The Evolution of Prion Virulence

Prions are a class of aggregative proteins that have been linked to several neurodegenerative disorders. Such illnesses are typically caused by misfolding of the PrP protein PrPSc, which coerces the benign conformation PrPc into an abnormal state. Though the biochemistry of prion replication has been studied thoroughly, the spontaneous emergence of novel strains, with different virulence, remains poorly understood. Novel strains are characterized by an altered PrPSc conformation, with distinct biochemical properties which affect their replication rate. This spontaneous emergence of variation in a population of replicating proteins is sufficient to allow a form of natural selection, in which novel confirmations function as "mutations" that produce distinct biochemical properties analogous to evolutionary "traits". Here we study the role played by this form of natural selection in shaping the characteristics of prion diseases. We develop a stochastic version of the nucleated polymerization model (SNPM) which allows us to study both inter- and intra-cellular competition between strains. We focus on the role of mutations that alter fragmentation rate, the key trait determining strain-dependent replication. Mutations to the fragmentation rate mimic prions undergoing a conformational change, that results in a new strain. We show that the evolution of fragmentation rate is subject to a transmission-virulence trade-off, in which strains that are more successful at co-opting PrPc within a cell (i.e. those which are more "virulent") are often less successful at invading uninfected cells (i.e. are less transmissible) and vice versa. We then extend this analysis to understand how certain biochemical constraints may introduce other trade-offs that may affect the direction of evolution. Of particular interest is the costs associated with optimizing either fragmentation or polymerization, which can lead to deterioration of the other process. We find that in the intra-cellular context, optimization of polymerization is favored, while fragmentation is more beneficial inter-cellularly. Lastly, we develop an ODE and spatial model that consider two strains which are subject to the transmission-virulence trade-off. We find that not only is specialization in either transmission or virulence necessary for strain coexistence to emerge, but that such dynamics can occur under limited resources. We also find that local infection is vital to maintaining strain coexistence when considering spatial effects.