Branching Patterns Of Neurons Research Articles

A micro-CT-based standard brain atlas of the bumblebee

In recent years, bumblebees have become a prominent insect model organism for a variety of biological disciplines, particularly to investigate learning behaviors as well as visual performance. Understanding these behaviors and their underlying neurobiological principles requires a clear understanding of brain anatomy. Furthermore, to be able to compare neuronal branching patterns across individuals, a common framework is required, which has led to the development of 3D standard brain atlases in most of the neurobiological insect model species. Yet, no bumblebee 3D standard brain atlas has been generated. Here we present a brain atlas for the buff-tailed bumblebee Bombus terrestris using micro-computed tomography (micro-CT) scans as a source for the raw data sets, rather than traditional confocal microscopy, to produce the first ever micro-CT-based insect brain atlas. We illustrate the advantages of the micro-CT technique, namely, identical native resolution in the three cardinal planes and 3D structure being better preserved. Our Bombus terrestris brain atlas consists of 30 neuropils reconstructed from ten individual worker bees, with micro-CT allowing us to segment neuropils completely intact, including the lamina, which is a tissue structure often damaged when dissecting for immunolabeling. Our brain atlas can serve as a platform to facilitate future neuroscience studies in bumblebees and illustrates the advantages of micro-CT for specific applications in insect neuroanatomy.

Topological characterization of neuronal arbor morphology via sequence representation: I--motif analysis.

BackgroundThe morphology of neurons offers many insights into developmental processes and signal processing. Numerous reports have focused on metrics at the level of individual branches or whole arbors; however, no studies have attempted to quantify repeated morphological patterns within neuronal trees. We introduce a novel sequential encoding of neurite branching suitable to explore topological patterns.ResultsUsing all possible branching topologies for comparison we show that the relative abundance of short patterns of up to three bifurcations, together with overall tree size, effectively capture the local branching patterns of neurons. Dendrites and axons display broadly similar topological motifs (over-represented patterns) and anti-motifs (under-represented patterns), differing most in their proportions of bifurcations with one terminal branch and in select sub-sequences of three bifurcations. In addition, pyramidal apical dendrites reveal a distinct motif profile.ConclusionsThe quantitative characterization of topological motifs in neuronal arbors provides a thorough description of local features and detailed boundaries for growth mechanisms and hypothesized computational functions.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0604-2) contains supplementary material, which is available to authorized users.

The flatness of bifurcations in 3D neuronal branching patterns

The geometry of bifurcations in natural branching systems often reflects optimization constraints during formation, leading to, for instance, a planar arrangement of the branches (segments). The present study aimed at testing whether bifurcations in 3D neuronal branching patterns also follow this general property. A measure for the flatness of bifurcations is the apex angle of the right circular cone enwrapping the bifurcation (cone angle) and earlier applied to dendritic bifurcations [1]. Recently, the cone angle was used by Kim et al. [2] in an analysis of bifurcations in Purkinje cells and retinal ganglion cells. As the cone angle distributions in these cells resembled those of random bifurcations it was concluded that the observed flatness already naturally emerges from random conditions. In the present study, a number of different geometrical measures of flatness has been developed and evaluated on their power for expressing the flatness of 3D bifurcations. These measures are applied to bifurcations from rat visual cortex pyramidal basal dendrites, and to random bifurcations (i.e., bifurcations with random oriented segments in 3D space). Frequency distributions of the various flatness measures of random and dendritic bifurcations appeared to be significantly different (Kolmogorov-Smirnov test). Dendritic bifurcations appeared to be more planar than random ones. In addition, parent segments in dendritic bifurcations have a strong preference to be aligned oppositely to the angular bisector of the daughter segments. These findings suggest that dendritic bifurcations are also formed under the influence of optimality constraints during the dendritic branching process. The flatness measure most strongly expressing the flatness of a 3D bifurcation was found to be the dihedral angle β between the daughters’ plane and the plane formed by the parent segment and the line in the daughters’ plane perpendicular to the angular bisector of the daughter segments. The dihedral angle β has a uniform distribution for random bifurcations but is highly skewed for dendritic ones (Fig. ​(Fig.11). Figure 1 Frequency distribution of the dihedral angle β of random bifurcations (horizontal line), and of basal dendritic bifurcations (dashed histogram). We conclude that 3D bifurcations in rat cortical pyramidal basal dendrites are significantly more flat than random bifurcations. In addition, parent segments are preferentially aligned opposite to the angular bisector of the daughter segments. These findings are in line with findings in tissue culture that neuritic bifurcations are subjected to elastic tensions [3], minimizing the distances between the nodes comprising the bifurcation.

