Journal of Neuroscience, Vol 12, 2403-2416, Copyright © 1992 by Society for Neuroscience
A parsimonious description of motoneuron dendritic morphology using computer simulation
RE Burke, WB Marks and B Ulfhake
Laboratory of Neural Control, National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, Maryland 20892.
Most quantitative descriptions of neuronal dendrite morphology involve
tabulations of measurements and correlations among them. The present work
is an attempt to extract from such data a parsimonious set of parameters
that are sufficient to describe the quantitative features of individual and
pooled dendrites, including their statistical variability. A relatively
simple stochastic (Monte Carlo) model was devised to simulate branching
dendritic trees. The necessary parameters were then derived directly from
measurements of 64 completely reconstructed dendrites belonging to six
gastrocnemius alpha- motoneurons, labeled by intracellular injection of
HRP. Comparison of actual and simulated dendrites was used to guide the
process of parameter extraction. The model included only two processes, one
to generate individual branches given their starting diameters and the
second to select starting diameters for the daughter branches produced at
dichotomous branching points. The stochastic process for branch generation
was controlled by probability functions for branching (Pbr) and for
terminating (Ptrm), together with a constant rate of branch taper. All
model parameters were fixed by motoneuron measurements except for branch
taper rate, which was allowed to vary within limits consistent with
observed taper rates in order to generate the appropriate total number of
branches. The simplest model (model 1), in which Pbr and Ptrm depended only
on local branch diameter, produced simulated dendrites that fit many, but
not all, characteristics of actual motoneuron dendrites. Two additional
properties produced significant improvements in the fit: (1) a small but
significant dependence of daughter diameters on the normalized starting
diameter of the parent branch, and (2) a dependence of Pbr and Ptrm on
distance from the soma as well as on local branch diameter. The process of
developing this model revealed unsuspected relations in the original data
that suggest the existence of fundamental mechanisms for morphological
control. The final model succinctly describes a large amount of data and
will enable quantitative comparisons between the dendritic structures of
different types of neurons, regardless of their relative sizes.
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