Role of filament annealing in the kinetics and thermodynamics of nucleated polymerization.

The formation of nanoscale protein filaments from soluble precursor molecules through nucleated polymerization is a common form of supra-molecular assembly phenomenon. This process underlies the generation of a range of both functional and pathological structures in nature. Filament breakage has emerged as a key process controlling the kinetics of the growth reaction since it increases the number of filament ends in the system that can act as growth sites. In order to ensure microscopic reversibility, however, the inverse process of fragmentation, end-to-end annealing of filaments, is a necessary component of a consistent description of such systems. Here, we combine Smoluchowski kinetics with nucleated polymerization models to generate a master equation description of protein fibrillization, where filamentous structures can undergo end-to-end association, in addition to elongation, fragmentation, and nucleation processes. We obtain self-consistent closed-form expressions for the growth kinetics and discuss the key physics that emerges from considering filament fusion relative to current fragmentation only models. Furthermore, we study the key time scales that describe relaxation to equilibrium.