Theoretical Analysis of the Ca 2+ Spark Amplitude Distribution

Abstract

A difficulty of using confocal microscopy to study Ca 2+ sparks is the uncertainty of the linescan position with respect to the source of Ca 2+ release. Random placement of the linescan is expected to result in a broad distribution of measured Ca 2+ spark amplitudes ( a) even if all Ca 2+ sparks were generated identically. Thus variations in Ca 2+ spark amplitude due to positional differences between confocal linescans and Ca 2+ release site are intertwined with variations due to intrinsic differences in Ca 2+ release properties. To separate these two sources of variations on the Ca 2+ spark amplitude, we determined the effect changes of channel current or channel open time—collectively called the source strength, α—had on the measured Ca 2+ spark amplitude histogram, N( a). This was done by 1) simulating Ca 2+ release, Ca 2+ and fluo-3 diffusion, and Ca 2+ binding reactions; 2) simulation of image formation of the Ca 2+ spark by a confocal microscope; and 3) using a novel automatic Ca 2+ 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 Ca 2+-bound fluo-3 is Gaussian, we show the following: 1) variations of Ca 2+ spark amplitude due to positional or intrinsic differences can be separated, and 2) f α ( α) can, in principle, be calculated from the Ca 2+ 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 Ca 2+ 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 Ca 2+ spark amplitude and decay time might be used to distinguish Ca 2+ sparks from different channel populations, noise can render the measured decay times meaningless for small amplitude Ca 2+ sparks.