The Shape of the Polymerization Rate in the Prion Equation

TL;DR

This paper models prion proliferation using a polymerization equation with size-dependent rates, employing power laws to match experimental data and improve upon previous constant-rate models.

Contribution

It introduces a novel approach using power laws for polymerization and fragmentation rates in prion models, enhancing the accuracy of shape predictions.

Findings

Recovered the shape of the polymerization rate from experimental data

Demonstrated the effectiveness of power law rates over constant coefficients

Improved modeling of prion strain fragmentation dependency

Abstract

We consider a polymerization (fragmentation) model with size-dependent parameters involved in prion proliferation. Using power laws for the different rates of this model, we recover the shape of the polymerization rate using experimental data. The technique used is inspired from an article of Zampieri et al. where the fragmentation dependency on prion strains is investigated. Our improvement is to use power laws for the rates whereas Zampieri et al. used a constant polymerization coefficient and linear fragmentation.