Prions are 'infectious proteins' that are able to replicate without the involvement of DNA or RNA. The mammalian prion, PrP, underlies neurodegenerative diseases such as scrapie in sheep, BSE in cattle and Creutzfeldt-Jakob disease in humans.
In brewer's yeast, Saccharomyces cerevisiae, several proteins are known to behave as prions, including Sup35p. Ordinarily, this protein exists as single soluble molecules (monomers). However, it can also exist in an alternative conformation which forms insoluble polymers. This is the prion form. Cells that contain the prion form are denoted [PSI+] and those in which all the Sup35p is in the monomeric form are [psi-].
Sup35p polymers are usually modelled as linear structures that can 'grow' by adding monomers and can 'replicate' by fragmenting. At any time, a [PSI+] yeast cell will contain a population of polymers of different sizes. The number and size of the polymers depends on the rates of growth and fragmentation, as well as the underlying rate of production of new Sup35p molecules and rates of degradation. Yeast cells reproduce by asymmetrical budding and cellular material, including Sup35p polymers, is passed from the mother to the daughter cell before the daughter separates completely from the mother. This enables the [PSI+] trait to be inherited by the daughter cell.
This paper describes a long-running collaboration between bioscientists and statisticians that is aimed at developing a quantitative understanding of the dynamics of the [PSI+] prion in yeast. We outline some of the stochastic models that we have developed and discuss the challenges of simulating dynamic processes within cells and inferring parameter values from indirect data. In particular, we discuss the extent to which stochastic approximations, SDEs in particular, can provide a useful bridge between deterministic (ordinary) differential equation models and direct simulation of all relevant molecular events within the cell.
Keywords: Stochastic approximation; Stochastic differential equation
Biography: Martin Ridout is Professor of Applied Statistics at the University of Kent. He is interested in stochastic modelling and statistics in diverse areas of application, particularly in biosciences and ecology. He is currently Joint Editor of Applied Statistics.