具有分数布朗运动的超统计福克-普朗克方程及其在细胞质内被动示踪剂中的应用

The Fokker-Planck equation of the superstatistical fractional Brownian motion with application to passive tracers inside cytoplasm.

作者信息

Runfola C, Vitali S, Pagnini G

机构信息

Department of Physics and Astronomy, University of Bologna, Viale Berti Pichat 6/2, I-40127 Bologna, Italy.

BCAM - Basque Center for Applied Mathematics, Alameda de Mazarredo 14, E-48009 Bilbao, Basque Country, Spain.

出版信息

R Soc Open Sci. 2022 Nov 2;9(11):221141. doi: 10.1098/rsos.221141. eCollection 2022 Nov.

DOI:10.1098/rsos.221141

PMID:36340511

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9627453/

Abstract

By collecting from literature data experimental evidence of anomalous diffusion of passive tracers inside cytoplasm, and in particular of subdiffusion of mRNA molecules inside live cells, we obtain the probability density function of molecules' displacement and we derive the corresponding Fokker-Planck equation. Molecules' distribution emerges to be related to the Krätzel function and its Fokker-Planck equation to be a fractional diffusion equation in the Erdélyi-Kober sense. The irreducibility of the derived Fokker-Planck equation to those of other literature models is also discussed.

摘要

通过从文献数据中收集被动示踪剂在细胞质内异常扩散的实验证据，特别是mRNA分子在活细胞内的亚扩散证据，我们得到了分子位移的概率密度函数，并推导了相应的福克 - 普朗克方程。分子分布呈现出与克拉策尔函数相关，其福克 - 普朗克方程在厄德利 - 科伯意义下是一个分数扩散方程。还讨论了所推导的福克 - 普朗克方程与其他文献模型方程的不可约性。