jps.21521

[ Pobierz całość w formacie PDF ]

phobic attractions is quantified by an attractive
contact-free-energy parameter (ehp), and is set to
values that typify native or non-native protein
Figure 2. Illustration of the qualitative and semi-
quantitative relationship between B22 and the standard
free energy of reversible oligomer formation. (A) Illus-
trative potential of mean force profiles between two
colloidal particles interacting with a combination of
screened electrostatic repulsions, solvophobic attrac-
tions, and steric hard sphere cores; different curves
correspond to increasing ionic strength. (B) Reduced
2nd osmotic virial coefficient and excess standard free
energy for dimer formation, as a function of ionic
strength at conditions slightly above or below the pI
(jZpj �10, solid curves) for folded (blue) and non-native
(red) model proteins; dashed curves are for pH pI
(jZpj �0). (C) Analogous curves to those in (B), but as
a function of net protein charge jZpj at fixed ionic
strength (low: I � 10 mM (solid), high: I > ca. 300 mM
(dashed)). s � 4 nm in all cases. For reference, estimates
Figure 2.
of K2,tr from hard-particle models give K2,tr 10 4 mM 1
with s � 4 nm.66
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 4, APRIL 2009 DOI 10.1002/jps
PREDICTING PROTEIN AGGREGATION RATES AND SHELF LIFE 1261
interactions under low or zero-charge state changes in b�F� can change the kinetics and
2
conditions (see also, Supporting Informa- thermodynamics of crystallization dramati-
tion).66,112 All curves in Figure 2 are for s � 4 cally.124,126 128 The much stronger dependence
nm, a typical mid-range value for pharmaceutical of protein solubility on the value b�F� may be due to
2
proteins and polypeptides. the fact that small changes in attraction strength
Illustrative Dg�a��r� profiles are shown in can dramatically alter the stability of the solid
12
Figure 2A as a function of ionic strength phase when long-range repulsions are greatly
(1:1 electrolyte) for an effective charge that is screened.111,115 Note that this and all arguments
appropriate for conditions reasonably below or based solely on isotropic or anisotropic colloidal
above the monomer pI (i.e., jZpj �10). interactions do not necessarily apply if one is
�a�
Figure 2B shows K2 and b�a� for jZpj �10, as a considering highly specific, strong contacts
2
function of ionic strength over a typical ex- between proteins that lead to essentially bind-
perimental range for a 1:1 electrolyte. ing-like interactions such as with multimeric
�a�
Figure 2C shows K2 and b�a� as a function of folded proteins. Such cases should instead be
2
jZpj for low ( 10 mM) and high ( 300 mM or treated directly in terms of the relevant equili-
higher) ionic strength with a 1:1 electrolyte. brium constants for dimer and oligomer forma-
Changing jZpj or k 1 in the model is physically tion, and those constants should in principle be
equivalent, respectively, to changing pH or measurable with techniques such as equilibrium
ionic strength of a formulation or processing AUC. Independent of the particular model one
condition. elects to use for Dg�a��r�, the relatively weak effect
12
�U� �F�
All the results in Figure 2 are only semi- that attraction strength has for K2 versus K2
quantitative, as they are illustrated using sim- supports the pragmatic use of b�F� as a surrogate
2
plified models for colloidal interactions. Those for b�U� in rationalizing aggregation-rate
2
limitations notwithstanding, Figure 2 highlights data.2,93,107
a number of important features of colloidal protein The above discussion must also be placed in
interactions and their relationship to b�F� and context by realizing that changing colloidal
2
�U�
K2 . One is that at low ionic strength the Debye interactions experimentally is most readily done
screening length is large compared to the size of a by changing solvent conditions. Such changes will
typical protein.111,124,125 As a result, an increase of almost invariably also change the thermo-
b�F� due to increasing protein charge corresponds dynamics and/or dynamics of other stages in
2
�U�
to a dramatic decrease in K2 . By contrast, b�U� aggregation. Therefore, in general the magnitude
2
and b�F� shift much more gradually and so are not and/or sign of colloidal interactions should not
2
�U�
necessarily sensitive indicators of changes in K2 be used on its own as a means to predict or
or kobs when electrostatic repulsions dominate. By rank aggregation propensity among proteins or
contrast, charges are almost completely screened different sample conditions. At a minimum,
at high ionic strength. Therefore, changing the unfolding free energy effects must be considered
charge state of a protein has little direct effect on simultaneously.2,93,107
�U�
the value of b�F� or K2 at high ionic strength Finally, when self-association is irreversible the
2
(Fig. 2C). Instead, the largest changes in asso- quantitative relation between b�F� and kobs is not
2
ciation free energy occur by unfolding or other always straightforward; even if one assumes the
means of altering the strength of surface attrac- rate coefficient for association �k�U�� is diffusion-
2
tions (Fig. 2B and C). limited and obeys colloidal models.71 Qualita-
Independent of the ionic strength effects, tively, however, increasing b�F� by altering the
2
�U� �F�
differences between K2 and K2 values at a strength and/or range of electrostatic interactions
given ionic strength are relatively small (less than is expected to correlate with decreasing k�U�.2,71
2 [ Pobierz całość w formacie PDF ]

Wątki