内皮细胞层维持与衰老的连续介质数学模型。

A continuum mathematical model of endothelial layer maintenance and senescence.

作者信息

Wang Ying, Aguda Baltazar D, Friedman Avner

机构信息

Mathematical Biosciences Institute, and Department of Mathematics, The Ohio State University Columbus, Ohio 43210, USA.

出版信息

Theor Biol Med Model. 2007 Aug 10;4:30. doi: 10.1186/1742-4682-4-30.

DOI:10.1186/1742-4682-4-30

PMID:17692115

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC1988791/

Abstract

BACKGROUND

The monolayer of endothelial cells (ECs) lining the inner wall of blood vessels deteriorates as a person ages due to a complex interplay of a variety of causes including cell death arising from shear stress of blood flow and cellular oxidative stress, cellular senescence, and decreased rate of replacement of dead ECs by progenitor stem cells.

RESULTS

A continuum mathematical model is developed to describe the dynamics of large EC populations of the endothelium using a system of differential equations for the number densities of cells of different generations starting from endothelial progenitors to senescent cells, as well as the densities of dead cells and the holes created upon clearing dead cells. Aging of cells is manifested in three ways, namely, losing the ability to divide when the Hayflick limit of 50 generations is reached, decreasing replication rate parameters and increasing death rate parameters as cells divide; due to the dependence of these rate parameters on cell generation, the model predicts a narrow distribution of cell densities peaking at a particular cell generation. As the chronological age of a person advances, the peak of the distribution - corresponding to the age of the endothelium - moves towards senescence correspondingly. However, computer simulations also demonstrate that sustained and enhanced stem cell homing can halt the aging process of the endothelium by maintaining a stationary cell density distribution that peaks well before the Hayflick limit. The healing rates of damaged endothelia for young, middle-aged, and old persons are compared and are found to be particularly sensitive to the stem cell homing parameter.

CONCLUSION

The proposed model describes the aging of the endothelium as being driven by cellular senescence, with a rate that does not necessarily correspond to the chronological aging of a person. It is shown that the age of the endothelium depends sensitively on the homing rates of EC progenitor cells.

摘要

背景

随着年龄增长，血管内壁的单层内皮细胞（ECs）会因多种因素的复杂相互作用而退化，这些因素包括血流剪切应力导致的细胞死亡、细胞氧化应激、细胞衰老以及祖干细胞对死亡ECs的替代率降低。

结果

建立了一个连续介质数学模型，使用从内皮祖细胞到衰老细胞的不同代细胞数量密度的微分方程组，以及死细胞密度和清除死细胞后产生的空洞密度，来描述内皮中大量ECs群体的动态变化。细胞衰老以三种方式表现出来，即当达到50代的海弗利克极限时失去分裂能力、随着细胞分裂复制速率参数降低以及死亡率参数增加；由于这些速率参数依赖于细胞代数，该模型预测细胞密度在特定细胞代数处达到峰值且分布狭窄。随着人的实际年龄增长，对应内皮年龄的分布峰值相应地向衰老方向移动。然而，计算机模拟还表明，持续增强的干细胞归巢可以通过维持在海弗利克极限之前达到峰值的稳定细胞密度分布来阻止内皮的衰老过程。比较了年轻人、中年人和老年人受损内皮的愈合率，发现其对干细胞归巢参数特别敏感。