Search

Voltage-dependent conductances in many spiking neurons are tuned to reduce action potential energy consumption, so improving the energy efficiency of spike coding. However, the contribution of voltage-dependent conductances to the energy efficiency of analogue coding, by graded potentials in dendrites and non-spiking neurons, remains unclear. We investigate the contribution of voltage-dependent conductances to the energy efficiency of analogue coding by modelling blowfly R1-6 photoreceptor membrane. Two voltage-dependent delayed rectifier K + conductances (DRs) shape the membrane's voltage response and contribute to light adaptation. They make two types of energy saving. By reducing membrane resistance upon depolarization they convert the cheap, low bandwidth membrane needed in dim light to the expensive high bandwidth membrane needed in bright light. This investment of energy in bandwidth according to functional requirements can halve daily energy consumption. Second, DRs produce negative feedback that reduces membrane impedance and increases bandwidth. This negative feedback allows an active membrane with DRs to consume at least 30% less energy than a passive membrane with the same capacitance and bandwidth. Voltage-dependent conductances in other non-spiking neurons, and in dendrites, might be organized to make similar savings., (© 2017 The Author(s).)

Flies use specialized photoreceptors R7 and R8 in the dorsal rim area (DRA) to detect skylight polarization. R7 and R8 form a tiered waveguide (central rhabdomere pair, CRP) with R7 on top, filtering light delivered to R8. We examine how the division of a given resource, CRP length, between R7 and R8 affects their ability to code polarization angle. We model optical absorption to show how the length fractions allotted to R7 and R8 determine the rates at which they transduce photons, and correct these rates for transduction unit saturation. The rates give polarization signal and photon noise in R7, and in R8. Their signals are combined in an opponent unit, intrinsic noise added, and the unit's output analysed to extract two measures of coding ability, number of discriminable polarization angles and mutual information. A very long R7 maximizes opponent signal amplitude, but codes inefficiently due to photon noise in the very short R8. Discriminability and mutual information are optimized by maximizing signal to noise ratio, SNR. At lower light levels approximately equal lengths of R7 and R8 are optimal because photon noise dominates. At higher light levels intrinsic noise comes to dominate and a shorter R8 is optimum. The optimum R8 length fractions falls to one third. This intensity dependent range of optimal length fractions corresponds to the range observed in different fly species and is not affected by transduction unit saturation. We conclude that a limited resource, rhabdom length, can be divided between two polarization sensors, R7 and R8, to optimize opponent coding. We also find that coding ability increases sub-linearly with total rhabdom length, according to the law of diminishing returns. Consequently, the specialized shorter central rhabdom in the DRA codes polarization twice as efficiently with respect to rhabdom length than the longer rhabdom used in the rest of the eye., Competing Interests: The authors declare there are no competing interests.

Capacitance limits the bandwidth of engineered and biological electrical circuits because it determines the gain-bandwidth product (GBWP). With a fixed GBWP, bandwidth can only be improved by decreasing gain. In engineered circuits, an inductance reduces this limitation through shunt peaking but no equivalent mechanism has been reported for biological circuits. We show that in blowfly photoreceptors a voltage-dependent K + conductance, the fast delayed rectifier (FDR), produces shunt peaking thereby increasing bandwidth without reducing gain. Furthermore, the FDR's time constant is close to the value that maximizes the photoreceptor GBWP while reducing distortion associated with the creation of a wide-band filter. Using a model of the honeybee drone photoreceptor, we also show that a voltage-dependent Na + conductance can produce shunt peaking. We argue that shunt peaking may be widespread in graded neurons and dendrites., (© 2016 The Author(s).)

Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na(+) and K(+) channels, with generator potential and graded potential models lacking voltage-gated Na(+) channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na(+) channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a 'footprint' in the generator potential that obscures incoming signals. These three processes reduce information rates by ∼50% in generator potentials, to ∼3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation.

