Comparison of Langevin and Markov channel noise models for neuronal signal generation.

The stochastic opening and closing of voltage-gated ion channels produce noise in neurons. The effect of this noise on the neuronal performance has been modeled using either an approximate or Langevin model based on stochastic differential equations or an exact model based on a Markov process model of channel gating. Yet whether the Langevin model accurately reproduces the channel noise produced by the Markov model remains unclear. Here we present a comparison between Langevin and Markov models of channel noise in neurons using single compartment Hodgkin-Huxley models containing either Na+ and K+, or only K+ voltage-gated ion channels. The performance of the Langevin and Markov models was quantified over a range of stimulus statistics, membrane areas, and channel numbers. We find that in comparison to the Markov model, the Langevin model underestimates the noise contributed by voltage-gated ion channels, overestimating information rates for both spiking and nonspiking membranes. Even with increasing numbers of channels, the difference between the two models persists. This suggests that the Langevin model may not be suitable for accurately simulating channel noise in neurons, even in simulations with large numbers of ion channels.

An energy budget for signaling in the grey matter of the brain.

Anatomic and physiologic data are used to analyze the energy expenditure on different components of excitatory signaling in the grey matter of rodent brain. Action potentials and postsynaptic effects of glutamate are predicted to consume much of the energy (47% and 34%, respectively), with the resting potential consuming a smaller amount (13%), and glutamate recycling using only 3%. Energy usage depends strongly on action potential rate--an increase in activity of 1 action potential/cortical neuron/s will raise oxygen consumption by 145 mL/100 g grey matter/h. The energy expended on signaling is a large fraction of the total energy used by the brain; this favors the use of energy efficient neural codes and wiring patterns. Our estimates of energy usage predict the use of distributed codes, with

Efficiency and complexity in neural coding.

Neural coding in the retina and lamina of fly compound eyes is amenable to detailed anatomical, physiological and theoretical analysis. This approach shows how identified cell signalling systems are optimized to maximize the transmission of information. Optimization reveals three familiar constraints, noise, saturation and bandwidth, and shows how coding can minimize their effects. Experiments reveal a fourth constraint, metabolic cost, whose properties favour the distribution of information among multiple pathways. The advantages of distributed codes will be offset by increasing complexity and the build up of noise. The optimization of coding in fly retina suggests that both noise and complexity will be reduced by matching each step in the system's operations to the input signal, and to the logical requirements of the network's ultimate function, pattern processing. This line of argument suggests tightly organized networks, laid out that information flows freely and independently, yet patterned so that the necessary contacts and transactions are made quickly and efficiently.

Variations in photoreceptor response dynamics across the fly retina.

Gradients in the spatial properties of retinal cells and their relation to image statistics are well documented. However, less is known of gradients in temporal properties, especially at the level of the photoreceptor for which no account exists. Using light flashes and white-noise-modulated light and current stimuli, we examined the spatial and temporal properties of a single class of photoreceptor (R1-6) within the compound eyes of male blowfly, Calliphora vicina. We find that there is a trend toward higher performance at the front of the eye, both in terms of spatiotemporal resolution and signal-to-noise ratio. The receptive fields of frontal photoreceptors are narrower than those of photoreceptors at the side and back of the eye and response speeds are 20% faster. The signal-to-noise ratio at high frequencies is also greatest at the front of the eye, allowing a 30-40% higher information rate. The power spectra of signals and noise indicate that this elevation of performance results both from shorter responses to individual photons and from a more reliable registration of photon arrival times. These distinctions are characteristic of adaptational changes that normally occur on increasing illumination. However, all photoreceptors were absorbing light at approximately the same mean photon rate during our recordings. We therefore suggest that frontal photoreceptors attain a higher state of light adaptation for a given photon rate. This difference may be achieved by a higher density of (Ca2+ permeable) light-gated channels. Consistent with this hypothesis, membrane-impedance measurements show that frontal photoreceptors have a higher specific conductance than other photoreceptors. This higher conductance provides a better temporal performance but is metabolically expensive. Across the eye, temporal resolution is not proportional to spatial (optical) resolution. Neither is it matched obviously to optic flow. Instead we examine the consequences of an improved temporal resolution in the frontal region for the tracking of small moving targets, a behavior exhibited by male flies. We conclude that the temporal properties of a given class of retinal neuron can vary within a single retina and that this variation may be functionally related to the behavioral requirements of the animal.

