Uniform Growth and Neuronal Integration.
oystein H. Olsen, Farzan Nadim, Andrew A. V. Hill and Donald H. Edwards.
Department of Biology, Emory University, Atlanta, GA 30322, the
Neuroscience and Behavior Program, Morrill Science Center (Biology),
University of Massachusetts, Amherst, MA 01003, and the Department of Biology,
Georgia State University, Atlanta, GA, 30302-4010.
APStracts 3:0095N, 1996.
SUMMARY AND CONCLUSIONS
1. The cable equations were analysed to determine the effects of two patterns
of uniform growth on the passive and active integrative properties of neurons.
2. During uniform isoelectrotonic growth, the diameters of all neuronal
processes increase as the square of their increase in length, while the
specific electrical properties and branch terminal conditions of the neuron
remain constant. An analytical inductive proof is given to show that, for any
neuron, uniform isoelectrotonic growth increases the input conductance
everywhere by the cube of the growth factor, but leaves the active and passive
spread of membrane potential within the neuron unchanged. The spread of
membrane voltage is unchanged because this pattern of growth enables both the
axial and membrane currents everywhere in the cell to increase by the cube of
the growth factor . Synaptic inputs would evoke the same responses in the
isoelectrotonically larger cell as in the smaller cell if the total
postsynaptic conductance of the synapse increased with the dendritic membrane
area. 3. During uniform isometric growth, the diameter and lengths of all
processes increase by the same factor, while the specific electrical
properties and branch terminal conditions remain constant. This pattern of
uniform growth increases the input conductance by the square of the growth
factor, and also increases the attenuation, delay and low-pass filtering of
the cell's responses. Voltage attenuation increases with isometric growth
because the axial current increases in proportion to growth, while the
membrane current increases in proportion to the square of the growth factor.
Isometric growth reduces the ability of distal synaptic inputs to affect the
membrane potential at proximal integrating sites, even after the synaptic
conductance has increased to compensate for the increased input conductance.
4. These two patterns of uniform growth help define the consequences of all
types of uniform growth for neuronal integration and responsiveness.
Received 26 February 1995; accepted in final form 13 May 1996.
APS Manuscript Number J154-6.
Article publication pending J. Neurophysiol.
ISSN 1080-4757 Copyright 1996 The American Physiological Society.
Published in APStracts on 5 June 96