Kiskowski Maria A, Hancock John F, Kenworthy Anne K
Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama 36688, USA.
Biophys J. 2009 Aug 19;97(4):1095-103. doi: 10.1016/j.bpj.2009.05.039.
Ripley's K-, H-, and L-functions are used increasingly to identify clustering of proteins in membrane microdomains. In this approach, aggregation (or clustering) is identified if the average number of proteins within a distance r of another protein is statistically greater than that expected for a random distribution. However, it is not entirely clear how the function may be used to quantitatively determine the size of domains in which clustering occurs. Here, we evaluate the extent to which the domain radius can be determined by different interpretations of Ripley's K-statistic in a theoretical, idealized context. We also evaluate the measures for noisy experimental data and use Monte Carlo simulations to separate the effects of different types of experimental noise. We find that the radius of maximal aggregation approximates the domain radius, while identifying the domain boundary with the minimum of the derivative of H(r) is highly accurate in idealized conditions. The accuracy of both measures is impacted by the noise present in experimental data; for example, here, the presence of a large fraction of particles distributed as monomers and interdomain interactions. These findings help to delineate the limitations and potential of Ripley's K in real-life scenarios.
里普利的K函数、H函数和L函数越来越多地用于识别膜微区中蛋白质的聚集情况。在这种方法中，如果在距离另一个蛋白质r范围内的蛋白质平均数量在统计上大于随机分布所预期的数量，则可识别出聚集（或聚类）。然而，目前尚不完全清楚该函数如何用于定量确定发生聚集的结构域的大小。在此，我们在理论化、理想化的背景下评估了通过对里普利K统计量的不同解释来确定结构域半径的程度。我们还评估了针对有噪声实验数据的测量方法，并使用蒙特卡罗模拟来区分不同类型实验噪声的影响。我们发现最大聚集半径近似于结构域半径，而在理想化条件下，用H(r)导数的最小值来确定结构域边界非常准确。这两种测量方法的准确性都受到实验数据中存在的噪声的影响；例如，在这里，存在大量以单体形式分布的粒子以及结构域间相互作用。这些发现有助于明确在实际情况中里普利K函数的局限性和潜力。
