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Neuron tracing and quantitative analyses of dendritic architecture reveal symmetrical three-way-junctions and phenotypes of git-1 in C. elegans

['Omer Yuval', 'Faculty Of Biology', 'Technion Israel Institute Of Technology', 'Haifa', 'School Of Computing', 'Faculty Of Engineering', 'Physical Sciences', 'University Of Leeds', 'Leeds', 'United Kingdom']

Date:None

Complex dendritic trees are a distinctive feature of neurons. Alterations to dendritic morphology are associated with developmental, behavioral and neurodegenerative changes. The highly-arborized PVD neuron of C. elegans serves as a model to study dendritic patterning; however, quantitative, objective and automated analyses of PVD morphology are missing. Here, we present a method for neuronal feature extraction, based on deep-learning and fitting algorithms. The extracted neuronal architecture is represented by a database of structural elements for abstracted analysis. We obtain excellent automatic tracing of PVD trees and uncover that dendritic junctions are unevenly distributed. Surprisingly, these junctions are three-way-symmetrical on average, while dendritic processes are arranged orthogonally. We quantify the effect of mutation in git-1, a regulator of dendritic spine formation, on PVD morphology and discover a localized reduction in junctions. Our findings shed new light on PVD architecture, demonstrating the effectiveness of our objective analyses of dendritic morphology and suggest molecular control mechanisms.

Here, we present an algorithmic approach for detection and classification of the tree-like dendrites of the PVD neuron in C. elegans worms. A key feature of our approach is to represent dendritic trees by a set of fundamental shapes, such as junctions and linear elements. By analyzing this dataset, we discovered several novel structural features. We have found that the junctions connecting branched dendrites have a three-way-symmetry, although the dendrites are arranged in a crosshatch pattern, and that the distribution of junctions varies across distinct sub-classes of the PVD’s dendritic tree. We further quantified subtle morphological effects due to mutation in the git-1 gene, a known regulator of dendritic spines. Our findings suggest molecular mechanisms for dendritic shape regulation and may help direct new avenues of research.

Funding: This work was supported by the Israel Science Foundation (grant 2751/20 to TS and 257/17 to BP). We thank the C. elegans knockout consortium for the git-1(ok1848) deletion allele generated by the C. elegans Gene Knockout Project at the Oklahoma Medical Research Foundation, and git-1(tm1962), generated by the National Bioresource Project, Tokyo, Japan. Some strains were provided by the Caenorhabditis Genetics Center, which is funded by National Institutes of Health Office of Research Infrastructure Programs (P40 OD010440). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Here, we present a computational tool for the automated segmentation and analysis of PVD neuronal architecture. Tracing neuronal processes from microscopy data is performed by a hybrid algorithm, combining a region-based active-contour model for feature extraction [ 47 – 49 ], with a deep learning network for image filtering [ 50 , 51 ] ( Fig 1D ). While the neuron tracing functions may be assisted by a human operator, segmentation operates in a fully autonomous mode and batch-processes multiple raw microscopy images. Following the tracing step, quantification and classification of the extracted features are performed algorithmically ( Fig 1D ). Finally, the tracing and analysis outputs are catalogued, stored and shared in a neuronal morphology database. We utilize the collected morphological data for two tasks: first, by analyzing an extensive set of quantified PVD structures, we aim to update the current histological knowledge of the PVD neuron. This detailed knowledge can afford insight into the underlying mechanisms that sculpt neuronal structures. Further, the morphological database is used to quantify the effect of git-1 mutation on the C. elegans PVD neuron during early adulthood. Thus, also demonstrating the use of the tool for the detection and quantification of subtle morphological differences as a result of mutations that were implicated in human disease.

Analysis of neuron architecture faces two fundamental challenges; foremost of which is the extraction of cellular features from microscopy images [ 39 ]. Due to the inherent noise associated with optical microscopy of living systems, identifying and isolating the relevant image portions is a technically difficult and error-prone process [ 40 – 42 ]. Following segmentation, there remains the second challenge of interpreting and analyzing the segmented structures. As neurons display elaborate and varied shapes, characterization of their morphologies requires complex metrics and classifications, often developed or adjusted for a specific cell type [ 8 , 9 , 43 ]. In particular, the dendritic arbors of PVD neurons are described in terms of visually-striking, repetitive morphological elements, referred to as ‘menorahs’ or multibranched candelabra [ 17 , 26 , 44 ] ( Fig 1B and 1C ). Characterization of the PVD dendritic morphology is therefore accomplished by annotation and quantification of the menorah structure ( Fig 1C ). Due to the intricacy of these challenges, both extraction and analysis of PVD morphology are usually performed semi-manually, using time-consuming methods that prohibit large-scale studies. In addition, human characterization of neuronal shapes is highly subjective and often not sensitive enough for subtle, small-scale structures, raising the need for a high-precision, unbiased, quantitative analysis of morphological features [ 17 , 21 , 44 , 45 ]. While multiple image-processing tools are utilized to assist in tracing of neuronal elements [ 40 – 42 , 46 ], most methods do not easily lend themselves to post-tracing quantitative analysis. Moreover, general-use segmentation algorithms do not consider how the geometry of the neuronal processes is related to the overall shape of the C. elegans organism. An integrated tool that combines detection, segmentation and analysis of the PVD’s dendritic tree is therefore required.

