title: Statistical mechanical treatments of protein amyloid formation.
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.
authors: Department of Physics, Drexel University, Philadelphia, PA 19104, USA.
authors: John S
authors: JS
authors: Schreck
authors: Jian-Min
authors: JM
authors: Yuan
mesh_terms: D000682:Amyloid / Q000737:chemistry*; D000818:Animals; D006801:Humans; D011506:Proteins / Q000737:chemistry
chemical_list: D000682:Amyloid; D011506:Proteins
references: Annu Rev Biophys Biophys Chem. 1989;18:93-111
references: 2660835
references: J Chem Phys. 2009 Sep 21;131(11):115104
references: 19778153
references: J Mol Biol. 2000 Mar 17;297(1):73-87
references: 10704308
references: Proc Natl Acad Sci U S A. 2003 May 27;100(11):6370-5
references: 12750461
references: Nature. 1997 Nov 13;390(6656):196-9
references: 9367160
references: Acc Chem Res. 2008 Oct;41(10):1309-18
references: 18937396
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 1):041914
references: 19905349
references: J Phys Chem B. 2012 May 10;116(18):5384-90
references: 22512540
references: Biophys Chem. 2011 Nov;159(1):14-23
references: 21530061
references: Science. 2009 Dec 11;326(5959):1533-7
references: 20007899
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 1):031922
references: 19905161
references: Proc Natl Acad Sci U S A. 2003 Jan 7;100(1):330-5
references: 12506200
references: Curr Opin Chem Biol. 2006 Oct;10(5):445-52
references: 16935548
references: Phys Rev Lett. 2010 Sep 3;105(10):108102
references: 20867550
references: J Biol Chem. 2009 Feb 20;284(8):4749-53
references: 18845536
references: Proc Natl Acad Sci U S A. 1998 May 26;95(11):6448-53
references: 9600986
references: Cell Mol Life Sci. 2011 Apr;68(8):1429-38
references: 20853129
references: Annu Rev Phys Chem. 2011;62:437-63
references: 21219143
references: J Mol Biol. 1962 Jan;4:10-21
references: 14482095
references: J Mol Biol. 1995 Oct 6;252(5):633-42
references: 7563079
references: Biophys Chem. 2002 Dec 10;101-102:255-65
references: 12488006
references: J Phys Chem B. 2013 May 30;117(21):6574-83
references: 23638987
references: J Chem Phys. 2012 Feb 14;136(6):065103
references: 22360223
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Apr;69(4 Pt 1):041908
references: 15169044
references: Nature. 2005 Jun 9;435(7043):773-8
references: 15944695
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Jun;81(6 Pt 1):061919
references: 20866452
references: J Phys Chem B. 2012 Jun 14;116(23):6611-7
references: 22126094
references: Nat Med. 2008 Aug;14(8):837-42
references: 18568035
references: Biophys J. 1994 Jul;67(1):349-55
references: 7919005
references: Nat Rev Mol Cell Biol. 2007 Feb;8(2):101-12
references: 17245412
references: Proc Natl Acad Sci U S A. 2002 Jan 8;99(1):150-4
references: 11756677
references: Acc Chem Res. 2006 Sep;39(9):584-93
references: 16981674
references: Biochemistry. 1999 Jul 13;38(28):8972-80
references: 10413470
references: Biophys J. 2013 Feb 5;104(3):533-40
references: 23442904
references: J Chem Phys. 2011 Dec 21;135(23):235102
references: 22191902
references: Proc Natl Acad Sci U S A. 2007 Jul 24;104(30):12494-9
references: 17636121
references: FEBS J. 2005 Dec;272(23):5950-61
references: 16302960
references: Proc Natl Acad Sci U S A. 2010 Feb 23;107(8):3487-92
references: 20133726
references: Biophys J. 1997 Jan;72(1):343-52
references: 8994619
references: J Am Chem Soc. 2009 Feb 18;131(6):2306-12
references: 19170581
references: Biophys J. 2008 Nov 15;95(10):4871-8
references: 18676659
references: Biophys J. 2011 Jan 19;100(2):450-8
references: 21244841
references: Biochemistry. 2006 Jan 17;45(2):498-512
references: 16401079
references: Proteins. 2007 Oct 1;69(1):58-68
references: 17596846
references: J Neurosci. 1999 Oct 15;19(20):8876-84
references: 10516307
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Nov;78(5 Pt 1):051904
references: 19113152
references: J Am Chem Soc. 2010 Mar 31;132(12):4266-80
references: 20218566
references: Protein Sci. 2006 Sep;15(9):2051-61
references: 16882994
references: Biopolymers. 1984 Dec;23(12):2879-90
references: 6525405
references: Biophys J. 2001 Sep;81(3):1805-22
references: 11509390
references: Structure. 2000 Sep 15;8(9):915-25
references: 10986459
references: Biopolymers. 1984 Sep;23(9):1701-24
references: 6478039
references: Methods Enzymol. 2006;412:285-99
references: 17046664
references: Cell. 2012 Mar 16;148(6):1188-203
references: 22424229
references: J Biol Chem. 2002 Jun 14;277(24):21140-8
references: 11912192
references: J Chem Phys. 2008 Dec 14;129(22):225101
references: 19071947
references: Biophys J. 2006 May 1;90(9):3134-45
references: 16603504
references: Curr Opin Struct Biol. 2003 Apr;13(2):146-59
references: 12727507
references: Biochem J. 2000 May 15;348 Pt 1:137-44
references: 10794724
references: J Chem Phys. 2008 Nov 7;129(17):175101
references: 19045373
references: Biochemistry. 2000 Oct 31;39(43):13269-75
references: 11052680
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Nov;72(5 Pt 1):051915
references: 16383653
references: Biochemistry. 1999 Oct 12;38(41):13560-73
references: 10521263
references: Biophys J. 2008 Jan 15;94(2):379-91
references: 17890392