Local diameter fully constrains dendritic size in basal but not apical trees of CA1 pyramidal neurons

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.

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

Background

The 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.

Results

Using 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.

Conclusions

The 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 material

The online version of this article (doi:10.1186/s12859-015-0604-2) contains supplementary material, which is available to authorized users.

Models and simulation of 3D neuronal dendritic trees using Bayesian networks

Neuron morphology is crucial for neuronal connectivity and brain information processing. Computational models are important tools for studying dendritic morphology and its role in brain function. We applied a class of probabilistic graphical models called Bayesian networks to generate virtual dendrites from layer III pyramidal neurons from three different regions of the neocortex of the mouse. A set of 41 morphological variables were measured from the 3D reconstructions of real dendrites and their probability distributions used in a machine learning algorithm to induce the model from the data. A simulation algorithm is also proposed to obtain new dendrites by sampling values from Bayesian networks. The main advantage of this approach is that it takes into account and automatically locates the relationships between variables in the data instead of using predefined dependencies. Therefore, the methodology can be applied to any neuronal class while at the same time exploiting class-specific properties. Also, a Bayesian network was defined for each part of the dendrite, allowing the relationships to change in the different sections and to model heterogeneous developmental factors or spatial influences. Several univariate statistical tests and a novel multivariate test based on Kullback-Leibler divergence estimation confirmed that virtual dendrites were similar to real ones. The analyses of the models showed relationships that conform to current neuroanatomical knowledge and support model correctness. At the same time, studying the relationships in the models can help to identify new interactions between variables related to dendritic morphology.

Parsimonious modelling allows generation of the dendrograms of primate striatal medium spiny and pallidal type II neurons using a stochastic algorithm

Data from quantitative three-dimensional analysis of primate striatal medium spiny neurons (MSNs) and pallidal type I and type II neurons were used to search for possible rules underlying the dendritic architecture of these cells. Branching and terminating probabilities per unit length of dendrite were computed from all available measurement points. In the three neuronal groups, terminating probabilities were found to be exponentially increasing functions of the path distance to soma. MSNs and type II branching probabilities could be accurately modelled with decreasing functions of both the metrical (exponential functions) and topological (power functions of the centrifugal branch order) distances to soma. Additionally, type II branching also slightly depended on the distance to the proximal tip of the supporting branches. Type I branching probabilities did not follow these rules accurately. Embedding the modelled probability functions in a stochastic algorithm allowed generation of dendrograms close to those of the real MSNs and pallidal type II neurons, while the algorithm failed to simulate type I dendrites. MSN and pallidal type II neuron branching and terminating probabilities are thus highly dependent on the position in the dendritic arbor. This relationship can be modelled with simple functions and has a strong incidence on the dendrogram structure of the cells concerned. The additional dependence of the branching probability on the within-branch position led us to propose an extension of a previous modelling study by Nowakowski and co-workers which could account for a large range of topological and metrical (length) dendritic tree structures.

Non-parametric algorithmic generation of neuronal morphologies

Generation algorithms allow for the generation of Virtual Neurons (VNs) from a small set of morphological properties. The set describes the morphological properties of real neurons in terms of statistical descriptors such as the number of branches and segment lengths (among others). The majority of reconstruction algorithms use the observed properties to estimate the parameters of a priori fixed probability distributions in order to construct statistical descriptors that fit well with the observed data. In this article, we present a non-parametric generation algorithm based on kernel density estimators (KDEs). The new algorithm is called KDE-NEURON: and has three advantages over parametric reconstruction algorithms: (1) no a priori specifications about the distributions underlying the real data, (2) peculiarities in the biological data will be reflected in the VNs, and (3) ability to reconstruct different cell types. We experimentally generated motor neurons and granule cells, and statistically validated the obtained results. Moreover, we assessed the quality of the prototype data set and observed that our generated neurons are as good as the prototype data in terms of the used statistical descriptors. The opportunities and limitations of data-driven algorithmic reconstruction of neurons are discussed.

Quantifying neuronal size: summing up trees and splitting the branch difference

Neurons vary greatly in size, shape, and complexity depending on their underlying function. Overall size of neuronal trees affects connectivity, area of influence, and other biophysical properties. Relative distributions of neuronal extent, such as the difference between subtrees at branch points, are also critically related to function and activity. This review covers neuromorphological research that analyzes shape and size to elucidate their functional role for different neuron types. We also introduce a novel morphometric, "caulescence", capturing the extent to which trees exhibit a main path. Neuronal tree types differ vastly in caulescence, suggesting potential neurocomputational correlates of this property.

L-Measure: a web-accessible tool for the analysis, comparison and search of digital reconstructions of neuronal morphologies

L-Measure (LM) is a freely available software tool for the quantitative characterization of neuronal morphology. LM computes a large number of neuroanatomical parameters from 3D digital reconstruction files starting from and combining a set of core metrics. After more than six years of development and use in the neuroscience community, LM enables the execution of commonly adopted analyses as well as of more advanced functions. This report illustrates several LM protocols: (i) extraction of basic morphological parameters, (ii) computation of frequency distributions, (iii) measurements from user-specified subregions of the neuronal arbors, (iv) statistical comparison between two groups of cells and (v) filtered selections and searches from collections of neurons based on any Boolean combination of the available morphometric measures. These functionalities are easily accessed and deployed through a user-friendly graphical interface and typically execute within few minutes on a set of approximately 20 neurons. The tool is available at http://krasnow.gmu.edu/cn3 for either online use on any Java-enabled browser and platform or download for local execution under Windows and Linux.

