The dynamic nonlinear behavior of fly photoreceptors evoked by a wide range of light intensities

Multiscale 'whole-cell' models to study neural information processing - New insights from fly photoreceptor studies

Understanding a neuron's input-output relationship is a longstanding challenge. Arguably, these signalling dynamics can be better understood if studied at three levels of analysis: computational, algorithmic and implementational (Marr, 1982). But it is difficult to integrate such analyses into a single platform that can realistically simulate neural information processing. Multiscale dynamical "whole-cell" modelling, a recent systems biology approach, makes this possible. Dynamical "whole-cell" models are computational models that aim to account for the integrated function of numerous genes or molecules to behave like virtual cells in silico. However, because constructing such models is laborious, only a couple of examples have emerged since the first one, built for Mycoplasma genitalium bacterium, was reported in 2012. Here, we review dynamic "whole-cell" neuron models for fly photoreceptors and how these have been used to study neural information processing. Specifically, we review how the models have helped uncover the mechanisms and evolutionary rules of quantal light information sampling and integration, which underlie light adaptation and further improve our understanding of insect vision.

Microsaccadic sampling of moving image information provides Drosophila hyperacute vision

Small fly eyes should not see fine image details. Because flies exhibit saccadic visual behaviors and their compound eyes have relatively few ommatidia (sampling points), their photoreceptors would be expected to generate blurry and coarse retinal images of the world. Here we demonstrate that Drosophila see the world far better than predicted from the classic theories. By using electrophysiological, optical and behavioral assays, we found that R1-R6 photoreceptors’ encoding capacity in time is maximized to fast high-contrast bursts, which resemble their light input during saccadic behaviors. Whilst over space, R1-R6s resolve moving objects at saccadic speeds beyond the predicted motion-blur-limit. Our results show how refractory phototransduction and rapid photomechanical photoreceptor contractions jointly sharpen retinal images of moving objects in space-time, enabling hyperacute vision, and explain how such microsaccadic information sampling exceeds the compound eyes’ optical limits. These discoveries elucidate how acuity depends upon photoreceptor function and eye movements.

Fruit flies have five eyes: two large compound eyes which support vision, plus three smaller single lens eyes which are used for navigation. Each compound eye monitors 180° of space and consists of roughly 750 units, each containing eight light-sensitive cells called photoreceptors. This relatively wide spacing of photoreceptors is thought to limit the sharpness, or acuity, of vision in fruit flies. The area of the human retina (the light-sensitive surface at back of our eyes) that generates our sharpest vision contains photoreceptors that are 500 times more densely packed.

Despite their differing designs, human and fruit fly eyes work via the same general principles. If we, or a fruit fly, were to hold our gaze completely steady, the world would gradually fade from view as the eye adapted to the unchanging visual stimulus. To ensure this does not happen, animals continuously make rapid, automatic eye movements called microsaccades. These refresh the image on the retina and prevent it from fading. Yet it is not known why do they not also cause blurred vision.

Standard accounts of vision assume that the retina and the brain perform most of the information processing required, with photoreceptors simply detecting how much light enters the eye. However, Juusola, Dau, Song et al. now challenge this idea by showing that photoreceptors are specially adapted to detect the fluctuating patterns of light that enter the eye as a result of microsaccades. Moreover, fruit fly eyes resolve small moving objects far better than would be predicted based on the spacing of their photoreceptors.

The discovery that photoreceptors are well adapted to deal with eye movements changes our understanding of insect vision. The findings also disprove the 100-year-old dogma that the spacing of photoreceptors limits the sharpness of vision in compound eyes. Further studies are required to determine whether photoreceptors in the retinas of other animals, including humans, have similar properties.

