Biology Reference
In-Depth Information
where K
Ca2
is the Ca
2
þ
association constant for the chelator in the singly proto-
nated form, HR. This provides some basics of the relationships for a single
chelator. However, more complicated solutions have multiple equilibria (e.g.,
other cations that bind EGTA and other Ca binding moieties) which cannot be
readily solved simultaneously in an analytical manner.
It should, however, be noted that it is simpler to go from free [Ca
2
þ
] to [Ca
t
],
especially with no Ca
2
þ
competitors. This is because all of the chelators which
might bind Ca
2
þ
will be in equilibrium with the same free [Ca
2
þ
]. Thus, one could
simply use a series of equations like
Eq. (7)
for di
erent chelators if you know the
values on the right-hand side. Then you can simply add up free [Ca
2
þ
] plus the
[CaR] values from the chelators to obtain the [Ca
t
]. If free [Ca
2
þ
] is not known
(or chosen) it requires multiple versions of equations like
Eq. (8)
to be solved
simultaneously. Thus, iterative computer programs are useful (see below).
V
B. Temperature, Ionic Strength, and pH Corrections
While the above explains the theoretical basis for calculating the pH e
ect on
K
0
Ca
, we should clarify how we normally correct for temperature, ionic strength,
and pH for the experimental conditions used. Again, those not interested in the
details can skip this section. Thus, the final apparent a
V
nity (or K
0
Ca
) should
include correction for temperature and ionic strength as well as pH. Indeed, both
proton a
Y
nity constants (e.g., K
Ca
) should be ad-
justed for the experimental temperature and ionic strength before adjusting for pH
as above.
Y
nity (K
H1
-K
H4
) and metal a
Y
1. Temperature Corrections
The standard way to correct equilibrium constants for changes in temperature
depends on knowledge of the enthalpy (
D
H) of the reaction.
0
0
log
10
K
¼ log
10
K þ D
H1
=T
1
=T
=
ð
2
:
303
R
Þ
ð10Þ
where temperature, T is in
K,
D
H is in kcal/mol and R is 1.9872
10
3
kcal/
(mol
K). Unfortunately, the
D
H values are not known for all the constants we
might like. For example, for EGTA they are known for the first two acid associa-
tion constants (K
H1
and K
H2
) and the higher a
nity Ca
2
þ
constant (K
Ca1
). This is
Y
generally su
cient for calculations with EGTA (see
Fig. 3
A). However, no
D
H
values have been reported for individual constants for BAPTA and Br
2
-BAPTA.
Harrison and Bers (1987)
measured the temperature dependence of the apparent
K
0
Ca
for BAPTA and Br
2
-BAPTA. We have fit that data, varying the value of the
D
H for K
Ca
. This is somewhat empirical because there is likely to also be tempera-
ture dependence of K
H1
-K
H4
. However, the data was well described using
D
H
values (for K
Ca
) of 4.7 and 5.53 kcal/mol for BAPTA and Br
2
-BAPTA, respectively
(see
Figs. 4 and 5
). Also, since BAPTA and Br
2
-BAPTA are almost completely
Y
