多细胞系统不表现出经典的布朗运动，而是异常扩散。尽管有这些证据，但由于以下几个原因，描述异常扩散背后的物理过程仍然是一个具有挑战性的问题。首先，不同的物理过程可以同时存在于一个系统中。其次，用于区分这些过程的常用工具基于渐近行为，而在大多数情况下，实验无法获得这种行为。最后，扩散模型的准确分析需要计算许多可观察量，因为不同的输运模式可能导致相同的扩散幂律 α，而α通常是从均方位移（MSD）中获得的。该领域的一个突出挑战是开发一种使用许多短轨迹的简单方案，以从经验数据中提取对扩散过程的准确评估的方法，这种方案适用于非专家级别的用户。在这里，我们使用深度学习来推断导致异常扩散的潜在过程。我们实现了一个神经网络，通过扩散类型对单粒子轨迹进行分类：布朗运动、分数布朗运动和连续时间随机行走。此外，我们证明了我们的网络架构可用于估计分数布朗运动的赫斯特指数和布朗运动的扩散系数，无论是在模拟数据还是实验数据上都有很好的适用性。与模拟轨迹上的平均 MSD 分析相比，这些网络在模拟轨迹上具有更高的准确性，而所需的轨迹数量仅为 25 步。在实验数据上进行测试时，网络和整体 MSD 分析都收敛到相似的值；然而，网络仅需要整体 MSD 分析所需轨迹数量的一半，即可达到相同的置信区间。最后，我们使用我们的方法从多个非常短的轨迹（10 步）中提取扩散参数。
