According to Strausfeld et al. [25
], the fly has four known pairs of neck nerves containing a total of 21 pairs of NMNs, only a subset of which respond to visual motion with changes in spike rate. The four nerves are referred to as the frontal nerve (FN), cervical nerve (CN), anterior dorsal nerve (ADN), and ventral cervical nerve (VCN). The NMNs these nerves contain innervate 21 pairs of neck muscles. In most cases each muscle receives input from only one NMN [24
Using extracellular recordings, we determined the local directional preferences () within the visual receptive fields of 47 wide-field NMNs in 38 flies. We defined wide-field NMNs as those that responded to our visual stimulus over a range of positions that was equal to or greater than 90° along the azimuth. The recordings were primarily taken from the nerves themselves and in some cases from the muscles that the NMNs innervate. When recording from the muscles, it was possible to isolate a single NMN's extracellular action potential waveform, but it was not possible to identify the nerve through which the unit was running with 100% confidence, as it is in nerve recordings. In these situations, we determined the nerve identity of the unit from the position of the electrode relative to the muscles and the known NMN-muscle connectivity [25
]. In such cases where the nerve that a unit belongs to was determined from the muscle recording site, the nerve to which it was attributed is marked with an asterisk
Characterizing the Visual Receptive Field of a NMN in the Left CN
Most neck muscles are thought to receive only one NMN input [25
]. In those recordings where we placed the electrodes near a NMN's innervated muscle, a slow waveform, most likely the muscle potential, could be seen to follow the NMN action potential in a 1:1 fashion (C). Thus, many of the NMN receptive field maps may also indicate the visual receptive field of the muscles the NMNs innervate. To our knowledge, this is the first time the visual receptive fields of muscles have been obtained.
Visual Receptive Fields of NMNs
Here we show example NMN receptive field maps that illustrate the range of different map types obtained from each nerve (–) - population data are shown later (,,S1
). The receptive field maps consist of local vectors plotted against azimuth and elevation. The azimuth and elevation indicate the horizontal and vertical angular position of a motion stimulus within the fly's visual field. The fly was oriented so that it was facing zero degrees azimuth and elevation. The orientation and length of each local vector in the receptive field maps indicate the NMN's local preferred direction of visual motion and relative motion sensitivity, respectively.
Receptive Field Maps for NMNs of the FN
Comparison of NMN and LPTC Receptive Field Maps
Comparison of the Distributions of Preferred Axes of Rotation for NMN and LPTC Populations
NMNs Are More Binocular and More Selective for Rotation Than LPTCs
All receptive field maps, except where noted, are plotted with respect to recordings from the left part of the nervous system. Maps derived from NMN recordings in the right part of the nervous system are mirror-transformed. To distinguish between the different examples we present, we have labeled them, e.g., FN NMN A, FN NMN B, etc. This naming convention is for convenience only and should not be taken to imply that the data come from any particular identified neuron.
Frontal Nerve NMNs
The FN is the biggest of the four neck motor nerves. NMNs running through this nerve innervate a variety of different neck muscles that, based on their anatomy [25
], could potentially be involved in head inclination (nose-up pitch), declination (nose-down pitch), unilateral adduction (yaw), and unilateral depression (roll). FN-innervated muscles may potentially also be involved in head extension/retraction—the only possible translational degree of freedom of the head [25
]. Milde et al. [23
] found that FN neurons were tuned to a variety of directions in the frontal visual field and to downward visual motion laterally—from this they concluded that FN units were sensitive to roll. Using our receptive field mapping approach, we were able to determine which self-motions the FN units were most sensitive to with a higher degree of accuracy. We found FN units with receptive fields that appear to be tuned for pitch, roll and pitch-roll intermediates.
Our first FN NMN example, FN NMN A (A), had a bilaterally symmetric receptive field with strong motion sensitivity in areas above the eye equator. In the frontal visual field, this NMN was most sensitive to vertical upward motion. Its directional preferences gradually became horizontal within the lateral visual field and eventually turned into a preference for almost vertical downward motion in the caudolateral visual field. The directional preferences were oriented along concentric circles around an area of low sensitivity at roughly ±90° azimuth. Such sensitivity minima, or singularities, within the receptive fields indicate the orientation of the neuron's “preferred rotation axis”, i.e. the axis about which the animal has to turn in order to most strongly activate the neuron. The rotation axis that this NMN preferred nearly coincides with the animal's transverse body axis, suggesting that FN NMN A would respond most strongly when the fly performs a nose-down pitch rotation.
