Journal of Neurophysiology, Vol 64, Issue 1 248-261, Copyright © 1990 by APS
Bifurcation analysis of nonlinear retinal horizontal cell models. II. Network properties
R. L. Winslow and S. Ma
Department of Physiology, University of Minnesota School of Medicine, Minneapolis.
1. We have previously presented a model of horizontal-cell soma isolated
from fish retina. The model consists of a synaptic conductance representing
input from photoreceptors in parallel with voltage-dependent membrane
currents. Membrane-current models are based on I-V curves measured in
isolated fish horizontal cells. Bifurcation theory was used to analyze
model properties. The major findings of this study were 1) the inward Ca2+
current must be inactivated to account for horizontal-cell resting
potentials and hyperpolarizing responses to light stimuli in a background
of dark, and 2) the synaptic conductance controls the bifurcation structure
of the model, with bistable behavior occurring at small and monostable
behavior occurring at larger values of the synaptic conductance. The
synaptic conductance at the point of transition from bistable to monostable
behavior corresponds to the activation of as few as 100 synaptic channels.
Thus tonic synaptic input from photoreceptors and inactivation of the
inward Ca2+ current act to "linearize" responses of isolated
horizontal-cell models. 2. The model described in this paper extends these
analyses to large networks of horizontal cells in which each cell is
coupled resistively to its nearest neighbors and is modeled with the use of
the full complement of nonlinear membrane currents. Network responses to
arbitrary patterns of conductance change (simulating inputs from
photoreceptors), current-, or voltage-clamp stimuli are computed using the
Newton iteration. The Newton descent direction is computed using either
conjugate gradient (CG) or preconditioned CG algorithms. 3. An analysis of
network stability properties is performed. Network I-V curves are computed
by voltage-clamping the center node and computing the current required to
maintain the clamp voltage. Computations are performed on networks of model
cells in which the Ca2+ current is fully activated and the synaptic
conductance is zero, thus making each cell as nonlinear as possible.
Coupling conductance values slightly greater than 100 pS provide a current
shunt sufficient to prevent the generation of Ca2+ action potentials in the
network. This coupling conductance corresponds to the conductance of as few
as two gap-junction channels and is more than two orders of magnitude less
than the coupling known to exist between pairs of cultured horizontal
cells.(ABSTRACT TRUNCATED AT 400 WORDS)
