Mathematical modeling of vascular endothelial layer maintenance: the role of endothelial cell division, progenitor cell homing, and telomere shortening

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Abstract
Maintenance of the endothelial cell (EC) layer of the vessel wall is essential for proper functioning of the vessel and prevention of vascular disorders. Replacement of damaged ECs could occur through division of surrounding ECs. Furthermore, EC progenitor cells (EPCs), derived from the bone marrow and circulating in the bloodstream, can differentiate into ECs. Therefore, these cells might also play a role in maintenance of the endothelial layer in the vascular system. The proliferative potential of both cell types is limited by shortening of telomeric DNA. Accelerated telomere shortening might lead to senescent vascular wall cells and eventually to the inability of the endothelium to maintain a continuous monolayer. The aim of this study was to describe the dynamics of EC damage and repair and telomere shortening by a mathematical model. In the model, ECs were integrated in a two-dimensional structure resembling the endothelium in a large artery. Telomere shortening was described as a stochastic process with oxidative damage as the main cause of attrition. Simulating the model illustrated that increased cellular turnover or elevated levels of oxidative stress could lead to critical telomere shortening and senescence at an age of 65 yr. The model predicted that under those conditions the EC layer could display defects, which could initiate severe vascular wall damage in reality. Furthermore, simulations showed that 5% progenitor cell homing/yr can significantly delay the EC layer defects. This stresses the potential importance of EPC number and function to the maintenance of vascular wall integrity during the human life span.