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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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Summary of protein conformation energies. A site could be occupied with a solvent cluster, denoted by n = 0 (square), or a protein, n = 1 (circles). Proteins may assume a particular conformation (sheet, black/solid circle; coil, white circle). A dilute q = 2 Potts model for sheet-coil conformations is shown, where nc = 1 and the free energies P1, K, R, and A are illustrated.
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f10-ijms-14-17420: Summary of protein conformation energies. A site could be occupied with a solvent cluster, denoted by n = 0 (square), or a protein, n = 1 (circles). Proteins may assume a particular conformation (sheet, black/solid circle; coil, white circle). A dilute q = 2 Potts model for sheet-coil conformations is shown, where nc = 1 and the free energies P1, K, R, and A are illustrated.

Mentions: To write down an effective Hamiltonian that can include the free energy A, the 1D or quasi-1D lattices used in constructing fibrils can be generalized to allow solvent clusters to occupy the lattice sites. For example, in Figure 10, a square represents a solvent cluster, whereas circle represents protein. Both solvent and proteins can occupy sites along 1D or quasi-1D lattices. By introducing a lattice gas model into the aggregate phase, a Potts Hamiltonian for the 1D lattice that quantifies the interactions between helix, sheet, or coil proteins and solvent can be written as [26]:


Statistical mechanical treatments of protein amyloid formation.

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

Summary of protein conformation energies. A site could be occupied with a solvent cluster, denoted by n = 0 (square), or a protein, n = 1 (circles). Proteins may assume a particular conformation (sheet, black/solid circle; coil, white circle). A dilute q = 2 Potts model for sheet-coil conformations is shown, where nc = 1 and the free energies P1, K, R, and A are illustrated.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f10-ijms-14-17420: Summary of protein conformation energies. A site could be occupied with a solvent cluster, denoted by n = 0 (square), or a protein, n = 1 (circles). Proteins may assume a particular conformation (sheet, black/solid circle; coil, white circle). A dilute q = 2 Potts model for sheet-coil conformations is shown, where nc = 1 and the free energies P1, K, R, and A are illustrated.
Mentions: To write down an effective Hamiltonian that can include the free energy A, the 1D or quasi-1D lattices used in constructing fibrils can be generalized to allow solvent clusters to occupy the lattice sites. For example, in Figure 10, a square represents a solvent cluster, whereas circle represents protein. Both solvent and proteins can occupy sites along 1D or quasi-1D lattices. By introducing a lattice gas model into the aggregate phase, a Potts Hamiltonian for the 1D lattice that quantifies the interactions between helix, sheet, or coil proteins and solvent can be written as [26]:

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