DNA-clustering in yeast (360G-Wellcome-211523_Z_18_Z)

We propose to describe mathematically the processes by which telomeres form clusters in the nuclei of yeast cells. It is thought that this is due to the presence of proteins which bind to the telomeres. We wish to investigate the processes which determine cluster size through: 1. forming a mathematical model of the attachment processes through which proteins bind to telomeres. This may involve a site exclusion process, whereby the protein binding rate slows due to the declining number of vacant protein binding sites as the telomere `fills up'; 2. constructing a mathematical model of the aggregation of telomere-protein complexes into clusters, and determine which rate parameters are key to controlling cluster size; 3. investigating the rate of equilibration of these processes. The models we construct will have the form of systems of coupled ordinary differential equations. Through a judicious choice of rate constants, explicit equilibrium solutions will be obtainable, allowing available data to be fitted. Numerical simulations of the process will also be performed, to verify that the equilibrium solutions are accessible within biologically realistic time periods.