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We develop a new analysis of the lateral geniculate nucleus (LGN) input to a cortical simple cell, demonstrating that this input is the sum of two terms, a linear term and a nonlinear term. In response to a drifting grating, the linear term represents the temporal modulation of input, and the nonlinear term represents the mean input. The nonlinear term, which grows with stimulus contrast, has been neglected in many previous models of simple cell response. We then analyze two scenarios by which contrast-invariance of orientation tuning may arise. In the first scenario, at larger contrasts, the nonlinear part of the LGN input, in combination with strong push-pull inhibition, counteracts the nonlinear effects of cortical spike threshold, giving the result that orientation tuning scales with contrast. In the second scenario, at low contrasts, the nonlinear component of LGN input is negligible, and noise smooths the nonlinearity of spike threshold so that the input-output function approximates a power-law function. These scenarios can be combined to yield contrast-invariant tuning over the full range of stimulus contrast. The model clarifies the contribution of LGN nonlinearities to the orientation tuning of simple cells and demonstrates how these nonlinearities may impact different models of contrast-invariant tuning.

A central theme in neural coding concerns the role of response variability and noise in determining the information transmission of neurons. This issue was investigated in single cells of the lateral geniculate nucleus of barbiturate-anesthetized cats by quantifying the degree of precision in and the information transmission properties of individual spike train responses to full field, binary (bright or dark), flashing stimuli. We found that neuronal responses could be highly reproducible in their spike timing (approximately 1-2 ms standard deviation) and spike count (approximately 0.3 ratio of variance/mean, compared with 1.0 expected for a Poisson process). This degree of precision only became apparent when an adequate length of the stimulus sequence was specified to determine the neural response, emphasizing that the variables relevant to a cell's response must be controlled to observe the cell's intrinsic response precision. Responses could carry as much as 3.5 bits/spike of information about the stimulus, a rate that was within a factor of two of the limit the spike train could transmit. Moreover, there appeared to be little sign of redundancy in coding: on average, longer response sequences carried at least as much information about the stimulus as would be obtained by adding together the information carried by shorter response sequences considered independently. There also was no direct evidence found for synergy between response sequences. These results could largely, but not entirely, be explained by a simple model of the response in which one filters the stimulus by the cell's impulse response kernel, thresholds the result at a fairly high level, and incorporates a postspike refractory period.

We study a recently proposed “correlation-based,” push-pull model of the circuitry of layer 4 of cat visual cortex. This model was previously shown to explain the contrast-invariance of cortical orientation tuning. Here we show that it can simultaneously account for several contrast-dependent (c-d) “nonlinearities” in cortical responses. These include an advance with increasing contrast in the temporal phase of response to a sinusoidally modulated stimulus; a change in shape of the temporal frequency tuning curve, so that higher temporal frequencies may give little or no response at low contrast but reasonable responses at high contrast; and contrast saturation that occurs at lower contrasts in cortex than in the lateral geniculate nucleus (LGN). In the context of the model circuit, these properties arise from a mixture of nonlinear cellular and synaptic mechanisms: short-term synaptic depression, spike-rate adaptation, contrast-induced changes in cellular conductance, and the nonzero spike threshold. The former three mechanisms are sufficient to explain the experimentally observed increase in c-d phase advance in cortex relative to LGN. The c-d changes in temporal frequency tuning arise as a threshold effect: voltage modulations in response to higher-frequency inputs are only slightly above threshold at lower contrast, but become robustly suprathreshold at higher contrast. The other three nonlinear mechanisms also play a crucial role in this result, allowing contrast dependence of temporal frequency tuning to coexist with contrast-invariance of orientation tuning. Contrast saturation, and the observation that responses to stimuli of increasing temporal frequency saturate at increasingly high contrasts, can be induced both by the model's push-pull inhibition and by synaptic depression. Previous proposals explained these nonlinear response properties by assuming contrast-invariant orientation tuning as a starting point, and adding normalization by shunting inhibition derived equally from cells of all preferred orientations. The present proposal simultaneously explains both contrast-invariant orientation tuning and these contrast-dependent nonlinearities and requires only processing that is local in orientation, in agreement with intracellular measurements.

Partially isolated cortical islands prepared in vivo become epileptogenic within weeks of the injury. In this model of chronic epileptogenesis, recordings from cortical slices cut through the injured area and maintained in vitro often show evoked, long- and variable-latency multiphasic epileptiform field potentials that also can occur spontaneously. These events are initiated in layer V and are synchronous with polyphasic long-duration excitatory and inhibitory potentials (currents) in neurons that may last several hundred milliseconds. Stimuli that are significantly above threshold for triggering these epileptiform events evoke only a single large excitatory postsynaptic potential (EPSP) followed by an inhibitory postsynaptic potential (IPSP). We investigated the physiological basis of these events using simulations of a layer V network consisting of 500 compartmental model neurons, including 400 principal (excitatory) and 100 inhibitory cells. Epileptiform events occurred in response to a stimulus when sufficient N-methyl-d-aspartate (NMDA) conductance was activated by feedback excitatory activity among pyramidal cells. In control simulations, this activity was prevented by the rapid development of IPSPs. One manipulation that could give rise to epileptogenesis was an increase in the threshold of inhibitory interneurons. However, previous experimental data from layer V pyramidal neurons of these chronic epileptogenic lesions indicate: upregulation, rather than downregulation, of inhibition; alterations in the intrinsic properties of pyramidal cells that would tend to make them more excitable; and sprouting of their intracortical axons and increased numbers of presumed synaptic contacts, which would increase recurrent EPSPs from one cell onto another. Consistent with this, we found that increasing the excitability of pyramidal cells and the strength of NMDA conductances, in the face of either unaltered or increased inhibition, resulted in generation of epileptiform activity that had characteristics similar to those of the experimental data. Thus epileptogenesis such as occurs after chronic cortical injury can result from alterations of intrinsic membrane properties of pyramidal neurons together with enhanced NMDA synaptic conductances.