FN NMN B (B) responded most strongly to oblique upward motion in the frontal visual field above the eye equator and was slightly less sensitive to motion in the right visual hemisphere. The global appearance of this NMN receptive field was similar to that of the VS8 LPTC [17
]: its preferred directions being oriented around a singularity at an azimuth of roughly −70°. Thus, the preferred rotation axis of FN NMN B lay between the longitudinal and transverse body axes, indicating that this NMN would probably respond best to nose-down pitch in combination with a slightly smaller roll component. Simultaneous recordings were often made from multiple FN NMNs with receptive fields similar to FN NMN B (B).
FN NMN C (C) had a binocular receptive field that covered the entire area tested in our experiments. The receptive field resembled an optic flow field generated during roll-rotation in combination with a subtle nose-down pitch. Accordingly, the NMN's preferred rotation axis was close to the fly's longitudinal body axis but slightly tipped downward frontally.
Ventral Cervical Nerve NMNs
The VCN hosts three NMNs innervating different oblique horizontal (OH) muscles. These muscles were suggested to be involved in the control of yaw rotations of the head [25
VCN NMNs (A) were recorded from the OH muscle group. They responded to motion across an area that covered the ipsilateral visual hemisphere. In contrast to most other NMNs, the VCN NMNs did not appear to receive contralateral input beyond the region of the eye's binocular overlap [26
The Receptive Field Maps of Two NMNs That Mainly Respond to Horizontal Motion
Yaw rotation of the fly results in horizontal motion in the same direction across both eyes, whereas forward translation motion of the fly results in horizontal motion in opposite directions either side of the focus of image expansion. Therefore, to distinguish between yaw rotation and translation, a neuron needs a binocular receptive field. In contrast to most of the other NMN receptive fields, the VCN NMN receptive field was mostly monocular. This type of NMN may therefore respond to both yaw rotation and translation of the fly. Besides potentially controlling yaw head movements, such NMNs may also be involved in the control of head retraction. In principle the oblique horizontal muscles which VCN NMNs innervate [25
] are suited to serve this function when simultaneously activated on either side of the neck motor system.
Anterior Dorsal Nerve NMNs
The ADN contains only two motor neurons, both of which supply the transversal horizontal (TH) muscles involved in rotations of the head around the vertical axis, i.e., yaw [25
ADN NMN A (B) was recorded from the TH muscle group. It had the smallest receptive field of all the NMNs presented in this account. The extent of the receptive field nearly reached 90° along the azimuth, and the neurons' sensitivity dropped sharply toward the dorsal and ventral visual field.
Other ADN receptive fields, such as ADN NMN B (A, also recorded from the TH muscle group), covered the entire area of the visual field examined. In a manner reminiscent of the HSE LPTC receptive field (B), such ADN NMNs showed the highest sensitivity to horizontal motion along the entire eye equator (A). Their motion sensitivity decreased toward both the dorsal and the ventral parts of the visual field. The singularity within this receptive field, though difficult to see in the cylindrical projection, lay at about +45° azimuth and +75° elevation, suggesting that this type of NMN would respond strongly during yaw rotation of the animal to the right.
Cervical Nerve NMNs
The CN contains several neck motor neurons that, among others, innervate muscles involved in head declination [25
]. Some of the units recorded from the CN were only sensitive to vertical downward motion in a very small portion of the frontal visual field (unpublished data). Because of their small receptive fields, the tuning of these units to self-motion could not be determined. We therefore excluded these units from the current analysis.
Wide-field CN NMNs were particularly sensitive to vertical downward motion in the frontal-to-frontolateral aspect of the contralateral visual field with a singularity at an azimuth of about −45° (C). The finding that the CN NMNs respond most strongly in the contralateral field is in agreement with Milde et al. [23
]. The CN NMNs were noticeably similar to the contralateral VS3 LPTC (D) [17
]. The distributions of the preferred directions and motion sensitivities within the CN NMN resembled optic-flow fields generated during nose-up banked turn to the left.
