  Protein molecules often self-assemble by means of non-covalent physical bonds
to form extended filaments, such as amyloids, F-actin, intermediate filaments,
and many others. The kinetics of filament growth is limited by the disassembly
rate, at which inter-protein bonds break due to the thermal motion. Existing
models often assume that the thermal dissociation of subunits occurs uniformly
along the filament, or even preferentially in the middle, while the well-known
propensity of F-actin to depolymerize from one end is mediated by biochemical
factors. Here, we show for a very general (and generic) model, using Brownian
dynamics simulations and theory, that the breakup location along the filament
is strongly controlled by the asymmetry of the binding force about the minimum,
as well as by the bending stiffness of the filament. We provide the basic
connection between the features of the interaction potential between subunits
and the breakup topology. With central-force (that is, fully flexible) bonds,
the breakup rate is always maximum in the middle of the chain, whereas for
semiflexible or stiff filaments this rate is either a minimum in the middle or
flat. The emerging framework provides a unifying understanding of biopolymer
fragmentation and depolymerization and recovers earlier results in its
different limits.
