Extended Data Fig. 9: Model for how heading and goal information is integrated in individual PFL3 neurons and predicting PFL3 output using FC2 activity as the goal signal.

a, Schematic for how PFL3 neurons integrate heading and goal information. Two inputs contribute to the membrane potential of a PFL3 cell. One input comes from the protocerebral bridge and yields a membrane potential signal, V_PB, in the PFL3 cell that is proportional to a cosine function of the difference between the fly’s heading angle, H, and the PFL3 cells’ preferred heading angle, H_pref. The other input comes from the fan-shaped body and results in the membrane potential signal, V_FB, in the PFL3 cell that is a cosine function of the difference between the fly’s goal angle, G, and the cell’s preferred goal angle, G_pref. The membrane potential measured at the soma, Vm, is dominated by V_PB because the fan-shaped body is electrotonically farther from the soma than the protocerebral bridge (consistent with the more modest goal-dependent changes in Vm, compared to spike rate, that we showed in Extended Data Fig. 7). The spike rate of the neuron is given by a nonlinear function of a sum of the cosine functions describing V_PB and V_FB (with V_FB scaled by a weighting factor d, reflecting the relative strengths of these two inputs at the spike initiation zone). b, Spike-rate vs Vm (spikes removed) curves from our whole-cell recordings. Data from different goal angles relative to the cell’s preferred heading are shown in different colors. We assume the relationship between the PFL3 Vm and spike rate would have been constant—i.e., not vary with goal direction—if we were measuring Vm at the spike initiation zone. The fact that this relationship depends on the fly’s goal angle in our somatic measurements, is, we believe, due to the somatic membrane potential predominantly reflecting heading input from the bridge and thus missing the goal-related Vm changes from the fan-shaped body. In the model, we assume that the spike-initiation zone has access to both the heading- and goal-related Vm signals. Each dot shows the mean across cells. Right PFL3 neurons were included by flipping the sign of the goal-to-preferred heading angle (Methods). c, The same curves as in panel b, but shifted along the horizontal axis in order to maximally align them. The black curve is a softplus function fit to the data points (see Methods for details). d, The shifts from panel c, plotted as a function of the goal angle of the corresponding spike-rate curve. The fact that these shifts have a roughly cosine shape as a function of the goal angle is consistent with: (1) the existence of a cosine-shaped goal input in the fan-shaped body (as our model assumes) and (2) our hypothesis that the voltage consequences of the goal in the fan-shaped body are not fully evident in the soma, thus requiring the Vm shift in the plot in panel b, to align all the curves to a common spike-rate vs. Vm underlying function (as our model assumes). e, Overlay of model predictions from Fig. 4f (lines) and calcium imaging results from Fig. 5d (open circles) for right and left LAL signals and for the R–L turning signal. f, The model error—i.e., the angular difference between the zero heading (the heading angle where the turning signal is zero and the slope is negative) and G (the goal angle)—as a function of G. g, An example virtual rotation trial from our FC2 imaging dataset alongside a computer-generated (i.e., synthetic) EPG/∆7 heading signal and the fly’s behaviour. The synthetic EPG/∆7 heading signal was generated using the term for the heading input in our PFL3 model, with the fly’s heading, H, taken to be the inverse of the bar angle. The rightmost column shows the predicted Right-Left (R-L) PFL3 activity from the model, when using the measured FC2 calcium signal (normalized) and the synthetic heading signal as model inputs (see Methods for details). h, Turning velocity as a function of predicted R-L asymmetry during the 2 s open-loop period of the bar jump. Each grey dot is a trial from our FC2 imaging dataset. Bar-jump trials used in Fig. 1 are shown in black. The example bar-jump trial in panel g is shown in red. i, Turning velocity as a function of measured R-L asymmetry (z-scored) during the 2 s open-loop period of the bar jump. Each grey dot is a trial from our PFL3 LAL imaging dataset. Trials selected using the same behavioural criteria as in Fig. 1 are shown in black. j, Predicted R-L asymmetry as a function of flies’ angular distance to goal angle (black) and turning velocity (grey) for FC2 imaging dataset. Mean ± s.e.m. across flies is shown (n = 10).

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