Biology Reference
In-Depth Information
Figure 6.14 The simplest reaction scheme for exogenous ligand binding to a
haemoglobin exhibiting endogenous hexacoordination. The axial ligands to the iron
in the starting material, Hb(6c), are the proximal histidine and X (e.g. Tyr B10 in CtrHb
or His E10 in Synechococcus 7002 GlbN). The pentacoordinate state with free distal site is
represented with Hb(5c). L represents an exogenous ligand (e.g. O
2
). The rate constants
are k
X
(s
1
) for the dissociation of X, k
þX
(s
1
) for its association, k
þL
(M
1
s
1
) for the
binding of L, and k
L
(s
1
) for its dissociation. Equilibrium constants are K
X
¼k
þX
/k
X
for
the association of X and K
L
¼
k
þL
/k
L
for the association of L.
histidine in order to bind an exogenous ligand. This additional step in the
binding process renders the evaluation of affinities and rate constants partic-
ularly complex. The simplest overall reaction is represented with two equi-
libria as in
Fig. 6.14
.
Depending on the relative values of the rate constants and the concen-
tration of ligand L, certain simplifications can be made to the equation rep-
resenting the observed changes in concentrations with time, and different
kinetic regimes can be distinguished. Two common assumptions are that
the dissociation of L is very slow (except of course when flashed off ),
and that L is in excess so that its concentration remains practically constant
throughout the course of the experiment (
Hargrove, 2000
). Under those
conditions, the second step is considered irreversible (
k
L
0) and the prod-
k
0
þ
L
is a pseudo first-order rate constant. Solving the set of
differential equations yields three eigenvalues,
l
1
,
l
2
and
l
3
. The first two are
given by
uct
k
þ
L
[L]
¼
q
k
X
þ
1
2
2
k
0
þ
L
l
1
,
2
¼
k
X
þ
k
þ
X
þ
ð
k
þ
X
þ
k
0
þ
L
Þ
4
k
X
k
0
þ
L
and the third,
3
, is 0 by conservation of mass (
Beard & Qian, 2008
). For
example, if
k
þ
X
and
k
X
k
0
þ
L
, the kinetics present a slow phase
corresponding to the product of
k
0
þ
L
by the rapid equilibrium fraction of
Hb(5c). Additional complexity is introduced when the pseudo first-order
approximation does not hold, and all scenarios are possible, depending on
the protein and the chosen conditions for the experiment. Within the
pseudo first-order regime and if the solution conditions (i.e. temperature,
l
