  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.
