Chemistry Reference
In-Depth Information
appears more progressive since small aggregates are formed initially which
grow in time.
14,18-20
When the electrostatic repulsion is weaker, either because
the pH is closer to the isoelectric point or because salt is added, the aggregates
appear more densely branched.
21,22
Scattering measurements can be used to determine the average structure of
aggregates over a range of length-scales between that of the size of an individual
protein molecule up
1 mm. Scattering techniques have the advantage that the
samples do not need to be specially treated and that average properties of the 3-D
structure are obtained. However, it is dicult to extract information on the
variability of the structures and on the connectivity, e.g., the degree of branching.
In addition, in order to eliminate the effect of interactions on the results, the
aggregates need to be highly dilute. Fortunately, most globular protein aggre-
gates are stable and can be diluted without modifying their structure. The
properties that can be derived using scattering techniques are illustrated in
Figure 3, where I/KC is plotted as function of the scattering wave vector q for
a dilute solution of idealized globular protein aggregates. The quantity I is the
excess scattering intensity over the solvent, C the concentration, and K an optical
constant.
23,24
The aggregates have a weight-average molar mass defined by
M
w
¼
Z
MC
ð
M
Þ
dM
=
C
;
B
ð
2
Þ
where C(M) is the weight concentration of aggregates with molar mass between
M and M+dM, and C the total concentration. They have a z-average radius
of gyration defined by
Z
MC
ð
M
Þ
R
g
dM
=
Z
MC
ð
M
Þ
dM
0
:
5
R
gz
¼
:
ð
3
Þ
10
10
M
w
10
9
L
p
-d
f
1/R
gz
10
8
10
7
-1
10
6
10
5
1/L
p
10
4
R
c
1/R
c
10
3
0.0001
0.001
0.01
0.1
1
R
g
q(nm
-1
)
Figure 3
Idealized structure of a globular protein aggregate (left) and the corresponding
q-dependent scattering intensity I (right) indicating the various parameters that
can be derived, as described in the text
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