Biomedical Engineering Reference
In-Depth Information
Table 1. Bilirubin - albumin binding constant (HSA human serum albumin, BSA
bovine serum albumin)
pH
T (°C)
High affinity sites
Low affinity sites
Reference
(M
-1
)
(M
-1
)
410
9
HSA
7.4
4
-
Gray et al., 1978
1.410
8
510
5
(a)
HSA
7.4
37
Jacobsen et al.,1977
310
6
1.410
5
(b)
HSA
8.5
24
Beaven et al.,1973
9.510
7
HSA
7.4
-
-
Petersen et al.,2000
6.810
7
4.510
6
÷510
6
(c)
HSA
7.4
-
Ostrow et al., 1994
1.310
8
2.410
6
(d)
HSA
-
5
Berde et al.,1979
1.210
8
4.910
6
(d)
HSA
-
23
Berde et al. 1979
6.410
7
2.610
6
(d)
HSA
-
37
Berde et al. 1979
510
7
−710
7
410
6
−510
6
BSA
7.4
25
Blauer et al.,1997
(a) Two sites at low affinity
(b) A third site is considered for high values of ionic strength
(c) A lot of low affinity sites in the range reported
(d) A third site is also considered
!
Μ
AB
2
−Μ
AB
−Μ
0
B
RT
C
AB
2
C
AB
C
B
K
2
= exp
=
(4)
where
C
B
,
C
A
are the free bilirubin and albumin concentration,
C
AB
and
C
AB
2
are the 1:1
and 1:2 albumin-bilirubin complex concentrations and
Μ
I
is the chemical potential of pure
component
i
at the temperature and pressure of the system. Values of the binding constants
reported in the literature (see Tab. 1) vary in a quite wide range; in any case,
K
1
values
in the range
10
7
−10
8
M
−1
and
K
2
values at least one order of magnitude lower are
widely accepted. On this basis, the formation of complexes involving secondary sites can
be neglected and only binding reaction (1) will henceforth be considered.
With this assumption, the fraction of unbound bilirubin can be calculated from total
albumin and bilirubin concentrations (
C
ALB
and
C
BIL
, respectively) by coupling equation (3)
with the following mass balance equations
C
BIL
= C
AB
+ C
B
(5)
C
ALB
= C
AB
+ C
A
(6)
In clinically interesting conditions
K
1
C
BIL
≫1
and, as far as
C
ALB
> C
BIL
, the unbound
fraction of bilirubin can be approximated as follows:
C
B
C
BIL
≈
1
K
1
(C
ALB
−C
BIL
)
≪1
(7)
Therefore, virtually all the bilirubin is present in the solution as AB complex (for example,
less than 1% of bilirubin is in the unbound form if the difference
C
ALB
−C
BIL
is greater than
10
−6
M), so that it may further be assumed that
C
AB
≈C
BIL
;
C
A
≈C
ALB
−C
BIL
(8)