Quantitative analysis of dendritic branching pattern of large neurons in human cerebellum

Dentate nucleus (nucleus dentatus) is the most distant of the cerebellar nuclei and the major system for information transfer in the cerebellum. So far, dendritic branches of four different kinds of large neurons of dentate nucleus, have been considered mainly qualitatively with no quantification of their morphological features. The aim of the study was to test the qualitative hypothesis that the human dentate nucleus is composed of various types of the large neurons by quantitative analysis of their dendritic branching patterns. Series of horizontal sections of the dentate nuclei were taken from 15 adult human brains, free of diagnosed neurological disorders. The 189 Golgi-impregnated images of large neurons were recorded by a digital camera connected to a light microscope. Dendritic branching patterns of digitized neuronal images were analyzed by modified Sholl and fractal analyses. The number of intersections (N(m)), critical radius (r(c)) and fractal dimension (D) of dendritic branching pattern for four types of the large neurons were calculated, statistically evaluated and analyzed. The results show that there is a significant difference between four neuronal types in one morphometric parameter at least. The present study is the first attempt to analyze quantitatively the dendritic branching pattern of neurons from the dentate nucleus in the human. The hypothesis that the four types of the large neurons exist in this part of human cerebellum is successfully supported.

Measuring neuronal branching patterns using model-based approach

Neurons have complex branching systems which allow them to communicate with thousands of other neurons. Thus understanding neuronal geometry is clearly important for determining connectivity within the network and how this shapes neuronal function. One of the difficulties in uncovering relationships between neuronal shape and its function is the problem of quantifying complex neuronal geometry. Even by using multiple measures such as: dendritic length, distribution of segments, direction of branches, etc, a description of three dimensional neuronal embedding remains incomplete. To help alleviate this problem, here we propose a new measure, a shape diffusiveness index (SDI), to quantify spatial relations between branches at the local and global scale. It was shown that growth of neuronal trees can be modeled by using diffusion limited aggregation (DLA) process. By measuring “how easy” it is to reproduce the analyzed shape by using the DLA algorithm it can be measured how “diffusive” is that shape. Intuitively, “diffusiveness” measures how tree-like is a given shape. For example shapes like an oak tree will have high values of SDI. This measure is capturing an important feature of dendritic tree geometry, which is difficult to assess with other measures. This approach also presents a paradigm shift from well-defined deterministic measures to model-based measures, which estimate how well a model with specific properties can account for features of analyzed shape.

Nonlinear anisotropic diffusion filtering of three-dimensional image data from two-photon microscopy

Two-photon microscopy in combination with novel fluorescent labeling techniques enables imaging of three-dimensional neuronal morphologies in intact brain tissue. In principle it is now possible to automatically reconstruct the dendritic branching patterns of neurons from 3-D fluorescence image stacks. In practice however, the signal-to-noise ratio can be low, in particular in the case of thin dendrites or axons imaged relatively deep in the tissue. Here we present a nonlinear anisotropic diffusion filter that enhances the signal-to-noise ratio while preserving the original dimensions of the structural elements. The key idea is to use structural information in the raw data-the local moments of inertia-to locally control the strength and direction of diffusion filtering. A cylindrical dendrite, for example, is effectively smoothed only parallel to its longitudinal axis, not perpendicular to it. This is demonstrated for artificial data as well as for in vivo two-photon microscopic data from pyramidal neurons of rat neocortex. In both cases noise is averaged out along the dendrites, leading to bridging of apparent gaps, while dendritic diameters are not affected. The filter is a valuable general tool for smoothing cellular processes and is well suited for preparing data for subsequent image segmentation and neuron reconstruction.

Axonal branching pattern of neurons of the subthalamic nucleus in primates.

