The intrinsic electrophysiological characteristics of fly lobula plate tangential cells: III. Visual response properties

Matched function of the neuropil processing optic flow in flies and crabs: the lobula plate mediates optomotor responses in Neohelice granulata

When an animal rotates (whether it is an arthropod, a fish, a bird or a human) a drift of the visual panorama occurs over its retina, termed optic flow. The image is stabilized by compensatory behaviours (driven by the movement of the eyes, head or the whole body depending on the animal) collectively termed optomotor responses. The dipteran lobula plate has been consistently linked with optic flow processing and the control of optomotor responses. Crabs have a neuropil similarly located and interconnected in the optic lobes, therefore referred to as a lobula plate too. Here we show that the crabs' lobula plate is required for normal optomotor responses since the response was lost or severely impaired in animals whose lobula plate had been lesioned. The effect was behaviour-specific, since avoidance responses to approaching visual stimuli were not affected. Crabs require simpler optic flow processing than flies (because they move slower and in two-dimensional instead of three-dimensional space), consequently their lobula plates are relatively smaller. Nonetheless, they perform the same essential role in the visual control of behaviour. Our findings add a fundamental piece to the current debate on the evolutionary relationship between the lobula plates of insects and crustaceans.

Neuronal circuits integrating visual motion information in Drosophila melanogaster

The detection of visual motion enables sophisticated animal navigation, and studies on flies have provided profound insights into the cellular and circuit bases of this neural computation. The fly's directionally selective T4 and T5 neurons encode ON and OFF motion, respectively. Their axons terminate in one of the four retinotopic layers in the lobula plate, where each layer encodes one of the four directions of motion. Although the input circuitry of the directionally selective neurons has been studied in detail, the synaptic connectivity of circuits integrating T4/T5 motion signals is largely unknown. Here, we report a 3D electron microscopy reconstruction, wherein we comprehensively identified T4/T5's synaptic partners in the lobula plate, revealing a diverse set of new cell types and attributing new connectivity patterns to the known cell types. Our reconstruction explains how the ON- and OFF-motion pathways converge. T4 and T5 cells that project to the same layer connect to common synaptic partners and comprise a core motif together with bilayer interneurons, detailing the circuit basis for computing motion opponency. We discovered pathways that likely encode new directions of motion by integrating vertical and horizontal motion signals from upstream T4/T5 neurons. Finally, we identify substantial projections into the lobula, extending the known motion pathways and suggesting that directionally selective signals shape feature detection there. The circuits we describe enrich the anatomical basis for experimental and computations analyses of motion vision and bring us closer to understanding complete sensory-motor pathways.

Calcium imaging of CPG-evoked activity in efferent neurons of the stick insect

The stick insect is a well-established experimental animal to study the neural basis of walking. Here, we introduce a preparation that allows combining calcium imaging in efferent neurons with electrophysiological recordings of motor neuron activity in the stick insect thoracic nerve cord. The intracellular free calcium concentration in middle leg retractor coxae motor neurons and modulatory octopaminergic DUM neurons was monitored after backfilling lateral nerve nl5 that contains the axons of these neurons with the calcium indicator Oregon Green BAPTA-1. Rhythmic spike activity in retractor and protractor motor neurons was evoked by pharmacological activation of central pattern generating neuronal networks and recorded extracellularly from lateral nerves. A primary goal of this study was to investigate whether changes in the intracellular free calcium concentration observed in motor neurons during oscillatory activity depend on action potentials. We show that rhythmic spike activity in leg motor neurons induced either pharmacologically or by tactile stimulation of the animal is accompanied by a synchronous modulation in the intracellular free calcium concentration. Calcium oscillations in motor neurons do not appear to depend on calcium influx through voltage-sensitive calcium channels that are gated by action potentials because Calcium oscillations persist after pharmacologically blocking action potentials in the motor neurons. Calcium oscillations were also apparent in the modulatory DUM neurons innervating the same leg muscle. However, the timing of calcium oscillations varied not only between DUM neurons and motor neurons, but also among different DUM neurons. Therefore, we conclude that the motor neurons and the different DUM neurons receive independent central drive.

A biophysical mechanism for preferred direction enhancement in fly motion vision

Seeing the direction of motion is essential for survival of all sighted animals. Consequently, nerve cells that respond to visual stimuli moving in one but not in the opposite direction, so-called 'direction-selective' neurons, are found abundantly. In general, direction selectivity can arise by either signal amplification for stimuli moving in the cell's preferred direction ('preferred direction enhancement'), signal suppression for stimuli moving along the opposite direction ('null direction suppression'), or a combination of both. While signal suppression can be readily implemented in biophysical terms by a hyperpolarization followed by a rectification corresponding to the nonlinear voltage-dependence of the Calcium channel, the biophysical mechanism for signal amplification has remained unclear so far. Taking inspiration from the fly, I analyze a neural circuit where a direction-selective ON-cell receives inhibitory input from an OFF cell on the preferred side of the dendrite, while excitatory ON-cells contact the dendrite centrally. This way, an ON edge moving along the cell's preferred direction suppresses the inhibitory input, leading to a release from inhibition in the postsynaptic cell. The benefit of such a two-fold signal inversion lies in the resulting increase of the postsynaptic cell's input resistance, amplifying its response to a subsequent excitatory input signal even with a passive dendrite, i.e. without voltage-gated ion channels. A motion detector implementing this mechanism together with null direction suppression shows a high degree of direction selectivity over a large range of temporal frequency, narrow directional tuning, and a large signal-to-noise ratio.

Non-uniform weighting of local motion inputs underlies dendritic computation in the fly visual system

The fly visual system offers a unique opportunity to explore computations performed by single neurons. Two previous studies characterized, in vivo, the receptive field (RF) of the vertical system (VS) cells of the blowfly (calliphora vicina), both intracellularly in the axon, and, independently using Ca²⁺ imaging, in hundreds of distal dendritic branchlets. We integrated this information into detailed passive cable and compartmental models of 3D reconstructed VS cells. Within a given VS cell type, the transfer resistance (TR) from different branchlets to the axon differs substantially, suggesting that they contribute unequally to the shaping of the axonal RF. Weighting the local RFs of all dendritic branchlets by their respective TR yielded a faithful reproduction of the axonal RF. The model also predicted that the various dendritic branchlets are electrically decoupled from each other, thus acting as independent local functional subunits. The study suggests that single neurons in the fly visual system filter dendritic noise and compute the weighted average of their inputs.

