a, Fraction of neurons with elevated firing rates (magenta) and suppressed firing rates (cyan) in response to tones during rest. A roughly equal number of neurons were excited by the reafferent frequency as were excited by other frequencies. b, Fraction of rest-responsive neurons with elevated firing rates (magenta) and suppressed firing rates (cyan) in response to tones of varying frequency during running. Nearly 50% of neurons were responsive to non-reafferent frequencies during running, whereas fewer than 25% were responsive to the reafferent frequency. c, Heat map showing response strength (tone-evoked rate – baseline rate) for neurons responsive to the expected reafferent frequency (left, n = 114 neurons, N = 11 mice) and another frequency (+2 octaves, n = 120 neurons, N = 11 mice) during rest. Neurons ordered by magnitude of response independently for each heat map. d, Response strengths of the neurons in c during running. Neurons are re-sorted by magnitude of response. Twenty-three per cent of neurons retained their response to the reafferent frequency during running, consistent with a sparse representation of expected reafferent sounds. e, Two alternative models for how locomotion-related suppression could change following aVR experience. In each model, the black curves show frequency tuning curves of three neurons during rest, red curves during running, and the green dashed line indicates the reafferent frequency. Across-neuron model: locomotion-related suppression is uniform across frequencies within a neuron but is strongest for neurons that are strongly responsive to the expected reafferent frequency. Within-neuron model: suppression is non-uniform at the single neuron level and regardless of how strongly the neuron responds to the expected reafferent frequency, suppression is always strongest at the reafferent frequency. f, Tuning curves for five example neurons measured during rest (black) and running (red). The best frequency (BF) for each neuron is shown by the blue triangle, and the reafferent frequency to which each mouse was acclimated is shown by the green dashed line. In all five neurons, locomotion-related suppression was strong at the reafferent frequency relative to other frequencies, regardless of the neuron’s best frequency. g, Neurons were sorted by their best frequency, measured relative to the reafferent frequency that each mouse experienced. Locomotion-related suppression at the expected reafferent frequency (green) and averaged across all non-reafferent frequencies (black). Regardless of a neuron’s best frequency, suppression was always strongest at the reafferent frequency, supporting the within-neuron model in e. Sample size: N = 11 mice, n = 314 neurons. Shaded regions show 95% confidence bounds estimated with a bootstrap analysis repeated 1,000 times. h, Probability of observing a minima in the gain function of individual neurons at each frequency, measured relative to the reafferent frequency. A substantial number of neurons had minima in their gain functions at the expected reafferent frequency, further supporting the within-neuron model in e. Sample size: N = 11 mice, n = 314 neurons. Shaded region shows a null distribution, which we estimated by randomly assigning to each neuron a reafferent frequency rather than using the actual frequency experienced by the mouse from which the neuron was recorded. This shuffling was performed 1,000 times and the 95% confidence bounds of the distribution were computed. Error bars show the 95% confidence bounds estimated from a bootstrap analysis repeated 1,000 times.