An alternative model to prion fragmentation based on the detailed balance between PrPSc and suPrP

Prion assemblies responsible for transmissible spongiform encephalopathies grow in the form of linear amyloid fibrils. Traditional models for prion growth and tissue-spreading have relied upon the assumption that propagation is based on the process of fragmentation, wherein an assembly literally breaks in two, creating additional templating interfaces. Recent experimental data shows that PrPSc assemblies are in detailed balance with an elementary oligomeric building block called suPrP. In the present work we compare the dynamics of the canonical model of induced-fragmentation to the model of PrPSc assemblies in detailed balance with suPrP. The model is a dynamical system describing the populations of fibrils of varying lengths as a function of time; we analyze the system via both analytical and numerical techniques. We demonstrate that the detailed balance between suPrP and PrPSc model can equivalently replace the induced-fragmentation model. This equivalence opens a new opportunity in an optimal control problem. ### Competing Interest Statement The authors have declared no competing interest.