Integrated Graduate Program in Physical and Engineering Biology, Yale University, New Haven, Connecticut 06520, USA.
Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA.
Phys Rev E. 2021 Mar;103(3-1):032405. doi: 10.1103/PhysRevE.103.032405.
Several recent experiments, including our own experiments in the fission yeast, Schizosaccharomyces pombe, have characterized the motions of gene loci within living nuclei by measuring the locus position over time, then proceeding to obtain the statistical properties of this motion. To address the question of whether a population of such single-particle tracks, obtained from many different cells, corresponds to a single mode of diffusion, we derive theoretical equations describing the probability distribution of the displacement covariance, assuming the displacement itself is a zero-mean multivariate Gaussian random variable. We also determine the corresponding theoretical means, variances, and third central moments. Bolstering the theory is good agreement between its predictions and the results obtained for various simulated and measured data sets, including simulated particle trajectories undergoing simple and anomalous diffusion, and the measured trajectories of an optically trapped bead in water, and in a viscoelastic polymer solution. We also show that, for sufficiently long tracks, each covariance distribution in all of these examples is well-described by a skew-normal distribution with mean, variance, and skewness given by the theory. However, for the experimentally measured motion of a gene locus in S. pombe, we find that the first two covariance distributions are wider than predicted, although the third and subsequent covariance distributions are well-described by theory. This observation suggests that the origin of the theory-experiment discrepancy in this case is associated with localization noise, which influences only the first two covariances. Thus, we hypothesized that the discrepancy is caused by locus-to-locus heterogeneity in the localization noise, of independent measurements of the same tagged site. Indeed, simulations implementing heterogeneous localization noise revealed that the excess covariance widths can be largely recreated on the basis of heterogeneous noise. Thus, we conclude that the motion of gene loci in fission yeast is consistent with a single mode of diffusion.
最近的几项实验，包括我们在裂殖酵母（Schizosaccharomyces pombe）中的实验，已经通过测量基因座在一段时间内的位置，来描述活细胞核内基因座的运动，并进一步获取该运动的统计特性。为了研究从许多不同细胞获得的这种单粒子轨迹的群体是否对应于单一的扩散模式，我们推导出了描述位移协方差概率分布的理论方程，假设位移本身是一个零均值多元高斯随机变量。我们还确定了相应的理论平均值、方差和第三中心矩。理论预测与各种模拟和测量数据集的结果之间的良好一致性为理论提供了支持，包括经历简单和异常扩散的模拟粒子轨迹，以及在水中和粘弹性聚合物溶液中光学捕获珠的测量轨迹。我们还表明，对于足够长的轨迹，在所有这些例子中，每个协方差分布都可以很好地用具有理论给出的均值、方差和偏度的斜正态分布来描述。然而，对于在 S. pombe 中基因座的实验测量运动，我们发现前两个协方差分布比预测的更宽，尽管第三个和后续的协方差分布与理论很好地相符。这一观察结果表明，在这种情况下理论与实验之间差异的原因与定位噪声有关，定位噪声仅影响前两个协方差。因此，我们假设差异是由同一标记位点的独立测量的定位噪声的基因座间异质性引起的。事实上，实现异质定位噪声的模拟表明，可以根据异质噪声在很大程度上再现多余的协方差宽度。因此，我们得出结论，裂殖酵母中基因座的运动与单一扩散模式一致。
