Stochastic kinetic treatment of protein aggregation and the effects of macromolecular crowding

Abstract

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.