Spatial Propagation of Protein Polymerization

We consider the spatial dependence of filamentous protein self-assembly. Through studying the cases where the spreading of aggregated material is dominated either by diffusion or by growth, we derive analytical results for the spatial evolution of filamentous protein aggregation, which we validate against Monte Carlo simulations. Moreover, we compare the predictions of our theory with experimental measurements of two systems for which we identify the propagation as either growth or diffusion controlled. Our results connect the macroscopic observables that characterize the spatial propagation of protein self-assembly with the underlying microscopic processes and provide physical limits on spatial propagation and prionlike behavior associated with protein aggregation.