Department of Physics, Drexel University, Philadelphia, PA 19104, USA.
Int J Mol Sci. 2013 Aug 23;14(9):17420-52. doi: 10.3390/ijms140917420.
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.
蛋白质聚集是一个重要的研究领域，因为它与神经退行性疾病的问题、生物材料的发展以及细胞结构（如细胞骨架）的生长密切相关。例如，蛋白质淀粉样纤维的自聚集是一个涉及多种物种和结构层次的复杂过程。然而，这种复杂性可以使用统计力学工具来处理，例如自由能、配分函数和转移矩阵。在本文中，我们综述了使用统计力学方法研究蛋白质聚集的一般策略，并表明正则和巨正则系综可以用于此类方法。巨正则方法特别方便，因为可以同时考虑组装和拆卸的竞争途径。使用统计力学的另一个优点是，对于纤维的所有热力学性质，例如形成的纤维数量，都可以作为初始蛋白质浓度的函数，得到数值上精确的解。此外，当有实验数据可供比较时，可以使用统计力学模型来拟合实验数据。
