Abstract
Telomeres are guanine-rich sequences at the end of chromosomes which shorten during each replication event and trigger cell cycle arrest and/or controlled death (apoptosis) when reaching a threshold length. The enzyme telomerase replenishes the ends of telomeres and thus prolongs the life span of cells, but also causes cellular immortalisation in human cancer. G-quadruplex (G4) stabilising drugs are a potential anticancer treatment which work by changing the molecular structure of telomeres to inhibit the activity of telomerase. We investigate the dynamics of telomere length in different conformational states, namely t-loops, G-quadruplex structures and those being elongated by telomerase. By formulating deterministic differential equation models we study the effects of various levels of both telomerase and concentrations of a G4-stabilising drug on the distribution of telomere lengths, and analyse how these effects evolve over large numbers of cell generations. As well as calculating numerical solutions, we use quasicontinuum methods to approximate the behaviour of the system over time, and predict the shape of the telomere length distribution. We find those telomerase and G4-concentrations where telomere length maintenance is successfully regulated. Excessively high levels of telomerase lead to continuous telomere lengthening, whereas large concentrations of the drug lead to progressive telomere erosion. Furthermore, our models predict a positively skewed distribution of telomere lengths, that is, telomeres accumulate over lengths shorter than the mean telomere length at equilibrium. Our model results for telomere length distributions of telomerase-positive cells in drug-free assays are in good agreement with the limited amount of experimental data available.
Highlights
Most normal cells cycle and divide a limited number of times, a discovery first made by Hayflick (1965), who grew normal human fibroblasts in culture and observed 60– 80 population doublings before apoptosis
The erosion of protective structures located at the ends of chromosomes, known as telomeres, during each replication is responsible for the limited lifespan of a cell, marking the ageing of cells and eventually triggering irreversible cell cycle exit and cell death when telomeres become critically short
We summarise the mechanisms of telomere length regulation in a simple model containing the states U, B, G and C respectively for the number of telomeres in the open (Uncapped/Unfolded) form, those Bound to telomerase (T), those in a G-quadruplex formation and those forming a Complex with the drug RHPS4 (R)
Summary
Most normal cells cycle and divide a limited number of times, a discovery first made by Hayflick (1965), who grew normal human fibroblasts in culture and observed 60– 80 population doublings before apoptosis. The erosion of protective structures located at the ends of chromosomes, known as telomeres, during each replication is responsible for the limited lifespan of a cell, marking the ageing of cells and eventually triggering irreversible cell cycle exit and cell death when telomeres become critically short. Mammalian telomeres are specialised nucleotide sequences that protect the end of chromosomes. The sequence of the repeat unit is TTAGGG in mammalian cells and human telomeres contain around 10–15 kilobasepairs per chromosome end at birth. About 3 basepairs are lost from one DNA strand on each round of cell division due to the end-replication problem. Oxidative stress in the from of reactive oxygen species, which accumulates over the lifespan of a cell, causes accidental lesion in the DNA and is assumed to be the cause of substantial telomere loss (Richter and von Zglinicki 2007; von Zglinicki et al 2005)
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