Identifying the determinants of neuronal energy consumption and their relationship to information coding is critical to understanding neuronal function and evolution. Three of the main determinants are cell size, ion channel density, and stimulus statistics. Here we investigate their impact on neuronal energy consumption and information coding by comparing single-compartment spiking neuron models of different sizes with different densities of stochastic voltage-gated Na(+) and K(+) channels and different statistics of synaptic inputs. The largest compartments have the highest information rates but the lowest energy efficiency for a given voltage-gated ion channel density, and the highest signaling efficiency (bits spike(-1)) for a given firing rate. For a given cell size, our models revealed that the ion channel density that maximizes energy efficiency is lower than that maximizing information rate. Low rates of small synaptic inputs improve energy efficiency but the highest information rates occur with higher rates and larger inputs. These relationships produce a Law of Diminishing Returns that penalizes costly excess information coding capacity, promoting the reduction of cell size, channel density, and input stimuli to the minimum possible, suggesting that the trade-off between energy and information has influenced all aspects of neuronal anatomy and physiology.

A balance between excitatory and inhibitory synaptic currents is thought to be important for several aspects of information processing in cortical neurons in vivo, including gain control, bandwidth and receptive field structure. These factors will affect the firing rate of cortical neurons and their reliability, with consequences for their information coding and energy consumption. Yet how balanced synaptic currents contribute to the coding efficiency and energy efficiency of cortical neurons remains unclear. We used single compartment computational models with stochastic voltage-gated ion channels to determine whether synaptic regimes that produce balanced excitatory and inhibitory currents have specific advantages over other input regimes. Specifically, we compared models with only excitatory synaptic inputs to those with equal excitatory and inhibitory conductances, and stronger inhibitory than excitatory conductances (i.e. approximately balanced synaptic currents). Using these models, we show that balanced synaptic currents evoke fewer spikes per second than excitatory inputs alone or equal excitatory and inhibitory conductances. However, spikes evoked by balanced synaptic inputs are more informative (bits/spike), so that spike trains evoked by all three regimes have similar information rates (bits/s). Consequently, because spikes dominate the energy consumption of our computational models, approximately balanced synaptic currents are also more energy efficient than other synaptic regimes. Thus, by producing fewer, more informative spikes approximately balanced synaptic currents in cortical neurons can promote both coding efficiency and energy efficiency.

The initiation and propagation of action potentials (APs) places high demands on the energetic resources of neural tissue. Each AP forces ATP-driven ion pumps to work harder to restore the ionic concentration gradients, thus consuming more energy. Here, we ask whether the ionic currents underlying the AP can be predicted theoretically from the principle of minimum energy consumption. A long-held supposition that APs are energetically wasteful, based on theoretical analysis of the squid giant axon AP, has recently been overturned by studies that measured the currents contributing to the AP in several mammalian neurons. In the single compartment models studied here, AP energy consumption varies greatly among vertebrate and invertebrate neurons, with several mammalian neuron models using close to the capacitive minimum of energy needed. Strikingly, energy consumption can increase by more than ten-fold simply by changing the overlap of the Na(+) and K(+) currents during the AP without changing the APs shape. As a consequence, the height and width of the AP are poor predictors of energy consumption. In the Hodgkin-Huxley model of the squid axon, optimizing the kinetics or number of Na(+) and K(+) channels can whittle down the number of ATP molecules needed for each AP by a factor of four. In contrast to the squid AP, the temporal profile of the currents underlying APs of some mammalian neurons are nearly perfectly matched to the optimized properties of ionic conductances so as to minimize the ATP cost.

Animal locomotion often depends upon stabilization reflexes that use sensory feedback to maintain trajectories and orientation. Such stabilizing reflexes are critically important for the blowfly, whose aerodynamic instability permits outstanding maneuverability but increases the demands placed on flight control. Flies use several sensory systems to drive reflex responses, and recent studies have provided access to the circuitry responsible for combining and employing these sensory inputs. We report that lobula plate VS neurons combine inputs from two optical sensors, the ocelli and the compound eyes. Both systems deliver essential information on in-flight rotations, but our neuronal recordings reveal that the ocelli encode this information in three axes, whereas the compound eyes encode in nine. The difference in dimensionality is reconciled by tuning each VS neuron to the ocellar axis closest to its compound eye axis. We suggest that this simple projection combines the speed of the ocelli with the accuracy of the compound eyes without compromising either. Our findings also support the suggestion that the coordinates of sensory information processing are aligned with axes controlling the natural modes of the fly's flight to improve the efficiency with which sensory signals are transformed into appropriate motor commands.

