Dynamics of unfolded protein aggregation

TL;DR

This paper models unfolded protein aggregation dynamics using a stochastic approach, deriving analytical solutions for the probability distribution and analyzing fluctuations, which vary between sub-Poisson, Poisson, and super-Poisson regimes.

Contribution

It extends the Lumry-Eyring model with a stochastic analytical solution for the probability distribution of unfolded proteins over time.

Findings

Probability distribution transitions from complex binomial to Poisson and then to Normal at large populations.

Fluctuations can be sub-Poisson, Poisson, or super-Poisson depending on conditions.

Analytical solutions provide insights into the stochastic dynamics of protein aggregation.

Abstract

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.