Energy as a constraint on the coding and processing of sensory information.

Neurons use significant amounts of energy to generate signals. Recent studies of retina and brain connect this energy usage to the ability to transmit information. The identification of energy-efficient neural circuits and codes suggests new ways of understanding the function, design and evolution of nervous systems.

Colour thresholds and receptor noise: behaviour and physiology compared.

Photoreceptor noise sets an absolute limit for the accuracy of colour discrimination. We compared colour thresholds in the honeybee (Apis mellifera) with this limit. Bees were trained to discriminate an achromatic stimulus from monochromatic lights of various wavelengths as a function of their intensity. Signal-to-noise ratios were measured by intracellular recordings in the three spectral types of photoreceptor cells. To model thresholds we assumed that discrimination was mediated by opponent mechanisms whose performance was limited by receptor noise. Most of the behavioural thresholds were close to those predicted from receptor signal-to-noise ratios, suggesting that colour discrimination in honeybees is affected by photoreceptor noise. Some of the thresholds were lower than this theoretical limit, which indicates summation of photoreceptor cell signals.

Accuracy of velocity estimation by Reichardt correlators.

Although a great deal of experimental evidence supports the notion of a Reichardt correlator as a mechanism for biological motion detection, the correlator does not signal true image velocity. This study examines the accuracy with which realistic Reichardt correlators can provide velocity estimates in an organism's natural visual environment. The predictable statistics of natural images imply a consistent correspondence between mean correlator response and velocity, allowing the otherwise ambiguous Reichardt correlator to act as a practical velocity estimator. Analysis and simulations suggest that processes commonly found in visual systems, such as prefiltering, response compression, integration, and adaptation, improve the reliability of velocity estimation and expand the range of velocities coded. Experimental recordings confirm our predictions of correlator response to broadband images.

Temperature and the temporal resolving power of fly photoreceptors.

A hot head gives an insect a clearer view of a moving world because warming reduces motion blur by accelerating photoreceptor responses. Over a natural temperature range, 19-34 degrees C, the speed of response of blowfly (Calliphora vicina) photoreceptors more than doubles, to produce the fastest functional responses recorded from an ocular photoreceptor. This acceleration increases temporal resolving power, as indicated by the corner frequency of the response power spectrum. When light adapted, the corner frequency increases from 53 Hz to 119 Hz with a Q10 of 1.9, and when dark adapted from 8 Hz to 32 Hz with a Q10 of 3.0. Temperature sensitivity originates in the phototransduction cascade, and is associated with signal amplification. The temperature sensitivity of photoreceptors must be taken into account when studying the mechanisms, function and ecology of vision, and gives a distinct advantage to insects that thermoregulate.

Photoreceptor performance and the co-ordination of achromatic and chromatic inputs in the fly visual system.

White noise techniques are used to compare the two photoreceptor sub-types in blowfly retina, the short visual fibres (R1-6) that code achromatic contrast, and the long visual fibres (R7 and R8) that together code wavelength distribution and polarisation plane. Measurements of signal and noise spectra and contrast gain, taken across a broad intensity range, permit a detailed comparison of coding efficiency under natural conditions of illumination. As a function of excitation (effective photons per photoreceptor per second; h upsilon/rec per s), adaptive changes in the long and short visual fibres are similar, suggesting that post-rhodopsin their phototransduction cascades are identical. Under identical natural daylight conditions (photons per cm2 per second; h upsilon/cm2 per s) short visual fibres catch more photons, thus operating with a higher signal to noise ratio and faster response, to consistently outperform the long visual fibres. Long visual fibres compensate for their poor quantum catch by having a higher absolute gain (mV/h upsilon) which at low light intensities enables them to achieve a level of contrast gain (mV/unit contrast) similar to the short visual fibres. Differences in signal to noise ratios are related to known differences in photoreceptor structure and synaptic frequency among visual interneurons. The principles of matching sensitivity and synapse number to quantum catch described here could explain analogous differences between chromatic and achromatic pathways in mammalian and amphibian retinas.

