Biomedical Engineering Reference
In-Depth Information
short-term regime from the long term regime. The short-term regime is the one in which the
anomalous diffusion applies. At the end of the short term interval (
t
t
c
), the self-similarity
of the system is lost, the surface is homogeneous, and regular diffusion applies.
¼
Pfeifer and Obert (1989)
state that the application of the above equation is contingent on the:
(a) analyte being uniformly distributed in the solution at time
t
equal to zero,
(b) binding being irreversible and first-order (
N
equals the number of analyte particles that
have reached the receptors), and
(c) binding occurring whenever an incoming analyte particle hits a receptor surface for the
first time. In other words, the “sticking” probability is one.
It is perhaps difficult to imagine any one or all of these conditions being satisfied for analyte-
receptor binding interactions occurring in continuous-flow reactors.
Given the extremely small volume of the flow channels there is a high probability of the
mixing of the analyte not being proper. This in turn may lead to analyte depletion in the flow
channel. Also, the binding cannot be assumed to be irreversible in all instances. There may be
cases of extremely fast binding and dissociation, especially for analytes with low affinity,
which can dissociate in the continuously flowing buffer without any regeneration reagent.
Condition (c) may be satisfied. However, it does not include the “sticking” probability in that
each collision leads to a binding event. Also, the presence of nonspecific binding, avidity
effects, and binding with reactions or binding of dissociated analytes may interfere with con-
dition (c) being satisfied. Furthermore, the equation makes assumptions about the number of
active sites, and the immobilized receptors. For example it states that the analyte binds to one
specific active site. The receptor cannot bind to more than one analyte molecule at a time
(1:1 binding). The equilibrium dissociation rate coefficient,
K
D
k
diss
/
k
assoc
can be calcu-
lated using the above models. The
K
D
value is frequently used in analyte-receptor reactions
occurring on biosensor surfaces. The ratio, besides providing physical insights into the
analyte
¼
receptor system, is of practical importance as it may be used to help determine
(and possibly enhance) the regenerability, reusability, stability, and other biosensor perfor-
mance parameters.
K
D
has the unit (sec)
[
D
f,diss
D
f,assoc
]/2
. This applies to both the single- as well
as the dual-fractal analysis. For example, for a single-fractal analysis,
K
D
has the units (sec)
[
D
fd
D
f
]/2
. Similarly,
for a dual-fractal analysis,
the affinity,
K
D1
has the units (sec)
[
D
fd1
D
fassoc1
]/2
[
D
fd2
D
fassoc2
]1/2
. Note the difference in the units of
the equilibrium dissociation rate coefficient obtained for the classical as well as the fractal-
type kinetics. Though the definition of the equilibrium dissociation rate coefficient is the
same in both types of kinetics (ratio of the dissociation rate coefficient to the association rate
coefficient), the difference(s) in the units of the different rate coefficients eventually leads to
a different unit for the equilibrium dissociation rate coefficient in the two types of kinetics.
This is not entirely unexpected as the classical kinetic analysis does not
and
K
D2
has the units (sec)
include the
