Dynamics of unfolded protein aggregation

Unfolded protein aggregation in cellular system is a problem causing various types of diseases depending on which type unfolded proteins aggregate. This phenomenon of aggregation may take place during production, storage, shipment or delivery in the cellular medium. In the present work, we studied a simplified and extended version of unfolded protein aggregation model by Lumry and Eyring using stochastic approach. We solved analytically the Master equation of the model for the probability distribution $P(x,t)$ of the unfolded protein population and the solution was found to be time dependent complex binomial distribution. In the large population limit $P(x,t)\sim \Lambda(x,t)\times Pois(x,t)$. Further, the distribution became Normal distribution at large population and mean of the distribution limit: $P(x,t)\sim\Lambda(x,t)\times N(\langle qx\rangle,\langle qx\rangle)$. The fluctuations inherent in the dynamics measured by Fano factor can have sub-Poisson, Poisson and super-Poisson at different situations.