Fig 1.
Left: A typical axospinous synapse (in the lower right-hand region of the electron micrograph). An axon terminal packed with small round vesicles of neurotransmitter (right) is closely apposed to a dendritic spine; at the junction a slightly increased electron density on the presynaptic plasma membrane (‘presynaptic active zone’) is precisely matched across the about 30 nm wide synaptic cleft by a dark extension into the dendritic spine, the ‘postsynaptic density.’ This synapse is perforated (the slight break in increased density halfway along the synapse). The membranous structure within the spine head is a ‘spine apparatus.’ Because of a fortunate plane of section, the plasma membrane of this spine is continuous with its parent dendritic shaft (left edge of photo), which contains longitudinally-sectioned microtubules. The scale bar represents 500 nm. Right: Cartoon diagramming the molecular architecture of an excitatory PSD-95-expressing synapse [19]. Basic biological knowledge about synapse structure and protein composition as depicted in this figure is used to inform the proposed query-based probabilistic algorithm.
Fig 2.
Three 1.277 μ m ×1.186 μ m images showing conjugate EM and IF data. The left panel has synapsin (green) and PSD-95 (red) data overlaid, marked by the colored boundary lines. The scale bar represents 500 nm. The presence of both presynaptic and postsynaptic channels indicates the presence of a synapse with high probability. The center panel shows the PSD-95 IF image and the right panel shows the synapsin IF image. On both images, the EM-identified synaptic cleft is marked by a blue box. While the proposed synapse detection method uses multiple synaptic markers, only two are shown here for visualization purposes.
Fig 3.
Fundamental steps of the proposed probabilistic synapse detection algorithm.
Fig 4.
These cumulative histograms show that typically ∼98% of voxels in the dataset lie below the threshold line indicated in red. The threshold lines are estimates based on visual inspection of the data.
Fig 5.
Cutout of size 2261×2501 pixels or 5.268×5.827μ m of the logarithm (for visualization purposes) of the IF raw data (left) and the corresponding image of the foreground probability map (right) of one slice of the PSD-95 antibody. The proposed approach clearly differentiates the high probability bright pixels from the background low probability pixels. The ‘dark’ rings around the puncta are an artifact of the deconvolution performed prior to image alignment, and its spatial extent has been taken into account in the spatially-oriented next steps of the algorithm. The AT data appears ‘quantized’ because it has been upsampled from its native 100 nm per pixel resolution to 2.33 nm per pixel to align the AT data with the EM data.
Fig 6.
The image on the left is the output from step one, a portion of a single slice of PSD-95 where each pixel codes the probability that it represents signal, not noise. The image on the right is the result of the corresponding probability map of each pixel belonging to a 2D punctum. Both images are cutouts of size 2261 × 2501 pixels or 5.268 × 5.827μ m.
Fig 7.
Top: Three consecutive slices of 2D puncta probability, given by Eq (3). Bottom: Factor image given by Eq (4) (left) and the corresponding 3D puncta probability, given by Eq (5), (right) of the center slice in the top row. Only those 2D puncta that actually span multiple slices are kept with high intensity (probability) in the combined result (bottom right). The green arrow points to an example of a probable punctum that spans multiple slices. The red arrow points to an example of a relatively-less probable punctum which does not span multiple slices and therefore is diminished in the output image. Each image is a cutout of size 2261 × 2501 pixels or 5.268 × 5.827μ m.
Fig 8.
Presynaptic and postsynaptic puncta adjacency.
The first row contains a cutout showing a PSD-95 punctum with a pixel highlighted in the center of the image. The second row contains synapsin cutouts with the search grid overlaid. For this example, K = 3, so shown is a 3 × 3 grid spanning 3 slices is shown. The brightest box is highlighted in green. Thus, the output value of the synaptic probability map at the pixel specific in the PSD-95 image is the average pixel value of the green box multiplied by the intensity value of the PSD-95 pixel.
Fig 9.
The output of the method, as described in Eq 8, where value at each voxel is the probability it belongs to a specific synapse subtype. Cutout of size 2261 × 2501 pixels or 5.268 × 5.827μ m.
Table 1.
Synaptic markers used in this work across the various datasets.
Not all markers were present in each dataset. Details, including the order of antibody application, can be found in [8] and [19].
Table 2.
The cAT datasets used for analysis [8].