A biomimetic fly photoreceptor model elucidates how stochastic adaptive quantal sampling provides a large dynamic range

Light intensities (photons s^-1  μm^-2 ) in a natural scene vary over several orders of magnitude from shady woods to direct sunlight. A major challenge facing the visual system is how to map such a large dynamic input range into its limited output range, so that a signal is neither buried in noise in darkness nor saturated in brightness. A fly photoreceptor has achieved such a large dynamic range; it can encode intensity changes from single to billions of photons, outperforming man-made light sensors. This performance requires powerful light adaptation, the neural implementation of which has only become clear recently. A computational fly photoreceptor model, which mimics the real phototransduction processes, has elucidated how light adaptation happens dynamically through stochastic adaptive quantal information sampling. A Drosophila R1-R6 photoreceptor's light sensor, the rhabdomere, has 30,000 microvilli, each of which stochastically samples incoming photons. Each microvillus employs a full G-protein-coupled receptor signalling pathway to adaptively transduce photons into quantum bumps (QBs, or samples). QBs then sum the macroscopic photoreceptor responses, governed by four quantal sampling factors (limitations): (i) the number of photon sampling units in the cell structure (microvilli), (ii) sample size (QB waveform), (iii) latency distribution (time delay between photon arrival and emergence of a QB), and (iv) refractory period distribution (time for a microvillus to recover after a QB). Here, we review how these factors jointly orchestrate light adaptation over a large dynamic range.

How a fly photoreceptor samples light information in time

A photoreceptor's information capture is constrained by the structure and function of its light‐sensitive parts. Specifically, in a fly photoreceptor, this limit is set by the number of its photon sampling units (microvilli), constituting its light sensor (the rhabdomere), and the speed and recoverability of their phototransduction reactions. In this review, using an insightful constructionist viewpoint of a fly photoreceptor being an ‘imperfect’ photon counting machine, we explain how these constraints give rise to adaptive quantal information sampling in time, which maximises information in responses to salient light changes while antialiasing visual signals. Interestingly, such sampling innately determines also why photoreceptors extract more information, and more economically, from naturalistic light contrast changes than Gaussian white‐noise stimuli, and we explicate why this is so. Our main message is that stochasticity in quantal information sampling is less noise and more processing, representing an ‘evolutionary adaptation’ to generate a reliable neural estimate of the variable world.

Graphics Processing Unit-Accelerated Code for Computing Second-Order Wiener Kernels and Spike-Triggered Covariance

Sensory neuroscience seeks to understand and predict how sensory neurons respond to stimuli. Nonlinear components of neural responses are frequently characterized by the second-order Wiener kernel and the closely-related spike-triggered covariance (STC). Recent advances in data acquisition have made it increasingly common and computationally intensive to compute second-order Wiener kernels/STC matrices. In order to speed up this sort of analysis, we developed a graphics processing unit (GPU)-accelerated module that computes the second-order Wiener kernel of a system's response to a stimulus. The generated kernel can be easily transformed for use in standard STC analyses. Our code speeds up such analyses by factors of over 100 relative to current methods that utilize central processing units (CPUs). It works on any modern GPU and may be integrated into many data analysis workflows. This module accelerates data analysis so that more time can be spent exploring parameter space and interpreting data.

Static and Dynamic Adaptation of Insect Photoreceptor Responses to Naturalistic Stimuli

We describe a new nonlinear dynamic model of insect phototransduction using a NLN (nonlinear, linear, nonlinear) block structure. The first nonlinear stage provides a single exponential decline in gain and mean following the start of light stimulation. The linear stage uses a two-parameter log-normal convolution model previously applied alone to insect photoreceptors. The final stage is a static quadratic function. The model fitted current and voltage responses of isolated single photoreceptors from three different insect species with reasonable fidelity when they were stimulated by naturalistic time series having wide bandwidth and contrast, over a light intensity range of >1:10⁴. Mean squared error values for receptor current and receptor potential varied over ~2–60%, with many values below 10%. Linear log-normal filter parameters did not vary strongly with species or light intensity. Initial gain reduction was only large for the highest light levels, while the time constant of gain and mean reduction decreased with light intensity. The final nonlinearity changed from positively to negatively quadratic with increasing light intensity, indicating a change from threshold, or expansion to saturating compression with greater signal strength. Photoreceptor information transmission was estimated by linear information capacity and signal entropy measurements of both experimental data and predicted outputs of the model for identical stimuli at each light level. Comparison of actual and predicted data indicated significant added noise during phototransduction, with information being progressively lost by nonlinear behavior with increasing light intensity.

