Directionality of growth and kinetics of branched fibril formation

Variance and higher moments in the sigmoidal self-assembly of branched fibrils

Self-assembly of functional branched filaments, such as actin filaments and microtubules, or dysfunctional ones, such as amyloid fibrils, plays important roles in many biological processes. Here, based on the master equation approach, we study the kinetics of the formation of the branched fibrils. In our model, a branched fibril has one mother branch and several daughter branches. A daughter branch grows from the side of a pre-existing mother branch or daughter branch. In our model, we consider five basic processes for the self-assembly of the branched filaments, namely, the nucleation, the dissociation of the primary nucleus of fibrils, the elongation, the fragmentation, and the branching. The elongation of a mother branch from two ends and the elongation of a daughter branch from two ends can, in principle, occur with four different rate constants associated with the corresponding tips. This leads to a pronounced impact of the directionality of growth on the kinetics of the self-assembly. Here, we have unified and generalized our four previously presented models of branched fibrillogenesis in a single model. We have obtained a system of non-linear ordinary differential equations that give the time evolution of the polymer numbers and the mass concentrations along with the higher moments as observable quantities.

Kinetics theories to understand the mechanism of aggregation of a protein and to design strategies for its inhibition

Protein aggregation phenomenon is closely related to the formation of amyloids which results in many neurodegenerative diseases like Alzheimer's, Parkinson's, Huntington's, and Amyotrophic Lateral Sclerosis. In order to prevent and treat these diseases, a clear understanding of the mechanism of misfolding and self-assembly of peptides and proteins is very crucial. The aggregation of a protein may involve various microscopic events. Multiple simulations utilizing the solutions of the master equation have given a better understanding of the kinetic profiles involved in the presence and absence of a particular microscopic event. This review focuses on understanding the contribution of these molecular events to protein aggregation based on the analysis of kinetic profiles of aggregation. We also discuss the effect of inhibitors, which target various species of aggregation pathways, on the kinetic profile of protein aggregation. At the end of this review, some strategies for the inhibition of aggregation that can be utilized by combining the chemical kinetics approach with thermodynamics are proposed.