A known regulator of dendritic morphogenesis and synaptic plasticity is GIT1: a GTPase activating protein for the small GTPase Arf (ADP ribosylation factor), as well as a focal adhesion scaffolding protein. Mutations in GIT1 have been linked with fear response and learning impairment, as well as reduced motor coordination and altered walking gait in rodents [ 29 , 30 ]. It has also been implicated in Huntington’s disease, Schizophrenia, and Attention Deficit and Hyperactivity Disorder (ADHD) [ 31 – 34 ]. Moreover, PIX (p21-activated kinase [PAK]-interacting exchange factor), the most prominent binding partner of GIT1, has been implicated in mental retardation in humans [ 35 ]. Several studies in rodent models have identified a link between GIT1 mutation and a reduction in the number of dendritic spines [ 29 , 36 , 37 ] and a recent report suggests it may have a structural role in the PVD as well [ 38 ].

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.

Over the past decade, the C. elegans bilateral PVD neuron has become a powerful model to study dendritic patterning, owing greatly to its stereotypical, highly ordered structure in the fourth larval stage and young adult ( Fig 1A ) [ 17 ]. The PVD neuron is located between the hypodermis and its basement membrane [ 17 , 18 ], and functions as a polymodal nociceptor, mechano- and thermo-sensor, and was suggested to play a role in proprioception–the sensing of body posture [ 18 , 19 ]. Two PVD cell bodies are born post-embryonically in the second larval stage (L2) and develop across the last three larval stages before adulthood (L2-L4), through a dynamic process of dendritic growth and retraction. By late L4 (typically within ~30 hours at 20°C), their complex dendritic arbor of repeating candelabra-shaped units extends almost the entire surface area of the worm [ 17 , 18 ]. This highly organized structure is made of tubular processes with diameters ranging between 35–60 nm [ 17 , 18 , 20 ]. Studies have implicated the PVD in a variety of functions, including self-fusion, aging and regeneration, and more recently for exploring structural aspects of neuropsychiatric and neurodegenerative diseases [ 17 , 21 – 25 ]. The relatively complex and high-order arborization of the PVD makes it an excellent model for studying the connection between structure and function in the nervous system [ 9 , 17 , 18 , 26 – 28 ].

The link between the information processing function of neurons and the intricate shapes of their dendritic processes has been the subject of over a century of extensive study [ 1 – 3 ]. Morphological features of dendritic arbors, such as length, diameter, and orientation have been related to neuronal functions [ 4 – 9 ], while deformations of the dendritic architecture have been associated with diseases and disorders [ 10 – 13 ]. Dendritic morphology varies significantly across species and across neuronal classes, which are often associated with distinct characteristic shapes [ 1 – 3 , 14 – 16 ].

The combined application of these segmentation procedures results in a dataset containing the position, dimensions, orientation and connectivity of the rectangular elements. Visual inspection confirms that this data serves as an efficient and faithful representation of the PVD shape (e.g. Fig 2N ). The abstracted nature of this representation facilitates post-segmentation analysis and may be used to combine multiple images to form larger datasets.

Sequential active contour segmentation is highly sensitive to the choice of the starting point, as well as image noise [ 47 , 55 ]. Since the active contour fitting was performed on the unclassified, original microscopy images, we overcame this limitation by utilizing the information contained in the CNN-derived skeleton to initialize and guide the active contour process. First, tips and vertices of the CNN skeleton are detected (pixels connected to either one, or more than two pixels, respectively). Skeletonized vertices serve as markers for dendritic junctions, and are used as the initial guess positions for fitting their shapes. Moreover, during the active contour tracing of the linear dendritic processes ( Fig 2B–2H ) we require the rectangular tracing elements to contain pixels of the CNN-derived skeleton from the corresponding skeleton segment. This constraint combines the benefits of deep learning and active contour fitting, and prevents divergence of the tracing into image regions that were classified as non-PVD by the CNN. Finally, we utilized the output of the tracing algorithm, as well as manual corrections, to update and retrain the CNN (see Fig 1D and S1 Text ). This feedback loop between the deep-learning classification module and the model-based fitting module is designed to enable a robust and adaptive extraction of the PVD neuron morphology from noisy images.