Fly Photoreceptors Encode Phase Congruency

More than five decades ago it was postulated that sensory neurons detect and selectively enhance behaviourally relevant features of natural signals. Although we now know that sensory neurons are tuned to efficiently encode natural stimuli, until now it was not clear what statistical features of the stimuli they encode and how. Here we reverse-engineer the neural code of Drosophila photoreceptors and show for the first time that photoreceptors exploit nonlinear dynamics to selectively enhance and encode phase-related features of temporal stimuli, such as local phase congruency, which are invariant to changes in illumination and contrast. We demonstrate that to mitigate for the inherent sensitivity to noise of the local phase congruency measure, the nonlinear coding mechanisms of the fly photoreceptors are tuned to suppress random phase signals, which explains why photoreceptor responses to naturalistic stimuli are significantly different from their responses to white noise stimuli.

Electrophysiological Method for Recording Intracellular Voltage Responses of Drosophila Photoreceptors and Interneurons to Light Stimuli In Vivo

Voltage responses of insect photoreceptors and visual interneurons can be accurately recorded with conventional sharp microelectrodes. The method described here enables the investigator to measure long-lasting (from minutes to hours) high-quality intracellular responses from single Drosophila R1-R6 photoreceptors and Large Monopolar Cells (LMCs) to light stimuli. Because the recording system has low noise, it can be used to study variability among individual cells in the fly eye, and how their outputs reflect the physical properties of the visual environment. We outline all key steps in performing this technique. The basic steps in constructing an appropriate electrophysiology set-up for recording, such as design and selection of the experimental equipment are described. We also explain how to prepare for recording by making appropriate (sharp) recording and (blunt) reference electrodes. Details are given on how to fix an intact fly in a bespoke fly-holder, prepare a small window in its eye and insert a recording electrode through this hole with minimal damage. We explain how to localize the center of a cell's receptive field, dark- or light-adapt the studied cell, and to record its voltage responses to dynamic light stimuli. Finally, we describe the criteria for stable normal recordings, show characteristic high-quality voltage responses of individual cells to different light stimuli, and briefly define how to quantify their signaling performance. Many aspects of the method are technically challenging and require practice and patience to master. But once learned and optimized for the investigator's experimental objectives, it grants outstanding in vivo neurophysiological data.

Dynamical feature extraction at the sensory periphery guides chemotaxis

Behavioral strategies employed for chemotaxis have been described across phyla, but the sensorimotor basis of this phenomenon has seldom been studied in naturalistic contexts. Here, we examine how signals experienced during free olfactory behaviors are processed by first-order olfactory sensory neurons (OSNs) of the Drosophila larva. We find that OSNs can act as differentiators that transiently normalize stimulus intensity—a property potentially derived from a combination of integral feedback and feed-forward regulation of olfactory transduction. In olfactory virtual reality experiments, we report that high activity levels of the OSN suppress turning, whereas low activity levels facilitate turning. Using a generalized linear model, we explain how peripheral encoding of olfactory stimuli modulates the probability of switching from a run to a turn. Our work clarifies the link between computations carried out at the sensory periphery and action selection underlying navigation in odor gradients.

DOI:http://dx.doi.org/10.7554/eLife.06694.001

Fruit flies are attracted to the smell of rotting fruit, and use it to guide them to nearby food sources. However, this task is made more challenging by the fact that the distribution of scent or odor molecules in the air is constantly changing. Fruit flies therefore need to cope with, and exploit, this variation if they are to use odors as cues.

Odor molecules bind to receptors on the surface of nerve cells called olfactory sensory neurons, and trigger nerve impulses that travel along these cells. While many studies have investigated how fruit flies can distinguish between different odors, less is known about how animals can use variation in the strength of an odor to guide them towards its source.