The optomotor response of the praying mantis is driven predominantly by the central visual field

The optomotor response has been widely used to investigate insect sensitivity to contrast and motion. Several studies have revealed the sensitivity of this response to frequency and contrast, but we know less about the spatial integration underlying this response. Specifically, few studies have investigated how the horizontal angular extent of stimuli influences the optomotor response. We presented mantises with moving gratings of varying horizontal extents at three different contrasts in the central or peripheral regions of their visual fields. We assessed the relative effectivity of different regions to elicit the optomotor response and modelled the dependency of the response on the angular extent subtended by stimuli at these different regions. Our results show that the optomotor response is governed by stimuli in the central visual field and not in the periphery. The model also shows that in the central region, the probability of response increases linearly with increase in horizontal extent up to a saturation point. Furthermore, the dependency of the optomotor response on the angular extent of the stimulus is modulated by contrast. We discuss the implications of our results for different modes of stimulus presentation and for models of the underlying mechanisms of motion detection in the mantis.

Common circuit design in fly and mammalian motion vision

Motion-sensitive neurons have long been studied in both the mammalian retina and the insect optic lobe, yet striking similarities have become obvious only recently. Detailed studies at the circuit level revealed that, in both systems, (i) motion information is extracted from primary visual information in parallel ON and OFF pathways; (ii) in each pathway, the process of elementary motion detection involves the correlation of signals with different temporal dynamics; and (iii) primary motion information from both pathways converges at the next synapse, resulting in four groups of ON-OFF neurons, selective for the four cardinal directions. Given that the last common ancestor of insects and mammals lived about 550 million years ago, this general strategy seems to be a robust solution for how to compute the direction of visual motion with neural hardware.

The role of models in the process of epistemic integration: the case of the Reichardt motion detector

Recent work on epistemic integration in the life sciences has emphasized the importance of integration in thinking about explanatory practice in science, particularly for articulating a robust alternative to reductionism and anti-reductionism. This paper analyzes the role of models in balancing the relative contributions of lower- and higher-level epistemic resources involved in this process. Integration between multiple disciplines proceeds by constructing a problem agenda (Love, Philos Sci 75(5): 874-886, 2008), a set of interrelated problems that structures the problem space of a complex phenomenon that is investigated by many disciplines. The usage of models, it is argued, mark changes in a phenomenon's problem agenda depending on the task that is expected of it. Particularly, it emphasizes the sensitivity of a problem agenda to changing attitudes in the solutions to the conceptual and empirical items constituting that agenda. The analysis will proceed by means of a case study, the Reichardt motion detector, a model that has been vital to the methodological and conceptual development of research on motion detection, especially in invertebrates. As will be seen, the history of the Reichardt model will exemplify the dynamic changes that occur in the interdisciplinary negotiations that comprise the active efforts of various sciences working to integrate their resources.

Cooperative integration and representation underlying bilateral network of fly motion-sensitive neurons

How is binocular motion information integrated in the bilateral network of wide-field motion-sensitive neurons, called lobula plate tangential cells (LPTCs), in the visual system of flies? It is possible to construct an accurate model of this network because a complete picture of synaptic interactions has been experimentally identified. We investigated the cooperative behavior of the network of horizontal LPTCs underlying the integration of binocular motion information and the information representation in the bilateral LPTC network through numerical simulations on the network model. First, we qualitatively reproduced rotational motion-sensitive response of the H2 cell previously reported in vivo experiments and ascertained that it could be accounted for by the cooperative behavior of the bilateral network mainly via interhemispheric electrical coupling. We demonstrated that the response properties of single H1 and Hu cells, unlike H2 cells, are not influenced by motion stimuli in the contralateral visual hemi-field, but that the correlations between these cell activities are enhanced by the rotational motion stimulus. We next examined the whole population activity by performing principal component analysis (PCA) on the population activities of simulated LPTCs. We showed that the two orthogonal patterns of correlated population activities given by the first two principal components represent the rotational and translational motions, respectively, and similar to the H2 cell, rotational motion produces a stronger response in the network than does translational motion. Furthermore, we found that these population-coding properties are strongly influenced by the interhemispheric electrical coupling. Finally, to test the generality of our conclusions, we used a more simplified model and verified that the numerical results are not specific to the network model we constructed.

Preserving neural function under extreme scaling

Important brain functions need to be conserved throughout organisms of extremely varying sizes. Here we study the scaling properties of an essential component of computation in the brain: the single neuron. We compare morphology and signal propagation of a uniquely identifiable interneuron, the HS cell, in the blowfly (Calliphora) with its exact counterpart in the fruit fly (Drosophila) which is about four times smaller in each dimension. Anatomical features of the HS cell scale isometrically and minimise wiring costs but, by themselves, do not scale to preserve the electrotonic behaviour. However, the membrane properties are set to conserve dendritic as well as axonal delays and attenuation as well as dendritic integration of visual information. In conclusion, the electrotonic structure of a neuron, the HS cell in this case, is surprisingly stable over a wide range of morphological scales.

Temporal and spatial adaptation of transient responses to local features

Interpreting visual motion within the natural environment is a challenging task, particularly considering that natural scenes vary enormously in brightness, contrast and spatial structure. The performance of current models for the detection of self-generated optic flow depends critically on these very parameters, but despite this, animals manage to successfully navigate within a broad range of scenes. Within global scenes local areas with more salient features are common. Recent work has highlighted the influence that local, salient features have on the encoding of optic flow, but it has been difficult to quantify how local transient responses affect responses to subsequent features and thus contribute to the global neural response. To investigate this in more detail we used experimenter-designed stimuli and recorded intracellularly from motion-sensitive neurons. We limited the stimulus to a small vertically elongated strip, to investigate local and global neural responses to pairs of local “doublet” features that were designed to interact with each other in the temporal and spatial domain. We show that the passage of a high-contrast doublet feature produces a complex transient response from local motion detectors consistent with predictions of a simple computational model. In the neuron, the passage of a high-contrast feature induces a local reduction in responses to subsequent low-contrast features. However, this neural contrast gain reduction appears to be recruited only when features stretch vertically (i.e., orthogonal to the direction of motion) across at least several aligned neighboring ommatidia. Horizontal displacement of the components of elongated features abolishes the local adaptation effect. It is thus likely that features in natural scenes with vertically aligned edges, such as tree trunks, recruit the greatest amount of response suppression. This property could emphasize the local responses to such features vs. those in nearby texture within the scene.

