  Investigation of protein self-assembly processes is important for the
understanding of the growth processes of functional proteins as well as
disease-causing amyloids. Inside cells, intrinsic molecular fluctuations are so
high that they cast doubt on the validity of the deterministic rate equation
approach. Furthermore, the protein environments inside cells are often crowded
with other macromolecules, with volume fractions of the crowders as high as
40%. We study protein self-aggregation at the cellular level using Gillespie's
stochastic algorithm and investigate the effects of macromolecular crowding
using models built on scaled-particle and transition-state theories. The
stochastic kinetic method can be formulated to provide information on the
dominating aggregation mechanisms in a method called reaction frequency (or
propensity) analysis. This method reveals that the change of scaling laws
related to the lag time can be directly related to the change in the
frequencies of reaction mechanisms. Further examination of the time evolution
of the fibril mass and length quantities unveils that maximal fluctuations
occur in the periods of rapid fibril growth and the fluctuations of both
quantities can be sensitive functions of rate constants. The presence of
crowders often amplifies the roles of primary and secondary nucleation and
causes shifting in the relative importance of elongation, shrinking,
fragmentation and coagulation of linear aggregates. Comparison of the results
of stochastic simulations with those of rate equations gives us information on
the convergence relation between them and how the roles of reaction mechanisms
change as the system volume is varied.