Optogenetics is a technique that allows neuroscientists to control the activities of individual nerve cells, simply by shining light on to them. Because fruit fly larvae are almost transparent, optogenetics can be used on freely moving animals. Now, Schulze, Gomez-Marin et al. have used optogenetics in these larvae to trigger patterns of activity in individual olfactory sensory neurons that mimic the activity patterns elicited by real odors. These virtual realities were then used to study, in detail, some of the principles that control the sensory navigation of a larva—as it moves using a series of forward ‘runs’ and direction-changing ‘turns’.

Olfactory sensory neurons responded most strongly whenever light levels changed rapidly in strength (which simulated a rapid change in odor concentration). On the other hand, these neurons showed relatively little response to constant light levels (i.e., constant odors). This indicates that the activity of olfactory sensory neurons typically represents the rate of change in the concentration of an odor. An independent study by Kim et al. found that olfactory sensory neurons in adult fruit flies also respond in a similar way.

Schulze, Gomez-Marin et al. went on to show that the signals processed by a single type of olfactory sensory neuron could be used to predict a larva's behavior. Larvae tended to turn less when their olfactory sensory neurons were highly active. Low levels and inhibition of activity in the olfactory sensory neurons had the opposite effect; this promoted turning. It remains to be determined how this relatively simple control principle is implemented by the neural circuits that connect sensory neurons to the parts of a larva's nervous system that are involved with movement.

DOI:http://dx.doi.org/10.7554/eLife.06694.002

Stochastic, adaptive sampling of information by microvilli in fly photoreceptors

Background

In fly photoreceptors, light is focused onto a photosensitive waveguide, the rhabdomere, consisting of tens of thousands of microvilli. Each microvillus is capable of generating elementary responses, quantum bumps, in response to single photons using a stochastically operating phototransduction cascade. Whereas much is known about the cascade reactions, less is known about how the concerted action of the microvilli population encodes light changes into neural information and how the ultrastructure and biochemical machinery of photoreceptors of flies and other insects evolved in relation to the information sampling and processing they perform.

Results

We generated biophysically realistic fly photoreceptor models, which accurately simulate the encoding of visual information. By comparing stochastic simulations with single cell recordings from Drosophila photoreceptors, we show how adaptive sampling by 30,000 microvilli captures the temporal structure of natural contrast changes. Following each bump, individual microvilli are rendered briefly (∼100–200 ms) refractory, thereby reducing quantum efficiency with increasing intensity. The refractory period opposes saturation, dynamically and stochastically adjusting availability of microvilli (bump production rate: sample rate), whereas intracellular calcium and voltage adapt bump amplitude and waveform (sample size). These adapting sampling principles result in robust encoding of natural light changes, which both approximates perceptual contrast constancy and enhances novel events under different light conditions, and predict information processing across a range of species with different visual ecologies.

Conclusions

These results clarify why fly photoreceptors are structured the way they are and function as they do, linking sensory information to sensory evolution and revealing benefits of stochasticity for neural information processing.

Neuronal encoding of object and distance information: a model simulation study on naturalistic optic flow processing

We developed a model of the input circuitry of the FD1 cell, an identified motion-sensitive interneuron in the blowfly's visual system. The model circuit successfully reproduces the FD1 cell's most conspicuous property: its larger responses to objects than to spatially extended patterns. The model circuit also mimics the time-dependent responses of FD1 to dynamically complex naturalistic stimuli, shaped by the blowfly's saccadic flight and gaze strategy: the FD1 responses are enhanced when, as a consequence of self-motion, a nearby object crosses the receptive field during intersaccadic intervals. Moreover, the model predicts that these object-induced responses are superimposed by pronounced pattern-dependent fluctuations during movements on virtual test flights in a three-dimensional environment with systematic modifications of the environmental patterns. Hence, the FD1 cell is predicted to detect not unambiguously objects defined by the spatial layout of the environment, but to be also sensitive to objects distinguished by textural features. These ambiguous detection abilities suggest an encoding of information about objects-irrespective of the features by which the objects are defined-by a population of cells, with the FD1 cell presumably playing a prominent role in such an ensemble.

