Abstract
A typical neuron signals to downstream cells when it is depolarized and fires sodium spikes. Some neurons, however, also fire calcium spikes when hyperpolarized. The function of such bidirectional signaling remains unclear in most circuits. Here, we show how a neuron class that participates in vector computation in the fly central complex employs hyperpolarization-elicited calcium spikes to invert two-dimensional mathematical vectors. By switching from firing sodium to calcium spikes, these neurons implement a ∼180° realignment between the vector encoded in the neuronal population and the fly's internal compass signal, thus inverting the vector. We show that calcium spikes rely on the T-type calcium channel Ca-α1T and argue via analytical and experimental approaches that these spikes enable vector computations in portions of angular space that would otherwise be inaccessible. These results reveal a seamless interaction between molecular, cellular, and circuit properties for implementing vector mathematics in the brain.