Binocular interactions underlying the classic optomotor responses of flying flies

In response to imposed course deviations, the optomotor reactions of animals reduce motion blur and facilitate the maintenance of stable body posture. In flies, many anatomical and electrophysiological studies suggest that disparate motion cues stimulating the left and right eyes are not processed in isolation but rather are integrated in the brain to produce a cohesive panoramic percept. To investigate the strength of such inter-ocular interactions and their role in compensatory sensory–motor transformations, we utilize a virtual reality flight simulator to record wing and head optomotor reactions by tethered flying flies in response to imposed binocular rotation and monocular front-to-back and back-to-front motion. Within a narrow range of stimulus parameters that generates large contrast insensitive optomotor responses to binocular rotation, we find that responses to monocular front-to-back motion are larger than those to panoramic rotation, but are contrast sensitive. Conversely, responses to monocular back-to-front motion are slower than those to rotation and peak at the lowest tested contrast. Together our results suggest that optomotor responses to binocular rotation result from the influence of non-additive contralateral inhibitory as well as excitatory circuit interactions that serve to confer contrast insensitivity to flight behaviors influenced by rotatory optic flow.

Flight activity alters velocity tuning of fly motion-sensitive neurons

Sensory neurons are mostly studied in fixed animals, but their response properties might change when the animal is free to move. Indeed, recent studies found differences between responses of sensory neurons in resting versus moving insects. Since the dynamic range of visual motion stimuli strongly depends on the speed at which an animal is moving, we investigated whether the visual system adapts to such changes in stimulus dynamics as induced by self-motion. Lobula plate tangential cells of flies lend themselves well to study this question because they are known to code for ego-motion based on optic-flow. We recorded the responses of the lobula plate tangential cell H1 to a visual pattern moving at different velocities under three different conditions: fixed flies before and after application of the octopamine agonist chlordimeform (CDM) and tethered flying flies. CDM has been previously shown to induce arousal in flies. We found that flying as well as the application of CDM significantly broadens the velocity tuning of H1 toward higher velocities.

Recording from two neurons: second-order stimulus reconstruction from spike trains and population coding

We study the reconstruction of visual stimuli from spike trains, representing the reconstructed stimulus by a Volterra series up to second order. We illustrate this procedure in a prominent example of spiking neurons, recording simultaneously from the two H1 neurons located in the lobula plate of the fly Chrysomya megacephala. The fly views two types of stimuli, corresponding to rotational and translational displacements. Second-order reconstructions require the manipulation of potentially very large matrices, which obstructs the use of this approach when there are many neurons. We avoid the computation and inversion of these matrices using a convenient set of basis functions to expand our variables in. This requires approximating the spike train four-point functions by combinations of two-point functions similar to relations, which would be true for gaussian stochastic processes. In our test case, this approximation does not reduce the quality of the reconstruction. The overall contribution to stimulus reconstruction of the second-order kernels, measured by the mean squared error, is only about 5% of the first-order contribution. Yet at specific stimulus-dependent instants, the addition of second-order kernels represents up to 100% improvement, but only for rotational stimuli. We present a perturbative scheme to facilitate the application of our method to weakly correlated neurons.

Candidate glutamatergic neurons in the visual system of Drosophila

The visual system of Drosophila contains approximately 60,000 neurons that are organized in parallel, retinotopically arranged columns. A large number of these neurons have been characterized in great anatomical detail. However, studies providing direct evidence for synaptic signaling and the neurotransmitter used by individual neurons are relatively sparse. Here we present a first layout of neurons in the Drosophila visual system that likely release glutamate as their major neurotransmitter. We identified 33 different types of neurons of the lamina, medulla, lobula and lobula plate. Based on the previous Golgi-staining analysis, the identified neurons are further classified into 16 major subgroups representing lamina monopolar (L), transmedullary (Tm), transmedullary Y (TmY), Y, medulla intrinsic (Mi, Mt, Pm, Dm, Mi Am), bushy T (T), translobula plate (Tlp), lobula intrinsic (Lcn, Lt, Li), lobula plate tangential (LPTCs) and lobula plate intrinsic (LPi) cell types. In addition, we found 11 cell types that were not described by the previous Golgi analysis. This classification of candidate glutamatergic neurons fosters the future neurogenetic dissection of information processing in circuits of the fly visual system.

Neurons with cholinergic phenotype in the visual system of Drosophila

The optic lobe of Drosophila houses about 60,000 neurons that are organized in parallel, retinotopically arranged columns. Based on the Golgi-staining method, Fischbach and Dittrich ([1989] Cell Tissue Res 258:441-475) determined that each column contains about 90 identified cells. Each of these cells is supposed to release one or two different neurotransmitters. However, for most cells the released neurotransmitter is not known. Here we characterize the vast majority of the neurons in the Drosophila optic lobe that release acetylcholine (Ach), the major excitatory neurotransmitter of the insect central nervous system. We employed a promoter specific for cholinergic neurons and restricted its activity to single or a few cells using the MARCM technique. This approach allowed us to establish an anatomical map of neurons with a cholinergic phenotype based on their branching pattern. We identified 43 different types of neurons with a cholinergic phenotype. Thirty-one of them match previously described members of nine different subgroups: Transmedullary (Tm), Transmedullary Y (TmY), Medulla intrinsic (Mi, Mt, and Pm), Bushy T (T), Translobula Plate (Tlp), and Lobula intrinsic (Lcn and Lt) neurons (Fischbach and Dittrich [1989]). Intriguingly, 12 newly identified cell types suggest that previous Golgi studies were not saturating and that the actual number of different neurons per column is higher than previously thought. This study and similar ones on other neurotransmitter systems will contribute towards a columnar wiring diagram and foster the functional dissection of the visual circuitry in Drosophila.

Neural action fields for optic flow based navigation: a simulation study of the fly lobula plate network

Optic flow based navigation is a fundamental way of visual course control described in many different species including man. In the fly, an essential part of optic flow analysis is performed in the lobula plate, a retinotopic map of motion in the environment. There, the so-called lobula plate tangential cells possess large receptive fields with different preferred directions in different parts of the visual field. Previous studies demonstrated an extensive connectivity between different tangential cells, providing, in principle, the structural basis for their large and complex receptive fields. We present a network simulation of the tangential cells, comprising most of the neurons studied so far (22 on each hemisphere) with all the known connectivity between them. On their dendrite, model neurons receive input from a retinotopic array of Reichardt-type motion detectors. Model neurons exhibit receptive fields much like their natural counterparts, demonstrating that the connectivity between the lobula plate tangential cells indeed can account for their complex receptive field structure. We describe the tuning of a model neuron to particular types of ego-motion (rotation as well as translation around/along a given body axis) by its ‘action field’. As we show for model neurons of the vertical system (VS-cells), each of them displays a different type of action field, i.e., responds maximally when the fly is rotating around a particular body axis. However, the tuning width of the rotational action fields is relatively broad, comparable to the one with dendritic input only. The additional intra-lobula-plate connectivity mainly reduces their translational action field amplitude, i.e., their sensitivity to translational movements along any body axis of the fly.

