No consistent relationship between gamma power and peak frequency in macaque primary visual cortex

Abstract

Neural activity in the gamma frequency range ("gamma") is elevated during active cognitive states. Gamma has been proposed to play an important role in cortical function, although this is debated. Understanding what function gamma might fulfill requires a better understanding of its properties and the mechanisms that generate it. Gamma is characterized by its spectral power and peak frequency, and variations in both parameters have been associated with changes in behavioral performance. Modeling studies suggest these properties are co-modulated, but this has not been established. To test the relationship between these properties, we measured local field potentials (LFPs) and neuronal spiking responses in primary visual cortex of anesthetized monkeys, for drifting sinusoidal gratings of different sizes, contrasts, orientations and masked with different levels of noise. We find that there is no fixed relationship between LFP gamma power and peak frequency, and neither is related to the strength of spiking activity. We propose a simple model that can account for the complex stimulus dependence we observe, and suggest that separate mechanisms determine gamma power and peak frequency.

Figure 1.

Architecture of the model. The model consisted of local excitatory (E) and inhibitory (I) components and a global (G) component. The local components provided input to each other (W_EI and W_IE) and to themselves (W_EE and W_II). The global component was driven by the E component (W_EG), and provided excitation to both E and I (W_GE and W_GI, respectively). Both E and I were driven by external input, I_E and I_I. Red indicates excitatory input or connections; blue indicates inhibition.

Figure 2.

Gamma power, peak frequency, and neuronal firing rate for different stimulus manipulations in V1. A, Left, Power spectra of LFP for gratings of different sizes (n = 209 sites). Dashed line indicates the gamma power for spontaneous activity. Middle, Peak frequency in the gamma range (thick red line) and normalized gamma power (thick black line). The faint lines indicate the average data from each animal. Dashed line indicates the gamma power for spontaneous activity. Right, Normalized neuronal responses (thick black line). Faint lines indicate the average data from each animal. B, Left, Power spectra of LFP for different levels of noise-masking (n = 228 sites). Middle, Peak frequency and normalized gamma power. Right, Normalized neuronal firing rate. C, Left, Power spectra of LFP for different stimulus contrasts (n = 90 sites). Middle, Peak frequency and normalized gamma power. Right, Normalized neuronal responses. D, Left, Power spectra of LFP for gratings of different orientations (n = 209 sites). Middle, Peak frequency and normalized gamma power. Right, Normalized neuronal responses. All error bars indicate SEM.

Figure 3.

Example simulation responses. A, Response of the E component to a small grating (r = 3), as a function of time. Note the strong mean response, and the presence of transient gamma fluctuations. Smaller gratings (r = 1 or 2) produced stronger responses, but too little gamma power to visualize in a single trial. B, Response of the E component to a large grating (r = 5). Note the decrease in mean response and enhancement of gamma band activity. C, D, Spectrogram of the epochs shown in A and B, respectively. Gamma activity is weaker and at a higher frequency for the small grating. Spectra were computed in a sliding 512 ms window, centered at the time indicated; spectra were smoothed for display only, by convolving a two-dimensional Gaussian kernel with the data.

Figure 4.

Simulated gamma power, peak frequency and neuronal firing rate for different stimulus manipulations. A, Left, Power spectra of LFP for gratings of different sizes Middle, Peak frequency in the gamma range (red) and normalized gamma power (black). Right, Normalized neuronal responses. B, Left, Power spectra of LFP for different levels of noise-masking. Middle, Peak frequency and normalized gamma power. Right, Normalized neuronal firing rate. C, Left, Power spectra of LFP for different stimulus contrasts. Middle, Peak frequency and normalized gamma power. Right, Normalized neuronal responses. D, Left, Power spectra of LFP for gratings of different orientations. Middle, Peak frequency and normalized gamma power. Right, Normalized neuronal responses.

Figure 5.

Dependence of model gamma power and peak frequency on input strength and time constants. A, Gamma power as a function of input strength for a large grating (r = 5). Input strength of 1 corresponds to values of R_max = 40, c = 1, MN = 0, θ = 0 for I_E, as in Equation 5; R_max = 32 for I_I. Weaker inputs were provided by scaling I_E and I_I by the values indicated on the abscissa. Different line shades correspond to simulations in which the model time constants (τ) were multiplied by the factor indicated. B, Same as A but for gamma peak frequency. C, Same as A but for response strength. D–F, Same as A–C but for small gratings (r = 1).