Uylings, Harry BM

van Pelt, Jaap

English

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Jaap van Pelt

Harry BM Uylings

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The flatness of bifurcations in 3D neuronal branching patterns

POSTER PRESENTATION Open Access
The flatness of bifurcations in 3D neuronal
branching patterns
Jaap van Pelt1*, Harry BM Uylings2
From Twentieth Annual Computational Neuroscience Meeting: CNS*2011
Stockholm, Sweden. 23-28 July 2011
The geometry of bifurcations in natural branching sys-
tems often reflects optimization constraints during for-
mation, 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 con-
cluded that the observed flatness already naturally
emerges from random conditions.
In the present study, a number of different geometri-
cal measures of flatness has been developed and evalu-
ated 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 dendri-
tic bifurcations appeared to be significantly different
(Kolmogorov-Smirnov test). Dendritic bifurcations
appeared to be more planar than random ones. In addi-
tion, parent segments in dendritic bifurcations have a
strong preference to be aligned oppositely to the angular
bisector of the daughter segments. These findings sug-
gest that dendritic bifurcations are also formed under
the influence of optimality constraints during the den-
dritic branching process. The flatness measure most
strongly expressing the flatness of a 3D bifurcation was
found to be the dihedral angle b 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 b has a uniform distribution for random bifurca-
tions but is highly skewed for dendritic ones (Fig. 1).
We conclude that 3D bifurcations in rat cortical pyra-
midal 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 dis-
tances between the nodes comprising the bifurcation.
* Correspondence: jaap.van.pelt@cncr.vu.nl
1Computational Neuroscience Group, Department of Integrative
Neurophysiology, CNCR, VU University Amsterdam, De Boelelaan 1085, 1081
HV Amsterdam, The Netherlands
Full list of author information is available at the end of the article
Figure 1 Frequency distribution of the dihedral angle b of random
bifurcations (horizontal line), and of basal dendritic bifurcations
(dashed histogram).
van Pelt and Uylings BMC Neuroscience 2011, 12(Suppl 1):P349
http://www.biomedcentral.com/1471-2202/12/S1/P349
© 2011 van Pelt and Uylings; licensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly cited.
Acknowledgments
This work was supported by EU BIO-ICT Project SECO (216593).
Author details
1Computational Neuroscience Group, Department of Integrative
Neurophysiology, CNCR, VU University Amsterdam, De Boelelaan 1085, 1081
HV Amsterdam, The Netherlands. 2Dept. Anatomy & Neuroscience, VU
University Medical Center, P.O. Box 7057, 1007 MB Amsterdam, The
Netherlands.
Published: 18 July 2011
References
1. Uylings HBM, Smit GJ: Three-dimensional branching structure of
pyramidal cell dendrites. Brain Research 1975, 87:55-60.
2. Kim Y, Sinclair R, De Schutter E: Local planar dendritic structure: a unique
biological phenomenon? BMC Neuroscience 2009, 10(Suppl I):P4.
3. Bray D: Mechanical tension produced by nerve cells in tissue culture. J.
Cell Sci 1979, 37:391-410.
doi:10.1186/1471-2202-12-S1-P349
Cite this article as: van Pelt and Uylings: The flatness of bifurcations in
3D neuronal branching patterns. BMC Neuroscience 2011 12(Suppl 1):
P349.
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van Pelt and Uylings BMC Neuroscience 2011, 12(Suppl 1):P349
http://www.biomedcentral.com/1471-2202/12/S1/P349
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Cite this article as: van Pelt and Uylings: The flatness of bifurcations in 3D neuronal branching patterns.

De Schutter E: Local planar dendritic structure: a unique biological phenomenon? BMC Neuroscience 2009, 10(Suppl I):P4. 3. Bray D: Mechanical tension produced by nerve cells in tissue culture.

GJ: Three-dimensional branching structure of pyramidal cell dendrites. Brain Research

Submit your next manuscript to BioMed Central and take full advantage of: • Convenient online submission • Thorough peer review • No space constraints or color ﬁgure charges • Immediate publication on acceptance

http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3240466

The flatness of bifurcations in 3D neuronal branching patterns

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