Stochastic characterization of small-scale algorithms for human sensory processing

Human sensory processing can be viewed as a functional H mapping a stimulus vector s into a decisional variable r. We currently have no direct access to r; rather, the human makes a decision based on r in order to drive subsequent behavior. It is this (typically binary) decision that we can measure. For example, there may be two external stimuli s([0]) and s([1]), mapped onto r([0]) and r([1]) by the sensory apparatus H; the human chooses the stimulus associated with largest r. This kind of decisional transduction poses a major challenge for an accurate characterization of H. In this article, we explore a specific approach based on a behavioral variant of reverse correlation techniques, where the input s contains a target signal corrupted by a controlled noisy perturbation. The presence of the target signal poses an additional challenge because it distorts the otherwise unbiased nature of the noise source. We consider issues arising from both the decisional transducer and the target signal, their impact on system identification, and ways to handle them effectively for system characterizations that extend to second-order functional approximations with associated small-scale cascade models.

A spatiotemporal white noise analysis of photoreceptor responses to UV and green light in the dragonfly median ocellus

Adult dragonflies augment their compound eyes with three simple eyes known as the dorsal ocelli. While the ocellar system is known to mediate stabilizing head reflexes during flight, the ability of the ocellar retina to dynamically resolve the environment is unknown. For the first time, we directly measured the angular sensitivities of the photoreceptors of the dragonfly median (middle) ocellus. We performed a second-order Wiener Kernel analysis of intracellular recordings of light-adapted photoreceptors. These were stimulated with one-dimensional horizontal or vertical patterns of concurrent UV and green light with different contrast levels and at different ambient temperatures. The photoreceptors were found to have anisotropic receptive fields with vertical and horizontal acceptance angles of 15° and 28°, respectively. The first-order (linear) temporal kernels contained significant undershoots whose amplitudes are invariant under changes in the contrast of the stimulus but significantly reduced at higher temperatures. The second-order kernels showed evidence of two distinct nonlinear components: a fast acting self-facilitation, which is dominant in the UV, followed by delayed self- and cross-inhibition of UV and green light responses. No facilitatory interactions between the UV and green light were found, indicating that facilitation of the green and UV responses occurs in isolated compartments. Inhibition between UV and green stimuli was present, indicating that inhibition occurs at a common point in the UV and green response pathways. We present a nonlinear cascade model (NLN) with initial stages consisting of separate UV and green pathways. Each pathway contains a fast facilitating nonlinearity coupled to a linear response. The linear response is described by an extended log-normal model, accounting for the phasic component. The final nonlinearity is composed of self-inhibition in the UV and green pathways and inhibition between these pathways. The model can largely predict the response of the photoreceptors to UV and green light.

Disentangling sub-millisecond processes within an auditory transduction chain

Every sensation begins with the conversion of a sensory stimulus into the response of a receptor neuron. Typically, this involves a sequence of multiple biophysical processes that cannot all be monitored directly. In this work, we present an approach that is based on analyzing different stimuli that cause the same final output, here defined as the probability of the receptor neuron to fire a single action potential. Comparing such iso-response stimuli within the framework of nonlinear cascade models allows us to extract the characteristics of individual signal-processing steps with a temporal resolution much finer than the trial-to-trial variability of the measured output spike times. Applied to insect auditory receptor cells, the technique reveals the sub-millisecond dynamics of the eardrum vibration and of the electrical potential and yields a quantitative four-step cascade model. The model accounts for the tuning properties of this class of neurons and explains their high temporal resolution under natural stimulation. Owing to its simplicity and generality, the presented method is readily applicable to other nonlinear cascades and a large variety of signal-processing systems.

