Biomedical Engineering Reference
In-Depth Information
Sagis and co-workers (Sagis et al.,
2004
) investigated the domain of a transparent
gel formed at low
-Lg ovalbumin or BSA concentrations from homogeneous solu-
tions by heating at low pH and for very extended times (up to 10 h). They excluded
from their analysis conditions where non-homogeneous gels could appear (with liquid
crystal inclusions; see below). For their amyloid
β
fibrillar systems, Sagis et al.(
2004
)
measured the frequency-independent G
0
values in the linear regime as a function of
protein concentration, and then
ttedthedataversus(c
−
c
0
) using a power law with
the exponent
, as a function of ionic strength. The range of concentrations inves-
tigated covered c/c
0
=0.01
γ
0.1. For all proteins, the authors found a decreasing c
0
with increasing ionic strength or decreasing Debye length, and for almost all samples
they found
-
2, which tends to suggest isotropic force percolation and a homoge-
neous network, even though others have reported a range of values from 1.8 to 2.5.
However, as pointed out above, this form of
γ ≈
fitting tends to produce a correlation
between
and c
0
.
They concluded, in contradiction to much other work, that there is no cross-linking of
the
γ
fibrils and that the results can be interpreted simply in terms of these very extended
and stiff strands, whose properties can be interpreted in terms of mesoscopic (liquid
crystalline) behaviour, as discussed in the next section. Assuming amyloid
fibrils are
semi-
exible rods, the critical percolation mass fraction was expressed according to the
model developed for charged semi-
fibres by Khokhlov and Semenov (
1981
)and
adapted from the Onsager treatment (Section 3.11) . The model requires an assumption
that we replace the chain contour length L
c
by its persistence length l
p
, so that the volume
fraction of objects at the isotropic
exible
-
nematic (I-N) transition is then written
d
eff
l
p
;
iso
≈ hαi
l
p
>>
d
eff
;
ð
9
:
1
Þ
where d
eff
is the effective diameter of the rods, which depends on the repulsion inter-
actions through the Debye length (lower salt levels yield less screening and therefore a
larger effective diameter), and
cient close to 1. The model suggests that the
persistence length is a control parameter for this critical concentration when L
c
>> l
p
:no
effect of the
〈
α
〉
is a coef
fibril length is expected for their estimates of c
0
. The persistence length was
deduced from TEM images while the effective diameter was calculated independently
using a theoretical model.
Figure 9.9
shows that this estimate of critical volume fraction increases with the
effective diameter of the semi-
fibres. The contour length L
c
was derived from
TEM images. Sagis and co-workers found a range of values for contour length from 0.2
to 5 μm and persistence lengths from 0.02 to 2 μm, and they suggested that the
persistence lengths in these systems were independent of ionic strength. Their value
for persistence length l
p
for
exible
β
-Lg is very large (l
p
= 1.6 μm), while for ovalbumin it is
smaller (l
p
= 300 nm). The contour lengths of
fibrils at pH 2 near their percolation
threshold vary between 2.5 and 4.5 μm for
-Lg and between 50 and 190 nm for
ovalbumin. The difference is somewhat surprising, but may re
β
ect the particular heating
regime adopted.
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