Contrast-Invariant Orientation Tuning in Cat Visual Cortex: Thalamocortical Input Tuning and Correlation-Based Intracortical Connectivity

Gabor-shaped cortical RFs. Lighter grays to white indicate positive values of Gabor function, corresponding to weights of ON-center LGN cells with centers at corresponding spatial positions; darker grays toblack indicate negative values of Gabor function, corresponding to weights of OFF-center cells. A, A full Gabor function, used to determine LGN inputs to a cortical cell in the conceptual model. B, Typical LGN inputs to a cortical cell in the computational model, after probabilistic sampling from the full Gabor (see Materials and Methods). These receptive fields are typical; different cortical cells may have different preferred orientations, spatial phase (relative locations of ON or OFF subregions), spatial location, and, in the computational model, different outcomes of the probabilistic sampling. Spatial frequency of sinusoid in Gabor function is 0.8 cycles/degree.

Tuning of total LGN input. A, Input to cortical cells in response to high (50%) and low (2.5%) contrast gratings at the preferred and null (orthogonal to preferred) orientations. High (50%) contrast and low (2.5%) contrast are shown.Curved traces show input in response to preferred orientation; black traces, average input (40 presentations) from computational model, using a sampled Gabor RF (as inB); gray curves, input for conceptual model, using connections from the full Gabor function (A).Gray straight lines show response in the conceptual model to a stimulus at the null orientation; in inset, these lines are repeated and compared to average input to null stimuli in computational model (black traces). Note that input to null stimulus at 50% contrast typically exceeds peak input to preferred stimulus at 2.5% contrast. Agreement of the two models for both preferred and null stimuli indicates that RF sampling and Poisson firing of LGN inputs have little effect. B, Tuning of mean (dashed lines) and mean plus first harmonic (solid lines) of thalamic input conductance. Lines show results from the conceptual model; solid circles show results from the computational model; error bars represent ±1 SD. Sum of mean plus first harmonic represents peak input during a cycle of the grating stimulus. Note that mean input is untuned for orientation, and mean input at high contrasts exceeds peak input to preferred orientation at low contrasts. Thus, although the first harmonic is well tuned, no single spike threshold can give tuned responses at both high and low contrasts. In this and subsequent figures showing orientation tunings, cells are grouped by preferred orientation in 10° bins, and orientation axis represents difference of stimulus orientation from preferred.

Contrast-invariant tuning. Response versus orientation for gratings of 2.5, 5, 10, 25, and 50% contrast.A, Computational model. B, Conceptual model. Both models yield contrast-invariant tuning at 5% contrast and above.

Increasing inhibition leads to sharper tuning. Tuning half-width at half-height (HWHH) versus level of inhibition for gratings of 2.5, 5, 10, 25, and 50% contrast. Thick solid(bottom) curve shows mean tuning HWHH above 5% for RFs with large subfield aspect ratios and narrow LGN tuning (matched to data from Jones and Palmer, 1987). Thick dashed(top) curve shows mean tuning HWHH for RFs with small subfield aspect ratios and broad LGN tuning (matched to data fromFerster et al. 1996). Level of inhibition is normalized so that 1 is the level that produces physiological half-widths for narrow LGN input (Fig. 4). Overlapping symbols indicate contrast-invariance. Tuning gradually sharpens with increased levels of inhibition. A, Computational model. B, Conceptual model. In conceptual model, tuning narrows slightly at 5% contrast for large levels of inhibition. This is attributable to the fact that spike threshold is optimized for default parameters, i.e., inhibition level of 1 (see Materials and Methods). Responses to 2.5% contrast gratings at high inhibition levels for both narrow (solid) and broad (dashed) LGN tuning are shown using thin lines. At very low contrast, conceptual model predicts much narrower tuning.

Behavior of model using correlation-based connectivity. Schematic representing behavior of the model in response to preferred (A) and null (B) stimuli. The excitatory cell described in Results is in the top left; its inhibitory antiphase partner is in the bottom right. E, Excitatory cells; I, inhibitory cells. Solid lines represent excitation and depolarization;open lines represent inhibition and hyperpolarization. Line thickness and size of RF icon represent magnitude of activity.Dashed lines represent correlation-based excitation, which is included in the complete computational model only (see Figs. 8-11). Some simulations were performed without cortical excitatory projections onto inhibitory neurons (gray dashed lines), but this did not substantially affect network behavior (see Fig.13B).

Inputs to a cortical cell given antiphase inhibition (inputs shown relative to background). A, Averaged computational model responses (40 presentations) to 50% contrast gratings. Excitatory LGN input is marked Ex.; intracortical inhibitory input is marked Inh. To compare excitatory and inhibitory inputs, synaptic conductances were converted to currents obtained if the cell was voltage-clamped at threshold.B, Peak synaptic current versus orientation for computational model. Responses are to single presentations of 50, 10, and 5% contrast gratings at 128°. Peak current is the first harmonic (F1) plus the mean (DC) of the stimulus-induced current (including excitation and inhibition). Error bars for 50% contrast are ±1 SD.Dotted line shows approximate threshold level that would lead to contrast-invariant tuning; actual threshold in computational model is determined independently from in vitro data (see Materials and Methods). C, Peak synaptic current versus orientation for conceptual model. Because there is no noise, true peak current is shown. Dotted line shows automatically selected threshold (see Materials and Methods). For both models, mean input decreases and modulation increases with contrast. Thresholds near the crossover point of net input tuning curves result in sharp, contrast-invariant tuning.