Contrast gain reduction in fly motion adaptation.

In many species, including humans, exposure to high image velocities induces motion adaptation, but the neural mechanisms are unclear. We have isolated two mechanisms that act on directionally selective motion-sensitive neurons in the fly's visual system. Both are driven strongly by movement and weakly, if at all, by flicker. The first mechanism, a subtractive process, is directional and is only activated by stimuli that excite the neuron. The second, a reduction in contrast gain, is strongly recruited by motion in any direction, even if the adapting stimulus does not excite the cell. These mechanisms are well designed to operate effectively within the context of motion coding. They can prevent saturation at susceptible nonlinear stages in processing, cope with rapid changes in direction, and preserve fine structure within receptive fields.

Sexual dimorphism matches photoreceptor performance to behavioural requirements.

Differences in behaviour exist between the sexes of most animal species and are associated with many sex-specific specializations. The visual system of the male housefly is known to be specialized for pursuit behaviour that culminates in mating. Males chase females using a high-acuity region of the fronto-dorsal retina (the 'love spot') that drives sex-specific neural circuitry. We show that love spot photoreceptors of the housefly combine better spatial resolution with a faster electrical response, thereby allowing them to code higher velocities and smaller targets than female photoreceptors. Love spot photoreceptors of males are more than 60% faster than their female counterparts and are among the fastest recorded for any animal. The superior response dynamics of male photoreceptors is achieved by a speeding up of the biochemical processes involved in phototransduction and by a tuned voltage-activated conductance that boosts the membrane frequency response. These results demonstrate that the inherent plasticity of phototransduction facilitates the tuning of the dynamics of visual processing to the requirements of visual ecology.

Adaptation and the temporal delay filter of fly motion detectors.

Recent accounts attribute motion adaptation to a shortening of the delay filter in elementary motion detectors (EMDs). Using computer modelling and recordings from HS neurons in the drone-fly Eristalis tenax, we present evidence that challenges this theory. (i) Previous evidence for a change in the delay filter comes from 'image step' (or 'velocity impulse') experiments. We note a large discrepancy between the temporal frequency tuning predicted from these experiments and the observed tuning of motion sensitive cells. (ii) The results of image step experiments are highly sensitive to the experimental method used. (iii) An apparent motion stimulus reveals a much shorter EMD delay than suggested by previous 'image step' experiments. This short delay agrees with the observed temporal frequency sensitivity of the unadapted cell. (iv) A key prediction of a shortening delay filter is that the temporal frequency optimum of the cell should show a large shift to higher temporal frequencies after motion adaptation. We show little change in the temporal or spatial frequency (and hence velocity) optima following adaptation.

Visual motion: dendritic integration makes sense of the world.

Flies use a system of specialised neurons to read the patterns of visual motion - optic flow - induced by the their movements. Recent experiments illustrate how the dendrites of these neurons reach out to assemble patterns of optic flow and encode them reliably.

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.

Spatio-temporal properties of motion detectors matched to low image velocities in hovering insects.

Our recent study [O'Carroll et al. (1996). Nature 382, 63-66) described a correlation between the spatio-temporal properties of motion detecting neurons in the optic lobes of flying insects and behaviour. We consider here theoretical properties of insect motion detectors at very low image velocities and measure spatial and temporal sensitivity of neurons in the lobula complex of two specialised hovering insects, the bee-fly Bombylius and the hummingbird hawkmoth, Macroglossum. The spatio-temporal optima of direction-selective neurons in these insects lie at lower velocities than those of other insects which we have studied, including large syrphid flies, which are also excellent hoverers. We argue that spatio-temporal optima reflect a compromise between the demands of diverse behaviour, which can involve prolonged periods of stationary, hovering flight followed by spectacular high speed pursuits of conspecifics. Males of the syrphid Eristalis which engage in such behaviour, have higher temporal frequency optima than females. High contrast sensitivity in these flies nevertheless results in reliable responses at very low image velocities. Neurons of Bombylius have two distinct velocity optima, suggesting that they sum inputs from two classes of motion correlator with different time constants. This also provides sensitivity to a large range of velocities.

