Statistical Mechanical Treatments of Protein Amyloid Formation

Abstract

Protein aggregation is an important field of investigation because it is closely related to the problem of neurodegenerative diseases, to the development of biomaterials, and to the growth of cellular structures such as cyto-skeleton. Self-aggregation of protein amyloids, for example, is a complicated process involving many species and levels of structures. This complexity, however, can be dealt with using statistical mechanical tools, such as free energies, partition functions, and transfer matrices. In this article, we review general strategies for studying protein aggregation using statistical mechanical approaches and show that canonical and grand canonical ensembles can be used in such approaches. The grand canonical approach is particularly convenient since competing pathways of assembly and dis-assembly can be considered simultaneously. Another advantage of using statistical mechanics is that numerically exact solutions can be obtained for all of the thermodynamic properties of fibrils, such as the amount of fibrils formed, as a function of initial protein concentration. Furthermore, statistical mechanics models can be used to fit experimental data when they are available for comparison.

Amyloid Fibril Solubility

“…refs. 3,5,25,26 ). Also, aggregation propensities might be predicted from protein physicochemical properties by using knowledge-based computational approaches [27][28][29][30] but they are not able to distinguish between different fibril structures.…”

“…Theoretically, a statistical mechanical description of the fibril solubility can be obtained in the case of linear aggregation in terms of molecular partition functions ( e.g. , refs , , , and ). Also, aggregation propensities might be predicted from protein physicochemical properties by using knowledge-based computational approaches, − but they are not able to distinguish between different fibril structures.…”

Dynamical protein interaction pathways: A molecular root to diseases

“…Additionally, a statistical mechanical approach to the formation of protein fibrils allows us to manipulate the magnitude of such aggregates. This approach gives the flexibility to quantify the assembly and disassembly of adjacent residues that bequeath one to fathom the molecular roots of diseases [58]. Also, the grand canonical ensembles are more sophisticated to visualize the signalling pathways.…”

“…Additionally, statistical mechanical treatments on the formation of protein fibrils allow us to manipulate the magnitude of β− sheet aggregates [70]. This approach gives the flexibility to quantify the assembly and disassembly of adjacent residues.…”