In addition to linear elements, the PVD arbors are characterized by junctions that connect dendritic branches ( Fig 2I ). We represented such junctions as circular elements, from which rectangular processes emanate radially. First, the position and size of the junctions are found by optimally fitting a circular mask ( Fig 2J ). Next, the dendritic processes that originate from each junction are detected by calculating the convolution score of rectangular masks across a range of orientations around the junction center ( Fig 2K ). The maxima of the score for different orientations correspond to the set of junctional angles, {α 1 , α 2 , α 3 }, that characterize the junction’s shape ( Fig 2L and 2M ).

In order to accurately extract the PVD morphology, we employed a simplified region-based active contour model to segment raw microscopy images [ 47 – 49 ]. Briefly, active contour methods detect morphological features by optimally fitting predefined shapes to the data. The optimization is influenced by “external forces” that attract the model shape to specific image elements, and “internal forces” that enforce intrinsic properties of the model shape, such as curvature [ 54 ]. Since the PVD dendrites have a tubular morphology with a slowly varying diameter, we represented the PVD shape by a series of discrete rectangular elements ( Fig 2B ; green rectangles). The fit score of each rectangular element (corresponding to the “external energy” of the active contour) is defined as the convolution of a rectangular mask with the image data. The score ranges from 0, corresponding to a mask containing no PVD elements (background, blue; Fig 2G and 2H ), to 1 for a mask containing only PVD elements (signal, green; Fig 2G and 2H ). The orientation of the dendritic process at each location is found by considering possible deviations from the orientation of the preceding element, where a 0° deviation indicates a locally linear segment ( Fig 2C ). The optimal orientation is defined as maximizing the mask convolution score ( Fig 2C and 2D ). The width of the rectangular mask is fitted at each point along the dendritic process by calculating the characteristic length at which the fit score decays with the rectangle width ( Fig 2E and 2F ; see arrows). Note that the fitted rectangular width does not indicate the actual diameter of the dendritic process, which falls below the resolving power of the microscopy setup, but rather the apparent fluorescent signal of the processes, which varies significantly throughout the PVD [ 17 ]. The length of the rectangular elements was taken as a twice the rectangular width (see S1 Table ). Once a section of the PVD has been fitted with a mask, the local background intensity in the vicinity of the dendrite is calculated and subtracted from the image data ( Fig 2G and 2H ). Thus, detection of dendritic processes is assisted by the segmentation of neighboring regions. Ultimately, the shape of the dendritic processes is represented by a connected chain of rectangles ( Fig 2B ). We regulated the continuity and smoothness of the representative chain (“internal energy” of the active contour) by constraining the orientations and widths of successive rectangles (see S1 Text ).

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.

Deep-learning algorithms are widely used for segmentation of microscopy data in general, and neuronal shapes in particular [ 51 , 52 ]. Here, we designed, trained and applied a convolutional neural network (CNN; S1 Fig ) in order to extract the neuron signal from images of one-day adult C. elegans ( Fig 1A ). The CNN acts to classify the fluorescent signal as either attributed to the PVD or to background noise and non-neuronal labeled components such as auto-fluorescent gut granules [ 53 ]. The CNN operates on small sub-regions of the image (see Fig 2A for an ensemble of raw and labeled regions), which are then re-assembled to reconstruct the full neuron image. The CNN outputs an image-sized array with values corresponding to the classification of each image pixel into PVD and non-PVD elements. Next, the CNN output is skeletonized, producing a pixel-wide, thin representation of the PVD shape (Figs 1D and S2C ). While the neural network is highly efficient in classification of microscopy images, we found that the CNN-derived shape is insufficient for a faithful representation of the PVD (see S2D Fig ).

Analysis of PVD shape

Following feature detection, we turned to construct a quantified characterization of the PVD architecture. In order to relate the structure of the dendritic arbor to the shape of the organism, we first defined an appropriate global system of coordinates. Subsequently, the extracted dataset of morphological elements was used to identify spatial patterns that represent intrinsic motifs of PVD organization. Classification of PVD elements according to such motifs is used to provide an idealized PVD representation, as well as a basis for quantitative comparison between phenotypes.

