Morphoelectrotonic Transforms - a Mathematica Package

Hagai Agmon-Snir hagai at helix.nih.gov
Fri May 26 09:36:51 EST 1995

           Mathematica Package for Morphoelectrotonic Transforms

A first version of a Mathematica package for rendering
Morphoelectrotonic Transforms (METs) of reconstructed dendritic
structures is available by anonymous ftp. This package provides means
for reading, transforming and rendering dendrites in various
METs. Also available are a sample Mathematica notebook and two public
domain morphological files with the appropriate format (we thank
Rodney Douglas for making his reconstructed neurons available to the
neuroscience public).

The Morphoelectrotonic Transform is described in (see abstract below):

Zador, A., Agmon-Snir, H., and Segev, I. 1995. The morphoelectrotonic
transform: a graphical approach to dendritic function. J. Neuroscience 15:

The files can be reached using the web at


or using ftp:

ftp bart.niddk.nih.gov
enter as anonymous, enter your email address as password and cd pub/hagai/MET.
All the files are ascii.

Any comments are welcome. For any help in customizing the package for
specific needs (or writing the code in other computer language),  call:

Hagai Agmon-Snir                      Tel: (301) 496-6136
Surface mail:                              (301) 496-4325
Mathematical Research Branch, NIDDK   Fax: (301) 402-0535
9190 Rockville Pike - Suite 350
Bethesda, MD 20814-3800

E-mail: hagai at helix.nih.gov

Tony Zador can be reached at zador at salk.edu. Idan Segev can reached at
idan at hujivms.huji.ac.il

Abstract of Zador et al., 1995:

Electrotonic structure of dendrites plays a critical role in neuronal
computational and plasticity.  In this paper we develop two novel measures
of electrotonic structure that describe intraneuronal signaling in
dendrites of arbitrary geometry.  The log-attenuation L_ij measures the
efficacy, and the propagation delay P_ij the speed, of signal transfer
between any two points i and j.  These measures are additive, in the sense
that if j lies between i and k, the total distance L_ik is just the sum of
the partial distances: L_ik = L_ij + L_jk, and similarly P_ik = P_ij +
P_jk.  This property serves as the basis for the morphoelectrotonic
transform (MET), a graphical mapping from morphological into electrotonic
space. In a MET, either P_ij or L_ij replace anatomical distance as the
fundamental unit and so provide direct functional measures of intraneuronal
signaling. The analysis holds for arbitrary transient signals, even those
generated by nonlinear conductance changes underlying both synaptic and
action potentials. Depending on input location and the measure of interest,
a single neuron admits many METs, each emphasizing different functional
consequences of the dendritic electrotonic structure.  Using a single layer
5 cortical pyramidal, we illustrate a collection of METs that lead to a
deeper understanding of the electrical behavior of its dendritic tree.  We
then compare this cortical cell to representative neurons from other brain
regions (cortical layer 2/3 pyramidal, region CA1 hippocampal pyramidal,
and cerebellar Purkinje). Finally, we apply the MET to electrical signaling
in dendritic spines, and extend this analysis to calcium signaling within
spines. Our results demonstrate that the MET provides a powerful tool for
obtaining a rapid and intuitive grasp of the functional properties of
dendritic trees.

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