The prion hypothesis, once a heretical violation of the central dogma of molecular biology, has become an accepted mechanism used to explain a host of progressive neurodegenerative diseases in mammals and heritable phenotypes in yeast. From the beginning, mathematical models have been an essential tool in studying prion and other protein misfolding/aggregation processes. In this work, we review some of the major mathematical studies that have contributed to our understanding of prion disease and discuss trends in current and future studies.
Part of the book: Prion
Prion diseases are a multi-scale biological phenomenon that requires understanding intracellular processes as well as how cells interact with each other and their environment. In mammals, prion diseases are progressive, untreatable, and fatal. Yeast prion phenotypes are harmless and reversible, which suggests a deep understanding of the reversal of prion phenotypes in yeast may be informative to mammalian diseases. In yeast, the loss of some prion phenotypes appears to be stochastic and spatially dependent, suggesting a cell-based model of yeast prion dynamics would be a powerful tool for comparisons with experimental results and hypothesis generation. In this work, we consider the components necessary to develop such a model that depicts both the biochemical-, intracellular-, and colony-level scales in yeast prion phenotypes. We first review the literature of mathematical models of the intracellular processes of prion disease. We then review common approaches to cell-based modeling of multicellular systems and how they have led to biological insights in other systems. This chapter ends with a discussion of future studies aimed at motivating how these two types of models can be coupled to produce multi-scale models of prion phenotypes.
Part of the book: Apolipoproteins, Triglycerides and Cholesterol