Relay cells in the mammalian lateral geniculate nucleus (LGN) are driven primarily by single retinal ganglion cells (RGCs). However, an LGN cell responds typically to less than half of the spikes it receives from the RGC that drives it, and without retinal drive the LGN is silent (Kaplan and Shapley, 1984). Recent studies, which used stimuli restricted to the receptive field (RF) center, show that despite the great loss of spikes, more than half of the information carried by the RGC discharge is typically preserved in the LGN discharge (Sincich et al., 2009), suggesting that the retinal spikes that are deleted by the LGN carry less information than those that are transmitted to the cortex. To determine how LGN relay neurons decide which retinal spikes to respond to, we recorded extracellularly from the cat LGN relay cell spikes together with the slow synaptic (‘S’) potentials that signal the firing of retinal spikes. We investigated the influence of the inhibitory surround of the LGN RF by stimulating the eyes with spots of various sizes, the largest of which covered the center and surround of the LGN relay cell's RF. We found that for stimuli that activated mostly the RF center, each LGN spike delivered more information than the retinal spike, but this difference was reduced as stimulus size increased to cover the RF surround. To evaluate the optimality of the LGN editing of retinal spikes, we created artificial spike trains from the retinal ones by various deletion schemes. We found that single LGN cells transmitted less information than an optimal detector could.
Firing-rate models provide a practical tool for studying signal processing in the early visual system, permitting more thorough mathematical analysis than spike-based models. We show here that essential response properties of relay cells in the lateral geniculate nucleus (LGN) can be captured by surprisingly simple firing-rate models consisting of a low-pass filter and a nonlinear activation function. The starting point for our analysis are two spiking neuron models based on experimental data: a spike-response model fitted to data from macaque (Carandini et al. J. Vis., 20(14), 1-2011, 2007), and a model with conductance-based synapses and afterhyperpolarizing currents fitted to data from cat (Casti et al. J. Comput. Neurosci., 24(2), 235-252, 2008). We obtained the nonlinear activation function by stimulating the model neurons with stationary stochastic spike trains, while we characterized the linear filter by fitting a low-pass filter to responses to sinusoidally modulated stochastic spike trains. To account for the non-Poisson nature of retinal spike trains, we performed all analyses with spike trains with higher-order gamma statistics in addition to Poissonian spike trains. Interestingly, the properties of the low-pass filter depend only on the average input rate, but not on the modulation depth of sinusoidally modulated input. Thus, the response properties of our model are fully specified by just three parameters (low-frequency gain, cutoff frequency, and delay) for a given mean input rate and input regularity. This simple firing-rate model reproduces the response of spiking neurons to a step in input rate very well for Poissonian as well as for non-Poissonian input. We also found that the cutoff frequencies, and thus the filter time constants, of the rate-based model are unrelated to the membrane time constants of the underlying spiking models, in agreement with similar observations for simpler models.
To understand how anatomy and physiology allow an organism to perform its function, it is important to know how information that is transmitted by spikes in the brain is received and encoded. A natural question is whether the spike rate alone encodes the information about a stimulus ( rate code ), or additional information is contained in the temporal pattern of the spikes ( temporal code ). Here we address this question using data from the cat Lateral Geniculate Nucleus (LGN), which is the visual portion of the thalamus, through which visual information from the retina is communicated to the visual cortex. We analyzed the responses of LGN neurons to spatially homogeneous spots of various sizes with temporally random luminance modulation. We compared the Firing Rate with the Shannon Information Transmission Rate , which quantifies the information contained in the temporal relationships between spikes. We found that the behavior of these two rates can differ quantitatively. This suggests that the energy used for spiking does not translate directly into the information to be transmitted. We also compared Firing Rates with Information Rates for X-ON and X-OFF cells. We found that, for X-ON cells the Firing Rate and Information Rate often behave in a completely different way, while for X-OFF cells these rates are much more highly correlated. Our results suggest that for X-ON cells a more efficient “temporal code” is employed, while for X-OFF cells a straightforward “rate code” is used, which is more reliable and is correlated with energy consumption.
LGN neurons can respond with extreme precision to a variety of temporally varying stimuli [1]. This precision requires non-linear processing of the stimulus and therefore cannot be described by standard linear (or linearnon-linear, LN) models. Rather, in previous work, we have found that precision arises through the interplay of an excitatory receptive field and a similarly tuned -but delayed -suppressive receptive field, allowing for fine time scales in the LGN response to arise in the brief window where excitation exceeds the suppression [2]. However, it is not clear whether such non-linear interaction arises in the retina, at the retinogeniculate synapse itself or involves other secondary LGN inputs.To investigate this, we applied a newly developed a Generalized Non-Linear Modeling (GNLM) framework to data involving the simultaneous recording of LGN neurons and their predominant retinal ganglion cell (RGC) input. This framework uses efficient maximum-likelihood optimization [3], adapted to include nested non-linear terms [2,4]. Using this novel approach, we simultaneously optimize the shape of postsynaptic currents resulting from RGC stimulation along with other non-linear excitatory and inhibitory elements tuned to the visual stimulus, based on the observed RGC and LGN spike trains alone. We also can directly characterize the non-linear elements in the RGC.We found that while there were subtle non-linear elements in the RGC response, they were amplified in that of the LGN. Consistent with previous reports [5], summation with a threshold explains a large part of the increased sparseness of LGN responses relative to those of the input RGC. However, an additional opposite-sign suppressive term was also present, possibly contributing to the pushpull nature of the LGN response observed in intracellular recordings [6]. In many cases, we also detected additional non-linear excitatory inputs, possibly resulting from other RGC inputs. Interestingly, such additional terms were much more sensitive to contrast than the dominant input, possible resulting in the well-known contrast gain control effects, though present both at the level of the retina and LGN.Thus, the GNLM modeling methods reveal how non-linear computation performed is performed the RG synapse, and allows for more general characterization of non-linear computation throughout the visual pathway. Butts DA, Jin JZ, Weng C, Alonso JM, Stanley GB: The computation underlying the precise timing of visual neuron spike trains.
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