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Does the nervous system "tune" itself to perform at peak efficiency? Optimal transmission of information in a single nerve cell occurs when the response is matched to the statistics of naturally occurring stimuli, such that all firing rates are used with equal probability and that redundant temporal correlations in the input are removed. Non-Hebbian, local learning rules are developed to adapt the voltage-dependent ionic conductances in Hodgkin-Huxley models of neurons with the goal of matching the neuron's response to the statistics of natural stimuli. These learning rules allow a nerve cell to maximize the amount of information transmitted about arriving stimuli. At a more detailed level, information transmission in neurons is limited by the noise in the input, defined as the root mean square of the fluctuations in the input. Three different performance measures are shown to scale identically as a function of the noise in simple models of neurons that have both a voltage and current threshold. These performance measures are: the probability of correctly detecting a constant input in a limited time, the signal-to-noise ratio in response to sinusoidal input, and the mutual information between an arbitrarily varying input and the output spike train of the model neuron. Of these, detecting a constant signal is the simplest and most fundamental quantity. For subthreshold signals, the model exhibits stochastic resonance, a non-zero noise amplitude that optimally enhances signal detection. In this case, noise paradoxically does not limit, but instead improves performance. Even though the noise amplitude can dwarf the signal, detection of a weak constant signal using stochastic resonance is still possible when the signal elicits on average only one additional spike. Stochastic resonance could thus play a role in neurobiological sensory systems, where speed is of the utmost importance and averaging over many individual spikes is not possible.

Information from the senses must be compressed into the limited range of firing rates generated by spiking nerve cells. Optimal compression uses all firing rates equally often, implying that the nerve cell's response matches the statistics of naturally occurring stimuli. Since changing the voltage-dependent ionic conductances in the cell membrane alters the flow of information, an unsupervised, non-Hebbian, developmental learning rule is derived to adapt the conductances in Hodgkin-Huxley model neurons. By maximizing the rate of information transmission, each firing rate within the model neuron's limited dynamic range is used equally often. An efficient neuronal representation of incoming sensory information should take advan(cid:173) tage of the regularity and scale invariance of stimulus features in the natural world. In the case of vision, this regularity is reflected in the typical probabilities of encountering particular visual contrasts, spatial orientations, or colors [1]. Given these probabilities, an optimized neural code would eliminate any redundancy, while devoting increased repre(cid:173) sentation to commonly encountered features. At the level of a single spiking neuron, information about a potentially large range of stimuli is compressed into a finite range of firing rates, since the maximum firing rate of a neuron is limited. Optimizing the information transmission through a single neuron in the presence of uniform, additive noise has an intuitive interpretation: the most efficient representation of the input uses every firing rate with equal probability. An analogous principle for non(cid:173) spiking neurons has been tested experimentally by Laughlin [2], who matched the statistics.

We investigate a model for neural activity that generates long range temporal correlations, 1/ f noise, and oscillations in global activity. The model consists of a two-dimensional sheet of leaky integrate-and- fire neurons with feedback connectivity consisting of local excitation and surround inhibition. Each neuron is independently driven by homogeneous external noise. Spontaneous symmetry breaking occurs, resulting in the formation of "hotspots" of activity in the network. These localized patterns of excitation appear as clusters that coalesce, disintegrate, or fluctuate in size while simultaneously moving in a random walk constrained by the interaction with other clusters. The emergent cross-correlation functions have a dual structure, with a sharp peak around zero on top of a much broader hill. The power spectrum associated with single units shows a 1/ f decay for small frequencies and is flat at higher frequencies, while the power spectrum of the spiking activity averaged over many cells-equivalent to the local field potential-shows no 1/ f decay but a prominent peak around 40 Hz.