Comparing auditory stimuli that give the same neural response within the framework of a computational model, the authors extract intermediary signal-processing steps with sub- millisecond temporal resolution

Interactions Between Light-Induced Currents, Voltage-Gated Currents, and Input Signal Properties inDrosophilaPhotoreceptors

Voltage-gated K+channels are important in neuronal signaling, but little is known of their interactions with receptor currents or their behavior during natural stimulation. We used nonparametric and parametric nonlinear modeling of experimental responses, combined with Hodgkin–Huxley style simulation, to examine the roles of K+channels in forming the responses of wild-type (WT) and Shaker mutant ( Sh14) Drosophila photoreceptors to naturalistic stimulus sequences. Naturalistic stimuli gave results different from those of similar experiments with white noise stimuli. Sh14responses were larger and faster than WT. Simulation indicated that, in addition to eliminating the Shaker current, the mutation changed the current flowing through light-dependent channels [light-induced current (LIC)] and increased the delayed rectifier current. Part of the change in LIC could be attributed to direct feedback from the voltage-sensitive ion channels to the light-sensitive channels by the membrane potential. However, we argue that other changes occur in the light detecting machinery of Sh14mutants, possibly during photoreceptor development.

Shaker K+ channels contribute early nonlinear amplification to the light response in Drosophila photoreceptors

We describe the contribution of rapidly inactivating Shaker K+ channels to the dynamic membrane properties of Drosophila photoreceptors. Phototransduction was measured in wild-type and Shaker mutant (Sh14) Drosophila photoreceptors by stimulating with white noise-modulated light contrast and recording the resulting intracellular membrane potential fluctuations. A second-order Volterra kernel series was used to characterize the nonlinear dynamic properties of transduction in the two situations. First-order kernels were indistinguishable in wild-type and Sh14 photoreceptors, indicating that the basic light transduction machinery was always intact. However, second-order kernels of Shaker mutants lacked a large, early amplification, indicating a novel role for Shaker K+ channels in amplifying and accelerating the voltage response of wild-type photoreceptors. A cascade model of two nonlinear static components surrounding one linear dynamic component was able to partially reproduce the experimental responses. Parameters obtained by fitting the model to the experimental data supported the hypothesis that normal Shaker K+ channels contribute an early, positive nonlinearity that partially offsets a later attenuating nonlinearity caused by membrane shunting.

The rate of information transfer of naturalistic stimulation by graded potentials

We present a method to measure the rate of information transfer for any continuous signals of finite duration without assumptions. After testing the method with simulated responses, we measure the encoding performance of Calliphora photoreceptors. We find that especially for naturalistic stimulation the responses are nonlinear and noise is nonadditive, and show that adaptation mechanisms affect signal and noise differentially depending on the time scale, structure, and speed of the stimulus. Different signaling strategies for short- and long-term and dim and bright light are found for this graded system when stimulated with naturalistic light changes.

Natural patterns of neural activity: how physiological mechanisms are orchestrated to cope with real life

Physiological mechanisms of neuronal information processing have been shaped during evolution by a continual interplay between organisms and their sensory surroundings. Thus, when asking for the functional significance of such mechanisms, the natural conditions under which they operate must be considered. This has been done successfully in several studies that employ sensory stimulation under in vivo conditions. These studies address the question of how physiological mechanisms within neurons are properly adjusted to the characteristics of natural stimuli and to the demands imposed on the system being studied. Results from diverse animal models show how neurons exploit natural stimulus statistics efficiently by utilizing specific filtering capacities. Mechanisms that allow neurons to adapt to the currently relevant range from an often immense stimulus spectrum are outlined, and examples are provided that suggest that information transfer between neurons is shaped by the system-specific computational tasks in the behavioral context.

Parallel cascade identification and its application to protein family prediction

Parallel cascade identification is a method for modeling dynamic systems with possibly high order nonlinearities and lengthy memory, given only input/output data for the system gathered in an experiment. While the method was originally proposed for nonlinear system identification, two recent papers have illustrated its utility for protein family prediction. One strength of this approach is the capability of training effective parallel cascade classifiers from very little training data. Indeed, when the amount of training exemplars is limited, and when distinctions between a small number of categories suffice, parallel cascade identification can outperform some state-of-the-art techniques. Moreover, the unusual approach taken by this method enables it to be effectively combined with other techniques to significantly improve accuracy. In this paper, parallel cascade identification is first reviewed, and its use in a variety of different fields is surveyed. Then protein family prediction via this method is considered in detail, and some particularly useful applications are pointed out.

