THEORETICAL-ANALYSIS OF THE CA2+ SPARK AMPLITUDE DISTRIBUTION

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 di fferences in Ca2+ release properties. To separate these two sources of variations on the Ca2+ spark amplitude, we determined the effect chan ges of channel current or channel open time-collectively called the so urce strength, alpha-had on the measured Ca2+ spark amplitude histogra m, N(a). This was done by 1) simulating Ca2+ release, Ca2+ and fluo3 d iffusion, and Ca2+ binding reactions; 2) simulation of image formation of the Ca2+ spark by a confocal microscope; and 3) using a novel auto matic Ca2+ spark detector, From these results we derived an integral e quation relating the probability density function of source strengths, f alpha(alpha), to N(a), which takes into account random positional v ariations between the source and linescan. In the special, but importa nt, case that the spatial distribution of Ca2+-bound fluo-3 is Gaussia n, we show the following: I)variations of Ca2+ spark amplitude due to positional or intrinsic differences can be separated, and 2) f alpha(a lpha) can, in principle, be calculated from the Ca2+ spark amplitude h istogram since N(a) is the sum of shifted hyperbolas, where the magnit udes of the shifts and weights depend on f alpha(alpha). 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 ampl itude and decay time might be used to distinguish Ca2+ sparks from dif ferent channel populations, noise can render the measured decay times meaningless for small amplitude Ca2+ sparks.