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Statistical mechanical treatments of protein amyloid formation.

Schreck JS, Yuan JM - Int J Mol Sci (2013)

Bottom Line: 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.Furthermore, statistical mechanics models can be used to fit experimental data when they are available for comparison.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, Drexel University, Philadelphia, PA 19104, USA.

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.

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Related in: MedlinePlus

Proteins or solvent clusters may occupy lattice sites, where the front-view (y–z plane) of an aggregate of Aβ(1–40) proteins is shown along with the interactions between proteins and solvent clusters. The nc = 2 nucleus is represented by dashed-dotted lines (free energy A denoting the nucleation). Dotted and solid lines illustrate interactions between sheet proteins. Double solid lines illustrate a protein-solvent interface. Dashed (blue) lines have no meaning.
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f11-ijms-14-17420: Proteins or solvent clusters may occupy lattice sites, where the front-view (y–z plane) of an aggregate of Aβ(1–40) proteins is shown along with the interactions between proteins and solvent clusters. The nc = 2 nucleus is represented by dashed-dotted lines (free energy A denoting the nucleation). Dotted and solid lines illustrate interactions between sheet proteins. Double solid lines illustrate a protein-solvent interface. Dashed (blue) lines have no meaning.

Mentions: Since nucleation cannot in reality occur in 1D, we consider a similar model for aggregates that positions the nucleus along the y-axis, as shown in Figure 6a and Figure 11. From this point of view the orientations of proteins in the nucleus are perpendicular to the direction of propagation (x-axis) of the fibrils, and the nucleus is now a multi-layer, 1D aggregate. The nuclei may assemble into proto-fibrils that grow longer on the quasi-1D lattice. An effective Hamiltonian for protein aggregation, including the quasi-1D nucleus, can be written:


Statistical mechanical treatments of protein amyloid formation.

Schreck JS, Yuan JM - Int J Mol Sci (2013)

Proteins or solvent clusters may occupy lattice sites, where the front-view (y–z plane) of an aggregate of Aβ(1–40) proteins is shown along with the interactions between proteins and solvent clusters. The nc = 2 nucleus is represented by dashed-dotted lines (free energy A denoting the nucleation). Dotted and solid lines illustrate interactions between sheet proteins. Double solid lines illustrate a protein-solvent interface. Dashed (blue) lines have no meaning.
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC3794734&req=5

f11-ijms-14-17420: Proteins or solvent clusters may occupy lattice sites, where the front-view (y–z plane) of an aggregate of Aβ(1–40) proteins is shown along with the interactions between proteins and solvent clusters. The nc = 2 nucleus is represented by dashed-dotted lines (free energy A denoting the nucleation). Dotted and solid lines illustrate interactions between sheet proteins. Double solid lines illustrate a protein-solvent interface. Dashed (blue) lines have no meaning.
Mentions: Since nucleation cannot in reality occur in 1D, we consider a similar model for aggregates that positions the nucleus along the y-axis, as shown in Figure 6a and Figure 11. From this point of view the orientations of proteins in the nucleus are perpendicular to the direction of propagation (x-axis) of the fibrils, and the nucleus is now a multi-layer, 1D aggregate. The nuclei may assemble into proto-fibrils that grow longer on the quasi-1D lattice. An effective Hamiltonian for protein aggregation, including the quasi-1D nucleus, can be written:

Bottom Line: 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.Furthermore, statistical mechanics models can be used to fit experimental data when they are available for comparison.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, Drexel University, Philadelphia, PA 19104, USA.

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.

Show MeSH
Related in: MedlinePlus