Simulation of motoneuron morphology in three dimensions. I. Building individual dendritic trees

Marks, W. B.; Burke, Robert E.

doi:10.1002/cne.21418

Cited by 20 publications

(32 citation statements)

References 47 publications

(90 reference statements)

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“…Interestingly, effective repulsion between the cell body and dendrites was introduced to reproduce realistic arbor shapes (45). Although the proposed repulsion can explain the straightness of dendritic branches and their centripetal orientation (45,70), it does not account for the distribution of the nearest-neighbor distance among branches (71). Here, based on the analysis of dendritic functionality, we proposed that effective repulsion exists among all segments of a dendritic arbor, not just between the cell body and dendrites.…”

Section: Discussionmentioning

confidence: 99%

Maximization of the connectivity repertoire as a statistical principle governing the shapes of dendritic arbors

Wen

Stepanyants

Elston³

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

120

127

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The shapes of dendritic arbors are fascinating and important, yet the principles underlying these complex and diverse structures remain unclear. Here, we analyzed basal dendritic arbors of 2,171 pyramidal neurons sampled from mammalian brains and discovered 3 statistical properties: the dendritic arbor size scales with the total dendritic length, the spatial correlation of dendritic branches within an arbor has a universal functional form, and small parts of an arbor are self-similar. We proposed that these properties result from maximizing the repertoire of possible connectivity patterns between dendrites and surrounding axons while keeping the cost of dendrites low. We solved this optimization problem by drawing an analogy with maximization of the entropy for a given energy in statistical physics. The solution is consistent with the above observations and predicts scaling relations that can be tested experimentally. In addition, our theory explains why dendritic branches of pyramidal cells are distributed more sparsely than those of Purkinje cells. Our results represent a step toward a unifying view of the relationship between neuronal morphology and function. Fig. 1). The dendritic arbor is a complex branching structure, which receives signals from thousands of other neurons and conducts them toward the cell body, where they are integrated. The axonal arbor typically spans a larger territory than a dendritic arbor and conducts signals from the cell body to synapses, where signals are transmitted to dendrites of thousands of other neurons (Fig. 1). The majority of synapses on neurons discussed below are formed on short dendritic protrusions called spines (Fig. 1). Because synaptic transmission requires a physical contact between dendrites and axons, dendritic arbor shape determines which axons are accessible to which dendrites (2-9). This suggests that the spatial distribution of dendrites is important for understanding brain function (10-15).Interestingly, dendritic arbor shape can vary widely among neurons of the same class and between different classes. Consider, for example, pyramidal cells, which comprise Ϸ80% of all neurons in the cerebral cortex (16). The total length of basal dendrites of pyramidal cells L, and the basal arbor radius R, defined as the rms distance between any 2 dendritic segments ( Fig. 2A), vary widely among different areas of the cortex (17-19). Furthermore, dendritic branches of pyramidal cells are distributed more sparsely than those of Purkinje cells, the principal neurons in the cerebellum (ref. 11 and Fig. 2B). To use these observations for inferring neuronal function, we need to identify principles governing arbor shape.We start by showing that, within pyramidal cell class, R and L, and the short-range correlation in the locations of dendrites within a cell, follow scaling laws. The corresponding exponents are related, suggesting that statistics of different arbors and different parts of the same arbor are governed by one principle. Second, we propose an explanation for these ...

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Section: Discussionmentioning

confidence: 99%

Maximization of the connectivity repertoire as a statistical principle governing the shapes of dendritic arbors

Wen

Stepanyants

Elston³

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

120

127

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“…Topology, along with trace centerlines (Fig. 1B), may also be relevant for studying growth or pathology processes (Hao and Shreiber, 2007; Meyer-Luehmann et al, 2008) and wiring principles (Stepanyants et al, 2004; Marks and Burke, 2007). For connectomics, higher branch orders and terminal regions (Fig.…”