Photoreceptors in metazoans can be grouped into two classes, with their photoreceptive membrane derived either from cilia or microvilli. Both classes use some form of the visual pigment protein opsin, which together with 11-cis retinaldehyde absorbs light and activates a G-protein cascade, resulting in the opening or closing of ion channels. Considerable attention has recently been given to the molecular evolution of the opsins and other photoreceptor proteins; much is also known about transduction in the various photoreceptor types. Here we combine this knowledge in an attempt to understand why certain photoreceptors might have conferred particular selective advantages during evolution. We suggest that microvillar photoreceptors became predominant in most invertebrate species because of their single-photon sensitivity, high temporal resolution, and large dynamic range, and that rods and a duplex retina provided primitive chordates and vertebrates with similar sensitivity and dynamic range, but with a smaller expenditure of ATP.

Accurate limb placement helps animals and robots to walk on substrates that are uneven or contain gaps. Visual information is important in controlling limb placement in walking mammals but has received little attention in insects. We investigated whether desert locusts walking along a horizontal ladder use vision to control limb placement. High-speed video analysis showed that locusts targeted their front legs to specific rungs in the absence of any previous contact, suggesting that visual information alone is sufficient for targeting single steps. Comparison between the proportions of missed steps before and after monocular occlusion showed that monocular visual information was used to place the ipsilateral but not the contralateral front leg. Accurate placement also depended upon mechanosensory inputs from the antennae and proprioceptive feedback from the ipsilateral but not the contralateral forelimb. Locusts also compensated for the loss of inputs to one eye by altering their stepping pattern. Changing the rung position after initiation of a step showed that targeting of the front leg depends on visual information acquired before but not during a step. The trajectory was only modified after missing the rung. Our data show that locusts walking in environments where footholds are limited use visual and mechanosensory information to place their front legs., (Copyright 2010 Elsevier Ltd. All rights reserved.)

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.

Why do vertebrates use rods and cones that hyperpolarize, when in insect eyes a single depolarizing photoreceptor can function at all light levels? We answer this question at least in part with a comprehensive assessment of ATP consumption for mammalian rods from voltages and currents and recently published physiological and biochemical data. In darkness, rods consume 10(8) ATP s(-1), about the same as Drosophila photoreceptors. Ion fluxes associated with phototransduction and synaptic transmission dominate; as in CNS, the contribution of enzymes of the second-messenger cascade is surprisingly small. Suppression of rod responses in daylight closes light-gated channels and reduces total energy consumption by >75%, but in Drosophila light opens channels and increases consumption 5-fold. Rods therefore provide an energy-efficient mechanism not present in rhabdomeric photoreceptors. Rods are metabolically less "costly" than cones, because cones do not saturate in bright light and use more ATP s(-1) for transducin activation and rhodopsin phosphorylation. This helps to explain why the vertebrate retina is duplex, and why some diurnal animals like primates have a small number of cones, concentrated in a region of high acuity.

Evolution of animal morphology, physiology and behaviour is shaped by the selective pressures to which they are subject. Some selective pressures act to increase the benefits accrued whilst others act to reduce the costs incurred, affecting the cost/benefit ratio. Selective pressures therefore produce a trade-off between costs and benefits that ultimately influences the fitness of the whole organism. The nervous system has a unique position as the interface between morphology, physiology and behaviour; the final output of the nervous system is the behaviour of the animal, which is a product of both its morphology and physiology. The nervous system is under selective pressure to generate adaptive behaviour, but at the same time is subject to costs related to the amount of energy that it consumes. Characterising this trade-off between costs and benefits is essential to understanding the evolution of nervous systems, including our own. Within the nervous system, sensory systems are the most amenable to analysing costs and benefits, not only because their function can be more readily defined than that of many central brain regions and their benefits quantified in terms of their performance, but also because recent studies of sensory systems have begun to directly assess their energetic costs. Our review focuses on the visual system in particular, although the principles we discuss are equally applicable throughout the nervous system. Examples are taken from a wide range of sensory modalities in both vertebrates and invertebrates. We aim to place the studies we review into an evolutionary framework. We combine experimentally determined measures of energy consumption from whole retinas of rabbits and flies with intracellular measurements of energy consumption from single fly photoreceptors and recently constructed energy budgets for neural processing in rats to assess the contributions of various components to neuronal energy consumption. Taken together, these studies emphasize the high costs of maintaining neurons at rest and whilst signalling. A substantial proportion of neuronal energy consumption is related to the movements of ions across the neuronal cell membrane through ion channels, though other processes such as vesicle loading and transmitter recycling also consume energy. Many of the energetic costs within neurons are linked to 3Na(+)/2K(+) ATPase activity, which consumes energy to pump Na(+) and K(+) ions across the cell membrane and is essential for the maintenance of the resting potential and its restoration following signalling. Furthermore, recent studies in fly photoreceptors show that energetic costs can be related, via basic biophysical relationships, to their function. These findings emphasize that neurons are subject to a law of diminishing returns that severely penalizes excess functional capacity with increased energetic costs. The high energetic costs associated with neural tissue favour energy efficient coding and wiring schemes, which have been found in numerous sensory systems. We discuss the role of these efficient schemes in reducing the costs of information processing. Assessing evidence from a wide range of vertebrate and invertebrate examples, we show that reducing energy expenditure can account for many of the morphological features of sensory systems and has played a key role in their evolution.