Axonal projections arising from the subthalamic nucleus (STN) in cynomolgus monkeys (Macaca fascicularis) were traced after labeling small pools (5-15 cells) of neurons with biotinylated dextran amine. Seventy-five single axons were reconstructed from serial sagittal sections with a camera lucida. Most of the STN labeled cells displayed five to eight long, sparsely spined dendrites that arborized mostly along the main axis of the nucleus. Based on their axonal targets, five distinct types of STN projection neurons have been identified: 1) neurons projecting to the substantia nigra pars reticulata (SNr), the internal (GPi) and external (GPe) segments of the globus pallidus (21.3%); 2) neurons targeting SNr and GPe (2. 7%); 3) neurons projecting to GPi and GPe (48%); 4) neurons targeting GPe only (10.7 %); and 5) neurons with axons that coursed toward the sriatum, but whose terminal arborization could not be visualized in detail (17.3%). Axons of the first two types bifurcated into rostral subthalamopallidal and caudal pallidonigral branches. However, the majority of STN axons had only a single branch that coursed rostrally toward the pallidum and striatum. These results reveal that, in contrast to current beliefs, the primate STN is not a monolithic entity. This nucleus harbors several subtypes of projection neurons, each endowed with a highly patterned set of collaterals. This organization allows STN neurons to exert a multifarious effect not only on the GPe, with which the STN is reciprocally connected, but also on the two major output structures of the basal ganglia, the SNr and the GPi.

Effect of Pruning on Dendritic Tree Topology

The variability in topological shapes of observed neuronal branching patterns can accurately be described by a simple model for random sequential growth. This finding is remarkable in view of the fact that the actual neuritic growth process can vary, and includes phases of regression and removal of branches which were not considered in the model. The aim of the present study is to investigate the influence of removal of branches on the topological structure of branching patterns as well as the effect of variable growth rules.A tree asymmetry index is used for the characterization of the topological structure of a tree. The mean value of the asymmetry index for a set of dendritic trees is sensitive to the mode of growth. The effect of removal of branches (“pruning”) on the topological structure of dendritic trees has been studied for several random pruning schemes, namely (i) removal of uniform randomly chosen subtrees, (ii) removal of uniform randomly chosen terminal segments, (iii) uniform random pruning during the growth process itself, and (iv) non-uniform random pruning schemes. It was found that the effect of pruning depends on both the mode of pruning and the mode of growth. Uniform random (terminal) pruning had no effect on the mean and standard deviation of the asymmetry index of trees grown with an order-independent mode of branching. Changes in the mean of the asymmetry index could occur either with non-uniform random pruning or when trees are grown according to an order-dependent mode of branching.The effect of variable growth rules was studied for several specific schemes, and it could be shown that they all result in a substantial increase in the variation in the asymmetry index of the trees.

Outgrowth patterns and directed growth of identified neurons induced by native substrates in culture.

In this study, we have tested how various identified leech neurons in culture grow on surfaces that they normally contact in situ. Neurons were cultured either on ganglion capsules from which neurons had been removed or on skin. On these substrates, outgrowth patterns were characteristic for each cell type. Retzius cells plated on capsules extended bundles of thick, fasciculated processes with few branching points and in the opposite direction a tangle of fine neurites. Anterior pagoda (AP) neurons plated on capsules extended two single processes in opposite directions but failed to grow on skin. Sensory P and N neurons on capsules extended multiple processes. On skin, P neurons extended only two long branches in opposite directions over the superficial body wall. N neurons on skin extended multiple processes. Varicosities were common in the processes of P and N neurons on capsules or skin. The branching patterns described here bore closer resemblance to those in the developing or adult nervous system than to those on Concanavalin A or laminin-enriched extract. Pairs of Retzius or AP neurons plated at a distance on the same capsule extended neurites from one neuron toward the other and formed contacts. Such directed growth failed in hybrid pairs of Retzius and AP neurons or in pairs plated on laminin-enriched extract or Concanavalin A. Our results suggest that multiple growth-promoting molecules anchored to the extracellular matrix may cooperate in regulating the branching pattern of neurons, fasciculation, and direction of growth.

Combining laser scanning confocal microscopy and electron microscopy in studies of the insect nervous system