PVD coordinate system It is convenient to describe the position of the extracted rectangular PVD elements by the natural coordinate system for C. elegans, defined by the moving frame ; where is locally tangential to the worm’s longitudinal axis, points along the local dorsal direction, and completes the orthonormal set by pointing in the direction of the worm’s right (see Fig 3A). The worm’s longitudinal axis is detected by morphological dilation and erosion image operations (see Figs 3B, S3A and S3B and S1 Text for details). PPT PowerPoint slide

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larger image TIFF original image Download: 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. https://doi.org/10.1371/journal.pcbi.1009185.g003 Since the PVD lies close to the worm’s body surface, positions of its dendritic elements may be given by only two coordinates: distance s along the longitudinal axis (defined as positive posteriorly towards the tail, with the origin anteriorly at the head; A-P in Figs 3B and S3B), and the azimuth angle ϕ relative to the axis (defined as positive for a counter-clockwise rotation about , such that azimuth is positive for dorsal elements, and negative for ventral; see Fig 3C). Note that two PVD neurons cover the worm laterally (PVDL, PVDR); this analysis addresses the PVD as viewed from the left. PVDR images were flipped to provide the same frame of reference. Although the worm’s body surface is curved, microscopy images are projected to the flat image plane defined by and vectors. Coordinates of an element in the image plane are therefore given by the distances (s, d), and the transformation between image and worm coordinates is given by ϕ = sin−1(d/r(s)), where r(s) is the radius of the worm at each point along the longitudinal midline axis. For each element of the dendrites, we defined the midline orientation angle θ of the local tangent, , relative to the longitudinal axis: θ = tan−1(dD/dS), where dD and dS are length components in the and directions respectively (see Fig 3D).

Three-way junctions’ angles are symmetric on average Our analysis has shown that PVD junctions connect segments that are, on average, perpendicular to each other. In order to test whether this arragment results from forces that orient the dendritic processes or from intrisic properties of the dendritic junctions, we analyzed the geometry of individual junctions. We found that PVD processes are predominantly connected by 3-way junctions (98.3% of all junctions), while 4-way junctions are scarce (1.7% of all junctions), and higher order junctions were not detected. Next, we determined the relative orientations of the dendritic processes at the points of their connection to the junctions. We observed that each 3-way junction is characterised by an ordered triplet of angles {α 1 , α 2 , α 3 }, where α 1 ≤α 2 ≤α 3 and α 1 +α 2 +α 3 = 360° (see Fig 5A for examples). Note that, in general, the junction angles differ from the orientations of the processes to which they are connected (see S5A Fig). After correcting for the distortion of the junction angles due to projection to the image plane (see Fig 3B and 3C and S1 Text for details), we found the averages for the smallest, intermediate and largest angles to be 〈α 1 〉 = 92°, 〈α 2 〉 = 119°, and 〈α 3 〉 = 149° (Fig 5B). Since the angles in a triplet are not independent, the means of the angle distributions do not correspond to the most abundant junction geometry. In order to reconstruct the charactersitic PVD junction, we used a Monte Carlo algorithm to simulate a range of possible junction geometries under deformation by random noise (see Figs 5C and S5B and S1 Text for details). In order to find the angle triplet and the angle variation that best characterize PVD junctions, we fitted the angle distributions of the simulated junctions with the experimentally determined distributions (Fig 5D and 5E; nondimensional fit residuals shown as a function of only α 1 and α 2 , since α 3 = 360°−α 1 −α 2 ). Angle triplets with lower residual errors indicate a better match with the experimental distributions. Importantly, our analysis shows that the experimental data is in best agreement with junction configurations close to the symmetric α 1 = α 2 = α 3 = 120° shape (Fig 5D). Moreover, the fit with the simulation reveals that the PVD junctions are somewhat varied: we found that junction angles are distributed around the symmetric configuration with a standard deviation of σ α = 18° (see S5B Fig; showing the fitted angle standard deviation, σ α , as a function of α 1 and α 2 ). While this variability of the junction angles allows for intrinsic junction configurations that may deviate from perfect three-way symmetry, these results demonstrate that the orthogonal arrangement of the PVD dendritic arbors (Figs 1C and 4A) is not a consequence of boundary conditions imposed by PVD junctions, but is rather determined by factors that align the processes themselves. The variability of junction geometry further indicates some mechanical flexibility of the junction structure. These findings may be used to guide future works in the search for the physical mechanisms that shape dendritic junctions. PPT PowerPoint slide