Intrinsic activity in the fly brain gates visual information during behavioral choices

The small insect brain is often described as an input/output system that executes reflex-like behaviors. It can also initiate neural activity and behaviors intrinsically, seen as spontaneous behaviors, different arousal states and sleep. However, less is known about how intrinsic activity in neural circuits affects sensory information processing in the insect brain and variability in behavior. Here, by simultaneously monitoring Drosophila's behavioral choices and brain activity in a flight simulator system, we identify intrinsic activity that is associated with the act of selecting between visual stimuli. We recorded neural output (multiunit action potentials and local field potentials) in the left and right optic lobes of a tethered flying Drosophila, while its attempts to follow visual motion (yaw torque) were measured by a torque meter. We show that when facing competing motion stimuli on its left and right, Drosophila typically generate large torque responses that flip from side to side. The delayed onset (0.1–1 s) and spontaneous switch-like dynamics of these responses, and the fact that the flies sometimes oppose the stimuli by flying straight, make this behavior different from the classic steering reflexes. Drosophila, thus, seem to choose one stimulus at a time and attempt to rotate toward its direction. With this behavior, the neural output of the optic lobes alternates; being augmented on the side chosen for body rotation and suppressed on the opposite side, even though the visual input to the fly eyes stays the same. Thus, the flow of information from the fly eyes is gated intrinsically. Such modulation can be noise-induced or intentional; with one possibility being that the fly brain highlights chosen information while ignoring the irrelevant, similar to what we know to occur in higher animals.

Central gating of fly optomotor response

We study the integration of multisensory and central input at the level of an identified fly motoneuron, the ventral cervical nerve motoneuron (VCNM) cell, which controls head movements of the animal. We show that this neuron receives input from a central neuron signaling flight activity, from two identified wide-field motion-sensitive neurons, from the wind-sensitive Johnston organ on the antennae, and from the campaniform sensillae of the halteres. We find that visual motion alone leads to only subthreshold responses. Only when it is combined with flight activity or wind stimuli does the VCNM respond to visual motion by modulating its spike activity in a directionally selective way. This nonlinear enhancement of visual responsiveness in the VCNM by central activity is reflected at the behavioral level, when compensatory head movements are measured in response to visual motion. While head movements of flies have only a small amplitude when flies are at rest, the response amplitude is increased by a factor of 30-40 during flight.

Wide-field motion integration in fly VS cells: insights from an inverse approach

Fly lobula plate tangential cells are known to perform wide-field motion integration. It is assumed that the shape of these neurons, and in particular the shape of the subclass of VS cells, is responsible for this type of computation. We employed an inverse approach to investigate the morphology-function relationship underlying wide-field motion integration in VS cells. In the inverse approach detailed, model neurons are optimized to perform a predefined computation: here, wide-field motion integration. We embedded the model neurons to be optimized in a biologically plausible model of fly motion detection to provide realistic inputs, and subsequently optimized model neuron with and without active conductances (g_Na, g_K, g_K(Na)) along their dendrites to perform this computation. We found that both passive and active optimized model neurons perform well as wide-field motion integrators. In addition, all optimized morphologies share the same blueprint as real VS cells. In addition, we also found a recurring blueprint for the distribution of g_K and g_Na in the active models. Moreover, we demonstrate how this morphology and distribution of conductances contribute to wide-field motion integration. As such, by using the inverse approach we can predict the still unknown distribution of g_K and g_Na and their role in motion integration in VS cells.

It is well established that neuronal morphology influences the computation performed by a single neuron. However, it remains largely unknown how these computations emerge from the interaction between dendritic morphology, the distribution of ion-channels and synaptic inputs. To investigate this neuronal morphology-function relationship we employ an inverse approach in which detailed model neurons are optimized to perform a predefined computation. In this work, we set to investigate how dendritic morphology contributes to wide-field motion integration in fly lobula plate tangential cells (LPTCs), cells of which the morphology is assumed to be linked to their function as wide-field motion integrators. The resulting optimized models perform well and share crucial features of LPTC morphology. By analysis of the optimized models, we revealed a match between morphological structures and physiological mechanisms required to perform wide-field motion integration, i.e., we explicitly show the morphology-function relationship in LPTC neurons. Moreover, the optimized distribution of ionic conductances gives rise to predictions about the distribution and role of these conductances in the real neurons. Finally, our findings provide an explanation of dendritic morphologies in terms of the computation they should perform.

An inverse approach for elucidating dendritic function

We outline an inverse approach for investigating dendritic function-structure relationships by optimizing dendritic trees for a priori chosen computational functions. The inverse approach can be applied in two different ways. First, we can use it as a "hypothesis generator" in which we optimize dendrites for a function of general interest. The optimization yields an artificial dendrite that is subsequently compared to real neurons. This comparison potentially allows us to propose hypotheses about the function of real neurons. In this way, we investigated dendrites that optimally perform input-order detection. Second, we can use it as a "function confirmation" by optimizing dendrites for functions hypothesized to be performed by classes of neurons. If the optimized, artificial, dendrites resemble the dendrites of real neurons the artificial dendrites corroborate the hypothesized function of the real neuron. Moreover, properties of the artificial dendrites can lead to predictions about yet unmeasured properties. In this way, we investigated wide-field motion integration performed by the VS cells of the fly visual system. In outlining the inverse approach and two applications, we also elaborate on the nature of dendritic function. We furthermore discuss the role of optimality in assigning functions to dendrites and point out interesting future directions.

Robust coding of ego-motion in descending neurons of the fly

In many species, motion-sensitive neurons responding to optic flow at higher processing stages are well characterized; however, less is known how this representation of ego-motion is further transformed into an appropriate motor response. Here, we analyzed in the blowfly Calliphora vicina the visuomotor transformation from motion-sensitive neurons in the lobula plate [V2 and vertical system (VS) cells] onto premotor descending neurons [descending neurons of the ocellar and vertical system (DNOVS) cells] feeding into the motor circuit of the fly thoracic ganglion. We found that each of these cells is tuned to rotation of the fly around a particular body axis. Comparing the responses of presynaptic and postsynaptic cells revealed that DNOVS cells have approximately the same tuning widths as V2 and VS cells. However, DNOVS signals cells are less corrupted by fluctuations arising from the spatial structure of the visual input than their presynaptic elements. This leads to a more robust representation of ego-motion at the level of descending neurons. Thus, when moving from lobula plate cells to descending neurons, the selectivity for a particular optic flow remains unaltered, but the robustness of the representation increases.

