Emergence of Multiplication in a Biophysical Model of a Wide-Field Visual Neuron for Computing Object Approaches: Dynamics, Peaks, & Fits

Many species show avoidance reactions in response to looming object approaches. In locusts, the corresponding escape behavior correlates with the activity of the lobula giant movement detector (LGMD) neuron. During an object approach, its firing rate was reported to gradually increase until a peak is reached, and then it declines quickly. The $\eta$-function predicts that the LGMD activity is a product between an exponential function of angular size $\exp(-\Theta)$ and angular velocity $\dot{\Theta}$, and that peak activity is reached before time-to-contact (ttc). The $\eta$-function has become the prevailing LGMD model because it reproduces many experimental observations, and even experimental evidence for the multiplicative operation was reported. Several inconsistencies remain unresolved, though. Here we address these issues with a new model ($\psi$-model), which explicitly connects $\Theta$ and $\dot{\Theta}$ to biophysical quantities. The $\psi$-model avoids biophysical problems associated with implementing $\exp(\cdot)$, implements the multiplicative operation of $\eta$ via divisive inhibition, and explains why activity peaks could occur after ttc. It consistently predicts response features of the LGMD, and provides excellent fits to published experimental data, with goodness of fit measures comparable to corresponding fits with the $\eta$-function.