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.
Highlights
Protein aggregation is an active, multidisciplinary science, with researchers and practitioners working in broad disciplines, including biophysics, medicine, biomaterials, and pharmaceuticals
The present article is only concerned with the fundamental investigations into the aggregation mechanisms of amyloid formation related to neurodegenerative disease
It is in a similar spirit that our statistical mechanical treatment of protein aggregation has been developed [21], which is the main subject of this article
Summary
Protein aggregation is an active, multidisciplinary science, with researchers and practitioners working in broad disciplines, including biophysics, medicine, biomaterials, and pharmaceuticals. The present article is only concerned with the fundamental investigations into the aggregation mechanisms of amyloid formation related to neurodegenerative disease. Analogous to a one-dimensional Ising model [14], Zimm and Bragg expressed the partition function in terms of transfer matrices and solved the problem analytically in the large polymerization limit, and for finite chains [8]. It is in a similar spirit that our statistical mechanical treatment of protein aggregation has been developed [21], which is the main subject of this article. Our formalism of the aggregation processes was stimulated by other statistical mechanical studies. These works will be briefly reviewed, along with conceptual developments of statistical mechanical techniques beyond those used in the.
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