Mathematical modeling confirms the length-dependency of telomere shortening

Telomeres, the ends of chromosomes, shorten with each cell division in human somatic cells, because of the end-replication problem, C-strand processing and oxidative damage. On the other hand, the reverse transcriptase telomerase can add back telomeric repeats at the telomere ends. It has been suggested that once telomeres have reached a critical length, cells cease proliferation, also known as senescence. Evidence is accumulating that telomere shortening and subsequent senescence might play a crucial role in life-threatening diseases. So far, mathematical models described telomere shortening as an autonomous process, where the loss per cell division does not depend on the telomere length itself. In this study, published measurements of telomere distributions in human fibroblasts and human endothelial cells were used to show that telomeres shorten in a length-dependent fashion. Thereafter, a mathematical model of telomere attrition was composed, in which a shortening factor and an autonomous loss were incorporated. It was assumed that the percentage of senescence was related to the percentage of telomeres below a critical length. The model was compared with published data of telomere length and senescence of human endothelial cells using the maximum likelihood method. This enabled the estimation of physiologically important parameters and confirmed the length-dependency of telomere shortening.