Abstract
Prions are proteins capable of adopting misfolded conformations and transmitting these conformations to other normally folded proteins. Prions are most commonly known for causing fatal neurodegenerative diseases in mammals but are also associated with several harmless phenotypes in yeast. A distinct feature of prion propagation is the existence of different phenotypical variants, called strains. It is widely accepted that these strains correspond to different conformational states of the protein, but the mechanisms driving their interactions remain poorly understood. This study uses mathematical modeling to provide insight into this problem. We show that the classical model of prion dynamics allows at most one conformational strain to stably propagate. In order to conform to biological observations of strain coexistence and co-stability, we develop an extension of the classical model by introducing a novel prion species consistent with biological studies. Qualitative analysis of this model reveals a new variety of behavior. Indeed, it allows for stable coexistence of different strains in a wide parameter range, and it also introduces intricate initial condition dependency. These new behaviors are consistent with experimental observations of prions in both mammals and yeast. As such, our model provides a valuable tool for investigating the underlying mechanisms of prion propagation and the link between prion strains and strain specific phenotypes. The consideration of a novel prion species brings a change in perspective on prion biology and we use our model to generate hypotheses about prion infectivity.
Highlights
Prion diseases are a class of neurodegenerative disorders in mammals associated with a change in the folded shape of the protein PrP
We note that the phenomenon of strains applies to prion diseases, and to other neurodegenerative disorders caused by prion-like mechanisms such as Alzheimer’s or Parkinson’s disease (Watts et al 2014; Cohen et al 2015)
Coexistence of strains was observed in yeast prions (Strbuncelj 2009), and our model shows that including an additional step in the polymerization pathway would give a reasonable explanation for this behavior
Summary
Prion diseases are a class of neurodegenerative disorders in mammals associated with a change in the folded shape (conformation) of the protein PrP. Previous mathematical studies of spontaneous prion formation have led to widespread acceptance of the nucleated polymerization model (Lansbury and Caughey 1995), which has been formulated under the assumption of either discrete or continuous aggregate sizes (Masel et al 1999; Greer et al 2006; Doumic et al 2009; Davis and Sindi 2015) This model reproduces qualitative and quantitative aspects of prion infection (Prüss et al 2006; Masel et al 1999), all the while being analytically tractable (Engler et al 2006). We note that our model exhibits qualitatively distinct behavior from the classical nucleated polymerization model Most importantly, it enables the coexistence of different strains (multiple strains present stably together), but it allows for simultaneous co-stability of different equilibria (dependency on initial conditions). 2 Background: the nucleated polymerization model can only predict single strain dominance
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