Calcium sparks were studied in frog intact skeletal muscle fibers using a home-built confocal scanner whose point-spread function was estimated to be ∼0.21 μm in x and y and ∼0.51 μm in z. Observations were made at 17–20°C on fibers from Rana pipiens and Rana temporaria. Fibers were studied in two external solutions: normal Ringer's ([K+] = 2.5 mM; estimated membrane potential, −80 to −90 mV) and elevated [K+] Ringer's (most frequently, [K+] = 13 mM; estimated membrane potential, −60 to −65 mV). The frequency of sparks was 0.04–0.05 sarcomere−1 s−1 in normal Ringer's; the frequency increased approximately tenfold in 13 mM [K+] Ringer's. Spark properties in each solution were similar for the two species; they were also similar when scanned in the x and the y directions. From fits of standard functional forms to the temporal and spatial profiles of the sparks, the following mean values were estimated for the morphological parameters: rise time, ∼4 ms; peak amplitude, ∼1 ΔF/F (change in fluorescence divided by resting fluorescence); decay time constant, ∼5 ms; full duration at half maximum (FDHM), ∼6 ms; late offset, ∼0.01 ΔF/F; full width at half maximum (FWHM), ∼1.0 μm; mass (calculated as amplitude × 1.206 × FWHM3), 1.3–1.9 μm3. Although the rise time is similar to that measured previously in frog cut fibers (5–6 ms; 17–23°C), cut fiber sparks have a longer duration (FDHM, 9–15 ms), a wider extent (FWHM, 1.3–2.3 μm), and a strikingly larger mass (by 3–10-fold). Possible explanations for the increase in mass in cut fibers are a reduction in the Ca2+ buffering power of myoplasm in cut fibers and an increase in the flux of Ca2+ during release.

The hypothesis is tested that enhanced green fluorescent protein (EGFP) can be used to quantify the aqueous spaces of living cells, using as a model transgenic Xenopus rods. Consistent with the hypothesis, regions of rods having structures that exclude EGFP, such as the mitochondrial-rich ellipsoid and the outer segments, have highly reduced EGFP fluorescence. Over a 300-fold range of expression the average EGFP concentration in the outer segment was approximately half that in the most intensely fluorescent regions of the inner segment, in quantitative agreement with prior X-ray diffraction estimates of outer segment cytoplasmic volume. In contrast, the fluorescence of soluble arrestin-EGFP fusion protein in the dark adapted rod outer segment was approximately threefold lower than predicted by the EGFP distribution, establishing that the fusion protein is not equilibrated with the cytoplasm. Arrestin-EGFP mass was conserved during a large-scale, light-driven redistribution in which ∼40% of the protein in the inner segment moved to the outer segment in less than 30 minutes.

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SummaryThe relaxation of fluorescence from diffraction-limited sources of photoactivatable green fluorescent protein (PAGFP) or sinks of photobleached enhanced GFP (EGFP) created by multiphoton photo-conversion was measured in solutions of varied viscosity (η), and in live, spherical Chinese hamster ovary (CHO) cells. Fluorescence relaxation was monitored with the probing laser fixed, or rapidly scanning along a line bisected by the photoconversion site. Novel solutions to several problems that hamper the study of PAGFP diffusion after multiphoton photoconversion are presented. A theoretical model of 3D diffusion in a sphere from a source in the shape of the measured multiphoton point-spread function was applied to the fluorescence data to estimate the apparent diffusion coefficient, D ap . The model incorporates two novel features that make it of broad utility. First, the model includes the no-flux boundary condition imposed by cell plasma membranes, allowing assessment of potential impact of this boundary on estimates of D ap . Second, the model uses an inhomogeneous source term that, for the first time, allows analysis of diffusion from sources produced by multiphoton photoconversion pulses of varying duration. For diffusion in aqueous solution, indistinguishable linear relationships between D ap and η −1 were obtained for the two proteins: for PAGFP, D aq = 89 ± 2.4 μm 2 s −1 (mean ± 95% confidence interval), and for EGFP D aq = 91 ± 1.8 μm 2 s −1 . In CHO cells, the application of the model yielded D ap = 20 ± 3 μm 2 s −1 (PAGFP) and 19 ± 2 μm 2 s −1 (EGFP). Furthermore, the model quantitatively predicted the decline in baseline fluorescence that accompanied repeated photobleaching cycles in CHO cells expressing EGFP, supporting the hypothesis of fluorophore depletion as an alternative to the oft invoked 'bound fraction' explanation of the deviation of the terminal fluorescence recovery from its pre-bleach baseline level. Nonetheless for their identical diffusive properties, advantages of PAGFP over EGFP were found, including an intrinsically higher signal/noise ratio with 488-nm excitation, and the requirement for ∼1/200th the cumulative light energy to produce data of comparable signal/noise.

In the OOA, refractive error is highly heritable. Hyperopia and myopia aggregate strongly in OOA families.

Quasi-least squares (QLS) is a two-stage computational approach for estimation of the correlation parameters in the framework of generalized estimating equations. We prove two general results for the class of mixed linear correlation structures: namely, that the stage one QLS estimate of the correlation parameter always exists and is feasible (yields a positive definite estimated correlation matrix) for any correlation structure, while the stage two estimator exists and is unique (and therefore consistent) with probability one, for the class of mixed linear correlation structures. Our general results justify the implementation of QLS for particular members of the class of mixed linear correlation structures that are appropriate for analysis of data from families that may vary in size and composition. We describe the familial structures and implement them in an analysis of optical spherical values in the Old Order Amish (OOA). For the OOA analysis, we show that we would suffer a substantial loss in efficiency, if the familial structures were the true structures, but were misspecified as simpler approximate structures. To help bridge the interface between Statistics and Medicine, we also provide R software so that medical researchers can implement the familial structures in a QLS analysis of their own data.

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