Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131-1141, USA.
Bull Math Biol. 2012 Jan;74(1):190-211. doi: 10.1007/s11538-011-9671-3. Epub 2011 Jul 13.
Cell biologists have developed methods to label membrane proteins with gold nanoparticles and then extract spatial point patterns of the gold particles from transmission electron microscopy images using image processing software. Previously, the resulting patterns were analyzed using the Hopkins statistic, which distinguishes nonclustered from modestly and highly clustered distributions, but is not designed to quantify the number or sizes of the clusters. Clusters were defined by the partitional clustering approach which required the choice of a distance. Two points from a pattern were put in the same cluster if they were closer than this distance. In this study, we present a new methodology based on hierarchical clustering to quantify clustering. An intrinsic distance is computed, which is the distance that produces the maximum number of clusters in the biological data, eliminating the need to choose a distance. To quantify the extent of clustering, we compare the clustering distance between the experimental data being analyzed with that from simulated random data. Results are then expressed as a dimensionless number, the clustering ratio that facilitates the comparison of clustering between experiments. Replacing the chosen cluster distance by the intrinsic clustering distance emphasizes densely packed clusters that are likely more important to downstream signaling events.We test our new clustering analysis approach against electron microscopy images from an experiment in which mast cells were exposed for 1 or 2 minutes to increasing concentrations of antigen that crosslink IgE bound to its high affinity receptor, FcϵRI, then fixed and the FcϵRI β subunit labeled with 5 nm gold particles. The clustering ratio analysis confirms the increase in clustering with increasing antigen dose predicted from visual analysis and from the Hopkins statistic. Access to a robust and sensitive tool to both observe and quantify clustering is a key step toward understanding the detailed fine scale structure of the membrane, and ultimately to determining the role of spatial organization in the regulation of transmembrane signaling.
细胞生物学家已经开发出了将金纳米颗粒标记在膜蛋白上的方法，然后使用图像处理软件从透射电子显微镜图像中提取金颗粒的空间点模式。以前，通过图像处理软件对所得模式使用霍普金斯统计量进行分析，该统计量可区分非聚集、适度聚集和高度聚集的分布，但不能用于定量簇的数量或大小。簇的定义采用分区聚类方法，该方法需要选择距离。如果两个模式中的点彼此之间的距离小于这个距离，则将它们放入同一簇中。在这项研究中，我们提出了一种基于层次聚类的新方法来定量聚类。计算了一个固有距离，这是在生物数据中产生最大数量簇的距离，从而无需选择距离。为了量化聚类程度，我们将正在分析的实验数据的聚类距离与来自模拟随机数据的聚类距离进行比较。然后，结果表示为无量纲数，即聚类比，这便于比较实验之间的聚类程度。用固有聚类距离代替选择的聚类距离，强调了可能对下游信号事件更为重要的密集聚集的簇。我们使用新的聚类分析方法来对抗电子显微镜图像，这些图像来自于一个实验，其中肥大细胞暴露于 1 或 2 分钟内，浓度逐渐增加的抗原，该抗原交联与高亲和力受体 FcεRI 结合的 IgE，然后固定并使用 5nm 金颗粒标记 FcεRIβ亚基。聚类比分析证实了与视觉分析和霍普金斯统计量预测的随着抗原剂量增加而增加的聚类。获得观察和定量聚类的稳健且敏感的工具是理解膜的详细精细结构并最终确定空间组织在跨膜信号转导调节中的作用的关键步骤。
