Biology Reference
In-Depth Information
a natural tendency to regard the relative change in intensity as reflecting an
equivalent relative change in [Ca
2
þ
]. For example, a doubling of intensity relative
to baseline (F/F
0
¼
1) is often used to infer a doubling of [Ca
2
þ
]. Such
an inference should never be made because it is always incorrect. A quantitative
analysis is presented below.
As shown in
Appendix 2
, the total fluorescence, F
T
, emitted by a solution of
Ca
2
þ
indicator is governed by the expression
2or
D
F/F
0
¼
F
T
/ Q
CaIn
e
CaIn
f
CaIn
þ Q
In
e
In
1
ð
f
CaIn
Þ
ð3Þ
ciencies of the Ca
2
þ
-bound
and Ca
2
þ
-free forms of the indicator, respectively,
e
CaIn
and
e
In
are the extinction
coe
where Q
CaIn
and Q
In
are the fluorescence quantum e
Y
cients of the two forms of the indicator at the excitation wavelength, and f
CaIn
is the fraction of the indicator that is in the Ca
2
þ
-bound form. Knowing that
f
CaIn
¼
Y
[Ca
2
þ
]/([Ca
2
þ
]
þ
K
d
), we can rewrite the expression to show its dependence
on [Ca
2
þ
] more explicitly:
Ca
2
þ
F
T
/ Q
In
e
In
þ Q
CaIn
e
CaIn
Q
In
e
In
ð
Þ
þ K
d
ð4Þ
Ca
2
þ
The only variable in the expression is [Ca
2
þ
]; all other parameters, being intrinsic
characteristics of a particular indicator, are constants. The above expression shows
that whereas [Ca
2
þ
] can range from 0 to any arbitrary positive value, the total
fluorescence, F
T
is bounded. This behavior is shown in
Fig. 13
. When [Ca
2
þ
]
0, all
of the indicator is Ca
2
þ
-free, and the fluorescence has a minimum value that
depends on the intrinsic brightness (Q
In
e
In
) of the Ca
2
þ
-free form of the indicator.
At saturating [Ca
2
þ
] ([Ca
2
þ
]
¼
K
d
), all of the indicator is Ca
2
þ
-bound, and the
fluorescence has a maximum value that depends on the intrinsic brightness
(Q
CaIn
e
CaIn
) of the Ca
2
þ
-bound form of the indicator. Once the indicator molecules
are saturated, further increasing [Ca
2
þ
] brings no increase in fluorescence. There-
fore, as can be seen from
Eq. (4)
and
Fig. 13
, fluorescence intensity is a nonlinear
function of [Ca
2
þ
]. This nonlinearity is the reason that a relative change in indica-
tor fluorescence does not imply an equal relative change in [Ca
2
þ
].
Figure 13
shows
that the discrepancy depends on the extent to which the indicator is already bound
to Ca
2
þ
: Starting from a relatively low [Ca
2
þ
], increasing [Ca
2
þ
] by an increment,
D
Ca
1
, results in a fluorescence increase,
D
F
1
. From the now-higher [Ca
2
þ
], a
further identical increment of
D
Ca
2
(
¼D
Ca
1
) brings a much smaller fluorescence
increase,
D
F
2
.
The error in using relative fluorescence changes to infer relative [Ca
2
þ
] changes
can be analyzed quantitatively for a specific example. Fluo-4 is a nonratiometric
indicator that is commonly used with 488-nm excitation. The extinction coe
Y
cient
binding Ca
2
þ
of Fluo-4
changes
only
by
a
few percent
upon
77,000 M
1
cm
1
at 488 nm); the Ca
2
þ
-bound form is at least 100
times more fluorescent than the Ca
2
þ
-free form (Q
CaIn
¼
(
e
In
e
CaIn
¼
0.14, Q
In
0.0014); and
345 nM. The quantitative relationship between [Ca
2
þ
] and fluorescence can
K
d
¼
