Theoretical analysis of the Ca2+ spark amplitude distribution

Leighton T. Izu, W. Gil Wier, C. William Balke

Research output: Contribution to journalArticlepeer-review

68 Scopus citations


A difficulty of using confocal microscopy to study Ca2+ sparks is the uncertainty of the linescan position with respect to the source of Ca2+ release. Random placement of the linescan is expected to result in a broad distribution of measured Ca2+ spark amplitudes (a) even if all Ca2+ sparks were generated identically. Thus variations in Ca2+ spark amplitude due to positional differences between confocal linescans and Ca2+ release site are intertwined with variations due to intrinsic differences in Ca2+ release properties. To separate these two sources of variations on the Ca2+ spark amplitude, we determined the effect changes of channel current or channel open time collectively called the source strength, α - had on the measured Ca2+ spark amplitude histogram, N(a). This was done by 1) simulating Ca2+ release, Ca2+ and fluo-3 diffusion, and Ca2+ binding reactions; 2) simulation of image formation of the Ca2+ spark by a confocal microscope; and 3) using a novel automatic Ca2+ spark detector. From these results we derived an integral equation relating the probability density function of source strengths, f(α)(α), to N(a), which takes into account random positional variations between the source and linescan. In the special, but important, case that the spatial distribution of Ca2+-bound fluo-3 is Gaussian, we show the following: 1) variations of Ca2+ spark amplitude due to positional or intrinsic differences can be separated, and 2) f(α)(α) can, in principle, be calculated from the Ca2+ spark amplitude histogram since N(a) is the sum of shifted hyperbolas, where the magnitudes of the shifts and weights depend on f(α)(α). In particular, if all Ca2+ sparks were generated identically, then the plot of 1/N(a) against a will be a straight line. Multiple populations of channels carrying distinct currents are revealed by discontinuities in the 1/N(a) plot. 3) Although the inverse relationship between Ca2+ spark amplitude and decay time might be used to distinguish Ca2+ sparks from different channel populations, noise can render the measured decay times meaningless for small amplitude Ca2+ sparks.

Original languageEnglish
Pages (from-to)1144-1162
Number of pages19
JournalBiophysical Journal
Issue number3
StatePublished - Sep 1998


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