Approaching object acceleration differentially affects the predictions of neuronal collision avoidance models

Abstract

The processing of visual information for collision avoidance has been investigated at the biophysical level in several model systems. In grasshoppers, the (so-called) $\eta$ model captures reasonably well the visual processing performed by an identified neuron called the lobular giant movement detector as it tracks approaching objects. Similar phenomenological models have been used to describe either the firing rate or the membrane potential of neurons responsible for visually guided collision avoidance in other animals. Specifically, in goldfish, the $\kappa$ model has been proposed to describe the Mauthner cell, an identified neuron involved in startle escape responses. In the vinegar fly, a third model was developed for the giant fiber neuron, which triggers last resort escapes immediately before an impending collision. One key property of these models is their prediction that peak neuronal responses occur at a fixed delay after the simulated approaching object reaches a threshold angular size on the retina. This prediction is valid for simulated objects approaching at a constant speed. We tested whether it remains valid when approaching objects accelerate. After characterizing and comparing the models’ responses to accelerating and constant speed stimuli, we find that the prediction holds true for the $\kappa$ and the giant fiber model, but not for the $\eta$ model. These results suggest that acceleration in the approach trajectory of an object may help distinguish and further constrain the neuronal computations required for collision avoidance in grasshoppers, fish and vinegar flies.