Model circuit of spiking neurons generating directional selectivity in simple cells
Authors: Maex R. , Orban G. A. 
Published: December 2017

1. We here consider the property of directional selectivity (DS) in simple cells of layer 4 of cat area 17 as an instance of a receptive field (RF) transformation between two monosynaptically connected neuron populations: the afferent geniculate (lateral geniculate nucleus, LGN) cells and their target, layer 4 simple cells. We have studied this particular RF transformation because the large set of experimental data available allowed us to restrain the synaptic organization of our model layer 4 circuitry. 2. The one-compartment, spiking model neurons of the layer 4 circuitry are excitatory (adapting) or inhibitory (nonadapting). They all have simple-cell RFs composed of two spatially separated ON and OFF subregions. The sequence of the subregions across the neurons' RFs, which is determined by the geniculocortical inputs they receive, varies independently from their preferred direction of stimulus motion, which is determined by spatial asymmetries in their corticocortical inputs. 3. Synaptic transmission in the model layer 4 circuitry is mediated via non-N-methyl-D-aspartate (non-NMDA) receptors (geniculocortical excitation), via NMDA receptors (corticocortical excitation), and via gamma-aminobutyric acid-A receptors (corticocortical inhibition). Excitatory and inhibitory cortical neurons receive the same afferents. However, excitatory neurons form efferent synapses exclusively with neurons having the same RF characteristics, and preferentially with those having the same RF position. Inhibitory neurons form synapses preferentially with neurons having different RF characteristics or adjacent RF positions. 4. By comparing the neurons' numerically computed responses to visual stimuli with those of actual simple cells, the topology of the corticocortical connections has been constrained. The experimental responses to stationary and moving, and to bar as well as grating, stimuli are consistently reproduced with a single constant parameter setting. 5. Subsequently, the model has been analyzed from a system-theoretic approach and has been manipulated in order to find the components critical for its proper functioning. Variations on the model have been simulated for evaluating the performance of alternative connection schemes. 6. Spatially opponent inhibition between model simple cells with antagonistic RF subregions is necessary for the restoration of linearity lost at the LGN output. It hyperpolarizes model simple cells when the contrast polarity of an efficient stimulus is reversed and prevents, particularly in directionally nonselective cells, a frequency doubling of the responses to sine wave gratings of low spatial frequencies. 7. Directionally opponent inhibition between model simple cells preferring opposite directions of motion is necessary for the generation of genuine DS (a ratio of firing rates > 2 for opposite directions of motion). 8. The corticocortical excitatory polysynaptic feedback loops in the model are able to provide the time delays needed to generate DS, and even to preserve DS at very low speeds. The strength spatial extension, and time course of this corticocortical feedback excitation, together with the dynamics of the geniculate afferents and the width of the RF, determine the tuning of model simple cells in the temporal and velocity domain. 9. The present model generates directionally selective responses to stimulus motion over distances smaller than the width of a single subregion and as small as the spacing between the afferent geniculate RFs. The direction-selective mechanism acts uniformly across the entire width of a subregion. Thus the position invariance of DS arises in the present model at the same level as DS itself. The same holds for the stimulus polarity (light vs. dark) invariance of DS. Consequently, there is no need for highly hierarchical models in which all these characteristics accumulate in simple cells by pooling from lower-order subunits or neurons.