Chemistry Reference
In-Depth Information
Table 1 Mean activity factors in sea water (3.5% salinity) at 298 K from
experiment
5,6
and simulation
7
Salt
g
(experimental)
g
(simulated)
Na
2
SO
4
0.37
0.37
K
2
SO
4
0.35
0.36
NaCl
0.67
0.67
KCl
0.66
0.66
CaSO
4
0.14
0.15
Let us take the calcium ion binding to the small chelator 5,5
0
-Br2BAPTA as
an example:
8
K
s
z}|{
c
ChCa
c
Ch
c
Ca
2
þ
g
ChCa
g
Ch
g
Ca
2
þ
:
Ch
þ
Ca
2
þ
Ð
ChCa
;
K
¼
ð
8
Þ
Since K is a true constant, we can write a relation between the stoichiometric
binding constants at two different salt concentrations as
g
ChCa
g
Ch
g
Ca
2
þ
g
I
ChCa
g
I
Ch
g
I
Ca
2
þ
K
s
¼
K
II
s
:
ð
9
Þ
The charge of the chelator (Ch) is -4e at neutral pH, and it is assumed to have a
radius of 7 A
˚
. When calcium ion is bound to the chelator it is simply modelled
by a reduction of the chelator charge from
4e to
2e. This simple model
captures the salt dependence from 1 mM to 1 M. Table 2 shows how the
stoichiometric binding constant K
s
varies with salt concentration. Both the
simulated and the DH results are in excellent agreement with experiment.
A quantitatively more correct alternative is to use the so-called Tanford-
Kirkwood (TK) model.
9
This takes the detailed charge distribution into
account and solves the electrostatic problem using a variant of the DH
approximation. The final result is the free energy for the macromolecule in a
salt solution. For a not too highly charged macromolecule, this is usually a very
efficient and reliable approach and the relevant equations are easily evaluated
numerically. Figure 3 shows how the calcium-binding constant to the small
protein calbindin D
9k
varies with salt concentration.
10
Both simulated and TK
results are based on the detailed charge distribution of the protein with the
calbindin structure obtained from an X-ray study.
11
The agreement between
the two theoretical approaches is excellent and so is the comparison with the
experimental results.
It is worthwhile to investigate the limitations of the TK approach, as one
should expect deviations from the simulated values for a really highly charged
protein. This is indeed the case, and Figure 4 reveals typical behaviour for the
binding of a charged ligand to an oppositely charged macromolecule or
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