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n apparent reaction order for monomer
s effective hard sphere diameter of a
loss; from m(t) at a single c0 value
protein monomer
c0 initial protein concentration
K2,tr equilibrium constant for dimerization
kobs observed rate coefficient for monomer
of hard spheres; accounting for transla-
loss, based on m(t)
tional or communal entropy contribu-
ðUÞ ðFÞ
F folded or native monomer conforma-
tions to K2 or K2
tional state
bðaÞ dimensionless or rescaled osmotic virial
2
U unfolded or partially unfolded, aggre-
coefficient; defined by Eq. (16).
gation-prone monomer conformational
jZpj absolute value of the net charge on the
state
surface of a protein monomer.
T temperature
Tref lowest temperature at which experi-
Ui reversible oligomer composed of i mono-
mental kobs values are available for
mers of U
extrapolation to lower temperatures;
Ux reversible prenucleus, composed of x
serves as a reference point temperature
monomers of U
in using Eqs. (19) and (20).
Aj irreversible aggregate composed of Ea,eff effective activation energy for tempera-
j monomers ture extrapolations of kobs; includes
Ax nucleus or smallest irreversible aggre- contributions from multiple stages of
gate; composed of x monomers. aggregation in some cases (cf. Tab. 5)
DG0 standard Gibbs free energy of unfolding G prefactor in Eq. (20); cf. Table 5
un
ku rate coefficient for unfolding
x number of monomers in a nucleus; must
kf rate coefficient for folding be greater than or equal to 2
Kun equilibrium constant for unfolding kB Boltzmann s constant
DOI 10.1002/jps JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 4, APRIL 2009
1272 WEISS, YOUNG, AND ROBERTS
tð0Þ intrinsic time scale for aggregate 11. Alford JR, Kwok SC, Roberts JN, Wuttke DS,
n
Kendrick BS, Carpenter JF, Randolph TW.
nucleation, such that [U] ¼ cref
2007. High concentration formulations of recom-
tð0Þ intrinsic time scale for aggregate
g
binant human interleukin-1 receptor antagonist:
growth by monomer addition, such that
I. Physical characterization. J Pharm Sci 97:3035
[U] ¼ cref
3050.
tð0Þ intrinsic time scale for aggregate
c
12. Eisenberg D, Nelson R, Sawaya MR, Balbirnie M,
growth by soluble aggregate-aggregate
Sambashivan S, Ivanova MI, Madsen AO, Riekel
association
C. 2006. The structural biology of protein aggrega-
tion diseases: Fundamental questions and some
answers. Acc Chem Res 39:568 575.
ACKNOWLEDGMENTS
13. Uversky VN, Fink AL. 2004. Conformational con-
straints for amyloid fibrillation: The importance of
CJR gratefully acknowledges financial support being unfolded. Biochim Biophys Acta 1698:131
153.
from the National Institutes of Health (R01
14. Raman B, Chatani E, Kihara M, Ban T, Sakai M,
E8006006) and support from Boehringer-Ingel-
Hasegawa K, Naiki H, Rao Ch M, Goto Y. 2005.
heim Pharmaceuticals, Pfizer Global R&D, and
Critical balance of electrostatic and hydrophobic
Merck Research Laboratories for projects from
interactions is required for beta 2-microglobulin
which ideas in this report have grown.
amyloid fibril growth and stability. Biochemistry
44:1288 1299.
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