Neuron model derivation.

<div><p>Accurate navigation often requires the maintenance of a robust internal estimate of heading relative to external surroundings. We present a model for angular velocity integration in a desert locust heading circuit, applying concepts from early theoretical work on heading circuits in mammals to a novel biological context in insects. In contrast to similar models proposed for the fruit fly, this circuit model uses a single 360° heading direction representation and is updated by neuromodulatory angular velocity inputs. Our computational model was implemented using steady-state firing rate neurons with dynamical synapses. The circuit connectivity was constrained by biological data, and remaining degrees of freedom were optimised with a machine learning approach to yield physiologically plausible neuron activities. We demonstrate that the integration of heading and angular velocity in this circuit is robust to noise. The heading signal can be effectively used as input to an existing insect goal-directed steering circuit, adapted for outbound locomotion in a steady direction that resembles locust migration. Our study supports the possibility that similar computations for orientation may be implemented differently in the neural hardware of the fruit fly and the locust.</p></div>