Bifurcation analysis of nonlinear retinal horizontal cell models. II. Network properties.

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)