Biomedical Engineering Reference
In-Depth Information
kinetics in the dissociation phase. The values of (a) the binding rate coefficient,
k
, and the
fractal dimension,
D
f
, for a single-fractal analysis, (b) the binding rate coefficients,
k
1
and
k
2
, and the fractal dimensions,
D
f1
and
D
f2
, for a dual-fractal analysis, and (c) the dissociation
rate coefficient,
k
d
, and the fractal dimension,
D
fd
, in the dissociation phase are given in
Tables 9.7
and
9.8
.
In this case, it is of interest to note that for a dual-fractal analysis as the fractal dimension
increases by a factor of 1.527 from a value of
D
f1
equal to 1.9644 to
D
f2
equal to 3.0, the
binding rate coefficient increases by a factor of 1.18 from a value of
k
1
equal to 25.515 to
k
2
equal to 30.2. In this case, an increase in the degree of heterogeneity or the fractal dimen-
sion on the biosensor surface leads to an increase in the binding rate coefficient.
Figure 9.7c
shows the binding and the dissociation phases for the 1.5 mM calcium
FRET-
based calcium biosensor employing troponin C (
Mank et al., 2006
). The external stimulation
frequency was 40 Hz for 2.2 s. Once again, a dual-fractal analysis is required to adequately
describe the kinetics in the binding phase. A single-fractal analysis is adequate to describe the
kinetics in the dissociation phase. The values of (a) the binding rate coefficient,
k
, and the
fractal dimension,
D
f
, for a single-fractal analysis, (b) the binding rate coefficients,
k
1
and
k
2
, and the fractal dimensions,
D
f1
and
D
f2
, for a dual-fractal analysis, and (c) the dissociation
rate coefficient,
k
d
, and the fractal dimension,
D
fd
, in the dissociation phase are given in
Tables 9.7
and
9.8
.
þ
In this case, it is of interest to note that for a dual-fractal analysis as the fractal dimension
increases by a factor of 1.423 from a value of
D
f1
equal to 1.6144 to
D
f2
equal to 2.2976, the
binding rate coefficient decreases by a factor of 0.747 from a value of
k
1
equal to 10.458 to
k
2
equal to 7.808. In this case, an increase in the degree of heterogeneity or the fractal dimension
on the biosensor surface leads to a decrease in the binding rate coefficient.
Figure 9.7d
shows the binding and the dissociation phases for the 10 mM calcium
FRET-
based calcium biosensor employing troponin C (
Mank et al., 2006
). The external stimulation
frequency was 160 Hz for 2.2 s. Once again, a dual-fractal analysis is required to adequately
describe the kinetics in the binding phase. A single-fractal analysis is adequate to describe the
kinetics in the dissociation phase. The values of (a) the binding rate coefficient,
k
, and the
fractal dimension,
D
f
, for a single-fractal analysis, (b) the binding rate coefficients,
k
1
and
k
2
, and the fractal dimensions,
D
f1
and
D
f2
, for a dual-fractal analysis, and (c) the dissociation
rate coefficient,
k
d
, and the fractal dimension,
D
fd
, in the dissociation phase are given in
Tables 9.7
and
9.8
.
þ
In this case, it is of interest to note that for a dual-fractal analysis as the fractal dimension
increases by a factor of 1.44 from a value of
D
f1
equal to 1.9486 to
D
f2
equal to 2.8129, the bind-
ing rate coefficient decreases by a factor of 0.793 from a value of
k
1
equal to 74.568 to
k
2
equal
to 59.148. In this case, an increase in the degree of heterogeneity or the fractal dimension on the
biosensor surface leads to a decrease in the binding rate coefficient.
