# Modeling retinal microcircuits for ganglion cells of different size

#### Abstract

As the ganglion cell receptive field center expands from central to peripheral retina, the distribution of sensitivity across the center remains Gaussian, but peak sensitivity declines. To identify anatomical circuitry that might explain this physiology, I measured the density of bipolar cell synapses on the dendritic membrane of beta (X) and alpha (Y) ganglion cells and the distribution of dendritic membrane across their dendritic fields. Both central and peripheral beta cells receive bipolar cell synapses at a density of $\sim$28/100 $\mu {\rm m}\sp2$ of dendritic membrane; central and peripheral alpha cells receive $\sim$13/100 $\mu {\rm m}\sp2$. The distribution of dendritic membrane across the dendritic field is dome-like; therefore the distribution of bipolar cell synapses is also dome-like. As the dendritic field enlarges, total postsynaptic membrane increases with field radius, but only linearly. Consequently, density of postsynaptic membrane in the dendritic field declines, and so does density of synapses within the field. The results suggest a simple model in which the receptive field center's Gaussian profile arises from the dome-like distribution of bipolar cell synapses across the dendritic field, and peak sensitivity is set by their average density in the dendritic field.^ I constructed anatomically correct compartmental models of three beta (X) ganglion cells that span a ten-fold range of dendritic field diameter and a ten-fold range in the number of bipolar cell synapses. For $\rm R\sb{m} = 50 k\Omega$-cm$\sp2$ and a quantal conductance of 100 pS, distal and proximal synapses are equally effective. Spatial summation is linear as long as no more than $\sim$5% of a cell's synapses are activated. All three cells show a dome-like distribution of sensitivity whose peak is 6-fold greater for the small cell. Temporal summation is linear for quantal rates up to about 50 quanta/synapse/sec. The simulations account for both the Gaussian-like sensitivity across the receptive field centers and the greater peak sensitivity of small ganglion cells by the density of excitatory synapses within the dendritic field. Linearity constrains the quantal conductance to be small, fast, and not too frequent; whereas signal-noise considerations constrain these parameters in the opposite direction. ^

#### Subject Area

Biology, Anatomy|Biology, Neuroscience|Engineering, Biomedical

#### Recommended Citation

Christian K Kier, "Modeling retinal microcircuits for ganglion cells of different size" (January 1, 1995). Dissertations available from ProQuest. Paper AAI9532218.
http://repository.upenn.edu/dissertations/AAI9532218

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