Nonlinear signal summation in magnocellular neurons of the macaque lateral geniculate nucleus

Abstract

Magnocellular (M-), but not parvocellular (P-), neurons of the macaque lateral geniculate nucleus (LGN) differ distinctively in their responses to counterphase-modulated and drifting gratings. Relative to stimulation with drifting gratings, counterphase modulation reduces the responses of M- cells in a band around 25 Hz, producing a "notch" in the temporal modulation transfer function (tMTF). The notch is prominent in nearly every M- cell with little variation in the temporal frequency at which it is deepest. The machinery responsible for the notch lies mostly outside the classical linear center. Directly driving the notching mechanism with annular gratings evokes no linear response but elicits a second harmonic (F2) modulation of the discharge accompanied by a drop in the mean discharge (F0). Analysis of the S- potential, which reveals inputs from ganglion cells, shows that 1) tMTFs of the afferent retinal ganglion cells are not notched and 2) during stimulation with annular gratings, the second harmonic component is present, but the drop in the F0 is largely absent from the responses of parasol ganglion cells. These results suggest that the notch is caused by the combined action of the linear response and the second harmonic response, both inherited from retina, and a suppression that originates after the retina. Our results reveal a distinctive signal transformation in the LGN and they show that nearly every M- cell exhibits a spatial nonlinearity like that observed in Y cells of the cat.

FIG. 1.

Temporal modulation transfer functions of lateral geniculate nucleus (LGN) cells. A: temporal modulation transfer functions (tMTFs) of a parvocellular (P-) cell (top) and a magnocellular (M-) cell (bottom) constructed from the responses to optimal spatial frequency gratings either drifted (filled symbols) or counterphase-modulated in the preferred phase (open symbols). B and C: population summaries of tMTFs for P- cells (top) and M- cells (bottom) from responses to drifting gratings (B) and counterphased gratings (C). D: the ratio of response in the counterphased condition to the response in the drifting condition. Gray lines are individual cells. Thick black lines are population averages. Thin black and colored lines identify the example cells. Inset: poststimulus time histograms (PSTHs) from the example cells for the 2 stimulation conditions (drifting in red and counterphased in green) folded to 1 stimulus cycle for the indicated temporal frequencies. Dashed lines in all PSTHs show the average spontaneous firing rate during the corresponding condition. Smooth black lines are best fits of the model (see methods and discussion). All PSTH scale bars denote 100 imp.s⁻¹.

FIG. 2.

Notching mechanism is contrast dependent. A: tMTFs for 2 M- cells collected with optimal spatial frequency gratings that were either drifted (top) or counterphase-modulated (bottom). Gratings were presented at either full contrast (open symbols) or at a contrast that evoked 25% of the maximal response, as determined by optimal drifting gratings (filled symbols). B and C: population summaries of tMTFs to optimal spatial frequency gratings at the c₂₅ (B) and at full contrast (C). D: the ratio of response in the high contrast condition to the response in the low contrast condition. Thin black lines indicate example cells. Other conventions as in Fig. 1.

FIG. 3.

Contrast response of M- cells at different temporal frequencies. A: contrast response of 2 M- cells to counterphase-modulated gratings at either a low temporal frequency (∼7 Hz; filled symbols) or at a temporal frequency that usually produced a notch (∼25 Hz; open symbols). B and C: population summaries of the contrast response to optimal spatial frequency gratings counterphased at a low temporal frequency (B) and at a notching temporal frequency (C). D: the ratio of response in the high temporal frequency condition to the response in the low temporal frequency condition. Other conventions as in Fig. 2.

FIG. 4.

Notching mechanism is spatially extended. A: tMTFs of an M- cell collected with counterphase-modulated gratings of optimal spatial frequency, at two sizes. The smaller (filled symbols) was the smallest size that evoked the largest response to drifting gratings of optimal spatial frequency. The larger (open symbols) was set to 8° and extended well beyond the linear center. B and C: population summaries of the tMTFs from responses to small (B) and large (C) stimuli. D: the ratio of response in the large condition to the response in the small condition. Other conventions as in Fig. 2.

