The optic flow field resulting from roll-rotation to the left (A) is plotted on the visual unit-sphere surrounding the fly (B) and in a 2D cylindrical projection (C). The orientation and length of each arrow indicates the direction and magnitude of local retinal image shifts at different positions within the spherical visual field.
(D) A small dot traveling on a circular path is used to characterize a LPTC's response to local motion at different positions in the fly's visual field. The response of the directional selective neuron is modulated by the changes of the dot's directional motion (for further details see [40] and Materials and Methods section). horizontal scale bar: 500 ms, vertical scale bar: 10 mV.
(E) Part of the receptive field map of the tangential cell VS6 as obtained by Krapp et al. [17] using the experimental procedure shown in (D). The orientation and length of the arrows indicate the local preferred direction and relative motion sensitivity at the respective position within the cell's receptive field. The green circle marks the approximate position of the cell's preferred axis of rotation. Note that the cell's local preferred directions are oriented along concentric circles centered on the preferred axis in a manner reminiscent of the motion vectors in a roll flow field (C) and (E).

The responses of the NMN are shown to oblique downward (A) and upward (B) motion of a grating moving perpendicular to its orientation at 60° azimuth and 45° elevation. The bottom traces and arrows give the time courses and directions of the visual stimuli, respectively. In (A) and (B), horizontal scale bar: 1 s, vertical scale bar: 0.05 mV.
(C) Extracellular hook electrode recording from a neck muscle close to the neck motor neuron, different from those shown in (A) and (B). Threshold-triggered waveforms are overlaid to show the 1:1 correspondence between a low-latency sharp waveform, most likely the neck motor neuron action potential, and the subsequent longer-latency wide waveform, most likely the muscle potential of the innervated muscle. Horizontal scale bar: 1 ms, vertical scale bar: 0.2 mV.
(D) Directional tuning curve of the same cell for which individual recording traces are shown in (A) and (B). The vertical gray line indicates the local preferred direction defined by the phase of the first harmonic obtained from the tuning curve's Fourier transform.
(E) and (F) Maps of the local preferred directions and motion sensitivities obtained at many different positions with the “dot method” (Figure 1D) and the “grating method”. The boxed arrow in (F) is derived from the directional tuning curve in (D). Black arrows indicate experimental results; grey arrows were obtained by interpolation (see Materials and Methods section for further explanation).

Black arrows indicate experimental results; gray arrows were obtained by interpolation. All receptive fields are transformed to appear as if they were taken from the left FN and were obtained using the grating stimulus. The change of local preferred directions within these maps is reminiscent of specific optic flow fields generated during pitch (A), a combination of pitch and roll (B), and almost pure roll rotation (C).

Both receptive fields are transformed to appear as if they were recorded from the left side of the nervous system.
(A) The receptive field of a VCN^* NMN recorded from the OH muscle group.
(B) A small ipsilateral receptive field of an ADN^* NMN that extends to nearly 90° along the azimuth. This NMN was recorded from the TH muscle group. In both (A) and (B) the asterisks indicate that the nerve assignment is based upon the NMN-muscle connectivity [25] and not on a direct recording from the nerve itself (see results). All data were obtained using the grating stimulus.

(A) The receptive field of an ADN* NMN, obtained using the grating stimulus. The recording was made from the TH muscle group. The known NMN-muscle connectivity [25] strongly suggests that this unit belongs to the ADN. The asterisk indicates that this nerve assignment is based on anatomical criteria. The receptive field of this NMN is similar to that of an identified HSE tangential cell shown in (B). Both the ADN NMN and the HSE LPTC have receptive fields reminiscent of the optic flow field induced by yaw rotation. HSE data were taken from [29].
(C) The receptive field obtained from a NMN in the left CN, using the dot stimulus, is similar to that of the contralateral identified VS3 tangential cell shown in (D). Both the CN and VS3 receptive fields are similar to an optic flow field generated during nose-up banked turn to the left (for further explanation see text). VS3 data were taken from [27].

(A) A fly aligned with the coordinate system we use to plot the data. The fly faces the green circle at 0° azimuth, 0° elevation. An example preferred axis of rotation is plotted as a red arrow to illustrate our plotting convention. The fly would have to rotate clockwise about the axis to maximally stimulate the cell whose preferred axis is represented by the red arrow.
(B) The preferred axes for all NMNs (red) and LPTCs (blue) plotted using the same convention as in (A). To account for the contralateral counterparts of the NMNs and LPTCs we duplicated all the receptive fields, mirror-transformed them about the y-axis and re-estimated the preferred axes for the transformed receptive fields. Note that because we only plot the clockwise portion of the preferred rotation axis, the duplication does not result in symmetry across the azimuth = 0° line in our plot.
(C) 2D cylindrical projection of the same data presented in (B); note that the 2D projection allows visualization of all the data, but introduces distortions so that the tightly packed clusters at the top and bottom appear spread out. See Figure S1 for information on which preferred axis corresponds to which cell type.
(D) Normalized spherical cross-correlation [30] between the two axis distributions shown in (B) and (C). The color of each square gives the correlation coefficient between the NMN and LPTC axis distributions shown in (B) and (C), given a relative rotation between the two. The position in the 3D plot gives the relative rotation between the two axis distributions around the three rotational degrees of freedom (α, β, and γ). The entire range of all possible rotations was tested with a spacing of 15°, but only the results lying along the orthogonal rotational degrees of freedom are shown for clarity.

The rotation selectivity ratio is plotted against the binocularity ratio for each NMN (red) and LPTC (blue). A binocularity ratio of 1 means that the neuron was equally sensitive to motion in both visual hemispheres, a value of 0 means that the neuron only responded to motion in one hemisphere. A rotation selectivity ratio of 0 means that we estimate the neuron only responds to translation-induced optic flow, 0.5 means we estimate the neuron responds to translation and rotation equally, 1 means the neuron only responds to rotation. See Materials and Methods for details on how the ratios were calculated. Histograms at the top and side show the distribution of binocularity and rotation selectivity ratios across the NMN and LPTC populations. The bin size is 0.1 for the binocularity histogram and 0.04 for the rotation selectivity histogram. For information on which data point corresponds to which cell type, see Figure S2.