Chemistry Reference
In-Depth Information
From the presented results follows a qualitative conclusion, that the gain in mass
0
or
R
g
, or decreasing
k
2
k
1
uptake increases while increasing
. As for parameters of
ε
binging intensity,
k
1
and
N
, there exists an optimal value, that leads to the peak in
gain. Roughly, these “peak” values are:
k
1
=
′
100
. This ¿ nding
is in contradiction with the results of Zhang et al. (2007), which states that the gain in
free solute uptake gradually increases with the ratio of binding sites concentration to
the bath concentration (
100
and
N
′
=
10
for
R
g
=
N
).
′
7.5.1 Transport of Matrix Binding Protein in Fibrin Gel
To show how the present model can be applied to a particular biological system, we
present an example of fibrin gel and mass transport of a plasmin-like protein inside
it. The parameters for this system are taken from the literature (see Table 1). The real
parameters are set to:
1
0.0001
1
s
m
2
kPa
50
μ
m
2
s
μ
c
0
=
1
μ
M
,
k
f
,
k
r
,
H
A
1
kPa
,
k
,
D
=
0.1
=
=
=
=
10000
μ
M
⋅
s
⋅
s
which correspond to the following non-dimensional parameters:
R
g
=
200
,
50
,
k
1
100
,
k
2
0.1
for
f
=
=
=
1
Hz
N
′
=
Figure 11 (A) represents the gain function for free, bound and total solute for these
parameters as a function of time in seconds. Figure 11(B) shows the gain function for
not binding solute for two frequencies:
f
1
Hz
and
f
=
0.1
Hz
as a function of time
=
1
Hz
, but stretched
in time by the order of 10 (see non-dimensional analog of this graph on Figure 4(B)
and use Equation (29) to transform normalized time into real). Since the average gain
monotonically decreases, the concentration front at higher frequency
will p
ropagate
further with respect to the deforming layer (“characteristic depth”
0.1
Hz
it is actually the same graph as for
f
=
in seconds. For
f
=
h
k
f
). There-
fore, if we measure the gain for different frequencies (but for the same strain ampli-
tude) at the same time moment, we get less gain for higher frequency.
From Figure 11 (A) it is easy to see that if the solute adheres to matrix with high
binding sites concentration, the shape of the gain curve is different compared with Fig-
ure 11(B) and Figure (3): it increases gradually to a peak value, then gradually decreas-
es. Consequently, measuring the gain at the same time for different frequencies does
not reÀ ect the effect of frequency, because it is unknown at what part of the curve this
time point falls. That is why, to investigate the effect of loading frequency on the trans-
port enhancement, we calculate the average gain for frequencies
f
H
A
⋅
=
10,1,0.1,0.01
Hz
at particular time for each frequency. This time points
t
f
are chosen in such a way
that the gains for non-binding solute at these times are equal (the value of the average
gain is 35%):
t
10
=
16000
s
. By these times the con-
centration front passes the same part of the deforming layer for each frequency. Thus,
the time points lie in corresponding parts of gain curves. The results are presented on
=
16
s
,
t
1
=
160
s
,
t
0.1
=
1600
s
,
t
0.01
=
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