Table 3.
Excitatory synapse detection queries for the cAT data.
Note that the size dimension in x, y correspond to the window width W in Eq (3) and the z range corresponds to the number of slices, j, mentioned in Eq (4).
Table 4.
Inhibitory synapse detection queries for the cAT data.
Table 5.
Results of excitatory and inhibitory synapse detection.
Precision is defined as the number of true positives detections / (true positive detections + false positive detections). Recall is defined as the number of true synapses detected / (true synapses detected + missed synapses). The value after the precision-recall values is the 95% confidence interval as computed by the Agresti-Coull method [23].
Fig 10.
The relationship between the precision and recall values across a series of thresholds for each cAT dataset. As detailed in the text, the threshold is for validation purposes, since the proposed framework outputs a confidence/probability.
Table 6.
State-of-the-art detection results for excitatory synapses from [8].
The value after the precision-recall values is the 95% confidence interval as computed by the Agresti-Coull method [23].
Fig 11.
Synaptogram showing the distribution of IF data for an EM identified synapse. Each column represents a single slice of data in the z direction, for a total of six slices. The first row (from the top) shows a manually labeled synaptic cleft, as identified in the EM volume. The EM data was used only for validation, since the method operates solely on the IF data. The second row shows the thresholded output of the proposed method, circled in red. Rows 3-6 show the corresponding foreground probability maps for each channel. PSD-95 is Postsynaptic Density 95, VGluT1 is Vesicular Glutamate Transporter 1, and NR1 is N-methyl-D-aspartate Receptor 1. PSD-95 and NR1 are both postsynaptic markers and tend to co-localize, while synapsin and VGluT1 are both presynaptic markers and tend to co-localize. The last row in the first panel shows the corresponding EM data. Each ‘block’ is 1.221μm × 1.233μm. The bottom panel shows enlarged, consecutive slices of the EM data, which was used to manually annotate the synapse. The scale bar on the lower left side is 500 nm.
Fig 12.
Synaptogram showing a ‘false positive.’ Presynaptic and postsynaptic proteins are visible and experts would often label this a synapse presented with IF data alone, but no synapse was identified in the corresponding EM section. The algorithm makes the same mistake as a human expert. Each ‘block’ is 1.069μ m ×1.011μ m. As before, the bottom panel shows enlarged, consecutive slices of the EM data, which was used to manually annotate the synapse. The scale bar on the lower left side is 500 nm.
Fig 13.
Synaptogram showing a ‘false negative.’ While the corresponding EM sections shows a synapse, there is insuficient synaptic IF signal available to justify the presence of a synapse using solely IF data. Again, the algorithm makes the same mistake a human expert would make when working only with the IF data. Each ‘block’ is 1.086μ m ×1.130μ m. As before, the bottom panel shows enlarged, consecutive slices of the EM data, which was used to manually annotate the synapse. The scale bar on the lower left side is 500 nm.
Table 7.
Excitatory synapse detection queries for the AT data.
Table 8.
Inhibitory synapse detection queries for the AT data.
Fig 14.
Top Left: Histogram of a slice of the probability map. Top Middle: Thresholded probability map, see text for details on the threshold selection. Top right: Probability map of one slice of a 13 μ m ×17 μ m region of the AT data on [19]. Bottom Row:. A series of pseudo-color images indicating the presence of the receptors PSD-95 (red), VGluT1 (blue), and synapsin (green) across three consecutive slices. Centroids of detected synapses containing all three receptors (query) are circled in black.
Fig 15.
Plots showing the variation of putative synapse density across different thresholds. In this first row, each curve represents a dataset in [19] and the red lines show the expected synaptic density. For excitatory synapses, the expected density is 0.9 synapses μ m3 ± 0.15μm3. For inhibitory synapses, the expected density is 0.1 synapses μ m3 ± 0.05μm3 [28] [29]. The first row shows the relationship between density and the threshold for each dataset, while the second row shows the average density of all the datasets as a function of the threshold. The error bars represent the standard error.
Fig 16.
Mouse barrel cortex layer density differences.
Plots showing the difference in synaptic density between Layer IV and Layer V for specific queries. The first two rows show the difference in density for each dataset. The last two rows show the average difference in density across all the datasets. The error bars represent the standard error. Each dataset was thresholded using the ‘optimal’ threshold value as determined from Fig 15.