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Volume electron microscopy together with computer-based image analysis are yielding neural circuit diagrams of ever larger regions of the brain. These datasets are usually represented in a cell-to-cell connectivity matrix and contain important information about prevalent circuit motifs allowing to directly test various theories on the computation in that brain structure. Of particular interest are the detection of cell assemblies and the quantification of feedback, which can profoundly change circuit properties. While the ordering of cells along the rows and columns doesn't change the connectivity, it can make special connectivity patterns recognizable. For example, ordering the cells along the flow of information, feedback and feedforward connections are segregated above and below the main matrix diagonal, respectively. Different algorithms are used to renumber matrices such as to minimize a given cost function, but either their performance becomes unsatisfying at a given size of the circuit or the CPU time needed to compute them scales in an unfavorable way with increasing number of neurons. Based on previous ideas, I describe an algorithm which is effective in matrix reordering with respect to both its performance as well as to its scaling in computing time. Rather than trying to reorder the matrix in discrete steps, the algorithm transiently relaxes the integer program by assigning a real-valued parameter to each cell describing its location on a continuous axis ('smooth-index') and finds the parameter set that minimizes the cost. I find that the smooth-index algorithm outperforms all algorithms I compared it to, including those based on topological sorting.

To study how the nervous system processes visual information, experimenters must record neural activity while delivering visual stimuli in a controlled fashion. In animals with a nearly panoramic field of view, such as flies, precise stimulation of the entire visual field is challenging. We describe a projector-based device for stimulation of the insect visual system under a microscope. The device is based on a bowl-shaped screen that provides a wide and nearly distortion-free field of view. It is compact, cheap, easy to assemble, and easy to operate using the included open-source software for stimulus generation. We validate the virtual reality system technically and demonstrate its capabilities in a series of experiments at two levels: the cellular, by measuring the membrane potential responses of visual interneurons; and the organismal, by recording optomotor and fixation behavior of Drosophila melanogaster in tethered flight. Our experiments reveal the importance of stimulating the visual system of an insect with a wide field of view, and we provide a simple solution to do so.

In natural environments, light intensities and visual contrasts vary widely, yet neurons have a limited response range for encoding them. Neurons accomplish that by flexibly adjusting their dynamic range to the statistics of the environment via contrast normalization. The effect of contrast normalization is usually measured as a reduction of neural signal amplitudes, but whether it influences response dynamics is unknown. Here, we show that contrast normalization in visual interneurons of Drosophila melanogaster not only suppresses the amplitude but also alters the dynamics of responses when a dynamic surround is present. We present a simple model that qualitatively reproduces the simultaneous effect of the visual surround on the response amplitude and temporal dynamics by altering the cells' input resistance and, thus, their membrane time constant. In conclusion, single-cell filtering properties as derived from artificial stimulus protocols like white-noise stimulation cannot be transferred one-to-one to predict responses under natural conditions.

The visual system must make predictions to compensate for inherent delays in its processing. Yet little is known, mechanistically, about how prediction aids natural behaviors. Here, we show that despite a 20-30ms intrinsic processing delay, the vertical motion sensitive (VS) network of the blowfly achieves maximally efficient prediction. This prediction enables the fly to fine-tune its complex, yet brief, evasive flight maneuvers according to its initial ego-rotation at the time of detection of the visual threat. Combining a rich database of behavioral recordings with detailed compartmental modeling of the VS network, we further show that the VS network has axonal gap junctions that are critical for optimal prediction. During evasive maneuvers, a VS subpopulation that directly innervates the neck motor center can convey predictive information about the fly's future ego-rotation, potentially crucial for ongoing flight control. These results suggest a novel sensory-motor pathway that links sensory prediction to behavior.

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.