Experimentally determining the synaptic interconnections between neurons in the nervous system is laborious and difficult in any animal species, but especially so in many invertebrates, including insects, where neurons generally have large, finely branching neuritic trees that form both pre- and postsynaptic specializations in dense neuropils with other neuritic trees. Electron microscopy is needed to identify synapses, but correlation of synapse type and location with the overall branching patterns of neurons, which are visible readily only in the light microscope or through extensive reconstruction of serial electron-microscope sections, is very difficult. In this paper, we present a simple method that we have developed (Sun et al. (1995) J. Histochem. Cytochem., 43: 329–335) that combines laser scanning confocal microscopy and electron microscopy for the study of synaptic relationships of neurons in the antennal lobe, the first central neuropil in the olfactory pathway, of the moth Manduca sexta. Briefly, neurons are labeled by intracellular injection with neurobiotin or biocytin, and then processed with a gold-particle tag for electron microscopic study and a fluorescent tag for confocal microscopy, and embedded in plastic. The fluorescence of the labeled neuron in the plastic blocks is imaged in three dimensions with laser scanning confocal microscopy and then the neuron is thin-sectioned at precisely chosen depths for electron microscopic study. The fluorescence pattern can be monitored repeatedly between episodes of thin-sectioning, and subtraction of a fluorescence image from the previous fluorescence image reveals which fluorescent processes have been sectioned. In this way, electron microscopic detail can be mapped onto a three-dimensional light microscopic image of the neuron.

IMPACT OF TOPOLOGICAL VARIABILITY ON DENDRITIC GEOMETRY

The development of neuronal branching patterns mainly proceeds by branching events at terminal segments. The randomness in the occurrences of these events is the major cause of the variability that is observed in the final topological structures of neuronal trees. A general observation in neuronal trees is the existence of a branch power relation between the diameters of the segments at branch points. Because of this correlation, total area and volume will become dependent on branching pattern topology. A quantitative assessment of this finding is given. How topological variation propagates into variation in total area and volume, using topological growth models for producing random tree topologies and a simple metrical parametrization is discussed.

Tree asymmetry--a sensitive and practical measure for binary topological trees.

The topological structure of a binary tree is characterized by a measure called tree asymmetry, defined as the mean value of the asymmetry of its partitions. The statistical properties of this tree-asymmetry measure have been studied using a growth model for binary trees. The tree-asymmetry measure appears to be sensitive for topological differences and the tree-asymmetry expectation for the growth model that we used appears to be almost independent of the size of the trees. These properties and the simple definition make the measure suitable for practical use, for instance for characterizing, comparing and interpreting sets of branching patterns. Examples are given of the analysis of three sets of neuronal branching patterns. It is shown that the variance in tree-asymmetry values for these observed branching patterns corresponds perfectly with the variance predicted by the used growth model.

Neuronal branching patterns and the economy of cortical wiring

Keeping the volume of connections in the cortex as low as possible may be an important evolutionary constraint on the design of the brain. Much as an engineer tries to arrange the components of a computer in such a way as to give efficient wiring, so the brain may have evolved a layout of neuronal types which gives an economical use of axonal 'wiring'. One key difference between computer and brain is that connections in the brain take the form of elaborate branching structures. It is argued here that certain features of cortical mapping, such as the stripes and patches seen within cortical areas, may be adaptations which allow efficient wiring by such structures. Some simple calculations are given to support this, using as models for axonal arbors certain branching patterns which give a low volume of wiring. In particular, it is shown that a pattern of stripes can give economical wiring when axon diameters follow a law dp = dp1 + dp2 with p greater than 4, where d1 and d2 are the diameters of the daughter branches and d that of the parent.

Analysis of binary trees when occasional multifurcations can be considered as aggregates of bifurcations

The geometrical properties of neurons are important for the way they function within neural circuits. The arborescent processes of neurons that are necessary for the transmission of the information are formed by branching and elongation of segments. In studies that model the outgrowth the tree structures have generally been considered as binary. However, multifurcations do occur. It will be shown that if the multifurcations can be considered as aggregates of bifurcations they may be included in the topological analysis of neuronal branching patterns.

Application of growth models to the topology of neuronal branching patterns

The variation in topological structure of branching patterns may contain essential information with respect to the way these branching patterns have grown. For the understanding of how growth modes finally result in a particular variety in topological patterns, model studies may provide indispensible tools. These studies imply the mathematical formulation of growth models and the development of statistical procedures to compare model predictions with observed data. Recent literature shows two main approached in these model studies, viz. subtree partition analysis (SPA) and vertex analysis. This paper will briefly review the current status with respect to SPA and will apply the model approach to sets of dendritic trees taken from pyramidal, multipolar non-pyramidal and from Purkinje cells. The results show that the topological properties of many dendrites are not in agreement with the hypothesis of random terminal growth and that substantial branching of intermediate segments and/or branching dependent of the position of segments in the tree (topological distance from the cell body) must be assumed. Only two parameters are required to incorporate these assumptions in the model. In all cases up to now it is possible to find parameter values such that the model predictions of topological properties are in agreement with the observations.