Figure 4. Two P-EN subpopulations mirror-symmetrically encode the fly’s rotational velocity.

(A) Example tuning curves of P-EN spike rate to the fly’s rotations as the fly walks in darkness. Angular velocities were binned in 12°/s bins and a sigmoid was fitted with bin counts used as weights (see Materials and methods for details). Mean spike rate and 95% confidence interval in black, sigmoidal fits in blue and red. (Ai) Tuning curve for a right P-EN neuron (same as in Figure 3). P-EN membrane potential changes were similar to the observed changes in spike rates (see Figure 4—figure supplement 1C for V_m tuning curve). (Aii) Tuning curve for a left P-EN neuron (see Figure 4—figure supplement 2A for example trace). (B) Fitted spike rates for the flies’ turns to the left versus right illustrate mirror-symmetric tuning properties of the left and right P-EN subpopulations. Spike rates were computed either at saturation or at an absolute rotational velocity of 200°/s, whichever was lower. Example cells from panel A are color coded. (C) Encoding of rotations by the two subpopulations is mirror-symmetric yet overlapping, that is, each P-EN subpopulation encodes rotations in both directions. Left: Normalized tuning curve fits for all P-EN neurons. Left hemisphere P-EN curves have been reflected for simplicity. Neurons plotted in A are color coded for comparison. Open circles mark each sigmoid’s half-maximum (inflexion point). Right: On average, the P-EN neurons’ receptive field for rotations is centered around 0°/s, where P-EN’s are half-maximally activated. Closed and open circles in the right subplot represent inflexion points of right and left P-EN tuning curves, respectively. Example cells from panel A are in blue and red. (D) Spike-triggered averages of angular velocities were constructed to characterize P-EN timing. Since P-EN neurons tend to spike at rest, all spikes with rotational velocities not exceeding 40°/s at any time in a one second window around the spike were excluded. Left: Membrane potential is plotted at top, angular velocity at bottom. Inset shows a magnification of the average spike shape. Right: The peak of the angular velocity precedes the spike in all P-ENs recorded. Example cells from panel A are in blue and red.

DOI: http://dx.doi.org/10.7554/eLife.23496.006

Figure 4—figure supplement 1. Extended data on P-EN rotational velocity tuning.

(A) Tuning curves for recordings in both experimental conditions (‘dark’ and ‘visual closed loop’) were well fit by a sigmoidal function. P value refers to unpaired t-test across conditions. Cells in the lower spectrum of R² values (<0.8) showed a higher variance around the mean, but no systematic deviation from the sigmoidal shape of the tuning curve. (B) Heat map of spike rate as a function of forward and angular velocity for the neuron plotted in Figure 3B. (C) Angular velocity tuning curve of the P-EN neuron plotted in Figure 4Ai, but relating membrane potential, rather than spike rate, to angular velocity. Mean membrane potential and 95% confidence intervals in black, sigmoidal fit in blue. (D) Each P-EN’s rate modulation was quantified as the absolute difference of fitted spike rates at saturation or at an absolute rotational velocity of 200°/s, whichever was lower (see inset in panel C). P-EN modulation appeared stronger in flies walking in darkness than in those with visual closed loop. P value refers to unpaired t-test across conditions. (E) Comparison of the fly’s dynamic range of rotations (‘behavioral bandwidth’) to the P-EN’s dynamic range for angular velocity encoding (‘P-EN coding bandwidth’, see inset in Panel C) for the two experimental conditions. Behavioral bandwidth was defined, for each fly, as the range between the 10^th and 90^th percentile of its rotational velocity distribution (in 50 ms bins, excluding velocities between −5 and 5°/s). P-value refers to a two-way ANOVA result across conditions (p-value for comparison of behavior to neural response: p=0.82). (F) Simulation of P-EN population activity based on electrophysiological recordings of 12 P-EN neurons. Spike rates of individual P-EN neurons were normalized to their respective mean spike rate across all bins. P-EN neurons from the left hemisphere were flipped so that population activity of ‘right P-ENs’ (blue) represents the mean of all cells. The tuning profile of ‘left P-ENs’ (red) was assumed to be the same, except mirror-symmetric around the y-axis (Figure 4C). The population activity (the sum of left and right P-EN neurons, green) was calculated as the linear sum of all 24 simulated P-EN neurons. (G) Generalized linear regression analysis of P-EN instantaneous spike rate relative to the fly’s turns, shown for the experiment plotted in Figure 3. The autocorrelation of the rotational velocity is plotted in black, the correlation coefficients for right and left turns with the neuron’s spike rate are plotted in blue and red, respectively. In brief, P-EN spike rates were regressed with rotations to the left and right as predictors, yielding a single pair of coefficients. A series of temporal shifts was introduced between rotations and spike train, giving rise to the temporal sequence plotted along the x-axis. The temporal shift that produced the maximum difference in left minus right turn coefficients was defined as the neurons response lag. This lag was positive for all P-EN neurons (that is, the neural response followed the change in rotational velocity). See Materials and methods for details. (H) P-EN response lag grouped by recording conditions. ‘STA’ refers to timing information extracted from spike triggered averages (see Figure 4D). ‘Regression’ refers to timing information obtained through fitting a generalized linear regression to the P-EN spike rate (see panel F and Materials and methods for details). P-value refers to a two-way ANOVA result across conditions (p-value for comparison of STA to regression: p=0.57). Timing information extracted from linear regression analysis of the membrane potential was similar to that extracted from generalized linear regression of spike rates (response lag V_m: 125 ± 21 ms, spike rates: 138 ± 83 ms, N = 8 for both groups, paired t-test: p=0.69).

DOI: http://dx.doi.org/10.7554/eLife.23496.007

Figure 4—figure supplement 2. Loose patch recordings.

(A) Example loose patch recording of a P-EN neuron located in the left hemisphere. (Ai) Plotted are the translational velocity (top row, gray), the accumulated rotation (second row, black) and the band-pass filtered extracellularly recorded potential changes (third row, black; see Materials and methods). Epochs of fast turning are highlighted in red and blue for left and right turns, respectively. Spike times are indicated with dots following the same color code. (Aii) Expanded view highlighting the spike shape of three events (left) in comparison to the average of all spikes recorded in this trial (right). Y-axis scale bar is the same for both panels. (B) Average spike shape across all events recorded in four consecutive epochs of five minute length. The traces in panel A are taken from the last epoch and illustrate the minimum quality criterion for inclusion of a recording in the final data set. In most recordings, spike amplitude decreased over time, and spike shape, particularly the post-spike hyperpolarization component, became less distinctive. Usually, but not always, this was accompanied by a slow increase in spike frequency. Experiments were terminated (and/or late trials excluded post-hoc) if the spike frequency increased notably, be it due to decreased signal-to-noise ratio and increased uncertainty in spike detection or, in rare cases, a partial break-in into the cell. (C) Threshold-based spike detection for trials included in the final dataset is robust, i.e. the number of detected spikes is largely constant in a ± 20% window around the chosen threshold.

DOI: http://dx.doi.org/10.7554/eLife.23496.008