Energy demands are becoming recognized as an important constraint on neural signaling. The olfactory glomerulus provides a well defined system for analyzing this question. Odor stimulation elicits high-energy demands in olfactory glomeruli where olfactory axons converge onto dendrites of olfactory bulb neurons. We performed a quantitative analysis of the energy demands of each type of neuronal element within the glomerulus. This included the volumes of each element, their surface areas, and ion loads associated with membrane potentials and synaptic activation as constrained by experimental observations. In the resting state, there was a high-energy demand compared with other brain regions because of the high density of neural elements. The activated state was dominated by the energy demands of action potential propagation in afferent olfactory sensory neurons and their synaptic input to dendritic tufts, whereas subsequent dendritic potentials and dendrodendritic transmission contributed only a minor share of costs. It is proposed therefore that afferent input and axodendritic transmission account for the strong signals registered by 2-deoxyglucose and functional magnetic resonance imaging, although postsynaptic dendrites comprise at least one-half of the volume of the glomerulus. The results further suggest that presynaptic inhibition of the axon terminals by periglomerular cells plays an important role in limiting the range of excitation of the postsynaptic cells. These results provide a new quantitative basis for interpreting olfactory bulb activation patterns elicited by odor stimulation.

It is generally assumed that axons use action potentials (APs) to transmit information fast and reliably to synapses. Yet, the reliability of transmission along fibers below 0.5 microm diameter, such as cortical and cerebellar axons, is unknown. Using detailed models of rodent cortical and squid axons and stochastic simulations, we show how conduction along such thin axons is affected by the probabilistic nature of voltage-gated ion channels (channel noise). We identify four distinct effects that corrupt propagating spike trains in thin axons: spikes were added, deleted, jittered, or split into groups depending upon the temporal pattern of spikes. Additional APs may appear spontaneously; however, APs in general seldom fail (<1%). Spike timing is jittered on the order of milliseconds over distances of millimeters, as conduction velocity fluctuates in two ways. First, variability in the number of Na channels opening in the early rising phase of the AP cause propagation speed to fluctuate gradually. Second, a novel mode of AP propagation (stochastic microsaltatory conduction), where the AP leaps ahead toward spontaneously formed clusters of open Na channels, produces random discrete jumps in spike time reliability. The combined effect of these two mechanisms depends on the pattern of spikes. Our results show that axonal variability is a general problem and should be taken into account when considering both neural coding and the reliability of synaptic transmission in densely connected cortical networks, where small synapses are typically innervated by thin axons. In contrast we find that thicker axons above 0.5 microm diameter are reliable.

Trade-offs between energy consumption and neuronal performance must shape the design and evolution of nervous systems, but we lack empirical data showing how neuronal energy costs vary according to performance. Using intracellular recordings from the intact retinas of four flies, Drosophila melanogaster, D. virilis, Calliphora vicina, and Sarcophaga carnaria, we measured the rates at which homologous R1-6 photoreceptors of these species transmit information from the same stimuli and estimated the energy they consumed. In all species, both information rate and energy consumption increase with light intensity. Energy consumption rises from a baseline, the energy required to maintain the dark resting potential. This substantial fixed cost, approximately 20% of a photoreceptor's maximum consumption, causes the unit cost of information (ATP molecules hydrolysed per bit) to fall as information rate increases. The highest information rates, achieved at bright daylight levels, differed according to species, from approximately 200 bits s(-1) in D. melanogaster to approximately 1,000 bits s(-1) in S. carnaria. Comparing species, the fixed cost, the total cost of signalling, and the unit cost (cost per bit) all increase with a photoreceptor's highest information rate to make information more expensive in higher performance cells. This law of diminishing returns promotes the evolution of economical structures by severely penalising overcapacity. Similar relationships could influence the function and design of many neurons because they are subject to similar biophysical constraints on information throughput.