Local and global motion preferences in descending neurons of the fly

For a moving animal, optic flow is an important source of information about its ego-motion. In flies, the processing of optic flow is performed by motion sensitive tangential cells in the lobula plate. Amongst them, cells of the vertical system (VS cells) have receptive fields with similarities to optic flows generated during rotations around different body axes. Their output signals are further processed by pre-motor descending neurons. Here, we investigate the local motion preferences of two descending neurons called descending neurons of the ocellar and vertical system (DNOVS1 and DNOVS2). Using an LED arena subtending 240° × 95° of visual space, we mapped the receptive fields of DNOVS1 and DNOVS2 as well as those of their presynaptic elements, i.e. VS cells 1–10 and V2. The receptive field of DNOVS1 can be predicted in detail from the receptive fields of those VS cells that are most strongly coupled to the cell. The receptive field of DNOVS2 is a combination of V2 and VS cells receptive fields. Predicting the global motion preferences from the receptive field revealed a linear spatial integration in DNOVS1 and a superlinear spatial integration in DNOVS2. In addition, the superlinear integration of V2 output is necessary for DNOVS2 to differentiate between a roll rotation and a lift translation of the fly.

Drosophila's view on insect vision

Within the last 400 million years, insects have radiated into at least a million species, accounting for more than half of all known living organisms: they are the most successful group in the animal kingdom, found in almost all environments of the planet, ranging in body size from a mere 0.1 mm up to half a meter. Their eyes, together with the respective parts of the nervous system dedicated to the processing of visual information, have long been the subject of intense investigation but, with the exception of some very basic reflexes, it is still not possible to link an insect's visual input to its behavioral output. Fortunately for the field, the fruit fly Drosophila is an insect, too. This genetic workhorse holds great promise for the insect vision field, offering the possibility of recording, suppressing or stimulating any single neuron in its nervous system. Here, I shall give a brief synopsis of what we currently know about insect vision, describe the genetic toolset available in Drosophila and give some recent examples of how the application of these tools have furthered our understanding of color and motion vision in Drosophila.

Structural homeostasis: compensatory adjustments of dendritic arbor geometry in response to variations of synaptic input

As the nervous system develops, there is an inherent variability in the connections formed between differentiating neurons. Despite this variability, neural circuits form that are functional and remarkably robust. One way in which neurons deal with variability in their inputs is through compensatory, homeostatic changes in their electrical properties. Here, we show that neurons also make compensatory adjustments to their structure. We analysed the development of dendrites on an identified central neuron (aCC) in the late Drosophila embryo at the stage when it receives its first connections and first becomes electrically active. At the same time, we charted the distribution of presynaptic sites on the developing postsynaptic arbor. Genetic manipulations of the presynaptic partners demonstrate that the postsynaptic dendritic arbor adjusts its growth to compensate for changes in the activity and density of synaptic sites. Blocking the synthesis or evoked release of presynaptic neurotransmitter results in greater dendritic extension. Conversely, an increase in the density of presynaptic release sites induces a reduction in the extent of the dendritic arbor. These growth adjustments occur locally in the arbor and are the result of the promotion or inhibition of growth of neurites in the proximity of presynaptic sites. We provide evidence that suggest a role for the postsynaptic activity state of protein kinase A in mediating this structural adjustment, which modifies dendritic growth in response to synaptic activity. These findings suggest that the dendritic arbor, at least during early stages of connectivity, behaves as a homeostatic device that adjusts its size and geometry to the level and the distribution of input received. The growing arbor thus counterbalances naturally occurring variations in synaptic density and activity so as to ensure that an appropriate level of input is achieved.

As the nervous system develops, an intricate web of connections forms between nerve cells, leading to the assembly of signalling networks that are capable of complex computations. However, the number and strength of connections formed between nerve cells varies. We ask how nerve cells deal with this variability so that the circuits they form are nicely matched to the functions they perform. Nerve cells are known to adjust their sensitivity to compensate for changes in the strengths of inputs they receive from other cells. In this study, we have identified a structural counterpart to this compensatory mechanism, and find that developing nerve cells respond to variation in the number of connections they receive by adjusting the size of their receiving structures (known as dendrites). Working with the same nerve cell in different embryos, we show that this cell reduces the size of its dendrites as the number of connections increases while allowing its dendrites to grow more extensively if inputs are reduced. These findings suggest that, at least during the early stages of wiring the nervous system, nerve cells regulate the growth of their dendrites, to compensate for variability and attain an optimal number of connections.

Structural homeostasis is defined as follows: developing neurons modify the growth of their dendrites to compensate for changes in synaptic density. This structural adjustment is mediated, at least in part, by postsynaptic PKA signalling.

Integration of lobula plate output signals by DNOVS1, an identified premotor descending neuron

Many motion-sensitive tangential cells of the lobula plate in blowflies are well described with respect to their visual response properties and the connectivity among them. They have large and complex receptive fields with different preferred directions in different parts of their receptive fields matching the optic flow that occurs during various flight maneuvers. However, much less is known about how tangential cells connect to postsynaptic neurons descending to the motor circuits in the thoracic ganglion and how optic flow is represented in these downstream neurons. Here we describe the physiology and the connectivity of a prominent descending neuron called DNOVS1 (for descending neurons of the ocellar and vertical system). We find that DNOVS1 is electrically coupled to a subset of vertical system cells. The specific wiring leads to a preference of DNOVS1 for rotational flow fields around a particular body axis. In addition, DNOVS1 receives input from interneurons connected to the ocelli.

Synapses in the fly motion-vision pathway: evidence for a broad range of signal amplitudes and dynamics

Synapses are generally considered to operate efficiently only when their signaling range matches the spectrum of prevailing presynaptic signals in terms of both amplitudes and dynamics. However, the prerequisites for optimally matching the signaling ranges may differ between spike-mediated and graded synaptic transmission. This poses a problem for synapses that convey both graded and spike signals at the same time. We addressed this issue by tracing transmission systematically in vivo in the blowfly's visual-motion pathway by recording from single neurons that receive mixed potential signals consisting of rather slow graded fluctuations superimposed with highly variable spikes from a small number of presynaptic elements. Both pre- and postsynaptic neurons were previously shown to represent preferred-direction motion velocity reliably and linearly at low fluctuation frequencies. To selectively assess the performance of individual synapses and to precisely control presynaptic signals, we voltage clamped one of the presynaptic neurons. Results showed that synapses can effectively convey signals over a much larger amplitude and frequency range than is normally used during graded transmission of visual signals. An explanation for this unexpected finding might lie in the transmission of the spike component that reaches larger amplitudes and contains higher frequencies than graded signals.

