Department of Mathematics, Texas A&M University-Commerce, Commerce, Texas.
The Hormel Institute, University of Minnesota, Austin, Minnesota.
Traffic. 2019 Nov;20(11):867-880. doi: 10.1111/tra.12690. Epub 2019 Oct 1.
Diffusion of proteins and lipids in lipid membranes plays a pivotal role in almost all aspects of cellular biology, including motility, exo-/endocytosis and signal transduction. For this reason, gaining a detailed understanding of membrane structure and function has long been a major area of cell biology research. To better elucidate this structure-function relationship, various tools have been developed for diffusion measurements, including Fluorescence Recovery After Photobleaching (FRAP). Because of the complexity of cellular microenvironments, biological diffusion is often correlated over time and described by a time-dependent diffusion coefficient, D(t), although the underlying mechanisms are not fully understood. Since D(t) provides important information regarding cellular structures, such as the existence of subresolution barriers to diffusion, many efforts have been made to quantify D(t) by FRAP assuming a single power law, D(t) = Γt where Γ and α are transport coefficient and anomalous exponent. However, straightforward approaches to quantify a general form of D(t) are lacking. In this study, we develop a novel mathematical and computational framework to compute the mean square displacement of diffusing molecules and diffusion coefficient D(t) from each individual time point of confocal FRAP data without the single power law assumption. Additionally, we developed an auxiliary equation for D(t) which can readily distinguish normal diffusion or single power law anomalous diffusion from other types of anomalous diffusion directly from FRAP data. Importantly, by applying this approach to FRAP data from a variety of membrane markers, we demonstrate the single power law anomalous diffusion assumption is not sufficient to describe various types of D(t) of membrane proteins. Lastly, we discuss how our new approaches can be applied to other fluorescence microscopy tools such as Fluorescence Correlation Spectroscopy (FCS) and Single Particle Tracking (SPT).
蛋白质和脂质在脂膜中的扩散在细胞生物学的几乎所有方面都起着关键作用，包括运动、胞吞/胞吐和信号转导。出于这个原因，长期以来，深入了解膜结构和功能一直是细胞生物学研究的主要领域。为了更好地阐明这种结构-功能关系，已经开发了各种用于扩散测量的工具，包括荧光漂白后恢复（FRAP）。由于细胞微环境的复杂性，生物扩散通常随时间相关，并由依赖时间的扩散系数 D(t) 来描述，尽管其潜在机制尚未完全理解。由于 D(t) 提供了有关细胞结构的重要信息，例如存在亚分辨率扩散障碍，因此已经做出了许多努力来通过 FRAP 假设单个幂律 D(t) = Γt 来量化 D(t)，其中 Γ 和 α 是传输系数和反常指数。然而，缺乏直接量化一般形式的 D(t) 的简单方法。在这项研究中，我们开发了一种新的数学和计算框架，无需单个幂律假设，即可从共焦 FRAP 数据的每个单独时间点计算扩散分子的均方位移和扩散系数 D(t)。此外，我们还为 D(t) 开发了一个辅助方程，该方程可以直接从 FRAP 数据中区分正常扩散或单个幂律反常扩散与其他类型的反常扩散。重要的是，通过将这种方法应用于来自各种膜标记物的 FRAP 数据，我们证明了单个幂律反常扩散假设不足以描述各种类型的膜蛋白的 D(t)。最后，我们讨论了如何将我们的新方法应用于其他荧光显微镜工具，如荧光相关光谱（FCS）和单粒子跟踪（SPT）。