A comparative computer simulation of dendritic morphology

Computational modeling of neuronal morphology is a powerful tool for understanding developmental processes and structure-function relationships. We present a multifaceted approach based on stochastic sampling of morphological measures from digital reconstructions of real cells. We examined how dendritic elongation, branching, and taper are controlled by three morphometric determinants: Branch Order, Radius, and Path Distance from the soma. Virtual dendrites were simulated starting from 3,715 neuronal trees reconstructed in 16 different laboratories, including morphological classes as diverse as spinal motoneurons and dentate granule cells. Several emergent morphometrics were used to compare real and virtual trees. Relating model parameters to Branch Order best constrained the number of terminations for most morphological classes, except pyramidal cell apical trees, which were better described by a dependence on Path Distance. In contrast, bifurcation asymmetry was best constrained by Radius for apical, but Path Distance for basal trees. All determinants showed similar performance in capturing total surface area, while surface area asymmetry was best determined by Path Distance. Grouping by other characteristics, such as size, asymmetry, arborizations, or animal species, showed smaller differences than observed between apical and basal, pointing to the biological importance of this separation. Hybrid models using combinations of the determinants confirmed these trends and allowed a detailed characterization of morphological relations. The differential findings between morphological groups suggest different underlying developmental mechanisms. By comparing the effects of several morphometric determinants on the simulation of different neuronal classes, this approach sheds light on possible growth mechanism variations responsible for the observed neuronal diversity.

Neurons in the brain have a variety of complex arbor shapes that help determine both their interconnectivity and functional roles. Molecular biology is beginning to uncover important details on the development of these tree-like structures, but how and why vastly different shapes arise is still largely unknown. We developed a novel set of computer models of branching in which measurements of real nerve cell structures digitally traced from microscopic imaging are resampled to create virtual trees. The different rules that the models use to create the most similar virtual trees to the real data support specific hypotheses regarding development. Surprisingly, the arborizations that differed most in the optimal rules were found on opposite sides of the same type of neuron, namely apical and basal trees of pyramidal cells. The details of the rules suggest that pyramidal cell trees may respond in unique and complex ways to their external environment. By better understanding how these trees are formed in the brain, we can learn more about their normal function and why they are often malformed in neurological diseases.

Successes and rewards in sharing digital reconstructions of neuronal morphology

The computer-assisted three-dimensional reconstruction of neuronal morphology is becoming an increasingly popular technique to quantify the arborization patterns of dendrites and axons. The resulting digital files are suitable for comprehensive morphometric analyses as well as for building anatomically realistic compartmental models of membrane biophysics and neuronal electrophysiology. The digital tracings acquired in a lab for a specific purpose can be often re-used by a different research group to address a completely unrelated scientific question, if the original investigators are willing to share the data. Since reconstructing neuronal morphology is a labor-intensive process, data sharing and re-analysis is particularly advantageous for the neuroscience and biomedical communities. Here we present numerous cases of "success stories" in which digital reconstructions of neuronal morphology were shared and re-used, leading to additional, independent discoveries and publications, and thus amplifying the impact of the "source" study for which the data set was first collected. In particular, we overview four main applications of this kind of data: comparative morphometric analyses, statistical estimation of potential synaptic connectivity, morphologically accurate electrophysiological simulations, and computational models of neuronal shape and development.

Optimization principles of dendritic structure

Background

Dendrites are the most conspicuous feature of neurons. However, the principles determining their structure are poorly understood. By employing cable theory and, for the first time, graph theory, we describe dendritic anatomy solely on the basis of optimizing synaptic efficacy with minimal resources.

Results

We show that dendritic branching topology can be well described by minimizing the path length from the neuron's dendritic root to each of its synaptic inputs while constraining the total length of wiring. Tapering of diameter toward the dendrite tip – a feature of many neurons – optimizes charge transfer from all dendritic synapses to the dendritic root while housekeeping the amount of dendrite volume. As an example, we show how dendrites of fly neurons can be closely reconstructed based on these two principles alone.

A new approach to reconstruction models of dendritic branching patterns

Quantitative models for characterising the detailed branching patterns of dendritic trees aim to explain these patterns either in terms of growth models based on principles of dendritic development or reconstruction models that describe an existing structure by means of a canonical set of elementary properties of dendritic morphology, which when incorporated into an algorithmic procedure will generate samples of dendrites that are statistically indistinguishable in both canonical and emergent features from those of the original sample of real neurons. This article introduces a conceptually new approach to reconstruction modelling based on the single assumption that dendritic segments are built from sequences of units of constant diameter, and that the distribution of the lengths of units of similar diameter is independent of location within a dendritic tree. This assumption in combination with non-parametric methods for estimating univariate and multivariate probability densities leads to an algorithm that significantly reduces the number of basic parameters required to simulate dendritic morphology. It is not necessary to distinguish between stem and terminal segments or to specify daughter branch ratios or dendritic taper. The procedure of sampling probability densities conditioned on local morphological features eliminates the need, for example, to specify daughter branch ratios and dendritic taper since these emerge naturally as a consequence of the conditioning process. Thus several basic parameters of previous reconstruction algorithms become emergent parameters of the new reconstruction process. The new procedure was applied successfully to a sample of 51 interneurons from lamina II/III of the spinal dorsal horn.