A mathematical finance approach to the stochastic and intermittent viscosity fluctuations in living cells.,Soft Matter

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A mathematical finance approach to the stochastic and intermittent viscosity fluctuations in living cells.
Soft Matter ( IF 2.9 ) Pub Date : 2020-05-18 , DOI: 10.1039/c9sm02534k
Claude L Bostoen ₁ , Jean-François Berret

Affiliation

Here we report on the viscosity of eukaryotic living cells, as a function of time, and on the application of stochastic models to analyze its temporal fluctuations. The viscoelastic properties of NIH/3T3 fibroblast cells are investigated using an active microrheological technique, where the magnetic wires, embedded into cells, are being actuated remotely. The data reveal anomalous transient responses characterized by intermittent phases of slow and fast rotation, revealing significant fluctuations. The time dependent viscosity is analyzed from a time series perspective by computing the autocorrelation functions and the variograms, two functions used to describe stochastic processes in mathematical finance. The resulting analysis gives evidence of a sub-diffusive mean-reverting process characterized by an autoregressive coefficient lower than 1. It also shows the existence of specific cellular times in the ranges 1–10 s and 100–200 s, not previously disclosed. The shorter time is found to be related to the internal relaxation time of the cytoplasm. To our knowledge, this is the first time that similarities are established between the properties of time series describing the intracellular metabolism and the statistical results from a mathematical finance approach. The current approach could be exploited to reveal hidden features from biological complex systems or to determine new biomarkers of cellular metabolism.

中文翻译：

一种数学财务方法，用于处理活细胞中的随机和间歇性粘度波动。

在这里，我们报告了真核生物细胞的粘度，时间的函数，以及随机模型在分析其时间波动方面的应用。使用主动微流变技术研究NIH / 3T3成纤维细胞的粘弹性质，其中嵌入细胞中的电磁线被远程驱动。数据揭示了异常的瞬态响应，其特征是缓慢旋转和快速旋转的间歇阶段，显示出明显的波动。通过计算自相关函数和变异函数（这两个函数用于描述数学金融中的随机过程），从时间序列角度分析了随时间变化的粘度。结果分析提供了亚扩散均值回复过程的证据，该过程的特征在于自回归系数小于1。它还显示了以前未披露的1-10 s和100-200 s范围内特定细胞时间的存在。发现较短的时间与细胞质的内部弛豫时间有关。据我们所知，这是首次在描述细胞内代谢的时间序列的属性与数学财务方法的统计结果之间建立相似性。可以利用当前方法来揭示生物复杂系统中的隐藏特征或确定细胞代谢的新生物标记。这是首次在描述细胞内代谢的时间序列属性与数学财务方法的统计结果之间建立相似性。可以利用当前方法来揭示生物复杂系统中的隐藏特征或确定细胞代谢的新生物标记。这是首次在描述细胞内代谢的时间序列属性与数学财务方法的统计结果之间建立相似性。可以利用当前方法来揭示生物复杂系统中的隐藏特征或确定细胞代谢的新生物标记。

更新日期：2020-07-01

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