PMC

The distribution of responses to drifting gratings across our sample population. Dark bars indicate neurons classified as complex (R₁/R₀ < 1) and open bars indicate neurons classified as simple (R₁/R₀ > 1). (a) The distribution of R₁/R₀ was significantly bimodal (Hartigan’s dip test, P < 0.02). Firing rate modulation values greater than 2.2 were included in the highest bin. (b–e) The distributions of V₁/V₀ (b),V₁ (c), V₀ (d) or spike threshold (measured relative to the resting potential; e) were not bimodal (Hartigan’s dip test, P > 0.5).

A comparison of the various measures of grating modulation and spatial segregation of ON and OFF responses. (a) The distribution of the spatial correlation coefficient from spike rate responses. Filled bars indicate the neurons for which both R₁/R₀ and the spatial correlation analysis was performed. The distribution is significantly bimodal (Hartigan’s dip test, P < 0.05) (b) The distribution of V₁/V₀. Filled bars indicate those neurons for which the spatial correlation of potential responses was analyzed. The distribution is not significantly bimodal (Hartigan’s dip test, P > 0.5). (c) The relationship between R₁/R₀ and the spatial correlation coefficient from spike rate responses (n = 80). (d) The relationship between R₁/R₀ and V₁/V₀ (n = 157). (e) The distribution of R₁/R₀. The distribution is significantly bimodal (Hartigan’s dip test, P < 0.05). (f) The relationship between the spatial correlation coefficients from spike rate and membrane potential responses (n = 92). Filled gray symbols and arrows correspond to the example neurons in . (g) The relationship between V₁/V₀ and the spatial correlation coefficients from membrane potential responses (n = 287). (h) The distribution of the spatial correlation coefficients from membrane potential responses. The distribution is not significantly bimodal (Hartigan’s dip test, P > 0.2). Filled bars indicate those neurons for which spatial maps were obtained from spike responses.

Intracellular responses to drifting gratings in four example neurons. Gratings had optimal orientation, spatial frequency and direction. (a) Responses of four neurons to a grating moving at 2 Hz and 64% contrast. The traces include 4 s of stimulation after 0.25 s of blank stimulus (0.1 s shown). The dashed line indicates each neuron’s resting membrane potential (V_rest). (b) Trial-averaged firing rate histograms (upper panel) and voltage traces. (c) Cycle-averaged firing rate histograms and voltage traces. Spikes were removed from voltage traces prior to averaging by using a 4-ms median filter. The spike responses of these cells (from top to bottom, in spikes/s) were as follows: R₀: 11.17, 21.00, 24.17, 13.06; R₁: 19.82, 24.51, 21.54, 3.68; the intracellular responses were (in mV) V₀: 5.49, 9.73, 13.77, 6.31; V₁: 8.25, 4.40, 4.69, 1.05. (d) Transformation between average voltage and firing rate. The blue symbols indicate the average firing rate when membrane potential is binned in 1-mV steps (error bars are s.e.m.). The red curve indicates the power-law function that best fit the data (see Methods).

The nonlinear transformation from the voltage modulation ratio to the firing rate modulation ratio. (a) The transformation between voltage and spiking response for two models: the solid line indicates the transformation for the power-law model and the dashed line indicates the transformation for the threshold-linear model (see Methods for details). (b) Transformations of membrane potential(V_m, traces) to firing rate (FR, filled bars) for two model voltage modulation ratios. Both panels show the membrane potential to firing rate transformation assuming the power-law model with an exponent p = 2. Top panel, V₁/V₀ = 0.24 and R₁/R₀ = 0.47; bottom panel, V₁/V₀ = 1.67 and R₁/R₀ = 1.5. (c) The nonlinear transformation of the voltage modulation ratio (abscissa) to the firing rate modulation ratio (ordinate) for power-law models with a threshold at V_rest and various exponents, including p = 2 (blue curve), p = 3 (red curve) and p = 5 (black curve). The curves are derived in the online, following Mechler and Ringach. Connected by the blue curve, each square shows the mapping of a particular voltage modulation ratio in model neurons that use the power law with exponent p = 2. Insets indicate the corresponding transformation of membrane potential (traces) to firing rate (filled bars). (d) An even distribution (green trace) and highly skewed distribution (orange trace) of the voltage modulation ratio. (e) The firing rate modulation distributions resulting from the even distribution (green trace) and skewed distribution (orange) found in (d) when transformed by the relationship dictated by the power law with exponent p = 2 (blue curve in (c)).