Influence of electrotonic structure and synaptic mapping on the receptive field properties of a collision-detecting neuron

The lobula giant movement detector (LGMD) is a visual interneuron of Orthopteran insects involved in collision avoidance and escape behavior. The LGMD possesses a large dendritic field thought to receive excitatory, retinotopic projections from the entire compound eye. We investigated whether the LGMD's receptive field for local motion stimuli can be explained by its electrotonic structure and the eye's anisotropic sampling of visual space. Five locust (Schistocerca americana) LGMD neurons were stained and reconstructed. We show that the excitatory dendritic field and eye can be fitted by ellipsoids having similar geometries. A passive compartmental model fit to electrophysiological data was used to demonstrate that the LGMD is not electrotonically compact. We derived a spike rate to membrane potential transform using intracellular recordings under visual stimulation, allowing direct comparison between experimental and simulated receptive field properties. By assuming a retinotopic mapping giving equal weight to each ommatidium and equally spaced synapses, the model reproduced the experimental data along the eye equator, though it failed to reproduce the receptive field along the ventral-dorsal axis. Our results illustrate how interactions between the distribution of synaptic inputs and the electrotonic properties of neurons contribute to shaping their receptive fields.

Nonlinear, binocular interactions underlying flow field selectivity of a motion-sensitive neuron

Neurons in many species have large receptive fields that are selective for specific optic flow fields. Here, we studied the neural mechanisms underlying flow field selectivity in lobula plate tangential cells (LPTCs) of the blowfly. Among these cells, the H2 cell responds preferentially to visual stimuli approximating rotational optic flow. Through double recordings from H2 and many other LPTCs, we characterized a bidirectional commissural pathway that allows visual information to be shared between the hemispheres. This pathway is mediated by axo-axonal electrical coupling of H2 and the horizontal system equatorial (HSE) cell located in the opposite hemisphere. Using single-cell ablations, we found that this pathway is sufficient to allow H2 to amplify and attenuate dendritic input during binocular visual stimuli. This is accomplished through a modulation of H2's membrane potential by input from the contralateral HSE cell, which scales the firing rate of H2 during visual stimulation but is not sufficient to induce action potentials.

Representation of behaviourally relevant information by blowfly motion-sensitive visual interneurons requires precise compensatory head movements

Flying blowflies shift their gaze by saccadic turns of body and head, keeping their gaze basically fixed between saccades. For the head, this results in almost pure translational optic flow between saccades, enabling visual interneurons in the fly motion pathway to extract information about translation of the animal and thereby about the spatial layout of the environment. There are noticeable differences between head and body movements during flight. Head saccades are faster and shorter than body saccades, and the head orientation is more stable between saccades than the body orientation. Here, we analyse the functional importance of these differences by probing visual interneurons of the blowfly motion pathway with optic flow based on either head movements or body movements, as recorded accurately with a magnetic search coil technique. We find that the precise head-body coordination is essential for the visual system to separate the translational from the rotational optic flow. If the head were tightly coupled to the body, the resulting optic flow would not contain the behaviourally important information on translation. Since it is difficult to resolve head orientation in many experimental paradigms, even when employing state-of-the-art digital video techniques, we introduce a 'headifying algorithm', which transforms the time-dependent body orientation in free flight into an estimate of head orientation. We show that application of this algorithm leads to an estimated head orientation between saccades that is sufficiently stable to enable recovering information on translation. The algorithm may therefore be of practical use when head orientation is needed but cannot be measured.

On the computations analyzing natural optic flow: quantitative model analysis of the blowfly motion vision pathway

For many animals, including humans, the optic flow generated on the eyes during locomotion is an important source of information about self-motion and the structure of the environment. The blowfly has been used frequently as a model system for experimental analysis of optic flow processing at the microcircuit level. Here, we describe a model of the computational mechanisms implemented by these circuits in the blowfly motion vision pathway. Although this model was originally proposed based on simple experimenter-designed stimuli, we show that it is also capable to quantitatively predict the responses to the complex dynamic stimuli a blowfly encounters in free flight. In particular, the model visual system exploits the active saccadic gaze and flight strategy of blowflies in a similar way, as does its neuronal counterpart. The model circuit extracts information about translation velocity in the intersaccadic intervals and thus, indirectly, about the three-dimensional layout of the environment. By stepwise dissection of the model circuit, we determine which of its components are essential for these remarkable features. When accounting for the responses to complex natural stimuli, the model is much more robust against parameter changes than when explaining the neuronal responses to simple experimenter-defined stimuli. In contrast to conclusions drawn from experiments with simple stimuli, optimization of the parameter set for different segments of natural optic flow stimuli do not indicate pronounced adaptational changes of these parameters during long-lasting stimulation.

Input organization of multifunctional motion-sensitive neurons in the blowfly

Flies rely heavily on visual motion cues for course control. This is mediated by a small set of motion-sensitive neurons called lobula plate tangential cells. A single class of these, the centrifugal horizontal (CH) neurons, play an important role in two pathways: figure-ground discrimination and flow-field selectivity. As was recently found, the dendrites of CH cells are electrically coupled with the dendritic tree of another class of neurons sensitive to horizontal image motion, the horizontal system (HS) cells. However, whether motion information arrives independently at both of these cells or is passed from one to the other is not known. Here, we examine the ipsilateral input circuitry to HS and CH neurons by selective laser ablation of individual interneurons. We find that the response of CH neurons to motion presented in front of the ipsilateral eye is entirely abolished after ablation of HS cells. In contrast, the motion response of HS cells persists after the ablation of CH cells. We conclude that HS cells receive direct motion input from local motion elements, whereas CH cells do not; their motion response is driven by HS cells. This connection scheme is discussed with reference to how the dendritic networks involved in figure-ground detection and flow-field selectivity might operate.

Neural image processing by dendritic networks

Convolution is one of the most common operations in image processing. Based on experimental findings on motion-sensitive visual interneurons of the fly, we show by realistic compartmental modeling that a dendritic network can implement this operation. In a first step, dendritic electrical coupling between two cells spatially blurs the original motion input. The blurred motion image is then passed onto a third cell via inhibitory dendritic synapses resulting in a sharpening of the signal. This enhancement of motion contrast may be the central element of figure-ground discrimination based on relative motion in the fly.

