Biomedical Engineering Reference
In-Depth Information
4.2.1
Complex Formation
Forming stable complexes is a passive action to finish with intruders. The stability
of a complex is characterized by its stability constant
K
stab
and calculated from the
equilibrium concentrations of the reaction between metal ion
M
with valence
nC
and ligand
L
with valence
m
:
mM
C
nL
D M
m
L
n
(4.1)
and the stability constant is expressed by:
ŒM
m
L
n
ŒM
K
stab
D
(4.2)
m
ŒL
n
Equation (
4.2
) has the same limitation as the equilibrium electrochemical potentials
given in Table
C.1
. It is correct only at infinite dilution. For practical purposes, one
should calculate the
conditional constant
, which takes into account activity instead
of concentration and all other reactions co-determining the 'naked' concentration
of the ion (definition of
activity
: see Appendix
C
). If the ligand has one or more acid
functions, e.g., -H
4
, [L] becomes pH dependent:
H
C
::: •
H
C
:
H
4
L
•
H
3
L
C
L
C
(4.3)
K
stab
at pH
The thermodynamic
for the
complex of Ni
2C
with glutathione are, respectively, 10
4:0
and 10
2:1
, not a marginal
difference! Workable stability constants should be calculated for the adequate pH
and taking into account all other competing reactions as well, easy to say but it was
and still is a daunting task. However, there is some light at the end of the tunnel: elec-
tronic databases with stability constants are available and computer programs allow
to model chemical equilibrium systems (IUPAC database for Stability Constants,
modeling programs such as HALTAFALL [
120
], MINAEQ
K
stab
(infinite dilution) and conditional
D 7
(more info available
on Internet); an older but basic comprehensive topic on complex formation is writ-
ten by Ringbom [
121
,
122
], or available in the series on Metal Ions in Biological
Systems, edited by Sigel [
123
]).
The undissociated compound in (
4.3
) was not merely an unbiased choice.
Ethylenediaminetetraacetic acid (EDTA) or its sodium salt has four binding sites
and is quoted as a multidentate or chelating ligand.
2
It remains after more than sixty
years an extremely versatile molecule.
C
2
The term
chelating ligand
comes from the old Greek word
meaning a lobster claw (or
pincette-like object). A cyanide ion CN
is an example of a unidentate ligand, having only one
binding site. EDTA was developed in the 1940s and was soon introduced in the analytical chemistry
lab as a selective titrant for a number of metal ions [124
]. It still is the case today and, moreover,
it found widespread use in medicine (chelation therapy for coronary artery disease, nephrology,
detoxification agent and so on).
K