A communication channel model for information transmission in the blowfly photoreceptor

Biological photoreceptors transduce and communicate information about visual stimuli to other neurons through a series of signal transformations among physical states such as concentration of a chemical species, current, or the number of open ion channels. We present a communication channel model to quantify the transmission and degradation of visual information in the blowfly photoreceptor cell. The model is a cascade of linear transfer functions and noise sources that are derived from fundamental principles whenever possible, and whose parameters are estimated from physiological data. We employ the model to calculate the information capacity of blowfly phototransduction; our results compare favorably with estimates of the capacity derived from experimental measurements by de Ruyter van Steveninck and Laughlin (Nature 379 (1996) 642-645) and Juusola (J. Gen. Physiol. 104 (1994) 593-621). The model predicts that photon shot noise and ion channel noise are the dominant noise sources that limits information transmission in the blowfly photoreceptor.

Information theoretical evaluation of parametric models of gain control in blowfly photoreceptor cells

Models are developed and evaluated that are able to describe the response of blowfly photoreceptor cells to natural time series of intensities. Evaluation of the models is performed using an information theoretical technique that evaluates the performance of the models in terms of a coherence function and a derived coherence rate (in bit/s). Performance is gauged against a maximum expected coherence rate determined from the repeatability of the response to the same stimulus. The best model performs close to this maximum performance, and consists of a cascade of two divisive feedback loops followed by a static nonlinearity. The first feedback loop is fast, effectively compressing fast and large transients in the stimulus. The second feedback loop also contains slow components, and is responsible for slow adaptation in the photoreceptor in response to large steps in intensity. Any remaining peaks that would drive the photoreceptor out of its dynamic range are handled by the final compressive nonlinearity.

Fast-acting compressive and facilitatory nonlinearities in light-adapted fly photoreceptors

Light-adapted fly photoreceptor cells were stimulated with brief positive and negative contrast flashes (contrast = delta I/I, I = intensity). Membrane potential responses to a wide range of flash intensities were well-fitted by a static nonlinearity followed by a compartmental model represented by a gamma function. However, the agreement improved if one parameter of the gamma function, n, varied quadratically with input light intensity. Response amplitude and time to peak were estimated from the fitted parameters. Response amplitude varied approximately linearly with contrast but showed nonlinear compression with the largest negative flashes. Reducing the background light level by 3 decades or hyperpolarizing the cell electrically produced stronger nonlinear compression with both contrast polarities. This is probably due to fast voltage-activated K+ channels. Responses to double flashes with varying time separations were well-fitted by summed gamma functions, allowing separation of the individual flash responses. There was no detectable time-dependent interaction between paired positive flashes at all separations. However, the response to two negative flashes was greater than the linear prediction at short separations, and this facilitatory nonlinearity decayed with a time constant of about 1 msec. The facilitation is probably related to resonant behavior in light-adapted photoreceptors and may be due to an IP3-induced intracellular Ca2+ release.

Transfer of graded potentials at the photoreceptor-interneuron synapse

To characterize the transfer of graded potentials and the properties of the associated noise in the photoreceptor-interneuron synapse of the blowfly (Calliphora vicina) compound eye, we recorded voltage responses of photoreceptors (R1-6) and large monopolar cells (LMC) evoked by: (a) steps of light presented in the dark; (b) contrast steps; and (c) pseudorandomly modulated contrast stimuli at backgrounds covering 6 log intensity units. Additionally, we made recordings from photoreceptor axon terminals. Increased light adaptation gradually changed the synaptic signal transfer from low-pass to band-pass filtering. This was accompanied by decreased synaptic delay and increased contrast gain, but the overall synaptic gain and the intrinsic noise (i.e., transmission noise) were reduced. Based on these results, we describe a descriptive synaptic model, in which the kinetics of the tonic transmitter (histamine) release from the photoreceptor axon terminals change with mean photoreceptor depolarization. During signal transmission, tonic transmitter release is augmented by voltage-dependent contrast-enhancing mechanisms in the photoreceptor axons that produce fast transients from the rising phases of the photoreceptor responses and add these enhanced voltages to the original photoreceptor responses. The model can predict the experimental findings and it agrees with the recently proposed theory of maximizing sensory information.