Assessing Cardiomyocyte Excitation-Contraction Coupling Site Detection From Live Cell Imaging Using a Structurally-Realistic Computational Model of Calcium Release

Figures

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  Figure 1. Finite element model of Ca2+ reaction-diffusion in an eight sarcomere section of a cardiomyocyte. (A) From an electron tomography imaging stack, myofibril and mitochondria regions were segmented from a slice at the depth of a z-disk. (C) This geometry was extruded 16 μm (in the direction shown as z here) to create a three-dimensional eight-sarcomere model. Mitochondrial regions shown in yellow; red volume indicates the myofibrillar and cytosolic region. (B) Statistical analysis of immuno-labeled microscopy data (RyR clusters shown in green) was used to determine inter-cluster spacing distributions. (D) RyR cluster locations in the model were defined at mitochondrial and myofibrillar border regions based on statistical spacing distributions. (E) A reaction-diffusion finite element model simulates the release of Ca2+ from the RyR clusters during the rising phase (first 30 ms) of the Ca2+ transient. Volume rendering of the fluorescence-bound Ca2+ (FCa) field shown at t = 15 ms.

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  Figure 2. Simulation of confocal fluorescence microscopy images from FE model results. (A) FE FCa field data (see Figure 1E) interpolated onto a regular grid with 53.75 nm resolution in each coordinate direction. Three-dimensional convolution of the interpolated FCa data with a (B) point spread function (PSF) produces blurring typical of confocal fluorescence microscopy data. (C) Blurred data resampled at a pixel resolution of 215 nm within the 22 simulated two-dimensional imaging planes in the volume. (A,C) are shown at a single time point, t = 15 ms.

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  Figure 3. Example of CaCLEAN detection and classification against modeled locations. (A) Simulated confocal fluorescence microscopy image at t = 15 ms for the densely packed cluster case (N = 123 per z-disk) with mitochondria. This represents one slice from the middle of the stack shown in Figure 2C. Modeled RyR cluster center locations within 280 nm of the imaging plane shown in magenta (also in B,C). (B) CaCLEAN map of the fluorescence signal. (C) Segmented clusters detected by CaCLEAN. (D) Statistical classification of detected cluster locations vs. actual (ground truth) modeled locations. Modeled release sites are represented by filled dots and detected sites are open circles. A correct detection is therefore represented by a green dot surrounded by a blue circle, while false positives (detection errors) are red circles and false negatives (missed modeled locations) are red dots.

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  Figure 4. Illustration of the admissible window parameter. The admissible window defines the distance tolerance from the simulated imaging plane for RyR cluster centers to be considered ground true positives. (A) Statistical classifier CaCLEAN results as a function of the admissible window for low cluster density, no mitochondrial barriers (case 3). Twenty two images were simulated with equidistant spacing through the model volume. Solid lines represent mean values and shaded regions indicate one standard deviation of values. Figure S1 shows similar results across the four model permutations. In (B–D) an example image slice is shown, with clusters considered TP (ground truth) for admissible windows of (B) 300 nm, (C) 640 nm, and (D) 1,000 nm in magenta. An oblique view is shown above, along with FCa model results at t = 15 ms. Below, an axial view perpendicular to the imaging plane is shown (looking through the modeled volume, with clusters outside the admissible window shown in white). The admissible window is indicated in pink shading.

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  Figure 5. Recall and precision of CaCLEAN applied to simulated microscopy data. Recall, precision and f1-score evaluated based on classification results. Shaded regions indicate one standard deviation of recall and precision values. The f1-score shown is evaluated based on the mean values for precision and recall (solid red and blue lines). In both cases shown, regions representing mitochondria act as barriers to diffusion. (A) A minimum spacing of 1 μm is enforced between modeled clusters of RyRs. (B) Cluster spacing is determined by statistical analysis of RyR cluster distributions from immuno-labeled super-resolution microscopy data.

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  Figure 6. Precision-recall curve for CaCLEAN in four models. Recall and precision mean values from results shown in Figure 5 plotted as a precision-recall curve. Higher values indicate better performance in each axis. Dashed line indicates the precision-recall break-even point, where recall = precision.

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  Figure 7. “Differential recall”: axial dependence of detection of true positive sites. Each curve shows the fraction of detected sites as a function of the distance z from the nominal focal plane. Differential recall at distance z is the fraction of all detected to modeled sites within 5 nm of that z depth i.e., within a 10 nm band centered about the distance z above and below the focal plane. A value of 1 is equivalent to the detection of all sites at a given z-depth. The various curves are calculated for different models, having a high or low density of sites and either using homogeneous diffusion (“no mito”) or obstacles to diffusion wherever mitochondria are (“with mito”). Data points shown are the result of applying a smoothing filter (see Figure S5 for the low density, no mito case shown in light brown). Solid lines indicate single-term Gaussian fits to the filtered data.