Anticipatory neural activity improves the decoding accuracy for dynamic head-direction signals

Insects and vertebrates harbor specific neurons that encode the animals head direction (HD) and provide an internal compass for spatial navigation. Each HD cell fires most strongly in one preferred direction. As the animal turns its head, however, HD cells in rat anterodorsal thalamic nucleus (ADN) and other brain areas fire already before their preferred direction is reached, as if the neurons anticipated the future head direction. This phenomenon has been explained at a mechanistic level but a functional interpretation is still missing. To close this gap, we use a computational approach based on the animals movement statistics and a simple model for the behavior of the ADN head-direction network. Network activity is read out using population vectors in a biologically plausible manner, so that only past spikes are taken into account. We find that anticipatory firing improves the representation of the present HD by reducing the motion-induced temporal bias inherent in causal decoding. The amount of anticipation observed in ADN enhances the precision of the HD compass read-out by up to 40%. In addition, our framework predicts that neural integration times not only reflect biophysical constraints, but also the statistics of natural stimuli; anticipatory tuning should be found whenever neurons encode sensory signals that change gradually in time.\n\nSignificance statementAcross different brain regions, populations of noisy neurons encode dynamically changing stimuli. Decoding a time-varying stimulus from the population response involves a trade-off: For short read-out times, stimulus estimates are unreliable as the number of stochastic spikes will be small; for long read-out times, estimates are biased because they lag behind the true stimulus. We show that optimal decoding relies not only on finding the right read-out time window, but requires neurons to anticipate future stimulus values. We apply this framework to the rodent head-direction system and show that the experimentally observed anticipation of future head directions can be explained at a quantitative level from the neuronal tuning properties, the network size, and the animals head-movement statistics.