Source: Luscher and Shiner (1990) Computation of action
potential propagation and presynaptic bouton activation in
terminal arborizations of different geometries. Biophys.
J. 58: 1377-1388.
The purposes of this model are: 1) to test the ability of
SNNAP to reproduce aspects of a model developed by Luscher
and Shiner (1990); and 2) demonstrate a method for modeling
branching structures. Only the first two figures in the
paper were reproduced by this model. Briefly, a parent
axon gives rise to 7 or 9 daughter branches (Fig. 1 of
Luscher and Shiner, 1990). An action potential is able to
propagating through the branch point with 7 daughter
branches, but fails to propagate when the number of
daughter branches is increased to 9. Briefly, the
properties of the model are homogenous and are described by
a Hodgkin-Huxley model that has been adjusted to 22.5 C.
Each process is described by 10 compartments and each
compartment is the equivalent of 0.2 x the resting space
Three simulations are included in this example:
F1_7brch.smu simulates conduction through a branch point
with 7 daughter branches (i.e., the equivalent of Luscher
and Shiner Fig. 1Bc (1990). The results of this simulation
are illustrated in Luscher_Shiner_Fig_1Bc.jpg.
F1_9brch.smu simulates conduction block at a branch point
with 9 daughter branches (i.e., the equivalent of Luscher
and Shiner Fig. 1Bd (1990). The results of this simulation
are illustrated in Luscher_Shiner_Fig_1Bd.jpg.
F2.smu simulates the increase in the amplitude of a
propagating spike as it approached a sealed end (i.e., the
equivalent of Luscher and Shiner Fig. 2 (1990). The
results of this simulation are illustrated in
While developing a model of a branched structure, one must
careful how to compute the cytoplasmic resistance at the
branch point. There are two methods. The first is
described by DeSchutter and Steuber (2001, Modeling simple
and complex active neurons. In: DeSchutter (Ed.)
Computational Neuroscience, CRC Press, New York, pp. 233-
258). The present simulation illustrates a second method.
A 'dumby' compartment (brch.neu) is used to link the
branches together. The biophysical properties of the
compartment are such that it doesn't significantly alter
the properties of the model and the coupling conductances
are adjusted as described by Parnas and Segev (1976, A
mathematical model for conduction of action potentials
along bifurcating axons. J. Physiol. (Lond.), 295: 323-