With the advent of neurogenetic methods, the neural basis of behavior is presently being analyzed in more and more detail. This is particularly true for visually driven behavior of Drosophila melanogaster where cell-specific driver lines exist that, depending on the combination with appropriate effector genes, allow for targeted recording, silencing and optogenetic stimulation of individual cell-types. Together with detailed connectomic data of large parts of the fly optic lobe, this has recently led to much progress in our understanding of the neural circuits underlying local motion detection. However, how such local information is combined by optic flow sensitive large-field neurons is still incompletely understood. Here, we aim to fill this gap by a dense reconstruction of lobula plate tangential cells of the fly lobula plate. These neurons collect input from many hundreds of local motion-sensing T4/T5 neurons and connect them to descending neurons or central brain areas. We confirm all basic features of HS and VS cells as published previously from light microscopy. In addition, we identified the dorsal and the ventral centrifugal horizontal, dCH and vCH cell, as well as three VSlike cells, including their distinct dendritic and axonal projection area.

Understanding the computational implications of specific synaptic connectivity patterns is a fundamental goal in neuroscience. In particular, the computational role of ubiquitous electrical synapses operating via gap junctions remains elusive. In the fly visual system, the cells in the vertical-system network, which play a key role in visual processing, primarily connect to each other via axonal gap junctions. This network therefore provides a unique opportunity to explore the functional role of gap junctions in sensory information processing. Our information theoretical analysis of a realistic VS network model shows that within 10 ms following the onset of the visual input, the presence of axonal gap junctions enables the VS system to efficiently encode the axis of rotation, θ, of the fly's ego motion. This encoding efficiency, measured in bits, is near-optimal with respect to the physical limits of performance determined by the statistical structure of the visual input itself. The VS network is known to be connected to downstream pathways via a subset of triplets of the vertical system cells; we found that because of the axonal gap junctions, the efficiency of this subpopulation in encoding θ is superior to that of the whole vertical system network and is robust to a wide range of signal to noise ratios. We further demonstrate that this efficient encoding of motion by this subpopulation is necessary for the fly's visually guided behavior, such as banked turns in evasive maneuvers. Because gap junctions are formed among the axons of the vertical system cells, they only impact the system's readout, while maintaining the dendritic input intact, suggesting that the computational principles implemented by neural circuitries may be much richer than previously appreciated based on point neuron models. Our study provides new insights as to how specific network connectivity leads to efficient encoding of sensory stimuli.

Optical illusions provide powerful tools for mapping the algorithms and circuits that underlie visual processing, revealing structure through atypical function. Of particular note in the study of motion detection has been the reverse-phi illusion. When contrast reversals accompany discrete movement, detected direction tends to invert. This occurs across a wide range of organisms, spanning humans and invertebrates. Here, we map an algorithmic account of the phenomenon onto neural circuitry in the fruit fly Drosophila melanogaster. Through targeted silencing experiments in tethered walking flies as well as electrophysiology and calcium imaging, we demonstrate that ON- or OFF-selective local motion detector cells T4 and T5 are sensitive to certain interactions between ON and OFF. A biologically plausible detector model accounts for subtle features of this particular form of illusory motion reversal, like the re-inversion of turning responses occurring at extreme stimulus velocities. In light of comparable circuit architecture in the mammalian retina, we suggest that similar mechanisms may apply even to human psychophysics.

Neuronal computation underlying detection of visual motion has been studied for more than a half-century. In Drosophila, direction-selective T4/T5 neurons show supralinear signal amplification in response to stimuli moving in their preferred direction, in agreement with the prediction made by the Hassenstein-Reichardt detector. Nevertheless, the molecular mechanism explaining how the Hassenstein-Reichardt model is implemented in T4/T5 cells has not been identified yet. In the present study, we utilized cell type-specific transcriptome profiling with RNA-seq to obtain a complete gene expression profile of T4/T5 neurons. We analyzed the expression of genes that affect neuronal computational properties and can underlie the molecular implementation of the core features of the Hassenstein-Reichardt model to the dendrites of T4/T5 neurons. Furthermore, we used the acquired RNA-seq data to examine the neurotransmitter system used by T4/T5 neurons. Surprisingly, we observed co-expression of the cholinergic markers and the vesicular GABA transporter in T4/T5 neurons. We verified the previously undetected expression of vesicular GABA transporter in T4/T5 cells using VGAT-LexA knock-in line. The provided gene expression dataset can serve as a useful source for studying the properties of direction-selective T4/T5 neurons on the molecular level.

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.

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.

