Information tuning of populations of neurons in primary visual cortex

Abstract

Neurons in macaque primary visual cortex (V1) show a diversity of orientation tuning properties, exhibiting a broad distribution of tuning width, baseline activity, peak response, and circular variance (CV). Here, we studied how the different tuning features affect the performance of these cells in discriminating between stimuli with different orientations. Previous studies of the orientation discrimination power of neurons in V1 focused on resolving two nearby orientations close to the psychophysical threshold of orientation discrimination. Here, we developed a theoretical framework, the information tuning curve, that measures the discrimination power of cells as a function of the orientation difference, deltatheta, of the two stimuli. This tuning curve also represents the mutual information between the neuronal responses and the stimulus orientation. We studied theoretically the dependence of the information tuning curve on the orientation tuning width, baseline, and peak responses. Of main interest is the finding that narrow orientation tuning is not necessarily optimal for all angular discrimination tasks. Instead, the optimal tuning width depends linearly on deltatheta. We applied our theory to study the discrimination performance of a population of 490 neurons in macaque V1. We found that a significant fraction of the neuronal population exhibits favorable tuning properties for large deltatheta. We also studied how the discrimination capability of neurons is distributed and compared several other measures of the orientation tuning such as CV with Chernoff distances for normalized tuning curves.

Figure 2.

The response tuning curves of six neurons in V1. Solid lines are models of tuning curves fitted to experimental results. Filled dots present the observed mean spike counts for 1 sec.

Figure 4.

A model of tuning curve λ(θ). λ(θ) = A + B₁ exp(–θ′²/2σ²) + B₂ exp(–θ″²/2σ²). θ′ (θ″) is the angle between θ and 90° (270°). For this example, A = 5, B₁ = B₂ = 20 σ = 22.5°.

Figure 1.

Mean and variance of spike counts of 490 neurons for preferred directions of each neuron. For each neuron, the number of spikes for one period of sinusoidal grating stimulus was counted. The average value of the ratio of variance and the mean is 1.9, but the distribution of the ratio between mean and variance has a peak at 1, which is the value for Poisson distributions.

Figure 3.

Plots of D_C(δθ) (i.e., examples of information tuning curves). Response tuning curves of corresponding neurons are shown in Figure 2.

Figure 5.

A surface plot of D_C(δθ) as a function of R_A andδθ.σ = 17.2°. The inset has plots of D_C(3°) and D_C(10°) as a function of R_A. The solid line is for D_C(3°). The dashed line is for D_C(10°).

Figure 6.

Plot of the half-width for relative baseline A_H as a function of angular difference δθ. The dependence on tuning width is revealed by comparing these curves for tuning width σ = 11.5, 17.2, and 22.9°.

Figure 7.

A plot D_C(δθ) as a function of tuning width σ and δθ. Relative baseline R_A = 0.

Figure 8.

Half-width for tuning widthσ,σ_H, andσ*. Solid lines are forσ_H. The dashed line is for optimal tuning width σ*. Relative baseline R_A = 0.

Figure 9.

Plots of D_C(3°) and D_C(45°) as functions of tuning width σ. Each line is for a different value of relative baseline R_A. From top to bottom, R_A = 0, 0.1, and 0.2, respectively.

Figure 10.

Optimal tuning width σ* for several different values of relative baseline R_A.

Figure 11.

Histograms of peak response M_B, baseline R_A, and response tuning widthσ for OS population (top graphs) and for DS population (bottom graphs). M_B is A + max{B₁, B₂}. R_A is A/M_B, where A is the baseline of the tuning curve and M_B is the peak response. See Figure 4 for the description of the model of the tuning curve.

Figure 12.

Scatter plots of D_C(δθ₁) and D_C(δθ₂) for 490 neurons in V1. For the three scatter plots, δθ₁ = 3° and δθ₂ = 10, 45, and 90°, respectively. d is a plot of correlation coefficients between D_C(3°) and D_C(δθ) as a function of δθ.

Figure 13.

Correlation between CV and D_C(δθ). a–c are scatter plots for δθ = 3, 45, and 90°, respectively. d is a plot of correlation coefficients between R_A and D_C(δθ).

Figure 14.

Plot of CV and D_C(90°). For the model of tuning curve, see Figure 4. For line (a), relative baseline R_A = 0 and tuning widthσ is from 8 to 40° (left side is for smallerσ). For line (b), σ is 20°, and R_A is from 0 to 0.2 (left side is for smaller R_A).

Figure 15.

Correlation between R_A and D_C(δθ) in the V1 population. a–c are scatter plots for δθ = 3, 45, and 180°, respectively. d is a plot of correlation coefficients between R_A and D_C(δθ).

Figure 16.

Correlation between σ and D_C(δθ) in the V1 population. a–c are scatter plots for δθ = 3,90, and 180°, respectively. d is a plot of correlation coefficients between σ and D_C(δθ).