Theoretical Studies of an Autocatalytic Prion Model

The Gillespie Algorithm is used to simulate a prion model so that the kinetics of the prions may be observed. The model is purely autocatalytic, that is, there is no fusion or fission of the infectious units. There is only conversion of PrP C into prions through a mechanism comprised of attaching PrP C to a PrP Sc p-mer, domain swapping, and splitting. It is well known that any model of an infectious disease must show exponential growth, which we show is the case with the presented model. We indeed find exponential growth in this model. Some conclusions based on a thorough sensitivity analysis of the parameters used in the model are also given. A brief introduction to proteins and their structure, prions, and the Gillespie Algorithm are provided as well.