Kepten Eldad, Bronshtein Irena, Garini Yuval
Physics Department & Institute of Nanotechnology, Bar Ilan University, Ramat Gan, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 May;87(5):052713. doi: 10.1103/PhysRevE.87.052713. Epub 2013 May 20.
The mean square displacement is a central tool in the analysis of single-particle tracking experiments, shedding light on various biophysical phenomena. Frequently, parameters are extracted by performing time averages on single-particle trajectories followed by ensemble averaging. This procedure, however, suffers from two systematic errors when applied to particles that perform anomalous diffusion. The first is significant at short-time lags and is induced by measurement errors. The second arises from the natural heterogeneity in biophysical systems. We show how to estimate and correct these two errors and improve the estimation of the anomalous parameters for the whole particle distribution. As a consequence, we manage to characterize ensembles of heterogeneous particles even for rather short and noisy measurements where regular time-averaged mean square displacement analysis fails. We apply this method to both simulations and in vivo measurements of telomere diffusion in 3T3 mouse embryonic fibroblast cells. The motion of telomeres is found to be subdiffusive with an average exponent constant in time. Individual telomere exponents are normally distributed around the average exponent. The proposed methodology has the potential to improve experimental accuracy while maintaining lower experimental costs and complexity.
均方位移是单粒子追踪实验分析中的核心工具，有助于揭示各种生物物理现象。通常，通过对单粒子轨迹进行时间平均，然后进行系综平均来提取参数。然而，当应用于进行反常扩散的粒子时，该过程存在两个系统误差。第一个误差在短时间滞后时很显著，是由测量误差引起的。第二个误差源于生物物理系统中的自然异质性。我们展示了如何估计和校正这两个误差，并改进对整个粒子分布的反常参数的估计。因此，即使在常规时间平均均方位移分析失败的相当短且有噪声的测量中，我们也能够表征异质粒子的系综。我们将此方法应用于3T3小鼠胚胎成纤维细胞中端粒扩散的模拟和体内测量。发现端粒的运动是亚扩散的，平均指数随时间恒定。单个端粒指数围绕平均指数呈正态分布。所提出的方法有可能提高实验精度，同时保持较低的实验成本和复杂性。