Adaptation of response transients in fly motion vision. II: Model studies

The so-called 'Reichardt detector' can successfully account for many properties of fly motion vision. In its simplest form, the signals derived from neighboring image locations become multiplied after a low-pass filter has delayed one of them. This operation is done twice in a mirror-symmetrical form and the resulting output signals become finally subtracted. As predicted by this model, fly neurons respond to a brief motion pulse with a sudden rise in activity followed by an exponential decay. The time constant of this decay has been shown to shorten when tested after presentation of an adapting motion stimulus. In terms of the detector model this inevitably implies that the time constant of the low-pass filter is adapting. Given that, one would expect a concomitant shift of the steady-state response towards higher velocities, which, however, could not be experimentally verified. Here, we show that given a model with an additional temporal high-pass filter in the cross-arms of the detector, only the high-pass filter determines the time course of the impulse response. Assuming consequently that the time constant of the high-pass filter is the locus of adaptation resolves the conflicts mentioned above. Moreover, such an elaborated model with an adaptive time-constant faithfully mimics a particular contrast-dependency of transient response oscillations observed in fly motion sensitive neurons.

Orientation tuning of motion-sensitive neurons shaped by vertical-horizontal network interactions

We measured the orientation tuning of two neurons of the fly lobula plate (H1 and H2 cells) sensitive to horizontal image motion. Our results show that H1 and H2 cells are sensitive to vertical motion, too. Their response depended on the position of the vertically moving stimuli within their receptive field. Stimulation within the frontal receptive field produced an asymmetric response: upward motion left the H1/H2 spike frequency nearly unaltered while downward motion increased the spike frequency to about 40% of their maximum responses to horizontal motion. In the lateral parts of their receptive fields, no such asymmetry in the responses to vertical image motion was found. Since downward motion is known to be the preferred direction of neurons of the vertical system in the lobula plate, we analyzed possible interactions between vertical system cells and H1 and H2 cells. Depolarizing current injection into the most frontal vertical system cell (VS1) led to an increased spike frequency, hyperpolarizing current injection to a decreased spike frequency in both H1 and H2 cells. Apart from VS1, no other vertical system cell (VS2-8) had any detectable influence on either H1 or H2 cells. The connectivity of VS1 and H1/H2 is also shown to influence the response properties of both centrifugal horizontal cells in the contralateral lobula plate, which are known to be postsynaptic to the H1 and H2 cells. The vCH cell receives additional input from the contralateral VS2-3 cells via the spiking interneuron V1.

FliMax, a novel stimulus device for panoramic and highspeed presentation of behaviourally generated optic flow

A high-speed panoramic visual stimulation device is introduced which is suitable to analyse visual interneurons during stimulation with rapid image displacements as experienced by fast moving animals. The responses of an identified motion sensitive neuron in the visual system of the blowfly to behaviourally generated image sequences are very complex and hard to predict from the established input circuitry of the neuron. This finding suggests that the computational significance of visual interneurons can only be assessed if they are characterised not only by conventional stimuli as are often used for systems analysis, but also by behaviourally relevant input.

Dendro-dendritic interactions between motion-sensitive large-field neurons in the fly

For visual course control, flies rely on a set of motion-sensitive neurons called lobula plate tangential cells (LPTCs). Among these cells, the so-called CH (centrifugal horizontal) cells shape by their inhibitory action the receptive field properties of other LPTCs called FD (figure detection) cells specialized for figure-ground discrimination based on relative motion. Studying the ipsilateral input circuitry of CH cells by means of dual-electrode and combined electrical-optical recordings, we find that CH cells receive graded input from HS (large-field horizontal system) cells via dendro-dendritic electrical synapses. This particular wiring scheme leads to a spatial blur of the motion image on the CH cell dendrite, and, after inhibiting FD cells, to an enhancement of motion contrast. This could be crucial for enabling FD cells to discriminate object from self motion.

Different mechanisms of calcium entry within different dendritic compartments

From our experiments combining in vivo calcium imaging and electrophysiology on fly vertical motion-sensitive cells (VS-cells) during visual stimulation, we infer different mechanisms of calcium entry within different dendritic compartments; while in the main dendritic branches calcium influx from extracellular space takes place only via voltage-activated calcium channels (VACCs), calcium enters the dendritic tips through VACCs as well as nicotinic acetylcholine receptors (nAChRs). Consequently, neuronal nACHRs of insects have to be assumed to be permeable to some extent for calcium under in vivo conditions.

Effects of mean firing on neural information rate

We investigated the effect of mean firing on the information rate of a spiking motion-sensitive neuron in the fly (H1-cell). In the control condition, the cell was stimulated repeatedly by identical zero-symmetrical white-noise motion. The mean firing rate was manipulated by adding a constant velocity offset either in the same area of the receptive field where the dynamic stimulus was displayed or in a separate one. We determined the information rate in the resulting spike trains in the time domain as the difference between the total and the noise entropy rate and found that the information rate increases with increasing mean firing under both stimulus conditions.

Recurrent network interactions underlying flow-field selectivity of visual interneurons

Motion-sensitive large-field neurons found at higher processing stages in many species often exhibit a remarkable selectivity for particular flow fields. However, the underlying neural mechanisms are not yet understood. We studied this problem in the so-called lobula plate tangential cells (LPTCs) of the fly. Investigating the connectivity between LPTCs by means of dual recordings, we find two types of connections: (1) heterolateral connections between LPTCs of both hemispheres and (2) ipsilateral connections between LPTCs within one lobula plate. The circuit is suitable to amplify incoming, dendritic signals in the case of rotatory flow fields and to reduce them in the case of other flow-field structures. In addition to feedforward connectivity, thus, the flow-field selectivity of LPTCs may be significantly attributable to recurrent excitation involving the network of large-field neurons in both brain hemispheres.

Membrane potential fluctuations determine the precision of spike timing and synchronous activity: a model study

It is much debated on what time scale information is encoded by neuronal spike activity. With a phenomenological model that transforms time-dependent membrane potential fluctuations into spike trains, we investigate constraints for the timing of spikes and for synchronous activity of neurons with common input. The model of spike generation has a variable threshold that depends on the time elapsed since the previous action potential and on the preceding membrane potential changes. To ensure that the model operates in a biologically meaningful range, the model was adjusted to fit the responses of a fly visual interneuron to motion stimuli. The dependence of spike timing on the membrane potential dynamics was analyzed. Fast membrane potential fluctuations are needed to trigger spikes with a high temporal precision. Slow fluctuations lead to spike activity with a rate about proportional to the membrane potential. Thus, for a given level of stochastic input, the frequency range of membrane potential fluctuations induced by a stimulus determines whether a neuron can use a rate code or a temporal code. The relationship between the steepness of membrane potential fluctuations and the timing of spikes has also implications for synchronous activity in neurons with common input. Fast membrane potential changes must be shared by the neurons to produce synchronous activity.

