Modelling prion dynamics in yeast

The word prion was coined by Nobel laureate Stanley Prusiner to describe the infectious agent in a group of fatal neurodegenerative diseases that includes scrapie in sheep, bovine spongiform encephalopathy (BSE) in cattle and variant Creutzfeldt-Jakob disease (vCJD) in humans. The infectious agent is a misfolded form of the protein, PrP, denoted PrPSc, which forms polymers that grow by recruiting molecules of the normal cellular form of the protein, PrPC. Once attached to the PrPSc complex, the PrPC molecule refolds into the prion conformation. A key property of prions is their ability to self-replicate, through a process known as nucleated polymerization. Nucleation refers to the fact that the minimal stable unit of PrPSc is a ‘nucleus’ or ‘seed’ consisting of several molecules. Very occasionally, such seeds can arise spontaneously; alternatively they are inherited or result from infection through eating meat from an infected animal. The seeds grow by polymerization and the polymers can subsequently fragment into two parts. Each fragment then acts as a separate seed, provided it is larger than the minimum stable size. This combination of growth and fragmentation provides the mechanism of replication. Yeast prions are a group of proteins in the budding yeast Saccharomyces cerevisiae that, though functionally unrelated to PrP, also self-replicate through nucleated polymerization and can be inherited through cell division. However, yeast prions are not associated with disease in S. cerevisiae. Tuite and Serio (2010) provide a recent overview of the biology. One widely-studied yeast prion is [PSI+], a prion form of the essential yeast-cell protein Sup35p. Sup35p is involved in ensuring that the translation of RNA transcripts into protein molecules terminates correctly. Normally it occurs as a soluble monomer (single molecule), but there is also a polymeric prion form that is insoluble. Yeast cells in which all the Sup35p is in the normal form are termed [psi−] whereas those that contain some Sup35p in the prion form are termed [PSI+]. A colour assay is available to distinguish the two types of cell. This paper gives an overview of a long-running collaboration between bioscientists and statisticians at the University of Kent, studying [PSI+]. We adopt a chronological approach, showing how initial phenomenological models have been refined progressively both to incorporate greater biological realism and to probe deeper into the underlying mechanisms. We begin by describing [PSI+] curing by the chemical guanidine hydrochloride (GdnHCl), which has been an important experimental technique for understanding [PSI+], and outline the stochastic models that we have developed to describe curing data. We then look at mathematical models of nucleated polymerization and conclude by outlining current and future areas of work.