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We explore the long-time behavior and equilibrium properties of a system of linear filaments growing through nucleated polymerisation. We show that the length distribution for breakable filaments evolves through two well defined limiting cases: first, a steady state distribution determined by the balance of breakage and elongation is reached; upon monomer depletion at the end of the growth phase, an equilibrium length distribution biased towards smaller filament fragments emerges. We furthermore compute the time evolution of the concentration of small oligomeric filament fragments. For frangible filaments, oligomers are present both at early times and at equilibrium, whereas in the absence of fragmentation, oligomers are only present in significant quantities at the beginning of the polymerisation reaction. Finally, we discuss the significance of these results for the biological consequences of filamentous protein aggregation.

Nucleated polymerization with secondary pathways. III. Equilibrium behavior and oligomer populations