Branching angles of pyramidal cell dendrites follow common geometrical design principles in different cortical areas

Local Microtubule and F-Actin Distributions Fully Constrain the Spatial Geometry of Drosophila Sensory Dendritic Arbors

Dendritic morphology underlies the source and processing of neuronal signal inputs. Morphology can be broadly described by two types of geometric characteristics. The first is dendrogram topology, defined by the length and frequency of the arbor branches; the second is spatial embedding, mainly determined by branch angles and straightness. We have previously demonstrated that microtubules and actin filaments are associated with arbor elongation and branching, fully constraining dendrogram topology. Here, we relate the local distribution of these two primary cytoskeletal components with dendritic spatial embedding. We first reconstruct and analyze 167 sensory neurons from the Drosophila larva encompassing multiple cell classes and genotypes. We observe that branches with a higher microtubule concentration tend to deviate less from the direction of their parent branch across all neuron types. Higher microtubule branches are also overall straighter. F-actin displays a similar effect on angular deviation and branch straightness, but not as consistently across all neuron types as microtubule. These observations raise the question as to whether the associations between cytoskeletal distributions and arbor geometry are sufficient constraints to reproduce type-specific dendritic architecture. Therefore, we create a computational model of dendritic morphology purely constrained by the cytoskeletal composition measured from real neurons. The model quantitatively captures both spatial embedding and dendrogram topology across all tested neuron groups. These results suggest a common developmental mechanism regulating diverse morphologies, where the local cytoskeletal distribution can fully specify the overall emergent geometry of dendritic arbors.

Distinct Relations of Microtubules and Actin Filaments with Dendritic Architecture

Microtubules (MTs) and F-actin (F-act) have long been recognized as key regulators of dendritic morphology. Nevertheless, precisely ascertaining their distinct influences on dendritic trees have been hampered until now by the lack of direct, arbor-wide cytoskeletal quantification. We pair live confocal imaging of fluorescently labeled dendritic arborization (da) neurons in Drosophila larvae with complete multi-signal neural tracing to separately measure MTs and F-act. We demonstrate that dendritic arbor length is highly interrelated with local MT quantity, whereas local F-act enrichment is associated with dendritic branching. Computational simulation of arbor structure solely constrained by experimentally observed subcellular distributions of these cytoskeletal components generated synthetic morphological and molecular patterns statistically equivalent to those of real da neurons, corroborating the efficacy of local MT and F-act in describing dendritic architecture. The analysis and modeling outcomes hold true for the simplest (class I), most complex (class IV), and genetically altered (Formin3 overexpression) da neuron types.

Comparing basal dendrite branches in human and mouse hippocampal CA1 pyramidal neurons with Bayesian networks

Pyramidal neurons are the most common cell type in the cerebral cortex. Understanding how they differ between species is a key challenge in neuroscience. A recent study provided a unique set of human and mouse pyramidal neurons of the CA1 region of the hippocampus, and used it to compare the morphology of apical and basal dendritic branches of the two species. The study found inter-species differences in the magnitude of the morphometrics and similarities regarding their variation with respect to morphological determinants such as branch type and branch order. We use the same data set to perform additional comparisons of basal dendrites. In order to isolate the heterogeneity due to intrinsic differences between species from the heterogeneity due to differences in morphological determinants, we fit multivariate models over the morphometrics and the determinants. In particular, we use conditional linear Gaussian Bayesian networks, which provide a concise graphical representation of the independencies and correlations among the variables. We also extend the previous study by considering additional morphometrics and by formally testing whether a morphometric increases or decreases with the distance from the soma. This study introduces a multivariate methodology for inter-species comparison of morphology.

Objective Morphological Classification of Neocortical Pyramidal Cells

A consensus on the number of morphologically different types of pyramidal cells (PCs) in the neocortex has not yet been reached, despite over a century of anatomical studies, due to the lack of agreement on the subjective classifications of neuron types, which is based on expert analyses of neuronal morphologies. Even for neurons that are visually distinguishable, there is no common ground to consistently define morphological types. The objective classification of PCs can be achieved with methods from algebraic topology, and the dendritic arborization is sufficient for the reliable identification of distinct types of cortical PCs. Therefore, we objectively identify 17 types of PCs in the rat somatosensory cortex. In addition, we provide a solution to the challenging problem of whether 2 similar neurons belong to different types or to a continuum of the same type. Our topological classification does not require expert input, is stable, and helps settle the long-standing debate on whether cell-types are discrete or continuous morphological variations of each other.

