Simon B. Laughlin

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 ≤15% of neurons simultaneously active, to reduce energy consumption and allow greater computing power from a fixed number of neurons. Functional magnetic resonance imaging signals are likely to be dominated by changes in energy usage associated with synaptic currents and action potential propagation.

The metabolic cost of neural information

We derive experimentally based estimates of the energy used by neural mechanisms to code known quantities of information. Biophysical measurements from cells in the blowfly retina yield estimates of the ATP required to generate graded (analog) electrical signals that transmit known amounts of information. Energy consumption is several orders of magnitude greater than the thermodynamic minimum. It costs 104 ATP molecules to transmit a bit at a chemical synapse, and 106 - 107 ATP for graded signals in an interneuron or a photoreceptor, or for spike coding. Therefore, in noise-limited signaling systems, a weak pathway of low capacity transmits information more economically, which promotes the distribution of information among multiple pathways.

Predictive coding: a fresh view of inhibition in the retina

Interneurons exhibiting centre-surround antagonism within their receptive fields are commonly found in peripheral visual pathways. We propose that this organization enables the visual system to encode spatial detail in a manner that minimizes the deleterious effects of intrinsic noise, by exploiting the spatial correlation that exists within natural scenes. The antagonistic surround takes a weighted mean of the signals in neighbouring receptors to generate a statistical prediction of the signal at the centre. The predicted value is subtracted from the actual centre signal, thus minimizing the range of outputs transmitted by the centre. In this way the entire dynamic range of the interneuron can be devoted to encoding a small range of intensities, thus rendering fine detail detectable against intrinsic noise injected at later stages in processing. This predictive encoding scheme also reduces spatial redundancy, thereby enabling the array of interneurons to transmit a larger number of distinguishable images, taking into account the expected structure of the visual world. The profile of the required inhibitory field is derived from statistical estimation theory. This profile depends strongly upon the signal: noise ratio and weakly upon the extent of lateral spatial correlation. The receptive fields that are quantitatively predicted by the theory resemble those of X-type retinal ganglion cells and show that the inhibitory surround should become weaker and more diffuse at low intensities. The latter property is unequivocally demonstrated in the first-order interneurons of the fly’s compound eye. The theory is extended to the time domain to account for the phasic responses of fly interneurons. These comparisons suggest that, in the early stages of processing, the visual system is concerned primarily with coding the visual image to protect against subsequent intrinsic noise, rather than with reconstructing the scene or extracting specific features from it. The treatment emphasizes that a neuron’s dynamic range should be matched to both its receptive field and the statistical properties of the visual pattern expected within this field. Finally, the analysis is synthetic because it is an extension of the background suppression hypothesis (Barlow & Levick 1976), satisfies the redundancy reduction hypothesis (Barlow 1961 a, b) and is equivalent to deblurring under certain conditions (Ratliff 1965).

A Simple Coding Procedure Enhances a Neuron's Information Capacity

Abstract The contrast-response function of a class of first order intemeurons in the flys compound eye approximates to the cumulative probability distribution of contrast levels in natural scenes. Elementary information theory shows that this matching enables the neurons to encode contrast fluctuations most efficiently.

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

SUMMARY 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 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.

Common strategies for light adaptation in the peripheral visual systems of fly and dragonfly

Summary1.Intracellular recordings from photoreceptors and large monopolar cells (LMCs) of the flyCalliphora stygia, and the dragonflyHemicordulia tau, were used to examine the peripheral light adaptation processes of the insect compound eye.2.Photoreceptor and lamina adaptation mechanisms were separated by comparing the response waveforms and intensity/response functions (plotted as V/log I curves) of receptors (Figs. 1 and 3) and LMCs (Figs. 2 and 4), subjected to identical regimes of adaptation.3.Photoreceptor adaptation occurs in two phases, a rapid one lasting 100 ms, and a slow phase taking up to 60 s to complete (Fig. 1). This adaptation shifts theV/logI curves to higher intensities without changing their shape or slope (Fig. 3). Adaptation is negligible at low intensities but with stronger adaptation range sensitivity changes approach proportionality to background increments (Fig. 7).4.Lamina adaptation mechanisms adjust the LMCV/logI curve in response to new background levels within 200 ms, producing a phasic response waveform within which background signals are annihilated (Figs. 1, 3, 8). The shape and amplitude of the saturated LMC ‘on’ and ‘off’ transient responses change with light adaptation (Figs. 2, 3).5.At all background intensities examined the slopes of the LMC V/log I curves remain about 8–10 times that of the photoreceptors under the same conditions, implying that lamina adaptation does not change the voltage gain of the first synapse. We propose that light induced depolarisation of the lamina extracellular space subtracts away the standing background signal from the photoreceptor terminals.6.During dark adaptation the faster lamina mechanism can be superimposed upon slower photoreceptor processes (Fig. 9).7.A comparison of our findings with studies of higher order neurons of the compound eye suggests that peripheral adaptation mechanisms play an important role in determining the response of the entire visual system.8.The peripheral light adaptation processes of fly and dragonfly are similar, and the intensity/response functions of retinula cells and LMCs resemble those of vertebrate cones and bipolar cells respectively (Fig. 11). We propose that this analogy has a functional basis. Both vertebrate and invertebrate systems use a ‘log transform-subtraction-multiplication” strategy to match the response bandwidth of peripheral neurons to the expected intensity fluctuation about any one mean, and in so doing maximise the image detail sent to higher centres.

Adaptation of the Motion-Sensitive Neuron H1 is Generated Locally and Governed by Contrast Frequency

Recordings from the motion-sensitive giant neuron H1 of the lobula plate of the fly Lucilia cuprina, indicate that small field, possibly retinotopic, units presynaptic to H1, adapt in response to motion in much the same way as photoreceptors do to their signal, light intensity. As a result their response is related to what we have called velocity contrast. This adaptation is shown to take place during or after the computation of motion, and is strongly dependent on contrast frequency (temporal frequency of a moving grating). Photometric contrast contributes much less to the rate of adaptation. This is best seen by the fact that at low contrast frequencies, strong photometric contrasts can saturate H1, and yet do not adapt H1 quickly. We propose that the dependence of the adaptation upon contrast frequency is a strategy for linking the radical changes of sensitivity and temporal resolution with adaptation to that signal parameter available to H1 that is most indicative of velocity change. The effects of changes in signal parameters not related to motion, such as sudden changes in photometric contrast, which might otherwise be construed as velocity changes, are reduced. Impulse response measurements confirm the increase in temporal resolution of velocity changes, during adaptation, as already known in adaptation to frequent impulses. The variable rate of adaptation means that the best measure of responsiveness is the peak instantaneous spike discharge rate. Taking this into account, the preferred contrast frequency of the H1 neuron in the unadapted state is 8-10 Hz, in close agreement with the optimum contrast frequency for initiating a landing response in tethered flies.

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, ∼20% of a photoreceptors 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 ∼200 bits s−1 in D. melanogaster to ∼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 photoreceptors 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.

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.