Chemistry Reference
In-Depth Information
The expression t = t
0
·
K
allows us to correlate the stability constant of complex
formation to the lifetime of the complex. Thus, the principal concept of molecular
biophysics regarding biomolecules:
structure - dynamics - function
can be reformu-
lated as:
structure - stability - function
. One may notice that such an approach highly
simplifi es and widens the time interval (from 10
− 10
s to 10
5
- 10
6
s and more) for inves-
tigating dynamic characteristics of macromolecules. A detailed description of the
derivation of formulae (2.2) is given in reference
28
.
2.2.2 Stability Constants of DNA - M
2+
Complexes
Stability Constants Determined by Graphical Methods Based on
Adsorption Isotherms
Different methods suitable for calculation of stability constants have been devel-
oped, for the most part based on linearization procedures of the law of mass
action.
38,39
The improvement of computer technology led to the development of
nonlinear curve fi tting algorithms;
40,41
among these the Scatchard and Klotz methods
have been widely used to analyze experimental data.
42,43
Let us describe, as an example, various models of Pb
2+
binding to DNA using
modifi ed Scatchard plots and two types of the Klotz graphical representation. Figure
2.1A shows the Scatchard plot. The intersection of the curves with the abscissa gives
the value
n
=
n
1
+
n
2
(
n
is the number of binding sites for Pb
2+
per phosphate group
of DNA at saturation). The intersection of the curves with the ordinate gives the
value of the binding constant (
K
):
Kn
=
k
1
n
1
+
k
2
n
2
.
43
The parameters are calculated
by the nonlinear least-squares fi t to the equations:
( ) +
( ) +
( )
rm
=
05
.
Br
B r
2
4
Cr
( )=+−+
(
)
Br
kn
kn
k
k r
11
2 2
1
2
( ) =
(
)
Cr
kkrn
+
n
−
r
12
1
2
Figure 2.1B illustrates the Klotz method with intercepts
a
1
,
a
2
,
a
3
,
a
4
for variables
r/m
and
r
, where two independent classes of binding sites are assumed.
anknk
ann
ank
=+
=+
+
1
1
1
2
2
2
1
2
System:
(
)
=
2
nk
22
2
a
1
2
31
(
nk
+
nk a
)
=
akk
2
12
21
4
2
12
It is seen from Table 2.2
44
that the parameters determined by the Klotz and
modifi ed Scatchard analysis methods are almost identical. Consequently, it can be
assumed that both models can be used to determine binding constants of Pb
2+
to
DNA. Based on the c
2
test, the Scatchard method (c
2
= 0.81) seems to give a better
estimate than the Klotz method (c
2
= 3.08).
45
