Neural coding of naturalistic motion stimuli.

We study a wide-field motion-sensitive neuron in the visual system of the blowfly Calliphora vicina. By rotating the fly on a stepper motor outside in a wooded area, and along an angular motion trajectory representative of natural flight, we stimulate the fly's visual system with input that approaches the natural situation. The neural response is analysed in the framework of information theory, using methods that are free from assumptions. We demonstrate that information about the motion trajectory increases as the light level increases over a natural range. This indicates that the fly's brain utilizes the increase in photon flux to extract more information from the photoreceptor array, suggesting that imprecision in neural signals is dominated by photon shot noise in the physical input, rather than by noise generated within the nervous system itself.

Efficiency and ambiguity in an adaptive neural code.

We examine the dynamics of a neural code in the context of stimuli whose statistical properties are themselves evolving dynamically. Adaptation to these statistics occurs over a wide range of timescales-from tens of milliseconds to minutes. Rapid components of adaptation serve to optimize the information that action potentials carry about rapid stimulus variations within the local statistical ensemble, while changes in the rate and statistics of action-potential firing encode information about the ensemble itself, thus resolving potential ambiguities. The speed with which information is optimized and ambiguities are resolved approaches the physical limit imposed by statistical sampling and noise.

Synergy in a neural code.

We show that the information carried by compound events in neural spike trains-patterns of spikes across time or across a population of cells-can be measured, independent of assumptions about what these patterns might represent. By comparing the information carried by a compound pattern with the information carried independently by its parts, we directly measure the synergy among these parts. We illustrate the use of these methods by applying them to experiments on the motion-sensitive neuron H1 of the fly's visual system, where we confirm that two spikes close together in time carry far more than twice the information carried by a single spike. We analyze the sources of this synergy and provide evidence that pairs of spikes close together in time may be especially important patterns in the code of H1.

On the application of information theory to neural spike trains.

The nervous system represents time-dependent signals in sequences of discrete action potentials or spikes are identical so that information is carried only in the spike arrival times. We show how to quantify this information, in bits, free from any assumptions about which features of the spike train or input waveform are most important. We apply this approach to the analysis of experiments on a variety of systems, including some where we confront severe sampling problems, and discuss some to the results obtained and hopes for future extensions.

The metabolic cost of neural information.

We derive experimentally based estimates of the energy used by neural mechanisms to code known quantities of information. Biophysical measurements from cells in the blowfly retina yield estimates of the ATP required to generate graded (analog) electrical signals that transmit known amounts of information. Energy consumption is several orders of magnitude greater than the thermodynamic minimum. It costs 10(4) ATP molecules to transmit a bit at a chemical synapse, and 10(6)-10(7) ATP for graded signals in an interneuron or a photoreceptor, or for spike coding. Therefore, in noise-limited signaling systems, a weak pathway of low capacity transmits information more economically, which promotes the distribution of information among multiple pathways.

Reproducibility and variability in neural spike trains.

To provide information about dynamic sensory stimuli, the pattern of action potentials in spiking neurons must be variable. To ensure reliability these variations must be related, reproducibly, to the stimulus. For H1, a motion-sensitive neuron in the fly's visual system, constant-velocity motion produces irregular spike firing patterns, and spike counts typically have a variance comparable to the mean, for cells in the mammalian cortex. But more natural, time-dependent input signals yield patterns of spikes that are much more reproducible, both in terms of timing and of counting precision. Variability and reproducibility are quantified with ideas from information theory, and measured spike sequences in H1 carry more than twice the amount of information they would if they followed the variance-mean relation seen with constant inputs. Thus, models that may accurately account for the neural response to static stimuli can significantly underestimate the reliability of signal transfer under more natural conditions.

Light adaptation and reliability in blowfly photoreceptors.

We characterize the reliability of response of blowfly photoreceptors at different light levels. These cells convey their information by graded potentials. Their reliability is quantified by the frequency-dependent contrast-normalized signal to noise ratio. Independently we estimate the effective photoconversion rate of the cells by counting individual photoconversion events, or quantum bumps, at calibrated low light levels. Comparing both results we quantify the statistical efficiency of photoconversion at higher light intensities, characterizing the transduction efficiency as a function of frequency. The light intensities used in these experiments ranged from about 300 to about 5 x 10(5) photoconversions per second per photoreceptor. Over most of this range, statistical efficiencies are within 50% at frequencies up to about 100 Hz.

Reading a neural code.

Traditional approaches to neural coding characterize the encoding of known stimuli in average neural responses. Organisms face nearly the opposite task--extracting information about an unknown time-dependent stimulus from short segments of a spike train. Here the neural code was characterized from the point of view of the organism, culminating in algorithms for real-time stimulus estimation based on a single example of the spike train. These methods were applied to an identified movement-sensitive neuron in the fly visual system. Such decoding experiments determined the effective noise level and fault tolerance of neural computation, and the structure of the decoding algorithms suggested a simple model for real-time analog signal processing with spiking neurons.