Initial condition of stochastic self-assembly

The formation of a stable protein aggregate is regarded as the rate limiting step in the establishment of prion diseases. In these systems, once aggregates reach a critical size the growth process accelerates and thus the waiting time until the appearance of the first critically sized aggregate is a key determinant of disease onset. In addition to prion diseases, aggregation and nucleation is a central step of many physical, chemical, and biological process. Previous studies have examined the first-arrival time at a critical nucleus size during homogeneous self-assembly under the assumption that at time t=0 the system was in the all-monomer state. However, in order to compare to in vivo biological experiments where protein constituents inherited by a newly born cell likely contain intermediate aggregates, other possibilities must be considered. We consider one such possibility by conditioning the unique ergodic size distribution on subcritical aggregate sizes; this least-informed distribution is then used as an initial condition. We make the claim that this initial condition carries fewer assumptions than an all-monomer one and verify that it can yield significantly different averaged waiting times relative to the all-monomer condition under various models of assembly.