An Optimization framework for Nonspiking Neuronal Networks and Aided Discovery of a Model for the Elementary Motion Detector

Abstract

We present a general optimization procedure that given a parameterized network of nonspiking conductance based compartmentally modeled neurons, tunes the parameters to elicit a desired network behavior. Armed with this tool, we address the elementary motion detector problem. Central to established theoretical models, the Hassenstein-Reichardt and Barlow-Levick detectors, are delay lines whose outputs from spatially separated locations are prescribed to be nonlinearly integrated with the direct outputs to engender direction selectivity. The neural implementation of the delays--which are substantial as stipulated by interomatidial angles--has remained elusive although there is consensus regarding the neurons that constitute the network. Assisted by the optimization procedure, we identify parameter settings consistent with the connectivity architecture and physiology of the Drosophila optic lobe, that demonstrates that the requisite delay and the concomitant direction selectivity can emerge from the nonlinear dynamics of small recurrent networks of neurons with simple tonically active synapses. Additionally, although the temporally extended responses of the neurons permit simple synaptic integration of their signals to be sufficient to induce direction selectivity, both preferred direction enhancement and null direction suppression is necessary to abridge the overall response. Finally, the characteristics of the response to drifting sinusoidal gratings are readily explained by the charging-up of the recurrent networks and their low-pass nature.