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 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, alpha--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 alpha (alpha), 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 Ca2+ spark amplitude due to positional or intrinsic differences can be separated, and 2) f alpha (alpha) 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 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 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.
Izu
L T
LT
Department of Medicine, University of Maryland School of Medicine, Baltimore 21201, USA.
Wier
W G
WG
Balke
C W
CW
D000814:Aniline Compounds; D000818:Animals; D055592:Biophysical Phenomena; D001703:Biophysics; D002118:Calcium / Q000378:metabolism*; D015220:Calcium Channels / Q000378:metabolism; D005456:Fluorescent Dyes; D018613:Microscopy, Confocal / Q000379:methods / Q000706:statistics & numerical data; D008954:Models, Biological; D008955:Models, Cardiovascular; D009206:Myocardium / Q000166:cytology / Q000378:metabolism; D012519:Sarcoplasmic Reticulum / Q000378:metabolism; D014966:Xanthenes
D000814:Aniline Compounds; D015220:Calcium Channels; D005456:Fluorescent Dyes; D014966:Xanthenes; C059715:Fluo-3; D002118:Calcium