Rob de Ruyter van Steveninck

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 104 ATP molecules to transmit a bit at a chemical synapse, and 106 - 107 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.

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.

Adaptive Rescaling Maximizes Information Transmission

Adaptation is a widespread phenomenon in nervous systems, providing flexibility to function under varying external conditions. Here, we relate an adaptive property of a sensory system directly to its function as a carrier of information about input signals. We show that the input/output relation of a sensory system in a dynamic environment changes with the statistical properties of the environment. Specifically, when the dynamic range of inputs changes, the input/output relation rescales so as to match the dynamic range of responses to that of the inputs. We give direct evidence that the scaling of the input/output relation is set to maximize information transmission for each distribution of signals. This adaptive behavior should be particularly useful in dealing with the intermittent statistics of natural signals.

Synergy in a Neural Code

We show that the information carried by compound events in neural spike trainspatterns of spikes across time or across a population of cellscan 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 flys 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.

Entropy and information in neural spike trains: Progress on the sampling problem

The major problem in information theoretic analysis of neural responses and other biological data is the reliable estimation of entropy-like quantities from small samples. We apply a recently introduced Bayesian entropy estimator to synthetic data inspired by experiments, and to real experimental spike trains. The estimator performs admirably even very deep in the undersampled regime, where other techniques fail. This opens new possibilities for the information theoretic analysis of experiments, and may be of general interest as an example of learning from limited data.

Neural coding of natural stimuli: information at sub-millisecond resolution

Our knowledge of the sensory world is encoded by neurons in sequences of discrete, identical pulses termed action potentials or spikes. There is persistent controversy about the extent to which the precise timing of these spikes is relevant to the function of the brain. We revisit this issue, using the motion – sensitive neurons of the fly visual system as a test case. New experimental methods allow us to deliver more nearly natural visual stimuli, comparable to those which flies encounter in free, acrobatic flight, and new mathematical methods allow us to draw more reliable conclusions about the information content of neural responses even when the set of possible responses is very large. We find that significant amounts of visual information are represented by details of the spike train at millisecond and sub-millisecond precision, even though the sensory input has a correlation time of ~60 ms; different patterns of spike timing represent distinct motion trajectories, and the absolute timing of spikes points to particular features of these trajectories with high precision. Under these naturalistic conditions, the systems information transmission rate still increases with higher photon flux, even though individual photoreceptors are counting more than one million photons per second. Further, exploiting the relatively slow dynamics of the stimulus, the system removes redundancy and so generates a more efficient neural code.

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 flys 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 flys 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.

Real-Time Encoding of Motion: Answerable Questions and Questionable Answers from the Fly’s Visual System

Much of what we know about the neural processing of sensory information has been learned by studying the responses of single neurones to rather simplified stimuli. The ethologists, however, have argued that we can reveal the full richness of the nervous system only when we study the way in which the brain deals with the more complex stimuli that occur in nature. On the other hand it is possible that the processing of natural signals is decomposable into steps that can be understood from the analysis of simpler signals. But even then, to prove that this is the case one must do the experiment and use complex natural stimuli. In the past decade there has been renewed interest in moving beyond the simple sensory inputs that have been the workhorse of neurophysiology, and a key step in this program has been the development of more powerful tools for the analysis of neural responses to complex dynamic inputs. The motion sensitive neurones of the fly visual system have been an important testing ground for these ideas, and there have been several key results from this work:

Reliability of Signal Transfer at a Tonically Transmitting, Graded Potential Synapse of the Locust Ocellar Pathway

We assessed the performance of a synapse that transmits small, sustained, graded potentials between two classes of second-order ocellar “L-neurons” of the locust. We characterized the transmission of both fixed levels of membrane potential and fluctuating signals by recording postsynaptic responses to changes in presynaptic potential. To ensure repeatability between stimuli, we controlled presynaptic signals with a voltage clamp. We found that the synapse introduces noise above the level of background activity in the postsynaptic neuron. By driving the presynaptic neuron with slow-ramp changes in potential, we found that the number of discrete signal levels the synapse transmits is ∼20. It can also transmit ∼20 discrete levels when the presynaptic signal is a graded rebound spike. Synaptic noise level is constant over the operating range of the synapse, which would not be expected if presynaptic potential set the probability for the release of individual quanta of neurotransmitter according to Poisson statistics. Responses to individual quanta of neurotransmission could not be resolved, which is consistent with a synapse that operates with large numbers of vesicles evoking small responses. When challenged with white noise stimuli, the synapse can transmit information at rates up to 450 bits/s, a performance that is sufficient to transmit natural signals about changes in illumination.

Bilocal visual noise as a probe of wide field motion computation.

Using an apparent visual motion stimulus with motion energies limited to specific separations in space and time, we study the computational structure of wide-field motion sensitive neurons in the fly visual brain. There is ample experimental evidence for correlation-based motion computation in many biological systems, but one of its central properties, namely that the response is proportional to the product of two bilocal signal amplitudes, remains to be tested. The design of the apparent motion stimuli used here allows us to manipulate the amplitudes of the bilocal input signals that serve as inputs to the computation. We demonstrate that the wide-field motion response of H1 and V1 neurons indeed shows bilinear behavior, even under contrast sign reversal, as predicted. But the response also varies inversely with contrast variance, an effect not described by the correlator operation. We also quantify the correlator contributions for different spatial and temporal separations. With suitable modification, the apparent motion stimuli used here can be applied to a broad range of neurophysiological as well as human psychophysical studies on motion perception.