Response variability of marmoset parvocellular neurons

Abstract

This study concerns the properties of neurons carrying signals for colour vision in primates. We investigated the variability of responses of individual parvocellular lateral geniculate neurons of dichromatic and trichromatic marmosets to drifting sinusoidal luminance and chromatic gratings. Response variability was quantified by the cycle-to-cycle variation in Fourier components of the response. Averaged across the population, the variability at low contrasts was greater than predicted by a Poisson process, and at high contrasts the responses were approximately 40% more variable than responses at low contrasts. The contrast-dependent increase in variability was nevertheless below that expected from the increase in firing rate. Variability falls below the Poisson prediction at high contrast, and intrinsic variability of the spike train decreases as contrast increases. Thus, while deeply modulated responses in parvocellular cells have a larger absolute variability than weakly modulated ones, they have a more favourable signal: noise ratio than predicted by a Poisson process. Similar results were obtained from a small sample of magnocellular and koniocellular ('blue-on') neurons. For parvocellular neurons with pronounced colour opponency, chromatic responses were, on average, less variable (10-15%, p<0.01) than luminance responses of equal magnitude. Conversely, non-opponent parvocellular neurons showed the opposite tendency. This is consistent with a supra-additive noise source prior to combination of cone signals. In summary, though variability of parvocellular neurons is largely independent of the way in which they combine cone signals, the noise characteristics of retinal circuitry may augment specialization of parvocellular neurons to signal luminance or chromatic contrast.

Figure 1. Analysis of the fundamental (first harmonic) response of an opponent parvocellular neuron in a?20 animal to red–green chromatic (RG) and luminance (LUM) flicker

A and B, post-stimulus histograms and rasters of responses to gratings at contrast of 0, 0.25 and 1.0. C, fundamental Fourier component z₁(n_trial, n_cycle) of responses to each stimulus cycle, for zero contrast (blue or grey) and a contrast of 1.0 (red or black). Each point's position in the complex plane represents a value of z₁(n_trial, n_cycle) (eqn (1)). The outer ellipse is the 1/e level curve of the Gaussian with mean and variance that match those of the data. The inner ellipse is a 95% confidence region on the average response, determined by the Hotelling T² test (Anderson, 1958). D, amplitude of mean first harmonic response |z₁(C) | (eqn (2)) as a function of contrast C. Error bars represent 95% confidence limits, as calculated by T²_circ (Victor & Mast, 1991). E, variability of the first harmonic response, plotted as , at each contrast C. Error bars represent 95% confidence limits, as calculated by an F statistic (see Appendix I).

Figure 2. Scattergrams of variance at C = 1.0 versus variance at C = 0 for the DC response (f₀), left column, and the fundamental Fourier component (f₁), right column

Top row, all dichromat neurons. Second row, non-opponent neurons from all trichromats. Third row, opponent neurons from Δ13 trichromats. Fourth row, opponent neurons from Δ20 trichromats. Variances plotted are V₀ and V₁, as defined by eqn (3). Error bars represent 95% confidence limits on the variance estimates for each neuron, as calculated by F statistics (see Appendix 1). While there is considerable scatter across the population, the average tendency is that of greater variance at the high contrast. Note that C = 1 for a chromatic stimulus has a much lower cone contrast than a C = 1 luminance stimulus, depending on phenotype (Table 1).

Figure 3. Response variance V_0,V₁ and V₂ for the DC response and the first two harmonics as a function of the mean firing rate z₀

Left column, Contrast = 0; right column, Contrast = 1. Data from all neurons, under all spatial and chromatic conditions. Dashed line, Poisson prediction (see text and Appendix II). Continuous line, linear (observed) regression.

Figure 4. Comparison of response variance V_k at constant response size under RG (abscissa) and LUM (ordinate) conditions for the DC response (f₀), left column, and the fundamental Fourier component (f₁), right column

The response size chosen for comparison is the midpoint of the range of overlap of the RG and LUM response amplitudes. Top row, all dichromat neurons. Second row, non-opponent neurons from all trichromats. Third row, opponent neurons from Δ13 trichromats. Fourth row: opponent neurons from Δ20 trichromats. For f₁ responses in Δ20 trichromats, there is a larger variance under LUM than RG conditions. There is a trend in the opposite direction for the other cell types. Variances plotted are V₀ and V₁, as defined by eqn (3) and interpolated by eqn (5), at constant response size. Error bars represent 95% confidence limits on the variance estimates for each neuron, and include the uncertainty of the variance estimates and the model error of the empirical variance versus mean relationship, eqn (5).

