Article Figures & Data
Figures
- Figure 1.
Model for contrast-dependent transformation between simple and complex cells in mammalian V1 neurons. A, Example of a model cell with a modulation ratio (F1/F0) that is greater than 1 (example cell 1, top), a model cell with F1/F0 between 0.5 and 1 (example cell 2, middle), and a cell with F1/F0 below 1 (example cell 3, bottom) at high contrasts. The top row represents the spiking rate of the cell and the bottom row is the underlying membrane potential of the cell. The black trace to the left shows responses of the cell to high contrasts and the light grey trace to the right shows responses to low contrasts. B, Black dots represent spiking rate at high contrast and grey dots represent spiking rate at low contrast. As the proportion of recurrent input increases (high contrast) the modulation ratio derived from the spiking rate (F1/F0) decreases. C, same as B but for membrane potential.
- Figure 2.
Threshold nonlinearity model (“iceberg” model) for a contrast-dependent transformation between simple and complex cells in mammalian V1 neurons. A, Spiking responses of a model neuron relative to contrast. As contrast increases, the spiking rate of the model neuron increases (right). The modulation ratio (F1/F0) decreases with increasing contrast due to relatively large increases in the mean spiking rate (F0) compared to the F1 component. B, Membrane potential responses of the model neuron relative to contrast. As the contrast increases, the amplitude of the membrane potential increases. The matched increases in the V0 and V1 components of the responses generate a steady modulation ratio (V1/V0) at all contrasts.
- Figure 3.
Intracellular responses of a mouse V1 simple cell to a drifting sinusoidal grating. Top panel: raw response to a sinusoidal grating with 100% contrast moving at 2 Hz at the cell's preferred orientation. The black trace represents the subthreshold membrane potential; spikes are shown in grey. The broken line indicates the resting membrane potential of the cell: −48.5 mV. Middle panel: trial-averaged (5 repeats) subthreshold voltage trace for the same cell, including the data in the top panel. Spikes are removed from voltage traces prior to averaging by calculating the derivative of the membrane potential and excluding rapid voltage excursions based on a derivative threshold. The grey shading shows the standard error of the mean. The mean membrane potential (mean V) and resting membrane potential (Vrest) for the trial-averaged subthreshold responses are shown respectively as dark grey and light grey broken lines. The voltage difference between the mean and resting membrane potential is defined as V0. Bottom panel: A visual representation of 4 cycles of the sinusoidal grating stimulus moving at 2 Hz (2 s in total).
- Figure 4.
The responses of two example mouse V1 cells (Cell A and Cell B) to drifting gratings (A & B). Left panel: cycle-averaged spiking rate (top panel) and membrane potential (bottom panel) responses to drifting sinusoidal gratings at different stimulus contrasts. From left to right, responses to a blank screen and five stimulus contrasts (blank, 4%, 8%, 16%, 32% and 64%) are shown for each cell. The broken lines represent spontaneous spiking rate and resting membrane potential (Vrest) for spiking rate (top panel) and membrane potential (bottom panel) responses, respectively. Right panel: The spiking modulation ratios (F1/F0, top panel) and the membrane potential modulation ratios (V1/V0, bottom panel) plotted as functions of contrast. The unity line, where F1/F0 = 1, is indicated as a broken line in the top panel. F0 and F1 values (top panel) and V0 and V1 values (bottom panel) are shown as functions of contrast.
- Figure 5.
Population results of mouse V1 cells recorded with drifting gratings (n = 20). A: Scatter plots of membrane potential modulation ratios (V1/V0) and B: spiking modulation ratios (F1/F0) at low (16%) and high (64%) contrasts. The diagonal broken lines indicate the unity lines, where the modulation ratios are the same at high and low contrasts. Compared to high contrasts, the modulation ratios showed significant increases at low contrasts in both membrane potential (one-sided t-test, p = 0.008) and spiking rate (one-sided t-test, p = 0.02). Red symbols represent cells that have F1/F0 > 1 (simple cells) at high contrast. Blue symbols represent cells that have F1/F0 < 1 (complex cells) at high contrast. In B, the horizontal and vertical broken lines indicate F1/F0 = 1. Data from the example cells in Figure 4 are marked as Cell A and Cell B on both A and B. Histograms of distributions of modulation ratios at high and low contrasts are plotted on the same scale next to the corresponding scatter plot axis. The broken lines indicate the means of the distributions. (A: * V1/V0 at low contrast: 4.55, V1/V0 at high contrast: 7.22).
- Figure 6.
Model responses of a simple and a complex cell to contrast-reversing gratings. A, Simple cell models (left) and complex cell models (right) have distinct responses to contrast reversing gratings. Four different spatial phases of the contrast reversing grating are shown in the top row and the receptive fields of the simple cell are shown below. The receptive field for the complex cell is not shown but reflects the quadrature pairs of simple cell receptive fields (Adelson and Bergen, 1985). Model responses to the contrast reversing grating are shown in the third row. B, Complex plane representation of the responses of the simple cell (left) and complex cell (right) at the first (F1, blue square) and second (F2, red circle) Fourier frequency. C, Amplitudes of the F1 and F2 frequencies projected onto the principle axis (see results).
- Figure 7.
Responses of an example mouse V1 cell (Cell C) to contrast-reversing gratings. A, Cycle-averaged spiking rate (top) and membrane potential (bottom) to contrast-reversing gratings at high (100%) stimulus contrasts for eight different spatial phases. From left to right, responses to a blank screen and spatial phases 0°, 45°, 90°, 135°, 180°, 225°, 270° and 315° are shown. B, F1 (blue) and F2 (red) values calculated from spiking rate (left panels) and membrane potential (right panels) are plotted separately as functions of spatial phases for high (100%) stimulus contrasts. C, Similar to A, but panels show responses at low (22%) stimulus contrast. D, Similar to B but at low (22%) stimulus contrast.
- Figure 8.
Population results of mouse V1 cells recorded with contrast-reversing gratings. A, B, Scatter plots of membrane potential modulation ratios (V2/V1) (A) and spiking modulation ratios (F2/F1) (B) at low (22% or 32%) and high (100%) contrasts. The diagonal broken lines indicate the unity lines, where the modulation ratio is the same at high and low contrasts. In B, the horizontal and vertical broken lines indicate F2/F1 = 1. Compared to high contrasts, the modulation ratios showed significant increases at low contrasts in both membrane potential responses (n = 21, one-sided t-test, p = 0.016) and spiking rate (n = 12; one-sided t-test, p = 0.021). Data from the example cell in Figure 7 is marked as Cell C on both A and B. Histograms of distributions of modulation ratios at high and low contrasts are plotted on the same scale next to the corresponding scatter plot axis. The broken lines indicate the means of the distributions.
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