Neuronal firing correlations are studied using simulations of a simple network model for a cortical column in a high-conductance state with dynamically balanced excitation and inhibition. Although correlations between individual pairs of neurons exhibit considerable heterogeneity, population averages show systematic behavior. When the network is in a stationary state, the average correlations are generically small: correlation coefficients are of order 1/N , where N is the number of neurons in the network. However, when the input to the network varies strongly in time, much larger values are found. In this situation, the network is out of balance, and the synaptic conductance is low, at times when the strongest firing occurs. However, examination of the correlation functions of synaptic currents reveals that after these bursts, balance is restored within a few milliseconds by a rapid increase in inhibitory synaptic conductance. These findings suggest an extension of the notion of the balanced state to include balanced fluctuations of synaptic currents, with a characteristic timescale of a few milliseconds.

We study the spike statistics of neurons in a network with dynamically balanced excitation and inhibition. Our model, intended to represent a generic cortical column, comprises randomly connected excitatory and inhibitory leaky integrate-and-fire neurons, driven by excitatory input from an external population. The high connectivity permits a mean field description in which synaptic currents can be treated as gaussian noise, the mean and autocorrelation function of which are calculated self-consistently from the firing statistics of single model neurons. Within this description, a wide range of Fano factors is possible. We find that the irregularity of spike trains is controlled mainly by the strength of the synapses relative to the difference between the firing threshold and the postfiring reset level of the membrane potential. For moderately strong synapses, we find spike statistics very similar to those observed in primary visual cortex.

We introduce a model of generalized Hebbian learning and retrieval in oscillatory neural networks modeling cortical areas such as hippocampus and olfactory cortex. Recent experiments have shown that synaptic plasticity depends on spike timing, especially on synapses from excitatory pyramidal cells, in hippocampus, and in sensory and cerebellar cortex. Here we study how such plasticity can be used to form memories and input representations when the neural dynamics are oscillatory, as is common in the brain (particularly in the hippocampus and olfactory cortex). Learning is assumed to occur in a phase of neural plasticity, in which the network is clamped to external teaching signals. By suitable manipulation of the nonlinearity of the neurons or the oscillation frequencies during learning, the model can be made, in a retrieval phase, either to categorize new inputs or to map them, in a continuous fashion, onto the space spanned by the imprinted patterns. We identify the first of these possibilities with the function of olfactory cortex and the second with the observed response characteristics of place cells in hippocampus. We investigate both kinds of networks analytically and by computer simulations, and we link the models with experimental findings, exploring, in particular, how the spike timing dependence of the synaptic plasticity constrains the computational function of the network and vice versa.

It is difficult to extract the information carried by neuronal responses about a set of stimuli because limited data samples result in biased es timates. Recently two improved procedures have been developed to calculate information from experimental results: a binning-and-correcting procedure and a neural network procedure. We have used data produced from a model of the spatiotemporal receptive fields of parvocellular and magnocellular lateral geniculate neurons to study the performance of these methods as a function of the number of trials used. Both procedures yield accurate results for one-dimensional neuronal codes. They can also be used to produce a reasonable estimate of the extra information in a three-dimensional code, in this instance, within 0.05-0.1 bit of the asymptotically calculated value—about 10% of the total transmitted information. We believe that this performance is much more accurate than previous procedures.