In the blowfly Calliphora vicina, lobula plate tangential cells (LPTCs) estimate self-motion by integrating local motion information from the compound eyes. Each LPTC is sensitive to a particular (preferred) rotation of the fly's head. The fly can also sense rotation using its three ocelli (simple eyes), by comparing the light intensities measured at each ocellus. We report that an individually identified tangential cell, V1, responds in an apparently rotation-specific manner to stimulation of the ocelli. This effect was seen with or without additional stimulation of the compound eye. We delivered stimuli to the ocelli which mimicked rotation of the fly's head close to that of the preferred axis of rotation of V1. Alternating between preferred and anti-preferred rotation elicited a strongly phasic response, the amplitude of which increased with the rate of change of light intensity at the ocelli. With combined stimulation of one compound eye and the ocelli, V1 displayed a robust response to ocellar stimuli over its entire response range. These findings provide the opportunity to study quantitatively the interactions of two different visual mechanisms which both encode the same variable--the animal's rotation in space.

Flies, like humans, experience a well-known consequence of adaptation to visual motion, the waterfall illusion. Direction-selective neurons in the fly lobula plate permit a detailed analysis of the mechanisms responsible for motion adaptation and their function. Most of these neurons are spatially non-opponent, they sum responses to motion in the preferred direction across their entire receptive field, and adaptation depresses responses by subtraction and by reducing contrast gain. When we adapted a small area of the receptive field to motion in its anti-preferred direction, we discovered that directional gain at unadapted regions was enhanced. This novel phenomenon shows that neuronal responses to the direction of stimulation in one area of the receptive field are dynamically adjusted to the history of stimulation both within and outside that area.

The action potential (AP) is transmitted by the concerted action of voltage-gated ion channels. Thermodynamic fluctuations in channel proteins produce probabilistic gating behavior, causing channel noise. Miniaturizing signaling systems increases susceptibility to noise, and with many cortical, cerebellar, and peripheral axons <0.5 mum diameter [1, 2 and 3], channel noise could be significant [4 and 5]. Using biophysical theory and stochastic simulations, we investigated channel-noise limits in unmyelinated axons. Axons of diameter below 0.1 microm become inoperable because single, spontaneously opening Na channels generate spontaneous AP at rates that disrupt communication. This limiting diameter is relatively insensitive to variations in biophysical parameters (e.g., channel properties and density, membrane conductance and leak) and will apply to most spiking axons. We demonstrate that the essential molecular machinery can, in theory, fit into 0.06 microm diameter axons. However, a comprehensive survey of anatomical data shows a lower limit for AP-conducting axons of 0.08-0.1 microm diameter. Thus, molecular fluctuations constrain the wiring density of brains. Fluctuations have implications for epilepsy and neuropathic pain because changes in channel kinetics or axonal properties can change the rate at which channel noise generates spontaneous activity.

Male houseflies use a sex-specific frontal eye region, the lovespot, to detect and pursue mates. We recorded the electrical responses of photoreceptors to optical stimuli that simulate the signals received by a male or female photoreceptor as a conspecific passes through its field of view. We analysed the ability of male and female frontal photoreceptors to code conspecifics over the range of speeds and distances encountered during pursuit, and reconstructed the neural images of these targets in photoreceptor arrays. A male's lovespot photoreceptor detects a conspecific at twice the distance of a female photoreceptor, largely through better optics. This detection distance greatly exceeds those reported in previous behavioural studies. Lovespot photoreceptors respond more strongly than female photoreceptors to targets tracked during pursuit, with amplitudes reaching 25 mV. The male photoreceptor also has a faster response, exhibits a unique preference for stimuli of 20-30 ms duration that selects for conspecifics and deblurs moving images with response transients. White-noise analysis substantially underestimates these improvements. We conclude that in the lovespot, both optics and phototransduction are specialised to enhance and deblur the neural images of moving targets, and propose that analogous mechanisms may sharpen the neural image still further as it is transferred to visual interneurones.

