Fig 1.
Tracing and feature extraction of the PVD neuron.
A. A maximum projection image of the PVD neuron in a young-adult wild-type C. elegans expressing fluorescent Kaede. A = anterior, P = posterior, D = dorsal, V = ventral. B. A characteristic ‘menorah’ structure, a repetitive pattern in the PVD’s dendritic arbor. C. A diagram of the menorah showing the conventional classification into branch orders. D. Outline of the algorithm for tracing and analysis of the PVD neuron. Starting with a grayscale raw image, dendritic processes are traced by fitting them with rectangular masks. This process is assisted by a skeleton, derived from a pre-trained convolutional neural network (CNN) used to constrain the orientation of the fitted elements. This results in accurate reconstruction of the PVD shape, that may be added to the CNN training set in order to refine its output for future analysis. The resulting neuron reconstruction can then be used to extract and quantify morphological features.
Fig 2.
Segmentation of the PVD using neural networks and active-contour models.
A. A convolutional neural network (CNN) is trained to detect PVD elements in noisy image patches, and to classify neuron and non-neuron pixels. The network gets a small image patch (top row, “Raw Image”), and returns a classified image array of the same size (middle row, “CNN Classification”). Green arrows show examples of correct classification of high-intensity autofluorescent gut granules, green arrowheads show examples of correct classification of complex morphologies, and red arrows show examples of incorrect classification of neuron pixels. The CNN output image is subsequently reduced to a topological skeleton (bottom row, “CNN Skeleton”). Orange arrows and arrowheads indicate cases in which the skeleton does not accurately capture the geometry of the neuron. These cases include over- and under-smoothing of neuronal processes (orange arrows), and deformed junction geometries (orange arrowheads). B. An illustration of the tracing process of a single neuronal segment. Sequential convolution of rectangles (green) is applied from the endpoints inwards until the segment is fully traced. C, D. The local orientation of a PVD element (C) is determined by the optimal alignment of a rectangular mask (blue) with the dendritic process (white), corresponding to the maximal convolution score (D, dashed lines represent detected deviation angle). E, F. Apparent local width of a PVD element (E) found using the decay rate (second derivative) of the convolution function (F, dashed line represents detected apparent width), using the orientation found in (C-D). G, H. The intensity and variation of the local background are determined by sampling the pixels within rectangles on both sides of the one found in C-F (G, blue rectangles for the background and green for the dendritic process). These are used to normalize the score and account for variation in background throughout the image and across images. Statistics were calculated using the nonparametric Mann–Whitney test. ***p < 0.0005. Error bars show the standard deviation. I-M. Determining the geometry of neuronal junctions–center point, radius, and angles. Given an approximate center point from the skeleton image (red dot in J), the precise center is detected by optimally fitting a circular mask to the binarized CNN image (green dot in J). Following the detection of the precise center and radius (J), a radially aligned rectangular mask (blue) is convolved against the greyscale image (K). Peaks in the convolution function (L) correspond to the detected local junctional angles (α; M). N. An example of a fully traced wild-type PVD neuron (same neuron as Fig 1A). Pink arrows indicate completely or partially untraced segments.
Fig 3.
The worm’s coordinate system and PVD feature extraction.
A. The coordinate system used to characterize the PVD neuron is defined by ; where
is locally tangential to the worm’s longitudinal axis,
points along the local dorsal direction, and
points in the direction of the worm’s right. B. Using the projection image of the non-planar PVD neuron, an outline image is generated using morphological operations applied to the neuron’s trace. This is used to find the neuron’s centerline and borderline. C. A schematic of the worm’s cross section. The azimuthal angle ϕ denotes the azimuthal position of PVD elements. r, radius at each point; d, distance. D. A schematic of the worm from a left/right side view. The angle θ denotes the orientation of PVD elements, defined as the angle between the longitudinal axis,
, and the local tangent,
. E, F. Visualization of the azimuthal angle ϕ (E) and distribution of the PVD elements for different ϕ angles (F, n = 10). The peaks at 0 and ±35° correspond to the primary (red) and tertiary (green, dorsal are positive and ventral are negative values) branches. Same neuron as Fig 1A. G, H. Visualization (G) and distribution (H) of orientation angle, θ, for PVD elements (n = 10). The distribution shows that most of the neuron’s length is either parallel (red) or perpendicular (green) to the midline. D = dorsal, V = ventral, L = left, R = right, A = anterior, P = posterior.
Fig 4.
Morphological characterization of the wild-type PVD.
A. Distribution of PVD elements by the azimuthal angle, ϕ, and midline orientation angle θ. Four distinct morphological classes are found: Class 1 (red), class 2 (green), class 3 (blue) and class 4 (yellow) (n = 10). B. The percentage of each of the morphological class found in (A); (n = 10). C. Visual example of the algorithmically-derived classification (same neuron as Fig 1A), closely resembling conventional branch-order classification scheme (see Fig 1C). D. Distribution of neuron length elements along the midline, classified as in C and averaged across worms (n = 10). E. Mean curvature of neuronal elements for each morphological class. Class 4 elements are the most curved, whereas class 3 elements are more curved than class 1 and 2, but less than class 4. The difference between class 2 and 4 is also statistically significant. Statistics were calculated using the nonparametric Mann–Whitney test. ***p < 0.0005. Error bars show the standard deviation (n = 10). Same neuron as Fig 1A. F. Example of a PVD neuron color-coded for curvature. Same neuron as Fig 1A.