NeuroPath2Path: Classification and elastic morphing between neuronal arbors using path-wise similarity

Neuron shape and connectivity affect function. Modern imaging methods have proven successful at extracting morphological information. One potential path to achieve analysis of this morphology is through graph theory. Encoding by graphs enables the use of high throughput informatic methods to extract and infer brain function. However, the application of graph-theoretic methods to neuronal morphology comes with certain challenges in term of complex subgraph matching and the difficulty in computing intermediate shapes in between two imaged temporal samples. Here we report a novel, efficacious graph-theoretic method that rises to the challenges. The morphology of a neuron, which consists of its overall size, global shape, local branch patterns, and cell-specific biophysical properties, can vary significantly with the cell's identity, location, as well as developmental and physiological state. Various algorithms have been developed to customize shape based statistical and graph related features for quantitative analysis of neuromorphology, followed by the classification of neuron cell types using the features. Unlike the classical feature extraction based methods from imaged or 3D reconstructed neurons, we propose a model based on the rooted path decomposition from the soma to the dendrites of a neuron and extract morphological features from each constituent path. We hypothesize that measuring the distance between two neurons can be realized by minimizing the cost of continuously morphing the set of all rooted paths of one neuron to another. To validate this claim, we first establish the correspondence of paths between two neurons using a modified Munkres algorithm. Next, an elastic deformation framework that employs the square root velocity function is established to perform the continuous morphing, which, as an added benefit, provides an effective visualization tool. We experimentally show the efficacy of NeuroPath2Path, NeuroP2P, over the state of the art.

Patterns of Dendritic Basal Field Orientation of Pyramidal Neurons in the Rat Somatosensory Cortex

The study of neuronal dendritic orientation is of interest because it is related to how neurons grow dendrites to establish the synaptic input that neurons receive. The dendritic orientations of neurons in the nervous system vary, ranging from rather heterogeneously distributed (asymmetric) to homogeneously distributed (symmetric) dendritic arbors. Here, we analyze the dendritic orientation of the basal dendrites of intracellularly labeled pyramidal neurons from horizontal sections of Layers II–VI of the hindlimb somatosensory (S1HL) cortex of 14-d-old (P14) rats. We used circular statistics and proposed two new graphical descriptive representations of the neuron. We found that the dendritic pattern of most neurons was asymmetric. Furthermore, we found that there is a mixture of different types of orientations within any given group of neurons in any cortical layer. In addition, we investigated whether dendritic orientation was related to the physical location within the brain with respect to the anterior, dorsal, posterior and ventral directions. Generally, there was a preference towards the anterior orientation. A comparison between layers revealed that the preference for the anterior orientation was more pronounced in neurons located in Layers II, III, IV, and Va than for the neurons located in Layers Vb and VI. The dorsal orientation was the least preferred orientation in all layers, except for Layers IV and Va, where the ventral orientation had the lowest preference. Therefore, the orientation of basal dendritic arbors of pyramidal cells is variable and asymmetric, although a majority has a single orientation with a preference for the anterior direction in P14 rats.

Sloppy morphological tuning in identified neurons of the crustacean stomatogastric ganglion

Neuronal physiology depends on a neuron’s ion channel composition and unique morphology. Variable ion channel compositions can produce similar neuronal physiologies across animals. Less is known regarding the morphological precision required to produce reliable neuronal physiology. Theoretical studies suggest that moraphology is tightly tuned to minimize wiring and conduction delay of synaptic events. We utilize high-resolution confocal microscopy and custom computational tools to characterize the morphologies of four neuron types in the stomatogastric ganglion (STG) of the crab Cancer borealis. Macroscopic branching patterns and fine cable properties are variable within and across neuron types. We compare these neuronal structures to synthetic minimal spanning neurite trees constrained by a wiring cost equation and find that STG neurons do not adhere to prevailing hypotheses regarding wiring optimization principles. In this highly modulated and oscillating circuit, neuronal structures appear to be governed by a space-filling mechanism that outweighs the cost of inefficient wiring.