Figure 5. Comparison of response variance V_k at as a function of response size ∣z_k∣ for RG and LUM conditions for the DC response (f₀), left column, and the fundamental Fourier component (f₁), right column

Top row, all dichromat neurons. Second row, non-opponent neurons from all trichromats. Third row, opponent neurons from Δ13 trichromats. Fourth row, opponent neurons from Δ20 trichromats. Variances plotted are V₀ and V₁, as defined by eqn (3) and interpolated by eqn (5). For f₁ responses in Δ20 trichromats, there is a larger variance under LUM than RG conditions at all response sizes. For f₀, the Poisson prediction V₀ =z₀ is also shown. All variances are somewhat greater than the Poisson prediction.

Figure 6. Dependence of response variance on core contrast

A, cone contrasts at the same criterion response amplitude as shown in Fig. 4 for RG and LUM conditions. The straight line corresponds to c_avg(RG) =c_avg(LUM). B, relationship of variance ratio to cone contrast ratio . Opponent neurons in Δ20 animals have a lower value of than opponent neurons in Δ13 animals, even at the same cone contrast ratio. Note that Contrast = 1 for a chromatic stimulus has a much lower cone contrast than a Contrast = 1 luminance stimulus, depending on phenotype (Table 1).

Figure 7. Analysis of the fundamental (first harmonic) responses of a magnocellular (MC) cell to luminance modulation, and of a koniocellular (KC) blue-on cell to short-wavelength-sensitive (SWS) cone-isolating modulation

A and C, post-stimulus histograms and raster plots of responses to gratings at contrast of 1.0. The upper panels in B and D show amplitude of mean first harmonic response |z₁(C) | (eqn (2)) as a function of contrast C. Error bars represent 95% confidence limits, as calculated by T²_circ (Victor & Mast, 1991). The lower panels show variability of the first harmonic response, plotted as , at each contrast C. Error bars represent 95% confidence limits, as calculated by an F statistic (see Appendix 1).

Figure 8. Scattergrams of variance at C = 1.0 versus variance at C = 0 for the DC response (F₀), left column, and the fundamental Fourier component (F₁), right column

Responses of magnocellular (MC) cells are shown in A and B. Responses of koniocellular (KC) blue-on cells are shown in C and D. Variances plotted are V₀ and V₁, as defined by eqn (3). Error bars represent 95% confidence limits on the variance estimates for each neuron, as calculated by F statistics (see Appendix 1). Values are pooled across chromatic stimulation conditions for MC and KC blue-on cells. The shaded area in each graph shows an envelope of PC cell responses from Fig. 4A. Outliers from the PC distribution were removed by iterative (3x) enclosure with a convex hull and removal of points at the hull vertices. Note that the majority of points for both MC and KC blue-on cells show greater variance at C = 1 than at C = 0, and thus lie within the PC cell envelope.

Figure 9. Response variance V₀, V₁ and V₂ for the DC response (F₀) and the first two harmonics (F₁, F₂) as a function of the DC amplitude (mean firing rate) z₀ in magnocellular (MC) and koniocellular (KC) blue-on cells

Left column, Contrast = 0; right column: Contrast = 1. The shaded area in each graph shows an envelope of PC cell responses from Fig. 5 for each contrast and harmonic. Outliers from the PC distribution were removed by iterative (3x) enclosure with a convex hull and removal of points at the hull vertices. Open symbols and thick continous lines show KC blue-on cells and linear regression line. Filled symbols and dotted lines show MC cells and linear regression. Thin continous lines show PC cell linear regressions from Fig. 5. Data from all neurons, under all spatial and chromatic conditions. Dashed line, Poisson prediction (see text and Appendix II). Note that for all populations the variance at high contrast falls below the Poisson prediction.

Figure 10

Distribution of probability (p) values from the empirical variance–mean relationship fits described in Appendix I.