A generalized linear model of the impact of direct and indirect inputs to the lateral geniculate nucleus

Abstract

Relay neurons in the lateral geniculate nucleus (LGN) receive direct visual input predominantly from a single retinal ganglion cell (RGC), in addition to indirect input from other sources including interneurons, thalamic reticular nucleus (TRN), and the visual cortex. To address the extent of influence of these indirect sources on the response properties of the LGN neurons, we fit a Generalized Linear Model (GLM) to the spike responses of cat LGN neurons driven by spatially homogeneous spots that were rapidly modulated by a pseudorandom luminance sequence. Several spot sizes were used to probe the spatial extent of the indirect visual effects. Our extracellular recordings captured both the LGN spikes and the incoming RGC input (S potentials), allowing us to divide the inputs to the GLM into two categories: the direct RGC input and the indirect input to which we have access through the luminance of the visual stimulus. For spots no larger than the receptive field center, the effect of the indirect input is negligible, while for larger spots its effect can, on average, account for 5% of the variance of the data and for as much as 25% in some cells. The polarity of the indirect visual influence is opposite to that of the linear receptive field of the neurons. We conclude that the indirect source of response modulation of the LGN relay neurons arises from inhibitory sources, compatible with thalamic interneurons or TRN.

Figure 1

An example extracellular voltage recording of an LGN neuron, corresponding to the cell in figure 5B. This record shows seven S potentials, which are large EPSPs driven by RGC input spikes. A “failed” S potential does not have a concomitant LGN spike, while a “successful” S potential is typically embedded within an LGN spike.

Figure 2

A schematic of the GLM that is fit to the recorded LGN data. The inputs to the model are the RGC input events x_t (S potential times; figure 1), the LGN cell spike time history n_t, and the luminance of the visual stimulus l_t. The linear filters acting on the inputs are D⃗ (blue), H⃗ (red) and K⃗; (green). A static nonlinearity f (equation 4) transforms the sum of filtered inputs to obtain the instantaneous firing rate of the neuron. The output spikes are generated as an inhomogeneous Poisson process with the rate parameter λ_t given by equation (1). The model inputs derive from the experimental data, while the linear filters are given by maximizing the likelihood of the model that reproduces the experimental LGN spike train. The temporal filter D⃗ represents the monosynaptic retinogeniculate transmission, and the filter K⃗ captures the effects of indirect visual inputs.

Figure 3

An example of the optimized linear temporal filters for A) an X-Off LGN neuron and B) an X-On LGN neuron. The error bars indicate the standard error of the optimization for each point (see Methods). The time course of the response of each cell, obtained by reverse correlation with checkerboard m-sequence stimuli (section 2.3), is shown in the insets. Each filter is normalized by the standard deviation of its corresponding input, so that the magnitude of the three filters may be compared directly.

Figure 4

The spike train of the GLM compared to the recorded (real) spike train of the LGN X-Off neuron from figure 3A, for the 128 repeated trials. A) The luminance of the visual stimulus is shown in the top panel; the RGC spikes (red) and the real LGN spikes (blue) are shown in the second panel. In the third panel the same RGC spikes (red) and the spike trains of the model LGN neuron (black) are illustrated. The ovals highlight the tendency of the RGC spikes to cluster before the LGN spikes both in the real data and the model. The fourth panel shows the instantaneous firing rate of the real (blue) and model (dotted black) LGN neurons averaged across trails. The bottom panel shows the variance of the firing rate for real (blue) and model (dotted black) LGN neuron across trials. B) The inter-spike-interval (ISI) distribution of the spike trains of the real (blue) and model (dotted black) LGN neurons.

Figure 5

The luminance filter K⃗ for several spot sizes (relative to the RF center size), A) for the representative Off cell corresponding to figure 3A and B) for a representative On cell corresponding to figure 3B. The error bars show the standard error of the optimization for each point (see Methods).

Figure 6

The performance of the GLMs and the contribution of the luminance filter (K⃗). A) The performance of the GLM in reproducing the real LGN spike trains in the repeated trials, calculated according to equation 5. The graph shows the performance of the full GLM (green) and the GLM without K⃗ filter (blue) as a function of the relative size of the stimulus spot, for the same Off cell as in figures 3A and 5A. B) Similar results for the representative On cell of figures 3B and 5B. C) The contribution of the luminance filter K⃗ in improving the performance of the GLM for the representative Off cell. D) The same results for the representative On cell. Error bars indicate the standard deviation over the 128 repeated trials in each case. Note that the contribution of the luminance filter is fairly small.

Figure 7

The average performance of the GLMs and the contribution of the luminance filter (K⃗) for different relative spot sizes. The performance of the model is calculated according to equation (5). The GLM predicts the LGN response better for small stimuli. The contribution of the luminance filter (K⃗) increases for larger stimuli. The error bars depict the standard error.

Figure 8

The contribution of the luminance filter K⃗ to the performance of the GLM for all 10 analyzed LGN neurons. The horizontal axis indicates the relative spot size. The vertical axis indicates the contribution of the K⃗ filter (in the percentage units illustrated in figure 6). Each marker shows the results for a single neuron and a specific stimulus size. The filled circles represent Off cells and open circles represent On cells. Each color corresponds to a distinct cell. The inset shows the identity of the cells that were also analyzed in two previous articles of our group.