ON and OFF spatial maps for both membrane potential and spikes. (a) The membrane potential responses of a neuron evoked by bright (top left panel) or dark stimuli (middle left panel). The traces indicate the stimulus-averaged membrane potential for a 135-ms duration following the stimulus onset for each spatial location. The color at each spatial location indicates the membrane potential in the analysis period, averaged between 50 and 80 ms after the stimulus was flashed. The significance region (black outline) selected for further analysis consisted of spatial locations in which either a dark or bright stimulus elicited a significant depolarization relative to the resting potential of the neuron (t-test, P < 0.05). The bottom two maps show spiking responses as stimulus-averaged spike rate histograms. The scattergrams to the right of the maps plot the amplitude of the ON response against the amplitude of the OFF response for each location within the significance region. Correlation coefficients for the scattergrams are shown at the upper right. (b–d) Different example neurons, same format. In response to moving gratings, the example neurons in panels a and b had R₁/R₀ values less than 1 and so were considered complex, whereas those in c and d had R₁/R₀ values greater than 1 and thus considered simple.

The nonlinear transformation from the voltage modulation ratio to the firing rate modulation ratio in primary visual cortex. (a) The voltage modulation ratio (abscissa) and firing rate modulation ratio (ordinate) are plotted for each cell in our sample population. Neurons were grouped by the exponent p that best fit the potential-to-firing rate relationship: p < 2.75 (blue symbols), p > 3.5 (black symbols) and p intermediate between these values (red symbols). The separation values were chosen to assure the same number of cells was found in each group. Blue, red and black lines indicate the predicted relationship between the potential modulation ratio and the rate modulation ratio for exponent values of 2, 3 and 5. Rate and potential modulation ratios greater than 2.2 are marked as 2.2. A single neuron had a negative voltage modulation ratio (due to a hyperpolarizing V₀ response to the optimal grating). The example neurons from are marked with open symbols. The distribution of the (b) voltage modulation ratio and (c) firing rate modulation ratio. Open and filled parts of bars indicate subsets of cells classified by the spike rate modulation as simple and complex cells. (d) Predicted and actual firing rate modulation ratios. The predicted firing rate modulation ratio is derived from the voltage modulation ratio and the exponent value. The solid line indicates a perfect relationship (identity) between the predicted and actual firing rate modulation ratios. The dashed line shows the linear regression between the predicted and actual firing rate modulation ratios.

The transformation between voltage modulation ratio and the firing rate modulation ratio in single cells. (a) Cycle averages of the firing rate response (top panels) and the membrane potential response to gratings of fixed (optimal) orientation, 2 Hz temporal modulation and different spatial frequencies (SF) for a single cell. (b) The V₁ and V₀ values shown as a function of the spatial frequency of the stimulus. (c) The corresponding R₁ and R₀ for the same cell. (d) For each spatial frequency that produced a measurable spike response, the voltage modulation ratio is plotted against the firing rate modulation ratio for the same cell shown in (a–c). The solid line indicates the model prediction given the exponent p that was estimated from the cell’s input-output function (not shown). The open symbol indicates the modulation ratios for the spatial frequency that elicited the largest R₀. (e–l) Same as shown in d for eight other neurons. The relationship between predicted and actual firing rate modulation ratios for the group of cells was high (R² = 0.71, slope = 0.91, not significantly different from 1 (P > 0.5), y-intercept = 0.13, significantly different from 0 (P < 0.05)). The cells included both simple and complex cells as defined by R₁/R₀ measured with the grating of optimal spatial frequency.