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.

^{2}; frame rate of 160 Hz) driven by a VSG 2/5 stimulator (Cambridge Research Systems, Cambridge, UK). Stimuli consisted of spatially homogeneous circular spots of various diameters, ranging from 0.5° to full field, modulated temporally according to a pseudorandom sequence (Reinagel & Reid, 2000; van Hateren, 1997). For each spot size, we presented a sequence of 256 stimulus segments of random luminance modulation, each 8 s long, in which 128 repeated segments (repeats) were interleaved with 128 nonrepeating segments (uniques). The entire stimulus run thus lasted 8 × 256 = 2048 s, during which the spot size was fixed. A filtered version of the repeated segment is shown in the top panel of Figure 4A.

*m*-sequence (Reid, Victor, & Shapley, 1997; Shutter, 1987). Neurons were classified as X or Y based on the responses to contrast reversal of fine gratings (Hochstein & Shapley, 1976). None of our Y cell recordings were sufficiently stable to be used in this work, so all the model results presented are for X cells. All cells were within 15° of the

*area centralis*. The RF center size was estimated by fitting a Difference of Gaussians (DOG) model to the spatial response map that resulted from the reverse correlation procedure. The center radius was taken to be twice the standard deviation of the Gaussian fit. In the figures, spot sizes are reported as a multiple of the estimated size of the RF center and are referred to as relative spot sizes.

*x*

_{ t },

*n*

_{ t }, and

*l*

_{ t }, which represent discrete time series for the RGC spikes (S potentials), LGN spikes, and the luminance of the visual stimulus at time

*t,*respectively. A distinct linear temporal filter is convolved with each source of input to the model: The filter

*x*

_{ t }), the filter

*n*

_{ t }) and models the spike-history effects on the present activity of the neuron, and the filter

*l*

_{ t }). The parameter

*b*is a constant offset that defines the background firing rate of the LGN neuron. Because of the presence of the constant

*b,*which represents the sum of all constant inputs to the function

*f,*the filters are mainly responsive to deviations of the corresponding inputs around their means. In line with this inherent separation of mean and variance in the model and in order to make the interpretation of the filter

^{2}) from the values

*l*

_{ t }at each time. After convolving the inputs with the filters, the result is fed into a nonlinear, monotonically increasing function

*f*to calculate the instantaneous firing rate

*λ*

_{ t }of the LGN neuron at time

*t*. The main role of

*f*is to capture nonlinear thresholding effects. Finally, the number of spikes in each time bin of duration

*d*

_{ t }is drawn from a Poisson distribution such that

*n*

_{ t }∼ Poiss(

*λ*

_{ t },

*dt*). Figure 2 depicts a schematic structure of the GLM and its components. An important feature of the GLM used here is that the visual input enters through two distinct routes: first, from the RGC spikes (

*x*

_{ t }) with its corresponding temporal filter

*l*

_{ t }), with its corresponding filter

*L*of the GLM producing the observed LGN spike train (

*O*) can be written as in Snyder and Miller (1991):

*c*is a constant unrelated to the model parameters. If

*f*(

*u*) is a convex function of its scalar argument

*u,*and log

*f*(

*u*) is concave in

*u,*then the above log-likelihood is guaranteed to be a concave function of the parameter

_{ ML }, which can be found easily by numerical ascent techniques. We use the standard Hessian-based estimate for the standard error of the optimization: diag[(∇

_{ θ ML }

^{2}

*L*)

^{−1}

_{ θ ML }

^{2}

*L*denotes the Hessian of the log-likelihood evaluated at the maximum likelihood estimate

*θ*

_{ ML }(Paninski, 2004; Paninski et al., 2007; Truccolo et al., 2005; see Figures 3 and 5). The function

*f*(

*u*) used here that satisfies the above conditions is

_{data}and PSTH

_{model}refer to the PSTH of the laboratory data and the GLM, respectively, and 〈·〉 denotes a time average across trials. We computed the PSTH using a bin width of 6.25 ms, equivalent to the frame interval of the 160 Hz stimulus presentation on the CRT. For each experimental condition, two GLMs are fit to the observed LGN spike trains. First, a full model that contains all the temporal filters (

*m*-sequence (see Recording of LGN spikes and S potentials section).

*t*. For times longer than that, these filters were effectively zero, and taking them into account only slowed down the optimization process. Moreover, using the repeated trials to cross-validate the model with filters having more time bins showed that adding redundant time bins to the model filters did not improve the fit, and eventually made the fit worse. This can be due to over-fitting of the model to the details of the noise in the data. With these considerations in mind, we found a 30-ms history to be appropriate for the GLM optimization.

*a priori*implementation of the specific biophysical properties. It is, therefore, more flexible in revealing the factors influencing the neural response.