Brains perform with remarkable efficiency, are capable of prodigious computation, and are marvels of communication. We are beginning to understand some of the geometric, biophysical, and energy constraints that have governed the evolution of cortical networks. To operate efficiently within these constraints, nature has optimized the structure and function of cortical networks with design principles similar to those used in electronic networks. The brain also exploits the adaptability of biological systems to reconfigure in response to changing needs.

Gap junctions have been shown to electrically couple cone photoreceptors: coupling blurs the image coded by cones, but this loss is offset by a decrease in noise. Electrical coupling thus improves the resolution of signals distributed across groups of cells.

We investigate the energy efficiency of signaling mechanisms that transfer information by means of discrete stochastic events, such as the opening or closing of an ion channel. Using a simple model for the generation of graded electrical signals by sodium and potassium channels, we find optimum numbers of channels that maximize energy efficiency. The optima depend on several factors: the relative magnitudes of the signaling cost (current flow through channels), the fixed cost of maintaining the system, the reliability of the input, additional sources of noise, and the relative costs of upstream and downstream mechanisms. We also analyze how the statistics of input signals influence energy efficiency. We find that energy-efficient signal ensembles favor a bimodal distribution of channel activations and contain only a very small fraction of large inputs when energy is scarce. We conclude that when energy use is a significant constraint, trade-offs between information transfer and energy can strongly influence the number of signaling molecules and synapses used by neurons and the manner in which these mechanisms represent information.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

The Shaker gene, responsible for A-type potassium channels in Drosophila muscle, encodes a large family of transcripts capable of generating a variety of kinetically distinct A channels when expressed in oocytes. We describe a distinct class of A channel encoded by the Shaker gene in a novel preparation of dissociated Drosophila photoreceptors. Whole-cell recordings reveal a rapidly inactivating A current that is absent in Shaker mutants and that can be readily isolated in cell-attached patches. Although very similar to their muscle counterparts, the photoreceptor A channels show a striking 40-50 mV negative shift in their voltage-operating range. Two mutations (ShE62 and T(1;Y)W32), which exclude only certain classes of Shaker transcripts, were used to show that photoreceptor A channels are encoded by multiple transcripts distinct from those encoding muscle A channels, while PCR techniques identified four transcripts (ShA1, ShA2, ShG1, and ShG2) in mRNA from dissected retina.

1. The membrane properties of the photoreceptors of the blowfly (Calliphora vicina) were investigated in situ by making intracellular recordings in the intact retina, using discontinuous single-electrode current and voltage clamp techniques. Single channels were investigated using inside-out patches from dissociated photoreceptors. 2. Photoreceptors have a resting potential in darkness of -60.4 +/- 6.6 mV (mean +/- S.D.; n = 43), a resting input resistance of 32 +/- 3 M omega (n = 11) and membrane time constant of 4.1 +/- 1 ms (n = 9). These values give a total cell capacitance of 0.13 nF and an effective membrane area of 1.3 x 10(-4) cm2. 3. Single-electrode voltage clamp reveals a voltage-sensitive outward current with an activation threshold at approximately -75 mV. This conductance has two kinetic components, the slower component activating at more depolarized levels. On the basis of its kinetics, a reversal potential of -85 +/- 6 mV (n = 6), sensitivity to intracellularly injected tetraethylammonium chloride (TEA), and its slow and partial inactivation (approximately 25%) this mechanism is classified as a delayed rectifier potassium conductance. 4. Voltage-sensitive potassium channels showing similar properties were found in excised inside-out patches from dissociated photoreceptors. Single-channel conductances are ca 20 pS for both fast and slow kinetic components, indicating a channel density in the intact cell of ca 2 microns -2. The reversal potential follows the Nernst slope for potassium ions. 5. The voltage dependence of the conductance was determined in patches containing channels of predominantly one or the other kinetic component. The midpoint of the activation curve is -65 mV for the fast and -50 mV for the slow component. Activation time constants (measured from a holding potential of -100 mV) are voltage dependent, and in the range 1-10 ms for the fast and 5-40 ms for the slow component. Both kinetic components are blocked by TEA (greater than 2.5 mM). The slow component is more sensitive to quinidine (greater than 200 microM), and the fast component to 4-aminopyridine (4-AP; greater than 200 microM). 6. In the intact preparation the outward current shows no dependence on light stimulation in the studied ranges of voltage (up to -25 mV) and intensity (up to 5.5 x 10(4) effective photons). Ensemble averages of channel openings in perfused inside-out patches show no dependence on calcium concentration in the range 10 nM-1.8 mM.(ABSTRACT TRUNCATED AT 400 WORDS)

1. The large monopolar cells (LMCs) of the fly, Calliphora vicina, visual system transmit graded potentials over distances of up to 1.0 mm. An electrical model was constructed to investigate the design principles relating their membrane parameters to signal transmission and filtering. 2. Using existing anatomical measurements, a cable model (van Hateren 1986) was fitted to the measured intracellular responses of the cells to injected current. The LMC has three functional components: a distal synaptic zone of low impedance, an axon with high specific membrane resistance (greater than 50.10(5) M omega.micron 2), and a high impedance proximal terminal. These components interact to transmit information efficiently. The low input impedance synaptic zone charges and discharges the axon rapidly, ensuring a good frequency response. The high resistance axon conducts signals with little decrement. The model shows that graded potential transmission in LMCs selectively filters synaptic noise and predicts the changes in response waveform that occur during transmission. 3. The parameters of the model were adjusted to determine the relative costs and benefits of alternative cable designs. The design used in LMCs is the most expensive and the most effective. It requires the largest currents to generate responses but transmits signals with least decrement. Parallel neurons in the fly visual system have fewer input synapses and this could low-pass filter their graded response.

Pulsatile injections of cyclic GMP into rod outer segments of the isolated toad retina cause transient depolarizations that are reduced in amplitude in proportion with the receptor potential by low Na+ Ringer's. This reduction in the amplitude of the cyclic GMP depolarization may be due to the direct effect of external Na+ concentration on dark current and an indirect effect resulting from the inactivation of a sodium-calcium exchange mechanism raising the intracellular Ca2+ concentration. By comparison the reduction in cyclic GMP response amplitude effected by illumination is accompanied by faster kinetics. This difference suggests that the reduced amplitude and speedier response reflect a light induced increase in phosphodiesterase (PDE) activity rather than the effects of Ca2+. Large doses of cyclic GMP can distort the kinetics of both the light response and the recovery from a depolarization caused by a pulse of cyclic GMP by similarly slowing both types of responses. This similarity in the kinetics of the cyclic GMP response and the initial hyperpolarizing phase of the receptor potential suggests that the kinetics of the initial phase of the receptor potential are controlled by light-mediated cyclic GMP hydrolysis.

1. In locust photoreceptors, the amplitude of the response to light pulses lasting less than 20 ms depends solely upon the number of absorbed photons, which can be estimated at low intensities by counting quantum bumps. Consequently, each receptor can be operated as a calibrated photon counter. 2. Three types of noise in receptor responses have been identified--extrinsic or photon noise and two types of intrinsic noise, dark noise (spontaneous activity) and transducer noise (noise in the transduction mechanism). The methods by which the noise sources are measured and identified involves measuring the responses to a train of flashes of constant intensity and converting these voltage values into a series of equivalent quantum catches. Because photon absorptions follow the Poisson distribution, the variance among equivalent catches due to photon noise equals the mean catch, and any excess variance represents intrinsic noise. 3. Dark noise is negligible: spontaneous signals (quantum bumps produced in darkness) occur less than ten times per hour at 25 degrees C, and the combined effects of membrane and electrode noise are unimportant at all but the highest intensities. 4. At low intensities transducer noise is responsible for more than 50% of all receptor noise (variance), and this rises to 90% when bright stimuli are presented to the dark-adapted eye. 5. Two simple models of transduction indicate that variations in the amplitudes and latencies of responses to single photons are a major source of transducer noise. 6. Transducer noise would be difficult to detect from an analysis of response noise alone, without knowledge of absolute photon catch, because in some important respects it mimics photon noise, e.g. it lowers the quantum efficiency without violating the square root relationship relating increment thresholds to mean intensity.