  Protein aggregation is of great importance in biology, e.g., in amyloid
fibrillation. The aggregation processes that occur at the cellular scale must
be highly stochastic in nature because of the statistical number fluctuations
that arise on account of the small system size at the cellular scale. We study
the nucleated reversible self-assembly of monomeric building blocks into
polymer-like aggregates using the method of kinetic Monte Carlo. Kinetic Monte
Carlo, being inherently stochastic, allows us to study the impact of
fluctuations on the polymerisation reactions. One of the most important
characteristic features in this kind of problem is the existence of a lag phase
before self-assembly takes off, which is what we focus attention on. We study
the associated lag time as a function of the system size and kinetic pathway.
We find that the leading order stochastic contribution to the lag time before
polymerisation commences is inversely proportional to the system volume for
large-enough system size for all nine reaction pathways tested. Finite-size
corrections to this do depend on the kinetic pathway.