FIG. 5.

Suppression of maintained discharge and generation of second harmonic from the region beyond the center of the receptive field. A: responses of an M- cell to annular gratings of varying inner diameter and 8° OD. Gratings were counterphase-modulated (5 Hz) at optimal spatial frequency (1.5 cycle/°). Blue triangles denote average firing rate (F0). Red circles denote amplitude of the first harmonic component of the discharge (F1). Green squares denote amplitude of the second harmonic component of the discharge (F2). Dashed lines indicate the spontaneous discharge response components. Inset: PSTHs folded to 1 stimulus cycle, for the indicated annulus inner diameters that elicited no F1 response component. Scale bar denotes 50 imp.s⁻¹. Dashed lines in all PSTHs show the average spontaneous firing rate. B: responses of an M- cell stimulated with counterphased annular gratings at a range of temporal frequencies. The inner diameter was the smallest that elicited no F1 response Inset: PSTHs folded to 1 stimulus cycle for the indicated temporal frequencies. Scale bar denotes 50 imp.s⁻¹. Dashed lines in all PSTHs show the average spontaneous firing rate. C–E: population summaries of F1 response (C), F0 response (after subtraction of the average maintained discharge) (D), and F2 response (E). Other conventions as in Fig. 2. F: relationship between the F2 elevation and the F0 suppression at the notch frequency. Example cell shown in black.

FIG. 6.

Spatial frequency tuning of suppression. A: responses of an M- cell stimulated with grating patches and annuli of different spatial frequencies, drifted at a notching temporal frequency. Triangles denote average firing rate (F0). Circles denote amplitude of the 1st harmonic component of the discharge (F1). Filled symbols show responses to grating patches; open symbols show responses to annular stimuli. Dashed lines indicate the spontaneous discharge. Smooth lines are best fits of the difference-of-Gaussians (DoG) model fitted to the F1 response to grating patches and the suppressive DoG model fitted to the F0 response to annular gratings, of inner diameter chosen so as not to evoke an appreciable F1 response at high spatial frequencies. B: a comparison of the receptive field center size with the subunit size estimated from the fits. Example cell shown in black.

FIG. 7.

Notching mechanism is absent in S- potentials. A and B: population summaries of tMTFs for LGN (top) and associated S- potentials (bottom) from responses to drifting gratings (A) and counterphase-modulated gratings (B). C: the ratio of response in the counterphased condition to the response in the drifting condition. D and E: population summaries of the S- potential F0 (after subtraction of the maintained discharge, D) and F2 (E) components of response to annuli of optimal spatial frequency counterphased at 7 temporal frequencies. Other conventions as in Fig. 2.

FIG. 8.

Model of M- cell response. A: the receptive fields of parasol retinal ganglion cells can be represented as the combination of linear Gaussian center and surround weighting functions (DoG; dark gray) and a bank of Gaussian subunits that generate rectified responses (middle gray). The subunit array outputs a signal that is constant in response to a drifting grating but is modulated at twice the stimulus frequency in response to a counterphased grating. Suppression arises after the retina, through pooling of signals from on- and off- LGN neurons across space and time (light gray). This results in a suppressive signal that is the same whether the stimulus is drifting or counterphased. The 3 signals are summed before passing through a static nonlinearity. Dashed black lines represent either baseline membrane potential or spike rate. B: DC response evoked by counterphase modulation. The DC suppression component of the notching mechanism can be construed as a mechanism that pools over on- and off-subunits (dark gray and light gray, respectively). At low contrast (left), the on- and off-signals cancel yielding no net pooled activity (thick black line). Rectification of the on- and off-responses to high-contrast stimuli (right) causes the pooled activity to elevate due to unequal cancellation. A sufficiently slow synapse (bottom) then acts to produce constant responses to counterphased stimuli. If this synapse is inhibitory, the result is a DC suppression in response to high contrast counterphased stimuli.