Fig 5.
The geometry of PVD junctions.
A. Examples of various PVD junction morphologies. Colors correspond to relative junctional angle size: smallest (red, α1), mid-size (green, α2) and largest (blue, α3). B. Each junction is described by three angles, corrected for distortion due to projection. The distributions of the smallest (red), mid-size (green) and largest (blue) angles are shown (n = 10 animals; 2620 junctions). The mean values of the angle distributions are 92°, 119° and 149°. C. A cartoon showing the effect of random variations in junction configuration. An intrinsic junction configuration (top) is deformed, resulting in one of the possible deformed configurations (bottom). D. Fit of Monte Carlo simulated angle distributions with the experimental distributions. The best fit to the experimental data is for a symmetrical configuration with a standard deviation of σα = 19° around the mean values ({α1 = 120°, α2 = 120°, α3 = 120°, σα = 19°}; configuration (4)). Circled numbers correspond to the simulation examples in (E). E. Examples of simulated junction configurations. Circled numbers correspond to the ones in (D) to show the residual error for each simulation. Solid lines indicate probability densities for simulated junctions, bars indicate frequencies from experimental data. (1) = {α1 = 90°,α2 = 90°,α3 = 180°,σα = 26°}, (2) = {α1 = 80°, α2 = 130°, α3 = 150°, σα = 17°}, (3) = {α1 = 94°, α2 = 118°, α3 = 148°, σα = 15°}, (4) = {α1 = 120°, α2 = 120°, α3 = 120°, σα = 19°}. Configuration (4) gives the best fit as shown in (D).
Fig 6.
Distributions of geometrical PVD elements in wild-type and git-1 mutant.
A. An image of a full PVD of a git-1 mutant, superimposed with color-coded morphological classes: class 1 (red), class 2 (green), class 3 (blue) and class 4 (yellow). B. Total PVD length for each morphological class for WT (blue) and git-1 mutant (red), normalized to the whole PVD midline length. C. The length density of junctions along the dendritic processes (reciprocal of the average length of dendrites between junctions normalized per 100 μm), for each morphological class. D. The length density of tips along the dendritic processes, normalized per 100μm, for each morphological class. E. The number of dendritic tips, normalized per 100μm of midline length, for each of the four morphological classes. F-I. Magnified regions of typical PVD morphologies in wild-type (F-G) and git-1 (H-I). Arrows show abnormal branching in git-1 compared to wild-type. This includes excess of junctions and tips, as well as neuronal processes that do not follow the pattern described in Figs 3 and 4. Dendritic segments color-coded according to classification as in panel A. In B-E, statistics were calculated using the nonparametric Mann–Whitney test. ***p < 0.0005, **p < 0.005, *p < 0.05. n = 10 wild-type animals, with 2620 junctions and 2228 tips. n = 10 git-1 animals, with 2631 junctions and 2308 tips. Bars show the mean value and error bars show the standard deviation.
Fig 7.
Behavioral characterization of git-1 mutants.
A-C. Characteristic tracks obtained by automated video analysis of six animals over three minutes, recorded at 7.5 frames per second (fps), for WT, git-1(tm1962) and git-1(ok1848) animals, respectively. For each genotype, the animals were recorded on a single plate, and the obtained tracks were separated for clarity. Red arrowheads indicate events where the track was lost (see Materials and Methods). D. Crawling wavelength automatically extracted and averaged over a three-minute, 7.5 fps recording. n = 31 WT; n = 15 git-1(tm1962); n = 33 git-1(ok1848). Student’s t test, ***p < 0.0005. Error bars represent the standard deviation. Values remain significant when normalized per worm length (results not shown). E. Crawling speed normalized by total worm length, automatically extracted and averaged over a three-minute, 7.5 fps recording. n = 31 WT; n = 15 git-1(tm1962); n = 33 git1(ok1848). Student’s t test, **p < 0.005. Error bars represent the standard deviation. Values remain significant when normalized per worm length (results not shown). F. Percentage of worms executing a harsh-touch-induced escape response. Results are not significant (p > 0.01) compared to WT for all genotypes except the harsh-touch insensitive mec-3(e1338). As a negative control, the gentle-touch insensitive mec-4(e1611) animals are used. n = 310 WT; n = 312 git-1(tm1962); n = 250 git-1(ok1848); n = 150 mec-4(e1611); n = 70 mec-3(e1338), n = 4 independent experiments for WT and git-1(tm1962) mutants, n = 3 independent experiments for git-1(ok1848) mutants and n = 2 independent experiments for mec-4 and mec-3 mutants. Fisher’s exact test, ***p < 0.0001. Error bars represent the standard deviation.