Synaptic interactions increase optic flow specificity

Representations of optic flow are encoded in fly tangential neurons by pooling the signals of many retinotopically organized local motion-sensitive inputs as well as of other tangential cells originating in the ipsi- and contralateral half of the brain. In the so called HSE cell, a neuron involved in optomotor course control, two contralateral input elements, the H1 and H2 cells, mediate distinct EPSPs. These EPSPs frequently elicit spike-like depolarizations in the HSE cell. The synaptic transmission between the H2 and the HSE cell is analysed in detail and shown to be very reliable with respect to the amplitude and time-course of the postsynaptic potential. As a consequence of its synaptic input, the HSE cell responds best to wide-field motion, such as that generated on the eyes when the animal turns about its vertical body axis. It is shown that the specificity of the HSE cell for this type of optic flow is much enhanced if rapid membrane depolarizations, such as large-amplitude EPSPs or spike-like depolarizations, are taken into account rather than the average membrane potential.

Local current spread in electrically compact neurons of the fly

Analyses of active and passive membrane properties predict an asymmetry in the spread of electrical current through a neuron. Simulated current injection into a large-diameter compartment of a biophysically realistic model neuron causes a local potential shift that can spread throughout the cell. In contrast, causing the same local potential shift in the dendritic tip of the same neuron results in only minimal changes in electrical potential in the rest of the cell. Using calcium as a reporter of electrical activity in neurons in the fly's lobula plate we find that current injected into the thick axon caused depolarization throughout the cell, whereas activation of a dendritic region remained local. These results have important implications for the ability of integrating neurons to perform local computations of synaptic input without additional hardware.

Spatial distribution and characteristics of voltage-gated calcium signals within visual interneurons

Most of our knowledge about insect calcium currents is derived from studies on cultured or dissociated somata. So far, only little data on calcium currents are available for neurons including their dendritic and presynaptic structures. Here we combined the switched-electrode voltage-clamp technique with optical recording using calcium-sensitive dyes in identified fly visual interneurons in vivo to characterize the voltage dependence and dynamics of calcium currents quantitatively and in a spatially resolved way. For all three cell types considered, i.e., centrifugal horizontal (CH), horizontal system (HS), and vertical system (VS) cells, the activation curve is rather flat and covers a voltage range from -60 to -20 mV in dendritic as well as presynaptic areas of the cells. The calcium increase is fastest for CH cells with a time constant of approximately 70 ms. In HS and VS cells, the time constant amounts to 400-700 ms. The calcium dynamics as determined in different regions of the cells are similar except for a small segment between the axon and the dendrite in HS and VS cells, where the calcium increase is significantly faster. In summary, the results show the existence of a low-voltage-activated calcium current with little or no inactivation in dendritic as well as presynaptic regions of fly lobula plate tangential cells.

The intrinsic electrophysiological characteristics of fly lobula plate tangential cells: II. Active membrane properties

The voltage-gated currents in the fly lobula plate tangential cells were examined using the switched electrode voltage clamp technique. In CH cells, two currents were identified (Figs. 1, 2): a slow calcium inward current and a delayed rectifying, noninactivating potassium outward current. HS and VS cells appear to possess similar currents to CH cells, but in addition, exhibit a fast-activating sodium inward current and a sodium-activated potassium outward current (Figs. 3, 4). While the delayed rectifying potassium current in all three cell classes is responsible for the observed outward rectification described previously (Borst and Haag, 1996), the sodium inward current produced the fast and irregular spikelike depolarizations found in HS and VS cells but not in CH cells: When the sodium current is blocked by either. TTX or intracellular QX314, no more action potentials can be elicited in HS cells under current-clamp conditions (Fig. 5). As is demonstrated in HS cells, space clamp conditions are sufficient to suppress synaptically induced action potentials (Fig. 6). The currents described above were incorporated with the appropriate characteristics into compartmental models of the cells (Fig. 7, 8). The anatomical and electrically passive membrane parameters of these cells were determined in a preceding paper (Borst and Haag, 1996). After fitting the current parameters to the voltage-clamp data (Fig. 9), the model cells qualitatively mimicked the fly tangential cells under current clamp conditions in response to current injection (Fig. 10). The simulations demonstrated that the electrical compactness seen in the HS and VS cells, either in passive models or in active models during continuous hyperpolarization, decreased significantly in the active models during continuous depolarization (Fig. 11). Active HS models reproduce the frequency-dependent amplification of current injected into their axon (Fig. 12).

The intrinsic electrophysiological characteristics of fly lobula plate tangential cells: I. Passive membrane properties

The passive membrane properties of the tangential cells in the fly lobula plate (CH, HS, and VS cells, Fig. 1) were determined by combining compartmental modeling and current injection experiments. As a prerequisite, we built a digital base of the cells by 3D-reconstructing individual tangential cells from cobalt-stained material including both CH cells (VCH and DCH cells), all three HS cells (HSN, HSE, and HSS cells) and most members of the VS cell family (Figs. 2, 3). In a first series of experiments, hyperpolarizing and depolarizing currents were injected to determine steady-state I-V curves (Fig. 4). At potentials more negative than resting, a linear relationship holds, whereas at potentials more positive than resting, an outward rectification is observed. Therefore, in all subsequent experiments, when a sinusoidal current of variable frequency was injected, a negative DC current was superimposed to keep the neurons in a hyperpolarized state. The resulting amplitude and phase spectra revealed an average steady-state input resistance of 4 to 5 M omega and a cut-off frequency between 40 and 80 Hz (Fig. 5). To determine the passive membrane parameters Rm (specific membrane resistance), Ri (specific internal resistivity), and Cm (specific membrane capacitance), the experiments were repeated in computer simulations on compartmental models of the cells (Fig. 6). Good fits between experimental and simulation data were obtained for the following values: Rm = 2.5 k omega cm2, Ri = 60 omega cm, and Cm = 1.5 microF/cm2 for CH cells; Rm = 2.0 k omega cm2, Ri = 40 omega cm, and Cm = 0.9 microF/cm2 for HS cells; Rm = 2.0 k omega cm2, Ri = 40 omega cm, and Cm = 0.8 microF/cm2 for VS cells. An error analysis of the fitting procedure revealed an area of confidence in the Rm-Ri plane within which the Rm-Ri value pairs are still compatible with the experimental data given the statistical fluctuations inherent in the experiments (Figs. 7, 8). We also investigated whether there exist characteristic differences between different members of the same cell class and how much the exact placement of the electrode (within +/-100 microns along the axon) influences the result of the simulation (Fig. 9). The membrane parameters were further examined by injection of a hyperpolarizing current pulse (Fig. 10). The resulting compartmental models (Fig. 11) based on the passive membrane parameters determined in this way form the basis of forthcoming studies on dendritic integration and signal propagation in the fly tangential cells (Haag et al., 1997; Haag and Borst, 1997).