Section: Introductionmentioning

confidence: 99%

The DIADEM Metric: Comparing Multiple Reconstructions of the Same Neuron

2011

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Digital reconstructions of neuronal morphology are used to study neuron function, development, and responses to various conditions. Although many measures exist to analyze differences between neurons, none is particularly suitable to compare the same arborizing structure over time (morphological change) or reconstructed by different people and/or software (morphological error). The metric introduced for the DIADEM (DIgital reconstruction of Axonal and DEndritic Morphology) Challenge quantifies the similarity between two reconstructions of the same neuron by matching the locations of bifurcations and terminations as well as their topology between the two reconstructed arbors. The DIADEM metric was specifically designed to capture the most critical aspects in automating neuronal reconstructions, and can function in feedback loops during algorithm development. During the Challenge, the metric scored the automated reconstructions of best-performing algorithms against manually traced gold standards over a representative data set collection. The metric was compared with direct quality assessments by neuronal reconstruction experts and with clocked human tracing time saved by automation. The results indicate that relevant morphological features were properly quantified in spite of subjectivity in the underlying image data and varying research goals. The DIADEM metric is freely released open source (http://diademchallenge.org) as a flexible instrument to measure morphological error or change in high-throughput reconstruction projects.

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“…In a detailed study of the architecture of dendritic trees of Cat alpha motoneurons, Marks and Burke (2007) found a similar left-skewed distribution for the angle between daughter branches (called dInterDau in their paper). From Figure 6C in their paper we estimated a mean value 50.7 and a SEM value of 2.2.…”

Section: Summary Discussion and Conclusionmentioning

confidence: 85%

The Flatness of Bifurcations in 3D Dendritic Trees: An Optimal Design

Pelt¹,

Uylings²

2012

Front. Comput. Neurosci.

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The geometry of natural branching systems generally reflects functional optimization. A common property is that their bifurcations are planar and that daughter segments do not turn back in the direction of the parent segment. The present study investigates whether this also applies to bifurcations in 3D dendritic arborizations. This question was earlier addressed in a first study of flatness of 3D dendritic bifurcations by Uylings and Smit (1975), who used the apex angle of the right circular cone as flatness measure. The present study was inspired by recent renewed interest in this measure. Because we encountered ourselves shortcomings of this cone angle measure, the search for an optimal measure for flatness of 3D bifurcation was the second aim of our study. Therefore, a number of measures has been developed in order to quantify flatness and orientation properties of spatial bifurcations. All these measures have been expressed mathematically in terms of the three bifurcation angles between the three pairs of segments in the bifurcation. The flatness measures have been applied and evaluated to bifurcations in rat cortical pyramidal cell basal and apical dendritic trees, and to random spatial bifurcations. Dendritic and random bifurcations show significant different flatness measure distributions, supporting the conclusion that dendritic bifurcations are significantly more flat than random bifurcations. Basal dendritic bifurcations also show the property that their parent segments are generally aligned oppositely to the bisector of the angle between their daughter segments, resulting in “symmetrical” configurations. Such geometries may arise when during neuronal development the segments at a newly formed bifurcation are subjected to elastic tensions, which force the bifurcation into an equilibrium planar shape. Apical bifurcations, however, have parent segments oppositely aligned with one of the daughter segments. These geometries arise in the case of side branching from an existing apical main stem. The aligned “apical” parent and “apical” daughter segment form together with the side branch daughter segment already geometrically a flat configuration. These properties are clearly reflected in the flatness measure distributions. Comparison of the different flatness measures made clear that they all capture flatness properties in a different way. Selection of the most appropriate measure thus depends on the question of research. For our purpose of quantifying flatness and orientation of the segments, the dihedral angle β was found to be the most discriminative and applicable single measure. Alternatively, the parent elevation and azimuth angle formed an orthogonal pair of measures most clearly demonstrating the dendritic bifurcation “symmetry” properties.

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Simulation of motoneuron morphology in three dimensions. I. Building individual dendritic trees

Cited by 20 publications

References 47 publications

Maximization of the connectivity repertoire as a statistical principle governing the shapes of dendritic arbors

Maximization of the connectivity repertoire as a statistical principle governing the shapes of dendritic arbors

The DIADEM Metric: Comparing Multiple Reconstructions of the Same Neuron

The Flatness of Bifurcations in 3D Dendritic Trees: An Optimal Design

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