Figure 2. Quantifying the effect of eye rotation on heading tuning curves. A–C, Schematic illustration of possible effects of eye rotation. Black curves represent responses to pure translation. Red and blue curves represent responses to combinations of translation and either rightward or leftward rotation, respectively. A, Schematic illustration of complete compensation for eye rotations. B, Schematic tuning of a cell with a forward heading preference (90°) that does not compensate for rotation, producing shifts of the peak and trough of the tuning curve in opposite directions. C, Schematic tuning of a cell with a lateral heading preference (180°, leftward) that does not compensate for rotation resulting in changes in tuning bandwidth without a shift in the heading preference. D–F, Illustration of steps in the computation of partial shifts. D, Tuning curves from a neuron responding to simulated translation and simulated rotation in the 2D environment. E, Both tuning curves are linearly interpolated and the translation+rotation tuning curve (blue) is vertically scaled and shifted to match the range of responses in the pure translation curve (black). F, Dashed lines indicate circularly shifted segments of the pure translation tuning curve that minimize the sum of squared error in each half of the translation+rotation tuning curve (0:180°, 180:360°). Partial shifts are indicated with arrows. Panels B, C, F show that the expected direction of the shift for each tuning curve half does not depend on heading preference.