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larger image TIFF original image Download: Fig 5. The geometry of PVD junctions. A. Examples of various PVD junction morphologies. Colors correspond to relative junctional angle size: smallest (red, α 1 ), mid-size (green, α 2 ) and largest (blue, α 3 ). 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 σ α = 19° around the mean values ({α 1 = 120°, α 2 = 120°, α 3 = 120°, σ α = 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) = {α 1 = 90°,α 2 = 90°,α 3 = 180°,σ α = 26°}, (2) = {α 1 = 80°, α 2 = 130°, α 3 = 150°, σ α = 17°}, (3) = {α 1 = 94°, α 2 = 118°, α 3 = 148°, σ α = 15°}, (4) = {α 1 = 120°, α 2 = 120°, α 3 = 120°, σ α = 19°}. Configuration (4) gives the best fit as shown in (D). https://doi.org/10.1371/journal.pcbi.1009185.g005

Distribution of network elements in wild-type and in git-1 mutant We next applied our quantitative morphological approach in order to characterize the role of GIT-1, a known regulator of dendritic spines, in shaping the PVD morphology. In order to quantify the effect of GIT-1, we extracted and analysed the PVD dendritic arbor for git-1(ok1848) mutant worms, utilizing the algorithm described for wild-type (WT) worms above (Figs 6A and S6A–S6I). As the most elementary metric for comparison, we quantified the length of dendritic processes detected in each worm. We found that the average total dendritic length was not affected in the mutant, with 6100±330μm (n = 10), compared to 6000±270μm in WT worms (n = 10). Next, we determined how PVD dendrites are distributed into the previously defined morphological classes, using the intrinsic class definitions determined for WT animals. We found that while the total length of PVD dendrites remain unchanged, its distribution into the classes was altered: the combined length of class-4 branches was decreased in the git-1 mutant compared to WT, whereas the length of class-3 was increased (see Fig 6B). Conversely, we found that the lengths of classes 1 and 2 were not changed considerably. PPT PowerPoint slide

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larger image TIFF original image Download: 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. https://doi.org/10.1371/journal.pcbi.1009185.g006 Next, we investigated the effect of git-1 mutation on the degree of arborization of the PVD dendrites. We define the one-dimensional junction density, ρ, as the number of three-way-junctions per unit length of the dendrites. The junction density is the reciprocal of the mean dendritic distance between neighboring junctions, and therefore constitutes a fundamental structural parameter of the PVD. We found that the overall density of junctions in the PVD of WT animals is 0.042±0.003μm−1, and is unchanged in git-1 mutant worms. Nevertheless, a more detailed analysis revealed that the junction density varies throughout the PVD, with significantly elevated junction densities found in the 2nd class, compared to the 1st and 4th classes (see Fig 6C). This trend was observed both in wild-type and git-1 mutants; however, our analysis has revealed a significant decrease in junction density of class 3 branches in the git-1 mutant, as compared to WT (Fig 6C). In addition to 3-way junctions and linear segments, the PVD architecture includes dendritic tips which terminate PVD processes. Such tips may represent sites at which applied mechanical forces can promote dendritic elongation or retraction, as well as potential sites of membrane fusion, leading to the formation of new 3-way junctions. We therefore sought to characterize the effect of git-1 on the number and distribution of terminal PVD branches. We found that the average number of tips in a wild-type PVD is 220±20 (n = 10 worms) and is essentially unchanged in git-1 mutants, with 230±20 (n = 10 worms). Similar to junction density, we characterized the density of terminal tips per unit length of PVD for branches of different classes. We found that the tip density in WT worms increases with class number, with the highest tip density found at 4th class (Fig 6D). This result is remarkable in contrast with the junction density, which is lowest at 4th class branches. In git-1 mutants both tip number and tip density of class 1 and 3 are increased compared to WT, while the number, but not density, of class-4 tips is reduced (Fig 6D and 6E). We note that while the reduction in class-4 tip number and length maintains a tip density similar to WT, this is not the case for class-3, where tip density is increased despite the increase in class-3 length (Fig 6B, 6D and 6E). While some, but not all, features of the WT and git-1 morphology can be confirmed by visual inspection and manual quantitative analyses (Fig 6F–6I; see S1 Text), the reliable detection of such nuanced differences demonstrates the power of our quantitative automated and objective approach. Taken together, these findings indicate a subtle but significant change in the morphology of the PVD in git-1 worms that is most prominent in tertiary-classed branches.

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