Biology Reference
In-Depth Information
common techniques has aimed to set in order the body of practical empirical
knowledge that underlies successful measurements of [Ca
2
þ
] through the use of
fluorescent indicators.
Appendix 1. The fraction of a polybasic acid that exists in a
particular state of protonation
The native forms of the Ca
2
þ
bu
ers and indicators discussed in this chapter are
polybasic acids; that is, they are species with multiple dissociable protons (e.g.,
H
4
EGTA). Almost invariably, the fully deprotonated species is the one that
actually binds Ca
2
þ
with high a
V
nity; therefore it is useful to be able to estimate
the fraction of the indicator or bu
Y
er in solution that actually exists in the fully
deprotonated form. In general, deprotonation of a polybasic acid is characterized
by a sequence of dissociation equilibria. For the specific example of a tetrabasic
acid, H
4
A, the sequence of stepwise dissociation reactions and the corresponding
equilibrium constants are:
V
H
3
A
H
þ
½
½
H
4
A
>
H
þ
þ
H
3
A
K
1
¼
½
H
4
A
H
þ
H
2
A
2
½
H
3
A
>
H
þ
þ
H
2
A
2
K
2
¼
H
3
A
½
H
þ
HA
3
½
H
2
A
2
>
H
þ
þ
HA
3
K
3
¼
H
2
A
2
A
4
H
þ
½
HA
3
>
H
þ
þ
A
4
K
4
¼
HA
3
If we define C
0
to be the total concentration of the acid, irrespective of the state
of protonation, then the fraction that is present as the fully deprotonated,
tetraanionic form, A
4
,is
A
4
a
4
¼
ðA1:1Þ
C
0
To derive a useful expression for
a
4
, we first recognize that the total concentration,
C
0
, encompasses the concentrations of all the possible protonated forms:
þ
þ
H
3
A
H
2
A
2
HA
3
A
4
C
0
¼
½
H
4
A
þ
½
þ
ðA1:2Þ
Because all the concentrations are related to each other through the dissociation
equilibrium constants, K
1
throughK
4
, the concentration of any particular protonated
species can be written in terms of the concentration of any other species. In the
present case, it is convenient to express all the concentrations in terms of [A
4
]:
