Voltage-dependent K+ channels improve the energy efficiency of signalling in blowfly photoreceptors.

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.

Optimizing the use of a sensor resource for opponent polarization coding.

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.

Shunt peaking in neural membranes.

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.

Balanced excitatory and inhibitory synaptic currents promote efficient coding and metabolic efficiency.

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 effect of cell size and channel density on neuronal information encoding and energy efficiency.

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.

Action potential energy efficiency varies among neuron types in vertebrates and invertebrates.

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.

Sensor fusion in identified visual interneurons.

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.

Phototransduction and the evolution of photoreceptors.

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.

Visual targeting of forelimbs in ladder-walking locusts.

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.

ATP consumption by mammalian rod photoreceptors in darkness and in light.

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.

Energy limitation as a selective pressure on the evolution of sensory systems.

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.

An energy budget for the olfactory glomerulus.

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.

Stochastic simulations on the reliability of action potential propagation in thin axons.

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.

Fly photoreceptors demonstrate energy-information trade-offs in neural coding.

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.

A motion-sensitive neurone responds to signals from the two visual systems of the blowfly, the compound eyes and ocelli.

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.

Global versus local adaptation in fly motion-sensitive neurons.

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.

Ion-channel noise places limits on the miniaturization of the brain's wiring.

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.

Neural images of pursuit targets in the photoreceptor arrays of male and female houseflies Musca domestica.

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.

Communication in neuronal networks.

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.