  While a significant body of investigations have been focused on the process
of protein self-assembly, much less is understood about the reverse process of
a filament breaking due to thermal motion into smaller fragments, or
depolymerization of subunits from the filament ends. Indirect evidence for
actin and amyloid filament fragmentation has been reported, although the
phenomenon has never been directly observed either experimentally or in
simulations. Here we report the direct observation of filament depolymerization
and breakup in a minimal, calibrated model of coarse-grained molecular
simulation. We quantify the orders of magnitude by which the depolymerization
rate from the filament ends $k_\mathrm{off}$ is larger than fragmentation rate
$k_{-}$ and establish the law $k_\mathrm{off}/k_- = \exp [( \varepsilon_\| -
\varepsilon_\bot) / k_\mathrm{B}T ] = \exp [0.5 \varepsilon / k_\mathrm{B}T ]$,
which accounts for the topology and energy of bonds holding the filament
together. This mechanism and the order-of-magnitude predictions are well
supported by direct experimental measurements of depolymerization of insulin
amyloid filaments.