Comparing Preferred Rotation Axes of NMN and LPTC Populations
The preferred rotation axis of a neuron is a convenient parameter to compare how the LPTC and NMN populations encode and control self-rotations. The preferred rotation axis is the body axis about which the fly would have to rotate to maximally excite a given neuron [28
]. We quantitatively estimated the preferred rotation axes of all 47 NMNs studied and a group of 28 LPTCs for which the binocular receptive field maps had previously been obtained [27
]. This was done by finding for each LPTC and NMN the rotation axis the animal would have to turn around to generate an optic flow field best matching the cell's receptive field map (see the Materials and Methods section). A second set of axes was obtained in the same manner from the mirror transformed NMN and LPTC receptive fields to account for the LPTCs and NMNs on the other side of the nervous system. This duplication of the dataset was based upon the well-supported assumption that bilateral symmetry exists in the LPTC and NMN populations [16
shows the preferred rotation axes of the LPTCs and NMNs in blue and red, respectively. Each arrow in B corresponds to the axis about which a fly would have to rotate clockwise to maximally stimulate a given neuron. For comparison, A shows a fly oriented in the same coordinate system. To show the preferred rotation axes on all sides of the sphere, we also plotted the axes against azimuth and elevation in a 2D cylindrical projection (C). The axes in the dorsal and ventral pole region of the cylindrical projection appear to be more scattered than they are in the spherical presentation (B). This distortion is due to the reduction of dimensions when transforming the data from the 3D spherical representation to a 2D cylindrical projection.
To quantify the relationship between the LPTC and NMN preferred rotation axes, we binned the two axis distributions into equi-angular bins (15° in azimuth and elevation at the equator) and then performed a normalized spherical cross-correlation [30
] between the two (D). The color values in D indicate the correlation coefficient, r
, between the binned NMN and LPTC preferred axes at different relative rotations between the two sets of axes. All possible combinations of the three rotational degrees of freedom (α, β, and γ) were tested with a resolution of 15°. There was a clear peak in the cross-correlation function at zero rotation (D), indicating that there was no systematic rotation between the NMN and LPTC preferred axes. At zero rotation, the correlation coefficient between the binned NMN and LPTC axes was r
= 0.57. Thus, almost a third (coefficient of determination r2
= 32%) of the variation in the measured NMN preferred rotation axes was related to the preferred axes of the LPTC population.
Binocularity and Rotation Selectivity
The most obvious difference between the receptive fields of many NMNs and LPTCs is that, while the VS LPTCs tended to have monocular receptive fields [17
], most NMNs responded to motion in both visual hemispheres. We quantified the degree of binocularity for each receptive field () by taking the ratio between the mean motion sensitivity in the left and right hemispheres (see the Materials and Methods section). The resulting binocularity ratio was 0.6 on average for the NMNs compared to 0.32 for the LPTCs. This increase in binocularity reflects a statistically significant difference between the two populations (p
, Student's two-sample t
Theoretical analysis has shown that sampling both visual hemispheres enables a system to distinguish more accurately between the rotation- and translation-induced components of optic flow [31
]. We investigated whether the increased binocularity of the NMNs was also accompanied by a higher rotation-selectivity than found for the more monocular LPTCs. To do so, we quantitatively estimated for each neuron its rotation selectivity ratio, which indicates the preference for rotation over translation based on the neuron's receptive field organization (see Materials and Methods
). The rotation selectivity ratio ranges from 0 to 1, where a ratio of 0 indicates the neuron was selective for only translation, 1 indicates selectivity for pure rotation, and 0.5 results from an equal selectivity to rotation and translation. For both the NMNs and the LPTCs, the more-binocular receptive fields tended to have a higher selectivity for rotation (). On average, the NMNs were more rotation-selective than the LPTCs. The LPTCs had a median rotation selectivity of 0.55 compared to a value of 0.65 for the NMNs. We found this 18% increase in rotation selectivity to be statistically significant (p
< 0.01, Mann-Whitney U test). When the NMN receptive fields were artificially made to be monocular by setting the motion sensitivity on their weakest side to zero, the distribution of rotation selectivities was no longer statistically different from those of the LPTCs (p
> 0.7, Mann-Whitney U test, median “monocularized” NMN rotation selectivity = 0.58). This suggests that the increased binocularity seen in the NMNs leads them to be more selective for rotation than the LPTCs.