Computational neuroscientists frequently encounter the challenge of parameter fitting--exploring a usually high dimensional variable space to find a parameter set that reproduces an experimental data set. One common approach is using automated search algorithms such as gradient descent or genetic algorithms. However, these approaches suffer several shortcomings related to their lack of understanding the underlying question, such as defining a suitable error function or getting stuck in local minima. Another widespread approach is manual parameter fitting using a keyboard or a mouse, evaluating different parameter sets following the users intuition. However, this process is often cumbersome and time-intensive. Here, we present a new method for manual parameter fitting. A MIDI controller provides input to the simulation software, where model parameters are then tuned according to the knob and slider positions on the device. The model is immediately updated on every parameter change, continuously plotting the latest results. Given reasonably short simulation times of less than one second, we find this method to be highly efficient in quickly determining good parameter sets. Our approach bears a close resemblance to tuning the sound of an analog synthesizer, giving the user a very good intuition of the problem at hand, such as immediate feedback if and how results are affected by specific parameter changes. In addition to be used in research, our approach should be an ideal teaching tool, allowing students to interactively explore complex models such as Hodgkin-Huxley or dynamical systems.

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.

Understanding the principles governing axonal and dendritic branching is essential for unravelling the functionality of single neurons and the way in which they connect. Nevertheless, no formalism has yet been described which can capture the general features of neuronal branching. Here we propose such a formalism, which is derived from the expression of dendritic arborizations as locally optimized graphs. Inspired by Ramón y Cajal's laws of conservation of cytoplasm and conduction time in neural circuitry, we show that this graphical representation can be used to optimize these variables. This approach allows us to generate synthetic branching geometries which replicate morphological features of any tested neuron. The essential structure of a neuronal tree is thereby captured by the density profile of its spanning field and by a single parameter, a balancing factor weighing the costs for material and conduction time. This balancing factor determines a neuron's electrotonic compartmentalization. Additions to this rule, when required in the construction process, can be directly attributed to developmental processes or a neuron's computational role within its neural circuit. The simulations presented here are implemented in an open-source software package, the "TREES toolbox," which provides a general set of tools for analyzing, manipulating, and generating dendritic structure, including a tool to create synthetic members of any particular cell group and an approach for a model-based supervised automatic morphological reconstruction from fluorescent image stacks. These approaches provide new insights into the constraints governing dendritic architectures. They also provide a novel framework for modelling and analyzing neuronal branching structures and for constructing realistic synthetic neural networks.

To comprehend the principles underlying sensory information processing, it is important to understand how the nervous system deals with various sources of perturbation. Here, we analyze how the representation of motion information in the fly's nervous system changes with temperature and luminance. Although these two environmental variables have a considerable impact on the fly's nervous system, they do not impede the fly to behave suitably over a wide range of conditions. We recorded responses from a motion-sensitive neuron, the H1-cell, to a time-varying stimulus at many different combinations of temperature and luminance. We found that the mean firing rate, but not firing precision, changes with temperature, while both were affected by mean luminance. Because we also found that information rate and coding efficiency are mainly set by the mean firing rate, our results suggest that, in the face of environmental perturbations, the coding efficiency is improved by an increase in the mean firing rate, rather than by an increased firing precision.

Dendrite morphology, a neuron's anatomical fingerprint, is a neuroscientist's asset in unveiling organizational principles in the brain. However, the genetic program encoding the morphological identity of a single dendrite remains a mystery. In order to obtain a formal understanding of dendritic branching, we studied distributions of morphological parameters in a group of four individually identifiable neurons of the fly visual system. We found that parameters relating to the branching topology were similar throughout all cells. Only parameters relating to the area covered by the dendrite were cell type specific. With these areas, artificial dendrites were grown based on optimization principles minimizing the amount of wiring and maximizing synaptic democracy. Although the same branching rule was used for all cells, this yielded dendritic structures virtually indistinguishable from their real counterparts. From these principles we derived a fully-automated model-based neuron reconstruction procedure validating the artificial branching rule. In conclusion, we suggest that the genetic program implementing neuronal branching could be constant in all cells whereas the one responsible for the dendrite spanning field should be cell specific.