Entropic Analysis of Protein Aggregation using Langevin Equations and Fokker–Planck Equations

Abstract

Protein aggregation is a sophisticated biological mechanism that can have detrimental consequences. It is recognized as the hallmark of neurodegenerative diseases, suffered by millions of people each year reported by World Health Organization, [Formula: see text]. Abnormal deposits of amyloid fibrils and/or oligomers accumulate in and around neurons causing irreparable damage that leads to severe deterioration of the surrounding brain tissue and cognitive function. As of now, early detection, therapeutic intervention and treatment options are extremely limited. Protein aggregation is known to be highly dynamic, irreversible process which is source of its difficulty to fully understand and remedy the problem. The design of our study is to interpret the mechanics of intrinsically disordered proteins that self-assemble into highly structured fibrils. The aim is to gain a deeper understanding of protein–protein interactions, environmental conditions and chaperone failure that attribute to the aggregation process. The complexity of the aggregation process cannot be modeled using statistical physics and statistical thermodynamics of equilibrium processes. There are numerous studies that suggest protein aggregation which is a non-equilibrium process. Based on non-equilibrium physics, one of the best ways to understand it is through the Langevin and Fokker–Planck equations. Langevin equations describe stochastic dynamics of non-equilibrium processes. The Fokker–Planck equation is used to calculate the probability distribution and explain the trend in entropy of a model independent protein aggregation process.