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First published online August 31, 2007
Journal of Experimental Biology 210, 3199-3208 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.006726
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Fast-scale adaptive changes of directional tuning in fly tangential cells are explained by a static nonlinearity

Peter Neri

Applied Vision Research Centre, City University, Northampton Square, London EC1V 0HB, UK


Figure 1
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  		Fig. 1. Stimuli, data analysis and modeling. (A) Stimuli consisted of Gabor patches that drifted in random directions at different locations within the receptive field of the neuron. During preliminary testing we presented 4x4 patches that covered the entire monitor (low-contrast patches in left-most frame) to obtain a vector map for a ~80°x80° portion of the receptive field (see Fig. 2B for an example). Subsequent testing only involved two patches (high-contrast), independently changing direction every 220 ms (in this figure the low-contrast patches indicate the other possible positions, but were not presented in the two-patch stimulus; in the full version of the stimulus (showing all patches) they were presented at high contrast). (B) We computed response surfaces for all possible directions of the patch at position 1 and time corresponding to when the response was measured (broken blue circle in A), together with all the possible directions of the preceding patch at position 2 (broken red circle in A). The specific combination shown in A is indicated by * in B (note that this panel does not show real data). A similar analysis was carried out for the preceding patch at the same location (broken white circle in A). (C–E) Schematic descriptions of three models that were tested in this paper. Proceeding from left to right, the nonlinear transducer (red) is placed at progressively earlier stages within the model. See Materials and methods for details of model implementation.

 

Figure 2
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  		Fig. 2. Example of data analysis for a V1 neuron. (A) Response to a full-field grating. (B) Vector map showing directional preference within the receptive field. (C) Response to individual patches at circled positions in B. (D) Response to two simultaneous patches. The direction of patch 1 is on the x axis, that of patch 2 on the y axis. (E,F) Computed as shown in Fig. 1B, responses to the patch at position 1 when preceded by the patch at position 1 (E) or 2 (F). (H–K) (H,I) were obtained from E and F after subtracting the average column, (J,K) after further subtracting the average row (see Materials and methods). (G) Slices across H along the positions indicated by coloured lines in H (black in G corresponds to the white rectangle in H). Arrows in G point to the direction of the y axis in H along which the slice was taken. Intensity in D–F,H,I shows firing rate plotted to the same scale where white is 88 Hz and black is –24 Hz (with respect to spontaneous firing of 43 Hz, indicated by dotted line in A). J and K plot Z scores (coloured for |Z|>2, blue for negative and red for positive). Smooth contours show interpolated surfaces with colour saturation and line thickness reflecting modulation intensity. Values are means ±1 s.e.m.; for N values, see Materials and methods.

 

Figure 3
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  		Fig. 3. Each pair of plots was computed as shown in Fig. 2J,K. `Same' is the average of Fig. 2J between patch 1 at t combined with patch 1 at t–{Delta}t and patch 2 at t combined with patch 2 at –{Delta}t. `Different' is the average of Fig. 2K between patch 1 at t combined with patch 2 at t–{Delta}t and patch 2 at t combined with patch 1 at t–{Delta}t. Six pairs are shown for six different cells (identity indicated by white labels). Notice that directional labeling on axes differs across neuronal types, reflecting differences in directional preference. For N values, see Materials and methods.

 

Figure 4
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  		Fig. 4. (A) Distribution of differences in preferred directions (on x axis in units of radians) within each pair of selected patches. For the majority of tests there was no difference in preferred direction (PrefDir.) between the two patches (peak at zero). (B) The response range of each patch is plotted against the response range of the other patch in the pair (the largest response range was plotted on the x axis for all tests). Response range was defined as the difference between the largest and the smallest responses on the directional tuning curve. Values are means ±1 s.e.m.; for N values, see Materials and methods.

 

Figure 5
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  		Fig. 5. (A) The number of significant (|Z|>2) pixels within `same' surfaces is plotted on the y axis against the corresponding measure for `different' surfaces on the x axis, for each tested pair of patches. (B) We computed the correlation between all possible pairs of `same' surfaces within the V1 (solid circles) and H1 (open circles) population separately (pairwise correlation), plotted on the y axis against the same measure for `different' surfaces on the x axis. (C) The modulation on `same' surfaces at the positions indicated by white triangles (negative diagonal) in Fig. 6D is plotted on the y axis (averaged between the two positions) against the modulation at the positions indicated by black triangles (positive diagonal) in units of impulses s–1. (D) We computed the Fourier power spectrum for each surface individually, and extracted power at four different orientations: horizontal, vertical and the two diagonals. Power oriented along the negative diagonal is plotted on the y axis against power along the positive diagonal on the x axis, for `same' (solid symbols) and `different' (open symbols) surfaces. Units are arbitrary. Power along horizontal and vertical orientations was similar to power oriented along the positive diagonal. In A,C,D: {blacktriangledown}{triangledown}, V1; {blacktriangleright}{triangleright}, H1; {blacktriangleup}{triangleup}, V2; {blacktriangleleft}{triangleleft}, H3. +ve, positive; –ve, negative.

 

Figure 6
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  		Fig. 6. (A) Data averaged across the entire neuronal population, after realigning preferred direction to {downarrow}. (B) Corresponding simulations for a linear model. (C–E) Simulations for the models depicted in Fig. 1C–E. For modeling results, surfaces plot average/{sigma} (comparable to Z score) for 100 simulations of each model. For N values, see Materials and methods.

 

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© The Company of Biologists Ltd 2007