Biology Reference
In-Depth Information
where we have omitted valency for simplicity. R (or R
4
) is the form which binds
Ca
2
þ
most avidly and it is convenient to transform
Eq. (1)
to one with an apparent
a
nity constant for Ca
2
þ
(K
0
Ca
) for a given pH
Y
Ca
¼
½
CaR
½
R
0
K
ð3Þ
½
Ca
½
R
½
R
t
½
CaR
or using
Eqs. (1) and (2)
½
R
0
Ca
¼ K
Ca
K
ð4Þ
½þ
R
½
HR
þ
½
H
2
R
þ
½
H
3
R
þ
½
H
4
R
Then it is a simple matter to show that
K
Ca
0
Ca
¼
K
2
3
4
H
þ
H
þ
H
þ
H
þ
1
þ
½
K
H1
½
þ
½
K
H1
K
H2
þ
½
K
H1
K
H2
K
H3
þ
½
K
H1
K
H2
K
H3
K
H4
ð5Þ
where K
H1
-K
H4
are the four acid association constants for the bu
er. Now if we
know K
Ca
, the pH, and K
H1
-K
H4
, we can calculate K
0
Ca
. This K
0
Ca
is thus the
apparent a
V
Y
nity for a given [H] where pH
¼
log10 ([H]/
g
H
), and
g
H
is the activity
cient for protons under the experimental conditions (see below). This K
0
Ca
is
the reciprocal of the dissociation constant, K
d
discussed in the previous section.
Eq. (3)
can also be manipulated to yield
coe
Y
0
Ca
R
½K
0
Ca
CaR
½
CaR
=
½
Ca
¼K
½
ð6Þ
which is the linearization for Scatchard plots of Bound/Free ([CaR]/[Ca]) versus
Bound ([CaR], where slope
[R
t
]). One can also solve for
[CaR] obtaining the familiar Michaelis-Menten form.
¼
-K
0
Ca
and x-intercept
¼
½
R
t
½
CaR
¼
ð7Þ
0
Ca
Ca
1
þ
1
=K
½
Þ
Solving for free [Ca] is more complicated because we do not know [CaR] a priori,
but substituting [CaR]
¼
[Ca
t
]
[Ca] we can get a quadratic solution
2
0
Ca
0
Ca
ð8Þ
Similar equations can be developed for Ca
2
þ
binding to the protonated form (e.g.,
H-EGTA) which also binds Ca
2
þ
with a lower a
½
Ca
þð½
R
t
½
Ca
t
þ
1
=K
Þ½
Ca
½
Ca
t
=K
¼
0
nity (e.g., see
Harrison and Bers,
1987
). For example, when we include Ca
2
þ
binding to the singly protonated form
of EGTA (or HR
3
) the following term must be added to the apparent a
Y
Y
nity
expression on the right-hand side of
Eq. (5)
K
Ca2
ð9Þ
2
H
þ
H
þ
H
þ
H
þ
3
1
=ð
½
K
H1
Þþ
1
þ
½
K
H2
þ
½
K
H2
K
H3
þ½
K
H2
K
H3
K
H4