DOI:http://dx.doi.org/10.7554/eLife.22352.001

Dendritic-branching angles of pyramidal neurons of the human cerebral cortex

In this article, we analyze branching angles of the basal dendrites of pyramidal neurons of layers III and V of the human temporal cortex. For this, we use a novel probability directional statistical distribution called truncated von Mises distribution that is able to describe more accurately the dendritic-branching angles than the previous proposals. Then, we perform comparative studies using this statistical method to determine similarities and/or differences between branches and branching angles that belong to different cortical layers and regions. Using this methodology, we found that common design principles exist and govern the patterns found in the different branches that compose the basal dendrites of human pyramidal cells of the temporal cortex. However, particular differences were found between supra and infragranular cells. Furthermore, we compared the branching angles of human layer III pyramidal neurons with data obtained in the previous studies in layer III of both the rat somatosensory cortex and of several cortical areas of the mouse. Finally, we study the branching angle differences between the humans that compose our data.

Dendritic branching angles of pyramidal cells across layers of the juvenile rat somatosensory cortex

The characterization of the structural design of cortical microcircuits is essential for understanding how they contribute to function in both health and disease. Since pyramidal neurons represent the most abundant neuronal type and their dendritic spines constitute the major postsynaptic elements of cortical excitatory synapses, our understanding of the synaptic organization of the neocortex largely depends on the available knowledge regarding the structure of pyramidal cells. Previous studies have identified several apparently common rules in dendritic geometry. We study the dendritic branching angles of pyramidal cells across layers to further shed light on the principles that determine the geometric shapes of these cells. We find that the dendritic branching angles of pyramidal cells from layers II-VI of the juvenile rat somatosensory cortex suggest common design principles, despite the particular morphological and functional features that are characteristic of pyramidal cells in each cortical layer. J. Comp. Neurol. 524:2567-2576, 2016. © 2016 Wiley Periodicals, Inc.

Numerical study of a cylinder model of the diffusion MRI signal for neuronal dendrite trees

We study numerically how the neuronal dendrite tree structure can affect the diffusion magnetic resonance imaging (dMRI) signal in brain tissue. For a large set of randomly generated dendrite trees, synthetic dMRI signals are computed and fitted to a cylinder model to estimate the effective longitudinal diffusivity D(L) in the direction of neurites. When the dendrite branches are short compared to the diffusion length, D(L) depends significantly on the ratio between the average branch length and the diffusion length. In turn, D(L) has very weak dependence on the distribution of branch lengths and orientations of a dendrite tree, and the number of branches per node. We conclude that the cylinder model which ignores the connectivity of the dendrite tree, can still be adapted to describe the apparent diffusion coefficient in brain tissue.

Bayesian networks in neuroscience: a survey

Bayesian networks are a type of probabilistic graphical models lie at the intersection between statistics and machine learning. They have been shown to be powerful tools to encode dependence relationships among the variables of a domain under uncertainty. Thanks to their generality, Bayesian networks can accommodate continuous and discrete variables, as well as temporal processes. In this paper we review Bayesian networks and how they can be learned automatically from data by means of structure learning algorithms. Also, we examine how a user can take advantage of these networks for reasoning by exact or approximate inference algorithms that propagate the given evidence through the graphical structure. Despite their applicability in many fields, they have been little used in neuroscience, where they have focused on specific problems, like functional connectivity analysis from neuroimaging data. Here we survey key research in neuroscience where Bayesian networks have been used with different aims: discover associations between variables, perform probabilistic reasoning over the model, and classify new observations with and without supervision. The networks are learned from data of any kind-morphological, electrophysiological, -omics and neuroimaging-, thereby broadening the scope-molecular, cellular, structural, functional, cognitive and medical- of the brain aspects to be studied.