A mathematical model of telomere length regulation and cellular senescence

Abstract

Telomeres play an essential role in chromosomal function and cell viability by preventing chromosome ends from being interpreted by the DNA damage response machinery as DNA breaks. In normal somatic cells, telomere length shortens with each cell replication. Both in vivo and in vitro telomere length correlates with the onset of senescence or apoptosis. Germ cells, stem cells and the majority of cancer cells express telomerase, an enzyme that extends telomere length and when expressed at sufficient levels can immortalize or extend the life span of a cell line.

It is believed that telomeres switch between two states: capped and uncapped. The telomere state determines its accessibility to telomerase and the onset of senescence. One hypothesis is that the t-loop, a large lariat-like structure, represents the capped state. In this thesis we model telomere state based on the biophysics of t-loop formation, allowing us to develop a single mathematical model that accounts for two processes: telomere length regulation for telomerase positive cells and cellular senescence in normal somatic cells.

To study telomere state we model chromatin as Worm-Like-Chain and include the effects of TRF2, a telomere binding protein implicated in t-loop formation. For telomerase positive cells we develop a deterministic model of telomere length regulation based on average telomere length, and a stochastic model based on a Kinetic-Monte-Carlo algorithm that reflects the inherent randomness of telomere biology. Finally we present a model of replicative senescence built upon the stochastic formulation.

The model predicts the steady state length distribution for telomerase positive cells, describes the time evolution of telomere length, and computes the life span of a cell line based on the levels of TRF2 and telomerase expression.

By fitting the model to a variety of experimental data we show that a model of telomere length regulation and cellular senescence based on telomere state is capable of replicating a wide range of experimental results. Our model supports the hypothesis of the t-loop as the protected telomere state.