Mathematical modelling of telomere dynamics - Qi, Qi (2011)
Telomeres are repetitive elements of DNA which are located at the ends of chromosomes. During cell division, telomeres on daughter chromomeres shorten until the telomere length falls below a critical level. This shortening restricts the number of cell divisions. In this thesis, we use mathematical modelling to study dynamics of telomere length in a cell in order to understand normal ageing (telomere shortening),Werner’s syndrome (a disease of accelerated ageing) and the immortality of cells caused by telomerase (telomere constant length maintenance). In the mathematical models we compared four possible mechanisms for telomere shortening. The simplest model assumes that a fixed amount of telomere is lost on each replication; the second supposes that telomere loss depends on telomere length; for the third case the amount of telomeres loss per division is fixed but the probability of dividing depends on telomere length; the fourth cases has both telomere loss and the probability of division dependent on telomere length. We start by developing Monte Carlo simulations of normal ageing using these four cases. Then we generalize the Monte Carlo simulations to consider Werner’s syndrome, where the extra telomeres are lost during replication accelerate the ageing process. In order to investigate how the distribution of telomere length varies with time, we derive, from the discrete model, continuum models for the four different cases. Results from the Monte Carlo simulations and the deterministic models are shown to be in good agreement. In addition to telomere loss, we also consider increases in telomere length caused by the enzyme telomerase, by appropriately extending the earlier Monte Carlo simulations and continuum models. Results from the Monte Carlo simulations and the deterministic models are shown to be in good agreement. We also show that the concentration of telomerase in cells can control their proliferative potential.