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.

Matched filtering by a photoreceptor membrane.

This study demonstrates how phototransduction cascades and membranes tune photoreceptor response dynamics to image quality, and eliminate noise introduced in cell signalling. Intracellular recordings from intact retina confirm that the light-adapted photoreceptors of the crane fly Tipula paludosa (Diptera; Tipulidae) have a slow response, appropriate for their visual ecology. To provide a slow response, the phototransduction cascade's impulse response fails to narrow with light-adaptation, despite reductions in the timescales of latency and quantum bumps. The photoreceptor membrane acts as a passive RC-filter, because light induced depolarization inactivates voltage-gated potassium currents. The frequency response of the membrane equals the cascade's and, as a result, the membrane is a matched filter that suppresses photon shot noise. This type of broad-band filter, matched to the predictable dynamics of preceding processes to remove noise, could be widely employed in vision and in many other chains of cellular communication.

Insect motion detectors matched to visual ecology.

To detect motion, primates, birds and insects all use local detectors to correlate signals sampled at one location in the image with those sampled after a delay at adjacent locations. These detectors can adapt to high image velocities by shortening the delay. To investigate whether they use long delays for detecting low velocities, we compared motion-sensitive neurons in ten species of fast-flying insects, some of which encounter low velocities while hovering. Neurons of bee-flies and hawkmoths, which hover, are tuned to lower temporal frequencies than those of butterflies and bumblebees, which do not. Tuning to low frequencies indicates longer delays and extends sensitivity to lower velocities. Hoverflies retain fast temporal tuning but use their high spatial acuity for sensing low-velocity motion. Thus an unexpectedly wide range of spatio-temporal tuning matches motion detection to visual ecology.

Visual ecology and voltage-gated ion channels in insect photoreceptors.

That particular membrane conductances are selected for expression to enable the efficient coding of biologically relevant signals is illustrated by recent work on insect photoreceptors. These studies exploit the richness of insect vision and the accessibility of insect photoreceptors to cellular analysis in both intact animal and isolated cell preparations. The distribution of voltage-gated conductances among photoreceptors of different species correlates with visual ecology. Delayed-rectifier K+ channels are found in the rapidly responding photoreceptors of fast-flying flies. The conductance's activation range and dynamics match light-induced signals, and enable a rapid response by reducing the membrane time constant. Slow-moving flies have slowly responding photoreceptors that lack the delayed rectifier, but express an inactivating K+ conductance that is metabolically less demanding. Complementing these findings, locust photoreceptor membranes are modulated diurnally. The delayed rectifier is exhibited during the day and the inactivating K+ current is exhibited at night. Insect photoreceptors also demonstrate the amplification of signals by voltage-gated Na+ channels. In drone-bee photoreceptors, voltage-gated Na+ channels combine with K+ channels to enhance the small transient signals produced by the image of a queen bee passing over the retina. This subthreshold amplifier operates most effectively over the range of light intensities at which drones pursue queens.

Retinal information capacity and the function of the pupil.

When the pupil is opened to increase sensitivity there is a loss of image sharpness due to aberrations. This trade-off between sensitivity and sharpness is analysed theoretically by calculating the information capacity of the retinal image. The analysis uses optical measurements of image sharpness made at different pupil diameters. At each luminance there is a pupil diameter that maximizes information capacity. This optimum is close to the diameter adopted under normal viewing conditions. The optimum is broad, consequently the system tolerates inaccurate adjustment. The benefits of correctly adjusting the pupil are evaluated. At low light levels the advantage is 68%, at intermediate levels it falls to around 20% but under daylight conditions it increases to 52%. These advantages suggest that the primary function of the pupillary light reflex is to maximize acuity over a wide range of luminances.