Stochastic Modeling and Simulation of Filament Aggregation in Alzheimer's Disease

Alzheimer's disease has been a serious problem for humankind, one without a promising cure for a long time now, and researchers around the world have been working to better understand this disease mathematically, biologically and computationally so that a better cure can be developed and finally humanity can get some relief from this disease. In this study, we try to understand the progression of Alzheimer's disease by modeling the progression of amyloid-beta aggregation, leading to the formation of filaments using the stochastic method. In a noble approach, we treat the progression of filaments as a random chemical reaction process and apply the Monte Carlo simulation of the kinetics to simulate the progression of filaments of lengths up to 8. By modeling the progression of disease as a progression of filaments and treating this process as a stochastic process, we aim to understand the inherent randomness and complex spatial-temporal features and the convergence of filament propagation process. We also analyze different reaction events and observe the events such as primary as well as secondary elongation, aggregations and fragmentation using different propensities for different possible reactions. We also introduce the random switching of the propensity at random time, which further changes the convergence of the overall dynamics. Our findings show that the stochastic modeling can be utilized to understand the progression of amyloid-beta aggregation, which eventually leads to larger plaques and the development of Alzheimer disease in the patients. This method can be generalized for protein aggregation in any disease, which includes both the primary and secondary aggregation and fragmentation of proteins.