Behavior of the full computational model.A, Orientation map used, and typical pattern of intracortical connections. There is one excitatory cell in every location of the cortical map (40 × 40 lattice) and one inhibitory cell in every fourth location (20 × 20 lattice). Cells were assigned preferred orientation according to illustrated 40 × 40 color map (red-green-blue-red representing 0–60–120–180°) (map is × mm from measurement in cat V1, provided by Michael Crair and Michael Stryker); RF spatial phases were assigned randomly to each cell, whereas retinotopic centers progress continuously across the map (described in Materials and Methods). Intracortical connections were assigned probabilistically according to RF correlations (excitatory connections, yielding roughly same-phase excitation) or anticorrelations (inhibitory connections, yielding roughly antiphase inhibition). A typical connectivity pattern is shown by the black and white squares, which illustrate locations of cells making inhibitory or excitatory intracortical synaptic connections, respectively, to the excitatory cell at thered X. Area of squares is proportional to connection strength. The distributions of excitatory and inhibitory connections across orientations are similar; on average, these distributions are identical. B, Theoretical distribution of connectivity as a function of the difference in preferred orientation (top) and the difference in spatial phase (bottom) between two cortical neurons with overlapping RF centers. Probability of excitatory connections is shown in red; inhibitory probabilities are shown inverted and in blue. All values are shown as percentage of maximal connection probability. The parametern_pow controls the width of tuning as a function of correlation (see Materials and Methods); n_pow = 6 (solid line) is the default value. Excitation and inhibition have identical spreads as a function of orientation difference but have opposite preferences for spatial phase. Distribution versus preferred orientation is averaged over cells of all spatial phases; distribution versus spatial phase averaged over cells of all preferred orientations, with spatial phase measured with respect to the center of the RF for all orientations. C–E, All responses are to 3 Hz, 0.8 cycle/degree sinusoidal grating. C, D, Firing rates of excitatory and inhibitory cells, versus orientation, as function of contrast (indicated by key in C). Error bars for the 50% contrast and 2.5% contrast responses are ±1 SD.E, Amplitude (F1) of excitatory cell voltage modulation, with and without the intracortical circuitry, versus difference of stimulus orientation from preferred. Dots, F1 for all 1600 excitatory cells; traces, means in 10° orientation bins, as in C, D. Blue, F1 for thalamocortical inputs alone; green, F1 with the full cortical circuit. Red trace is the thalamocortical response scaled to the peak response of the full cortical circuit. Note that thalamocortical and full circuit have same tuning, as in Ferster et al. (1996).

Example traces. Voltage (V_m) and conductance in response to a 3 Hz sinusoidal grating at 50% contrast. AMPA, GABA-A, synaptic conductances with background subtracted (converted to currents at threshold as in Fig. 7A). AHP, Spike-triggered potassium conductance. Bars show stimulus orientation relative to preferred (vertical). Top row shows orientation differences spaced at 30° intervals; bottom row shows model behavior at orientations between 0 and 30°. Excitation and inhibition arrive out of phase and have similar orientation tuning. Inhibition dominates at the null.

Orientation tuning of peak excitatory current (dot-dashed line) and inhibitory current (solid line) at 50% contrast (peak current equals DC+F1; see Fig. 7B). Dotted line shows excitatory current scaled and translated to match maxima and minima of inhibitory currents. Peak inhibition is larger than excitation at all orientations, but the tuned components of excitation and inhibition have nearly identical shape.

Orientation tuning narrows with increasing spatial frequency of a sinusoidal grating (3 Hz). A, Tuning of the F1 voltage modulation for the full circuit (top) and with LGN excitation only (middle). Tuning curves, from widest to narrowest, represent response to spatial frequencies 0.4 (dot-dashed), 0.56 (thin), 0.8 (thick), and 1.13 (dashed) cycles/degree, respectively; each curve is normalized to its peak response.Thicker line is the spatial frequency used for simulations in other figures. The bottom shows the difference between the normalized tuning curves: LGN input F1 and full circuit F1 closely match. B, Half-width at half height versus spatial frequency for 5, 10, 25, and 50% contrast gratings. Orientation tuning remains contrast invariant over a broad range of spatial frequencies.Inset, Spatial frequency tuning curve at the preferred orientation and 50% contrast.

Orientation tuning after blocking inhibition in a single cell [as in Nelson et al. (1994)]. Tuning curves derived when inhibitory and adaptation currents are blocked within a single cell (see Materials and Methods). Dotted line shows tuning with inhibitory blockade only; solid line shows the tuning when negative current equal to the mean inhibitory synaptic current at background is injected into the cell. Dashed line shows tuning without blockade for comparison. Inhibitory blockade with current injection has little effect on tuning. Notice, however, a slight (1.9 Hz) rise in the response to null stimuli. Contrast equals 50%.