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Upper bound
Q CaIn ε CaIn
Δ
F 2
Δ F 1
Lower bound
Q In ε In
0
0
[Ca 2+ ]
Fig. 13 Indicator fluorescence intensity is a nonlinear function of [Ca 2 þ ]. At [Ca 2 þ ] ¼ 0, all indica-
tor molecules in solution are in the Ca 2 þ -free form, and indicator fluorescence is at the lower
bound. Whereas [Ca 2 þ ] can range from 0 to any arbitrarily large value, indicator fluorescence
cannot exceed an upper bound, which is reached when all indicator molecules in solution are in
the Ca 2 þ -bound form. The relationship between fluorescence intensity and [Ca 2 þ ] is hyperbolic.
The consequence is that successive equal increments in [Ca 2 þ ] do not result in equal increments of
fluorescence intensity (compare the fluorescence increments D F 1 and D F 2 resulting from two equal
increments in [Ca 2 þ ]).
be calculated by using these parameters in Eq. (4) . Figure 14 shows the relative
change in Fluo-4 fluorescence for di
erent increments in [Ca 2 þ ], up to a 10-fold
V
change ([Ca 2 þ ]/[Ca 2 þ ] 0 ¼
10). Because resting [Ca 2 þ ] i is typically in the range 50-
100 nM, the starting [Ca 2 þ ] was assumed to be [Ca 2 þ ] 0 ¼
75 nM for the calculation.
Figure 14 shows clearly that the relative change in fluorescence is never a good
measure of the true relative change in [Ca 2 þ ]. F/F 0 significantly underestimates
[Ca 2 þ ]/[Ca 2 þ ] 0 , and the error increases severely as the change in [Ca 2 þ ] becomes
larger.
VII. Measuring [Ca 2 þ ] in Mitochondria
As mentioned in Section II , when cells are incubated with the AM ester of
Rhod-2, the indicator preferentially loads into mitochondria. The structures of
two fluorescent dyes, TMRM and TMRE, which also accumulate preferentially
into mitochondria, and Rhod-2 AM are shown in Fig. 15 A. The positively charged
structure in these molecules that enables preferential loading into mitochondria
is highlighted with thick lines in Fig. 15 A. Figure 15 B shows that, rather than
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